Research ArticleFlettner Rotor Concept for Marine ApplicationsA Systematic Study

A De Marco S Mancini C Pensa G Calise and F De Luca

Department of Industrial Engineering University of Naples Federico II Via Claudio 21 80125 Naples Italy

Correspondence should be addressed to S Mancini simonemanciniuninait

Received 19 January 2016 Revised 31 May 2016 Accepted 15 June 2016

Academic Editor Ryoichi Samuel Amano

Copyright copy 2016 A De Marco et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The concept of Flettner rotor a rotating cylinder immersed in a fluid current with a top-mounted disk has been analyzed bymeansof unsteady Reynolds averaged Navier-Stokes simulations with the aim of creating a suitable tool for the preliminary design of theFlettner rotor as a shiprsquos auxiliary propulsion system The simulation has been executed to evaluate the performance sensitivity ofthe Flettner rotor with respect to systematic variations of several parameters that is the spin ratio the rotor aspect ratio the effectof the end plates and their dimensions The Flettner rotor device has been characterized in terms of lift and drag coefficients andthese data were compared with experimental trends available in literature A verification study has been conducted in order toevaluate the accuracy of the simulation results and the main sources of numerical uncertainty All the simulation results were usedto achieve a surrogate model of lift and drag coefficients This model is an effective mathematical tool for the preliminary designof Flettner rotor Finally an example of assessment of the Flettner rotor performance as an auxiliary propulsion device on a realtanker ship is reported

1 Introduction

In the era in which most of the worldrsquos attention is focusedon improving energy savings the use of spinning cylindersas an auxiliary naval propulsion system has become a realityFlettner rotors are rotating cylinders that when immersed ina fluid stream are able to produce fluid dynamic lift usingthe Magnus effect This idea is due to the German engineerAnton Flettner who studied in the 1920s the effectiveness ofspinning cylinders as a shiprsquos propulsion systemThis kind ofpropulsion systems was enrolled for the first time in 1925-1926 on the Buckau ship shown in Figure 1(a) This shipused two rotors to augment the propulsion power of its for-mer conventional sailing rigs However further commercialdevelopment of the FRs did not take place before the twenty-first century Nowadays with increasing fuel prices and ageneral growing sensibility about green and environmental-protection policies the FRs are being seriously reconsideredas viable green ship propulsion devices In 2010 Enercon awind energy company launched a Flettner-powered cargoship named E-Ship 1 Figure 1(b) On E-Ship 1 the FRs areused to assist the diesel engine as reported in the Enercon

technical report [1] the owner declares that thanks to thisdevice a 30 reduction of fuel consumption is achieved E-Ship 1 is in current use and has been recounted to cover morethan 17000 sea miles with no mention of particular problemsabout the FRs [1]

2 Literature Overview

The capability of infinite length rotating cylinders to produceaerodynamic forces was studied for the first time at theLangley NACA Laboratory by Reid [2] he found that inparticular conditions such simple devices are capable ofdeveloping very high values of the lift coefficient and of theaerodynamic efficiency (ie the lift-to-drag ratio) Thom [3]presented an experimental work on rotating cylinders withemphasis on the effects of the Reynolds number (Re) surfaceconditions aspect ratio and end plates disks describingthe device in terms of lift drag and torque coefficientsSuccessively Swanson [4] clarified the physics underpinningthe FR thus highlighting the nature of the circulation aroundthe rotating cylinder More recently a comprehensive study

Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2016 Article ID 3458750 12 pageshttpdxdoiorg10115520163458750

2 International Journal of Rotating Machinery

(a) (b)

Figure 1 Buckau first Flettnerrsquos ship (a) and E-Ship 1 by Enercon wind company (b)

on the functioning of FR was conducted by Da-Qing et al[5] This work presents a numerical study of aerodynamicperformance of Flettner rotors at a high Re (16 sdot 10

6) inrelation to the change of spin ratio (SR) and aspect ratio(AR) Special attention is paid to the formation of vortexstructures and the relationship between wake instability andfluctuation of aerodynamic loads This paper also reportsstatistical expressions correlating 119862

119871and 119862

119863with SR

The aerodynamic coefficients of an FR depend on variousparameters (geometrical and functional) In the followingsubsections the most important parameters are briefly sum-marized

21 Spin Ratio The amount of aerodynamic force generatedby a rotating cylinder that is an FR is mainly dependenton the SR (or velocity ratio also named 120572) which accountsfor the angular speed Ω the FR diameter 119889 and the freestream velocity 119880 as shown in Figure 2The flow phenomenaaround a 3D circular cylinder are rather complex and featureboth tip vortices and an alternate vortex shedding betweenthe rotor sides Seifert [6] highlights that vortex sheddingoccurs for Re all the way up to at least 80 sdot 10

6 and thatthe extension of the vortices depends also on the Strouhalnumber (St) The St represents the degree of unsteadinessof the oscillating flow past the rotating cylinder In Mittaland Kumar [7] a detailed analysis of St regimes for rotatingcylinders is presented Low Strouhal numbers (St lt 10

minus4)indicate long eddy formations hence the flow is consideredquasi-steady According to Badalamenti and Prince [8] theshedding phenomena are also influenced by SR small spinratios cause long eddy formations while higher SRs causeconsiderably short eddies Thus the Karman vortex street isseen for SR le 2 when large eddies are formed and shedalternately on the two sides of the cylinder Conversely vortexformation and shedding can no longer be seen for 20 le SR lt

30 and for 30 le SR lt 35 quasi-steady-states are observableAt SR = 35 a second shedding mode is found

Swanson [4] pointed out that lift and drag of a rotatingcylinder at SR lt 10 show a significant dependency on ReThe effects of Re aremore evident on lift at Re gt 6times10

4 whichis also confirmed by Gowree and Prince [9] When SR gt 25

Lift

DragH

U

Ω

de

d

Figure 2 Sketch of the FR with end plate and main relevantparameters

and Re gt 4 times 104 drag and lift curves have a slightly growing

trend for increasing Re

22 Aspect Ratio Themain shape factor of an FR is the aspectratio AR which significantly influences the FR effectivenessin producing aerodynamic forces The AR of FR devicewhich is the ratio between height and diameter modifies itsaerodynamic efficiency as for higher aspect ratios the FRdevice behaves much like a wing with tip vortices that takepart in the lift production An important consideration ispresented by Swanson [4] who observed that the smaller theaspect ratio the smaller the maximum lift obtained and thesmaller the velocity ratio at which this maximum is reachedSwanson also demonstrated that for very high aspect ratiothe lift can reach higher values than themaximum theoreticallimit predicted by Prandtlrsquos classical theory [10] An extensivecomparison of the main data available in the literature on FR

International Journal of Rotating Machinery 3

performances both experimental and numerical ones alongwith some considerations can be found in De Marco et al[11]

23 End Plate The idea of applying an end plate on FRto optimize its aerodynamic efficiency was first suggestedby Prandtl [10] The presence of an end plate modifies the3D flow phenomena at the tip of the FR augmenting theldquoeffective ARrdquo of the rotor Thom [3] investigated the effectof large end plates with a diameter ratio 119889

119890119889 = 30 where 119889

119890

is the diameter of the end plate disk (Figure 2)The FR with end plate also called Thom disk is able

to produce almost double the lift at high velocity ratios forexample SR = 20 In Badalamenti and Prince [12] it isshown that for a cylinder with AR = 51 and diameter ratiosranging from 11 to 30 the effects of the increases 119889

119890119889 and

AR are similar Increasing the 119889119890119889 value a higher lift value

is generated by the FR and such value occurs at higher SR aswell (see Seifert [6]) Thouault et al [13] presented a detailedanalysis of the effects of end plate dimensions on the FRefficiency based on experiments and numerical simulations

A discussion of how the end plate size is related to SR inorder to achieve optimal performances of the FR is presentedby Seifert [6] In his work Seifert observes that at low spinratio (SR = 10) smaller plates generally give lightly smallerdrag for applications at moderate spin ratio (10 lt SR lt

30) larger plates are preferred so as to delay the increase ininduced drag while for high spin ratio applications (SR gt

30) smaller plates are again more desirable

24 Marine Application of FR Concerning the use of FRfor marine applications not many research papers are avail-able in the literature An overview of the applications ofthe Magnus effect devices in the marine field is given inMorisseau [14] The Magnus effect devices can be used asroll stabilizers water propellers and air generator such asFR Moreover this paper reports an interesting preliminaryanalysis of retrofitting of a single screw US Navy auxiliaryship with five FRs More recently in Pearson [15] a ldquofirst-stagerdquo assessment is found in practical limitations as well asnegative side effects of retrofitting Flettner rotors to a ship Allthese considerations are collected in order to create a softwaremodel for a preliminary analysis of the viability of retrofittingFR to a defined ship before any progression onto analyzingspecific scenario benefits or other detailed investigations Alimit of this work is in the estimation of FR performanceswhich are evaluated only as a function of SR The softwarepresented assumes a universal FR geometry with 119889

119890119889 = 15

and AR = 5 (based on Prandtlrsquos study [10]) and evaluates 119862119871

and119862119863of this FR then the performances of FR are evaluated

changing SR in the range 00sim80Traut et al [16] explore the potential for harnessing wind

power for shipping applications Numerical models of thetwo main wind power technologies FR and towing kite arelinked with wind data along a set of five trade routes Theresults of their analysis give an estimation of the average windpower contribution on a defined route For a single FR thedelivered power is in a range between 193 and 373 kW and

Figure 3 Estraden ship latest FR installation

for the towing kite between 127 and 461 kW The FR has avariability of the delivered power smaller than the towingkite due to the different dependencies on wind speed anddirection The average power contribution coming from anFR is higher than that coming from the kite on some routesand lower on others But an advantage of FR is that thecontribution would be expected to increase almost linearlywith the number of devices installed on the same ship (in thisrespect a quantitative study of interference effects is lackingin the literature) For this reason for instance installing threeFRs on a 5500DWT (dead weight tonnage) general cargocarrier could provide on average more than half the powerrequired by the main engine under typical slow steamingconditions

25 Aim of the Work The present research extends previousinvestigations presented in De Marco et al [17] and in DeMarco et al [11] in order to assess in a systematic way theeffect of the FR key parameters that is the AR SR and theend plate diameter on the device performance Furthermorethe mutual interaction effects of these parameters on theaerodynamic forces generated by FR are investigated Theanalyzed ranges of variation of the key parameters havebeen chosen considering technologically plausible marineapplications of the FR concept

3 Flettner Rotor Installationsand Reference Data

To choose the ranges of the key parameters some constraintshave been taken into account For instance one has toconsider the currently available technology as well as thepracticality in marine applications Another important factoris the vortex shedding risk (first and second mode) whichdepends on the mutual interaction between AR and SRConsequently the limits of AR and SR have been identifiedby the analysis of some real FR installations on board

The known installations of FR and their reference dataare summarized in Table 1 The first two examples Buckauand Barbara are not in service while the two ships E-Ship-1 and Estraden (Figure 3) are currently operated byNorth European owners for commercial purposes In allof these examples a Thom disk is used and the AR are inthe range 55sim70 This range is taken as a reference for the

4 International Journal of Rotating Machinery

Table 1 Geometric performance and structural related parameters collected from all-known rotor ships

Ship (year) Buckau (1924) Barbara (1926) E-Ship 1 (2010) Estraden (2014)Type Retrofit Newbuild Newbuild RetrofitHeight (m) 156 170 270 190Diameter (m) 28 40 40 30Aspect ratio 56 43 68 63End plate Yes Yes Yes YesMaterial Zinc coated steel Aluminum NA CompositeMax rpm 1350 1500 NA 2500

Table 2 Values of analyzed variables

Variables ValuesSR 10 15 20 30AR 20 40 60 80119889119890119889 10 20 30

investigations presented here It is observed that the angularrotor speeds have increased over the years thus allowinghigher SR However the SR values of interest for marineapplication remain in the range 10 to 30 For example SR =

25 is obtained for a typical relative wind velocity of 20 kn(10ms) a reasonable diameter of 30m and a rotation speedof 160 rpm

4 Numerical Experiments

Systematic variations of FR configurations have been inves-tigated by means of URANS simulations in incompressibleflow All the analyses have been performed using the com-mercially available computational fluid dynamics softwareCD adapco STAR-CCM+ v 906 The simulations were con-ducted using the same approach such as the oversetchimeragrid technique described in De Marco et al [17] and in DeMarco et al [11] Furthermore fairly wide ranges of the keyparameters that is AR SR and 119889

119890119889 have been examined

as detailed in the Table 2 and displayed in Figure 4 Thecharacteristics of FRs were evaluated in terms of lift anddrag coefficients and aerodynamic efficiencyThe simulationshave been launched on the computer cluster of the SCoPEsupercomputing centre at the University of Naples ldquoFedericoIIrdquo using up to 120 CPUs in parallel

41 Simulation Setup The rotating motion of the FR wassimulated using the oversetchimera mesh methodologywith distance-weighted interpolation method This methodwhich is especially suitable for rotational movements usesan interpolation factor inversely proportional to the distancefrom acceptor cell to donor cell as indicated in CD adapcoUserrsquos Guide [18]

Hybridmesh approach coupling unstructured and struc-tured mesh has been used for all the simulations Thecomputational domain contains two regions the backgroundnonrotating region and the overlapped rotating region(Figure 5) For the background and overlapped region an

AR

1 2 3

24

68

ded

Figure 4 Sketch of all geometry of FRs tested

unstructured grid approach was used while a structuredboundary layer mesh was created near the FR surface Thechoice of hybrid mesh approach is justified by the fact thatthis is a suitable compromise between accuracy and compu-tational effort compared with the Cartesian mesh as shownin the 2D preliminary study reported in De Marco et al [11]Furthermore the grid set up allowed a nondimensional walldistance (y+) value approximately equal to 10

The chosen URANS-solving algorithm uses a first-orderforward Euler scheme for the temporal discretization animplicit element-based finite volume method and a segre-gated flow approachwith second-order upwind discretizationof the convective terms A fully turbulent approach with 119896-120596Shear Stress-Transport (SST) turbulencemodel has been used(a comparison with other turbulence model is reported inFigure 9) All of the properties of the numerical solver aresummarized in Table 3

It has to be noted that the simulation time step is afunction of the angular speed Ω For the convergence of thenumerical scheme as a rule of thumb there is a limitationon themaximum cell-based Courant-Friedrichs-Lewy (CFL)number in a time stepTherefore the higher the angular speedthe lower the time step

42 Computational Domain and Boundary Conditions Abox-shaped domain has been created around the cylinder

International Journal of Rotating Machinery 5

Table 3 Summary of the numerical simulation setup

Pressure link Pressure Convectionterm

Temporaldiscretization Time step (s) Iteration per

time stepTurbulencemodel

Oversetinterpolation

scheme

Simple Standard 2nd order 1st orderFunction ofangular speed

(Ω)11 119896-120596 SST Distance

weighted

(a)

Overset region

Backgroundregion

Interface

(b)

Figure 5 Section of the computational grid (a) Close-up views of the hybrid mesh (b)

Inletvelocity

Inletvelocity

Inletvelocity

Symmetry plane

Pressure outlet

15d

5d275d

35H

Figure 6 Boundary conditions and domain dimensions in functionof the main dimensions of FR (119867 119889)

geometry as seen in Figure 6 In order to reduce the compu-tational effort only half the domain has been considered anda symmetry plane has been assumed containing the cylinderaxis and parallel to the free stream velocity A velocity inletboundary condition has been set on the front side of thedomain with a prescribed velocity this inlet velocity also hasbeen used to control the SR of the rotor keeping constantits angular speed Ω On the bottom and the top side of thedomain a symmetry boundary condition also is used On therear side of the domain surface a pressure outlet boundarycondition has been imposed with a relative pressure of value0 Pa An axial-symmetrical zone surrounding the rotor hadto be modeled overlapping the rotating mesh (fixed with therotor) and the underlying nonmoving mesh domain Thisturned out to be a necessary grid treatment for using theoverset mesh methodology

43 Numerical Uncertainty Analysis In order to assess thenumerical setup and to evaluate the simulation numericaluncertainty 119880SN a verification study has been performed

The benchmark experimental data are derived fromBadalamenti and Prince [8 12] and are related to an FR withAR = 51 (cylinder height 119867 = 045m) diameter of 119889 =

00889m and the Thom disk on the top of this FR with119889119890= 01778m (corresponding to 119889

119890119889 = 20)

According to the Oberkampf and Blottner [19] verifica-tion is defined as a process for assessing simulation numericaluncertainty 119880SN The simulation numerical error and uncer-tainty are composed of a grid convergence error (120575

119866) iterative

convergence error (120575119868) time step convergence error (120575TS)

and other parameters (120575119875) Therefore the numerical error is

the sum

120575SN = 120575119866

+ 120575119868+ 120575TS + 120575

119875 (1)

and the simulation numerical uncertainty is given by theformula

1198802

SN = 1198802

119866+ 1198802

119868+ 1198802

TS + 1198802

119875 (2)

where 119880119866 119880119868 119880TS and 119880

119875are the uncertainties arising

from the grid iterative time step and other parametersrespectively (see Stern et al [20])

The numerical uncertainty evaluation was performedusing two different methods the grid convergence index(GCI) method and the correction factor (CF) method Thegeneral form of the uncertainty evaluation based on thegeneralized Richardson extrapolation (RE) method can bewritten as follows

119880119896= 119865119878(

12057621119896

119903119901119896

119896minus 1

) (3)

where 12057621119896

is the solution changes for the 119896-input parameterbetween the solutions (fine (119878

1119896) to medium (119878

2119896) and coarse

(1198783119896)) 119903119896is the constant refinement ratio (recommended

6 International Journal of Rotating Machinery

values between radic2 and 2) 119901119896is the observed order of

accuracy and 119865119878is the safety factor Furthermore another

parameter is the convergence ratio (119877119896) which provides

information about the convergencedivergence of a solutionThe 119877

119896value was determined by the following ratio

119877119896=

12057621119896

12057632119896

(4)

The two different solution verification methods used in thisstudy differ in the choice of safety factor (119865

119878)

The GCI method proposed by Roache [21 22] is usedextensively and it is recommended for example by theAmerican Society of Mechanical Engineers (ASME) [23]and the American Institute of Aeronautics and Astronautics(AIAA) [24] Roache recommended for careful grid studies(three or more grids analyzed) 125 as the 119865

119878value

The other method used is the CF described in Stern et al[20] that uses a variable value of 119865

119878 In the CFmethod unlike

in the GCI method the uncertainty of the error dependson how close the solutions are to the asymptotic rangeThe expressions to assess the uncertainties were reported byWilson et al [25]

The verification study has been carried out for the criticalpoints of SR = 20 and SR = 25 in terms of 119862

119863estimation

errorThe iterative uncertainties are estimated by the fluctua-

tions of the time-history of the results in the last few periodsas indicated in Stern et al [20] Specifically as reported in (5)119880119868are estimated by half the difference of the maximum value

(119878119880) and the minimum value (119878

119871) of the final time-history of

the results

119880119868=

1003816100381610038161003816100381610038161003816

1

2(119878119880

minus 119878119871)

1003816100381610038161003816100381610038161003816 (5)

Then the grid uncertainty has been evaluated by the follow-ing expressions that is (6) for the GCI method and (7) forthe CF method

119880119896= 125 sdot

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

(6)

119880119896

=

[96 (1 minus 119862119896)2+ 11]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 lt 0125

[210038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 + 1]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 ge 0125

(7)

where 119865119878is equal to 125 and 119862

119896is the correction factor

Verification results using three systematically refined gridswith the refinement ratio (119903

119866) equal to radic2 are shown in

Table 5 The grid sizes range from 09M to 19M grid pointsand the three grids tested are shown in Table 4

Because 0 lt 119877119866

lt 1 monotonic convergence isachieved for 119862

119871and 119862

119863 where 119877

119866is convergence ratio for

the grid calculated according to (4) The uncertainty valuesare reported in Table 5

Table 4 The three grids tested

Grids CellsGrid A Coarse 0933 sdot 10

6

Grid B Medium 1320 sdot 106

Grid C Fine 1867 sdot 106

The values of simulation uncertainty reported in Table 5show that119880SN for 119862

119863is higher than119880SN for 119862

119871 due to much

larger errors in the estimation of 119862119863than of 119862

119871for SR = 20

and SR = 25Iterative convergence is achieved for all simulations and

119880119868is found to be negligible with respect to grid errors

similarly to what happens in other engineering applications(eg Wilson et al [26] and Xing et al [27])

Moreover the verification procedure cannot be com-pleted with the validation phase due to the lack of experi-mental uncertainty dataTherefore only the results related tosimulation numerical uncertainty are reported in Table 5

The numerical results of the verification study have beencompared with the experimental data as shown in Figure 7The comparison highlighted that no significant improvementin the 119862

119871and 119862

119863evaluation is detected between coarse

medium and fine mesh case However increasing the gridpoints increases the calculation effort as shown in Figure 8

For the reasons mentioned above the grid of Case B hasbeen assumed as the reference mesh This grid guarantees anacceptable solutionwithout an excessive computational effort(such as in Case C)

The comparison between experimental data and numer-ical results for SR in the range from 00 to 25 reportedin Figure 9 shows a good agreement in particular for 119862

119871

Regarding 119862119863 the CFD simulations give reliable results for

SR lt 15 and the error increases at higher values of SRlikewise highlighted in Thouault et al [13] and Da-Qing etal [5]

As shown in Table 5 it can be observed that for 119862119863the

comparison error (119864) is much greater than 119880SN Accordingto Oberkampf and Blottner [19] and Stern et al [20] it canbe said that when 119864 is much greater than the uncertaintyit is necessary to improve the simulations models It iswell known that one of the main sources of the modelingsimulation error is the turbulence models Nevertheless ashighlighted in Figure 9 comparing the different two-equationturbulence models that is 119896-120596 SST and Realizable 119896-120576 nosignificant differences are appreciableThe 119896-120596 SST is used asturbulencemodel for all the subsequent simulations howevera different simulation approach is required for an accurate119862

119863

evaluation at high SR

5 Results

The results of the simulations performed into the variableranges indicated in Table 2 are reported in terms of the so-called response curvesThese curves shown in Figure 10 rep-resent the values of 119862

119871and 119862

119863and aerodynamic efficiency

keeping constant 119889119890119889 of the FRThis representation is useful

because it permits us to clearly recognize the relationships

International Journal of Rotating Machinery 7

65 64 62

231213 199

Case A Case B Case C

SR 25SR 20

0

10

20

30

40

CL

erro

r

(a)

331 322 314

363 359 356

Case A Case B Case C0

10

20

30

40

C

Der

ror

SR 25SR 20

(b)

Figure 7 119862119871and 119862

119863percentage error between numerical (three mesh cases tested) and experimental data at SR = 20 and 25

Case A Case B Case C

CPU

tim

e per

tim

e ste

p (s

)

0

1000

2000

3000

Figure 8 Computational time required for the grids tested

Exp dataCFD k-εCFD k-120596 SST

minus1000102030405060708090

100

CL

05 10 15 20 2500SR

(a)

00

20

40

60

80

100

CD

05 10 15 20 2500SR

Exp dataCFD k-εCFD k-120596 SST

(b)

Figure 9 Comparison between CFD results and experimental data for lift (a) and drag (b) coefficient using mesh Case B and two differentturbulence models

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 International Journal of Rotating Machinery

(a) (b)

Figure 1 Buckau first Flettnerrsquos ship (a) and E-Ship 1 by Enercon wind company (b)

on the functioning of FR was conducted by Da-Qing et al[5] This work presents a numerical study of aerodynamicperformance of Flettner rotors at a high Re (16 sdot 10

6) inrelation to the change of spin ratio (SR) and aspect ratio(AR) Special attention is paid to the formation of vortexstructures and the relationship between wake instability andfluctuation of aerodynamic loads This paper also reportsstatistical expressions correlating 119862

119871and 119862

119863with SR

The aerodynamic coefficients of an FR depend on variousparameters (geometrical and functional) In the followingsubsections the most important parameters are briefly sum-marized

21 Spin Ratio The amount of aerodynamic force generatedby a rotating cylinder that is an FR is mainly dependenton the SR (or velocity ratio also named 120572) which accountsfor the angular speed Ω the FR diameter 119889 and the freestream velocity 119880 as shown in Figure 2The flow phenomenaaround a 3D circular cylinder are rather complex and featureboth tip vortices and an alternate vortex shedding betweenthe rotor sides Seifert [6] highlights that vortex sheddingoccurs for Re all the way up to at least 80 sdot 10

6 and thatthe extension of the vortices depends also on the Strouhalnumber (St) The St represents the degree of unsteadinessof the oscillating flow past the rotating cylinder In Mittaland Kumar [7] a detailed analysis of St regimes for rotatingcylinders is presented Low Strouhal numbers (St lt 10

minus4)indicate long eddy formations hence the flow is consideredquasi-steady According to Badalamenti and Prince [8] theshedding phenomena are also influenced by SR small spinratios cause long eddy formations while higher SRs causeconsiderably short eddies Thus the Karman vortex street isseen for SR le 2 when large eddies are formed and shedalternately on the two sides of the cylinder Conversely vortexformation and shedding can no longer be seen for 20 le SR lt

30 and for 30 le SR lt 35 quasi-steady-states are observableAt SR = 35 a second shedding mode is found

Swanson [4] pointed out that lift and drag of a rotatingcylinder at SR lt 10 show a significant dependency on ReThe effects of Re aremore evident on lift at Re gt 6times10

4 whichis also confirmed by Gowree and Prince [9] When SR gt 25

Lift

DragH

U

Ω

de

d

Figure 2 Sketch of the FR with end plate and main relevantparameters

and Re gt 4 times 104 drag and lift curves have a slightly growing

trend for increasing Re

22 Aspect Ratio Themain shape factor of an FR is the aspectratio AR which significantly influences the FR effectivenessin producing aerodynamic forces The AR of FR devicewhich is the ratio between height and diameter modifies itsaerodynamic efficiency as for higher aspect ratios the FRdevice behaves much like a wing with tip vortices that takepart in the lift production An important consideration ispresented by Swanson [4] who observed that the smaller theaspect ratio the smaller the maximum lift obtained and thesmaller the velocity ratio at which this maximum is reachedSwanson also demonstrated that for very high aspect ratiothe lift can reach higher values than themaximum theoreticallimit predicted by Prandtlrsquos classical theory [10] An extensivecomparison of the main data available in the literature on FR

International Journal of Rotating Machinery 3

performances both experimental and numerical ones alongwith some considerations can be found in De Marco et al[11]

23 End Plate The idea of applying an end plate on FRto optimize its aerodynamic efficiency was first suggestedby Prandtl [10] The presence of an end plate modifies the3D flow phenomena at the tip of the FR augmenting theldquoeffective ARrdquo of the rotor Thom [3] investigated the effectof large end plates with a diameter ratio 119889

119890119889 = 30 where 119889

119890

is the diameter of the end plate disk (Figure 2)The FR with end plate also called Thom disk is able

to produce almost double the lift at high velocity ratios forexample SR = 20 In Badalamenti and Prince [12] it isshown that for a cylinder with AR = 51 and diameter ratiosranging from 11 to 30 the effects of the increases 119889

119890119889 and

AR are similar Increasing the 119889119890119889 value a higher lift value

is generated by the FR and such value occurs at higher SR aswell (see Seifert [6]) Thouault et al [13] presented a detailedanalysis of the effects of end plate dimensions on the FRefficiency based on experiments and numerical simulations

A discussion of how the end plate size is related to SR inorder to achieve optimal performances of the FR is presentedby Seifert [6] In his work Seifert observes that at low spinratio (SR = 10) smaller plates generally give lightly smallerdrag for applications at moderate spin ratio (10 lt SR lt

30) larger plates are preferred so as to delay the increase ininduced drag while for high spin ratio applications (SR gt

30) smaller plates are again more desirable

24 Marine Application of FR Concerning the use of FRfor marine applications not many research papers are avail-able in the literature An overview of the applications ofthe Magnus effect devices in the marine field is given inMorisseau [14] The Magnus effect devices can be used asroll stabilizers water propellers and air generator such asFR Moreover this paper reports an interesting preliminaryanalysis of retrofitting of a single screw US Navy auxiliaryship with five FRs More recently in Pearson [15] a ldquofirst-stagerdquo assessment is found in practical limitations as well asnegative side effects of retrofitting Flettner rotors to a ship Allthese considerations are collected in order to create a softwaremodel for a preliminary analysis of the viability of retrofittingFR to a defined ship before any progression onto analyzingspecific scenario benefits or other detailed investigations Alimit of this work is in the estimation of FR performanceswhich are evaluated only as a function of SR The softwarepresented assumes a universal FR geometry with 119889

119890119889 = 15

and AR = 5 (based on Prandtlrsquos study [10]) and evaluates 119862119871

and119862119863of this FR then the performances of FR are evaluated

changing SR in the range 00sim80Traut et al [16] explore the potential for harnessing wind

power for shipping applications Numerical models of thetwo main wind power technologies FR and towing kite arelinked with wind data along a set of five trade routes Theresults of their analysis give an estimation of the average windpower contribution on a defined route For a single FR thedelivered power is in a range between 193 and 373 kW and

Figure 3 Estraden ship latest FR installation

for the towing kite between 127 and 461 kW The FR has avariability of the delivered power smaller than the towingkite due to the different dependencies on wind speed anddirection The average power contribution coming from anFR is higher than that coming from the kite on some routesand lower on others But an advantage of FR is that thecontribution would be expected to increase almost linearlywith the number of devices installed on the same ship (in thisrespect a quantitative study of interference effects is lackingin the literature) For this reason for instance installing threeFRs on a 5500DWT (dead weight tonnage) general cargocarrier could provide on average more than half the powerrequired by the main engine under typical slow steamingconditions

25 Aim of the Work The present research extends previousinvestigations presented in De Marco et al [17] and in DeMarco et al [11] in order to assess in a systematic way theeffect of the FR key parameters that is the AR SR and theend plate diameter on the device performance Furthermorethe mutual interaction effects of these parameters on theaerodynamic forces generated by FR are investigated Theanalyzed ranges of variation of the key parameters havebeen chosen considering technologically plausible marineapplications of the FR concept

3 Flettner Rotor Installationsand Reference Data

To choose the ranges of the key parameters some constraintshave been taken into account For instance one has toconsider the currently available technology as well as thepracticality in marine applications Another important factoris the vortex shedding risk (first and second mode) whichdepends on the mutual interaction between AR and SRConsequently the limits of AR and SR have been identifiedby the analysis of some real FR installations on board

The known installations of FR and their reference dataare summarized in Table 1 The first two examples Buckauand Barbara are not in service while the two ships E-Ship-1 and Estraden (Figure 3) are currently operated byNorth European owners for commercial purposes In allof these examples a Thom disk is used and the AR are inthe range 55sim70 This range is taken as a reference for the

4 International Journal of Rotating Machinery

Table 1 Geometric performance and structural related parameters collected from all-known rotor ships

Ship (year) Buckau (1924) Barbara (1926) E-Ship 1 (2010) Estraden (2014)Type Retrofit Newbuild Newbuild RetrofitHeight (m) 156 170 270 190Diameter (m) 28 40 40 30Aspect ratio 56 43 68 63End plate Yes Yes Yes YesMaterial Zinc coated steel Aluminum NA CompositeMax rpm 1350 1500 NA 2500

Table 2 Values of analyzed variables

Variables ValuesSR 10 15 20 30AR 20 40 60 80119889119890119889 10 20 30

investigations presented here It is observed that the angularrotor speeds have increased over the years thus allowinghigher SR However the SR values of interest for marineapplication remain in the range 10 to 30 For example SR =

25 is obtained for a typical relative wind velocity of 20 kn(10ms) a reasonable diameter of 30m and a rotation speedof 160 rpm

4 Numerical Experiments

Systematic variations of FR configurations have been inves-tigated by means of URANS simulations in incompressibleflow All the analyses have been performed using the com-mercially available computational fluid dynamics softwareCD adapco STAR-CCM+ v 906 The simulations were con-ducted using the same approach such as the oversetchimeragrid technique described in De Marco et al [17] and in DeMarco et al [11] Furthermore fairly wide ranges of the keyparameters that is AR SR and 119889

119890119889 have been examined

as detailed in the Table 2 and displayed in Figure 4 Thecharacteristics of FRs were evaluated in terms of lift anddrag coefficients and aerodynamic efficiencyThe simulationshave been launched on the computer cluster of the SCoPEsupercomputing centre at the University of Naples ldquoFedericoIIrdquo using up to 120 CPUs in parallel

41 Simulation Setup The rotating motion of the FR wassimulated using the oversetchimera mesh methodologywith distance-weighted interpolation method This methodwhich is especially suitable for rotational movements usesan interpolation factor inversely proportional to the distancefrom acceptor cell to donor cell as indicated in CD adapcoUserrsquos Guide [18]

Hybridmesh approach coupling unstructured and struc-tured mesh has been used for all the simulations Thecomputational domain contains two regions the backgroundnonrotating region and the overlapped rotating region(Figure 5) For the background and overlapped region an

AR

1 2 3

24

68

ded

Figure 4 Sketch of all geometry of FRs tested

unstructured grid approach was used while a structuredboundary layer mesh was created near the FR surface Thechoice of hybrid mesh approach is justified by the fact thatthis is a suitable compromise between accuracy and compu-tational effort compared with the Cartesian mesh as shownin the 2D preliminary study reported in De Marco et al [11]Furthermore the grid set up allowed a nondimensional walldistance (y+) value approximately equal to 10

The chosen URANS-solving algorithm uses a first-orderforward Euler scheme for the temporal discretization animplicit element-based finite volume method and a segre-gated flow approachwith second-order upwind discretizationof the convective terms A fully turbulent approach with 119896-120596Shear Stress-Transport (SST) turbulencemodel has been used(a comparison with other turbulence model is reported inFigure 9) All of the properties of the numerical solver aresummarized in Table 3

It has to be noted that the simulation time step is afunction of the angular speed Ω For the convergence of thenumerical scheme as a rule of thumb there is a limitationon themaximum cell-based Courant-Friedrichs-Lewy (CFL)number in a time stepTherefore the higher the angular speedthe lower the time step

42 Computational Domain and Boundary Conditions Abox-shaped domain has been created around the cylinder

International Journal of Rotating Machinery 5

Table 3 Summary of the numerical simulation setup

Pressure link Pressure Convectionterm

Temporaldiscretization Time step (s) Iteration per

time stepTurbulencemodel

Oversetinterpolation

scheme

Simple Standard 2nd order 1st orderFunction ofangular speed

(Ω)11 119896-120596 SST Distance

weighted

(a)

Overset region

Backgroundregion

Interface

(b)

Figure 5 Section of the computational grid (a) Close-up views of the hybrid mesh (b)

Inletvelocity

Inletvelocity

Inletvelocity

Symmetry plane

Pressure outlet

15d

5d275d

35H

Figure 6 Boundary conditions and domain dimensions in functionof the main dimensions of FR (119867 119889)

geometry as seen in Figure 6 In order to reduce the compu-tational effort only half the domain has been considered anda symmetry plane has been assumed containing the cylinderaxis and parallel to the free stream velocity A velocity inletboundary condition has been set on the front side of thedomain with a prescribed velocity this inlet velocity also hasbeen used to control the SR of the rotor keeping constantits angular speed Ω On the bottom and the top side of thedomain a symmetry boundary condition also is used On therear side of the domain surface a pressure outlet boundarycondition has been imposed with a relative pressure of value0 Pa An axial-symmetrical zone surrounding the rotor hadto be modeled overlapping the rotating mesh (fixed with therotor) and the underlying nonmoving mesh domain Thisturned out to be a necessary grid treatment for using theoverset mesh methodology

43 Numerical Uncertainty Analysis In order to assess thenumerical setup and to evaluate the simulation numericaluncertainty 119880SN a verification study has been performed

The benchmark experimental data are derived fromBadalamenti and Prince [8 12] and are related to an FR withAR = 51 (cylinder height 119867 = 045m) diameter of 119889 =

00889m and the Thom disk on the top of this FR with119889119890= 01778m (corresponding to 119889

119890119889 = 20)

According to the Oberkampf and Blottner [19] verifica-tion is defined as a process for assessing simulation numericaluncertainty 119880SN The simulation numerical error and uncer-tainty are composed of a grid convergence error (120575

119866) iterative

convergence error (120575119868) time step convergence error (120575TS)

and other parameters (120575119875) Therefore the numerical error is

the sum

120575SN = 120575119866

+ 120575119868+ 120575TS + 120575

119875 (1)

and the simulation numerical uncertainty is given by theformula

1198802

SN = 1198802

119866+ 1198802

119868+ 1198802

TS + 1198802

119875 (2)

where 119880119866 119880119868 119880TS and 119880

119875are the uncertainties arising

from the grid iterative time step and other parametersrespectively (see Stern et al [20])

The numerical uncertainty evaluation was performedusing two different methods the grid convergence index(GCI) method and the correction factor (CF) method Thegeneral form of the uncertainty evaluation based on thegeneralized Richardson extrapolation (RE) method can bewritten as follows

119880119896= 119865119878(

12057621119896

119903119901119896

119896minus 1

) (3)

where 12057621119896

is the solution changes for the 119896-input parameterbetween the solutions (fine (119878

1119896) to medium (119878

2119896) and coarse

(1198783119896)) 119903119896is the constant refinement ratio (recommended

6 International Journal of Rotating Machinery

values between radic2 and 2) 119901119896is the observed order of

accuracy and 119865119878is the safety factor Furthermore another

parameter is the convergence ratio (119877119896) which provides

information about the convergencedivergence of a solutionThe 119877

119896value was determined by the following ratio

119877119896=

12057621119896

12057632119896

(4)

The two different solution verification methods used in thisstudy differ in the choice of safety factor (119865

119878)

The GCI method proposed by Roache [21 22] is usedextensively and it is recommended for example by theAmerican Society of Mechanical Engineers (ASME) [23]and the American Institute of Aeronautics and Astronautics(AIAA) [24] Roache recommended for careful grid studies(three or more grids analyzed) 125 as the 119865

119878value

The other method used is the CF described in Stern et al[20] that uses a variable value of 119865

119878 In the CFmethod unlike

in the GCI method the uncertainty of the error dependson how close the solutions are to the asymptotic rangeThe expressions to assess the uncertainties were reported byWilson et al [25]

The verification study has been carried out for the criticalpoints of SR = 20 and SR = 25 in terms of 119862

119863estimation

errorThe iterative uncertainties are estimated by the fluctua-

tions of the time-history of the results in the last few periodsas indicated in Stern et al [20] Specifically as reported in (5)119880119868are estimated by half the difference of the maximum value

(119878119880) and the minimum value (119878

119871) of the final time-history of

the results

119880119868=

1003816100381610038161003816100381610038161003816

1

2(119878119880

minus 119878119871)

1003816100381610038161003816100381610038161003816 (5)

Then the grid uncertainty has been evaluated by the follow-ing expressions that is (6) for the GCI method and (7) forthe CF method

119880119896= 125 sdot

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

(6)

119880119896

=

[96 (1 minus 119862119896)2+ 11]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 lt 0125

[210038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 + 1]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 ge 0125

(7)

where 119865119878is equal to 125 and 119862

119896is the correction factor

Verification results using three systematically refined gridswith the refinement ratio (119903

119866) equal to radic2 are shown in

Table 5 The grid sizes range from 09M to 19M grid pointsand the three grids tested are shown in Table 4

Because 0 lt 119877119866

lt 1 monotonic convergence isachieved for 119862

119871and 119862

119863 where 119877

119866is convergence ratio for

the grid calculated according to (4) The uncertainty valuesare reported in Table 5

Table 4 The three grids tested

Grids CellsGrid A Coarse 0933 sdot 10

6

Grid B Medium 1320 sdot 106

Grid C Fine 1867 sdot 106

The values of simulation uncertainty reported in Table 5show that119880SN for 119862

119863is higher than119880SN for 119862

119871 due to much

larger errors in the estimation of 119862119863than of 119862

119871for SR = 20

and SR = 25Iterative convergence is achieved for all simulations and

119880119868is found to be negligible with respect to grid errors

similarly to what happens in other engineering applications(eg Wilson et al [26] and Xing et al [27])

Moreover the verification procedure cannot be com-pleted with the validation phase due to the lack of experi-mental uncertainty dataTherefore only the results related tosimulation numerical uncertainty are reported in Table 5

The numerical results of the verification study have beencompared with the experimental data as shown in Figure 7The comparison highlighted that no significant improvementin the 119862

119871and 119862

119863evaluation is detected between coarse

medium and fine mesh case However increasing the gridpoints increases the calculation effort as shown in Figure 8

For the reasons mentioned above the grid of Case B hasbeen assumed as the reference mesh This grid guarantees anacceptable solutionwithout an excessive computational effort(such as in Case C)

The comparison between experimental data and numer-ical results for SR in the range from 00 to 25 reportedin Figure 9 shows a good agreement in particular for 119862

119871

Regarding 119862119863 the CFD simulations give reliable results for

SR lt 15 and the error increases at higher values of SRlikewise highlighted in Thouault et al [13] and Da-Qing etal [5]

As shown in Table 5 it can be observed that for 119862119863the

comparison error (119864) is much greater than 119880SN Accordingto Oberkampf and Blottner [19] and Stern et al [20] it canbe said that when 119864 is much greater than the uncertaintyit is necessary to improve the simulations models It iswell known that one of the main sources of the modelingsimulation error is the turbulence models Nevertheless ashighlighted in Figure 9 comparing the different two-equationturbulence models that is 119896-120596 SST and Realizable 119896-120576 nosignificant differences are appreciableThe 119896-120596 SST is used asturbulencemodel for all the subsequent simulations howevera different simulation approach is required for an accurate119862

119863

evaluation at high SR

5 Results

The results of the simulations performed into the variableranges indicated in Table 2 are reported in terms of the so-called response curvesThese curves shown in Figure 10 rep-resent the values of 119862

119871and 119862

119863and aerodynamic efficiency

keeping constant 119889119890119889 of the FRThis representation is useful

because it permits us to clearly recognize the relationships

International Journal of Rotating Machinery 7

65 64 62

231213 199

Case A Case B Case C

SR 25SR 20

0

10

20

30

40

CL

erro

r

(a)

331 322 314

363 359 356

Case A Case B Case C0

10

20

30

40

C

Der

ror

SR 25SR 20

(b)

Figure 7 119862119871and 119862

119863percentage error between numerical (three mesh cases tested) and experimental data at SR = 20 and 25

Case A Case B Case C

CPU

tim

e per

tim

e ste

p (s

)

0

1000

2000

3000

Figure 8 Computational time required for the grids tested

Exp dataCFD k-εCFD k-120596 SST

minus1000102030405060708090

100

CL

05 10 15 20 2500SR

(a)

00

20

40

60

80

100

CD

05 10 15 20 2500SR

Exp dataCFD k-εCFD k-120596 SST

(b)

Figure 9 Comparison between CFD results and experimental data for lift (a) and drag (b) coefficient using mesh Case B and two differentturbulence models

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

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International Journal of

International Journal of Rotating Machinery 3

performances both experimental and numerical ones alongwith some considerations can be found in De Marco et al[11]

23 End Plate The idea of applying an end plate on FRto optimize its aerodynamic efficiency was first suggestedby Prandtl [10] The presence of an end plate modifies the3D flow phenomena at the tip of the FR augmenting theldquoeffective ARrdquo of the rotor Thom [3] investigated the effectof large end plates with a diameter ratio 119889

119890119889 = 30 where 119889

119890

is the diameter of the end plate disk (Figure 2)The FR with end plate also called Thom disk is able

to produce almost double the lift at high velocity ratios forexample SR = 20 In Badalamenti and Prince [12] it isshown that for a cylinder with AR = 51 and diameter ratiosranging from 11 to 30 the effects of the increases 119889

119890119889 and

AR are similar Increasing the 119889119890119889 value a higher lift value

is generated by the FR and such value occurs at higher SR aswell (see Seifert [6]) Thouault et al [13] presented a detailedanalysis of the effects of end plate dimensions on the FRefficiency based on experiments and numerical simulations

A discussion of how the end plate size is related to SR inorder to achieve optimal performances of the FR is presentedby Seifert [6] In his work Seifert observes that at low spinratio (SR = 10) smaller plates generally give lightly smallerdrag for applications at moderate spin ratio (10 lt SR lt

30) larger plates are preferred so as to delay the increase ininduced drag while for high spin ratio applications (SR gt

30) smaller plates are again more desirable

24 Marine Application of FR Concerning the use of FRfor marine applications not many research papers are avail-able in the literature An overview of the applications ofthe Magnus effect devices in the marine field is given inMorisseau [14] The Magnus effect devices can be used asroll stabilizers water propellers and air generator such asFR Moreover this paper reports an interesting preliminaryanalysis of retrofitting of a single screw US Navy auxiliaryship with five FRs More recently in Pearson [15] a ldquofirst-stagerdquo assessment is found in practical limitations as well asnegative side effects of retrofitting Flettner rotors to a ship Allthese considerations are collected in order to create a softwaremodel for a preliminary analysis of the viability of retrofittingFR to a defined ship before any progression onto analyzingspecific scenario benefits or other detailed investigations Alimit of this work is in the estimation of FR performanceswhich are evaluated only as a function of SR The softwarepresented assumes a universal FR geometry with 119889

119890119889 = 15

and AR = 5 (based on Prandtlrsquos study [10]) and evaluates 119862119871

and119862119863of this FR then the performances of FR are evaluated

changing SR in the range 00sim80Traut et al [16] explore the potential for harnessing wind

power for shipping applications Numerical models of thetwo main wind power technologies FR and towing kite arelinked with wind data along a set of five trade routes Theresults of their analysis give an estimation of the average windpower contribution on a defined route For a single FR thedelivered power is in a range between 193 and 373 kW and

Figure 3 Estraden ship latest FR installation

for the towing kite between 127 and 461 kW The FR has avariability of the delivered power smaller than the towingkite due to the different dependencies on wind speed anddirection The average power contribution coming from anFR is higher than that coming from the kite on some routesand lower on others But an advantage of FR is that thecontribution would be expected to increase almost linearlywith the number of devices installed on the same ship (in thisrespect a quantitative study of interference effects is lackingin the literature) For this reason for instance installing threeFRs on a 5500DWT (dead weight tonnage) general cargocarrier could provide on average more than half the powerrequired by the main engine under typical slow steamingconditions

25 Aim of the Work The present research extends previousinvestigations presented in De Marco et al [17] and in DeMarco et al [11] in order to assess in a systematic way theeffect of the FR key parameters that is the AR SR and theend plate diameter on the device performance Furthermorethe mutual interaction effects of these parameters on theaerodynamic forces generated by FR are investigated Theanalyzed ranges of variation of the key parameters havebeen chosen considering technologically plausible marineapplications of the FR concept

3 Flettner Rotor Installationsand Reference Data

To choose the ranges of the key parameters some constraintshave been taken into account For instance one has toconsider the currently available technology as well as thepracticality in marine applications Another important factoris the vortex shedding risk (first and second mode) whichdepends on the mutual interaction between AR and SRConsequently the limits of AR and SR have been identifiedby the analysis of some real FR installations on board

The known installations of FR and their reference dataare summarized in Table 1 The first two examples Buckauand Barbara are not in service while the two ships E-Ship-1 and Estraden (Figure 3) are currently operated byNorth European owners for commercial purposes In allof these examples a Thom disk is used and the AR are inthe range 55sim70 This range is taken as a reference for the

4 International Journal of Rotating Machinery

Table 1 Geometric performance and structural related parameters collected from all-known rotor ships

Ship (year) Buckau (1924) Barbara (1926) E-Ship 1 (2010) Estraden (2014)Type Retrofit Newbuild Newbuild RetrofitHeight (m) 156 170 270 190Diameter (m) 28 40 40 30Aspect ratio 56 43 68 63End plate Yes Yes Yes YesMaterial Zinc coated steel Aluminum NA CompositeMax rpm 1350 1500 NA 2500

Table 2 Values of analyzed variables

Variables ValuesSR 10 15 20 30AR 20 40 60 80119889119890119889 10 20 30

investigations presented here It is observed that the angularrotor speeds have increased over the years thus allowinghigher SR However the SR values of interest for marineapplication remain in the range 10 to 30 For example SR =

25 is obtained for a typical relative wind velocity of 20 kn(10ms) a reasonable diameter of 30m and a rotation speedof 160 rpm

4 Numerical Experiments

Systematic variations of FR configurations have been inves-tigated by means of URANS simulations in incompressibleflow All the analyses have been performed using the com-mercially available computational fluid dynamics softwareCD adapco STAR-CCM+ v 906 The simulations were con-ducted using the same approach such as the oversetchimeragrid technique described in De Marco et al [17] and in DeMarco et al [11] Furthermore fairly wide ranges of the keyparameters that is AR SR and 119889

119890119889 have been examined

as detailed in the Table 2 and displayed in Figure 4 Thecharacteristics of FRs were evaluated in terms of lift anddrag coefficients and aerodynamic efficiencyThe simulationshave been launched on the computer cluster of the SCoPEsupercomputing centre at the University of Naples ldquoFedericoIIrdquo using up to 120 CPUs in parallel

41 Simulation Setup The rotating motion of the FR wassimulated using the oversetchimera mesh methodologywith distance-weighted interpolation method This methodwhich is especially suitable for rotational movements usesan interpolation factor inversely proportional to the distancefrom acceptor cell to donor cell as indicated in CD adapcoUserrsquos Guide [18]

Hybridmesh approach coupling unstructured and struc-tured mesh has been used for all the simulations Thecomputational domain contains two regions the backgroundnonrotating region and the overlapped rotating region(Figure 5) For the background and overlapped region an

AR

1 2 3

24

68

ded

Figure 4 Sketch of all geometry of FRs tested

unstructured grid approach was used while a structuredboundary layer mesh was created near the FR surface Thechoice of hybrid mesh approach is justified by the fact thatthis is a suitable compromise between accuracy and compu-tational effort compared with the Cartesian mesh as shownin the 2D preliminary study reported in De Marco et al [11]Furthermore the grid set up allowed a nondimensional walldistance (y+) value approximately equal to 10

The chosen URANS-solving algorithm uses a first-orderforward Euler scheme for the temporal discretization animplicit element-based finite volume method and a segre-gated flow approachwith second-order upwind discretizationof the convective terms A fully turbulent approach with 119896-120596Shear Stress-Transport (SST) turbulencemodel has been used(a comparison with other turbulence model is reported inFigure 9) All of the properties of the numerical solver aresummarized in Table 3

It has to be noted that the simulation time step is afunction of the angular speed Ω For the convergence of thenumerical scheme as a rule of thumb there is a limitationon themaximum cell-based Courant-Friedrichs-Lewy (CFL)number in a time stepTherefore the higher the angular speedthe lower the time step

42 Computational Domain and Boundary Conditions Abox-shaped domain has been created around the cylinder

International Journal of Rotating Machinery 5

Table 3 Summary of the numerical simulation setup

Pressure link Pressure Convectionterm

Temporaldiscretization Time step (s) Iteration per

time stepTurbulencemodel

Oversetinterpolation

scheme

Simple Standard 2nd order 1st orderFunction ofangular speed

(Ω)11 119896-120596 SST Distance

weighted

(a)

Overset region

Backgroundregion

Interface

(b)

Figure 5 Section of the computational grid (a) Close-up views of the hybrid mesh (b)

Inletvelocity

Inletvelocity

Inletvelocity

Symmetry plane

Pressure outlet

15d

5d275d

35H

Figure 6 Boundary conditions and domain dimensions in functionof the main dimensions of FR (119867 119889)

geometry as seen in Figure 6 In order to reduce the compu-tational effort only half the domain has been considered anda symmetry plane has been assumed containing the cylinderaxis and parallel to the free stream velocity A velocity inletboundary condition has been set on the front side of thedomain with a prescribed velocity this inlet velocity also hasbeen used to control the SR of the rotor keeping constantits angular speed Ω On the bottom and the top side of thedomain a symmetry boundary condition also is used On therear side of the domain surface a pressure outlet boundarycondition has been imposed with a relative pressure of value0 Pa An axial-symmetrical zone surrounding the rotor hadto be modeled overlapping the rotating mesh (fixed with therotor) and the underlying nonmoving mesh domain Thisturned out to be a necessary grid treatment for using theoverset mesh methodology

43 Numerical Uncertainty Analysis In order to assess thenumerical setup and to evaluate the simulation numericaluncertainty 119880SN a verification study has been performed

The benchmark experimental data are derived fromBadalamenti and Prince [8 12] and are related to an FR withAR = 51 (cylinder height 119867 = 045m) diameter of 119889 =

00889m and the Thom disk on the top of this FR with119889119890= 01778m (corresponding to 119889

119890119889 = 20)

According to the Oberkampf and Blottner [19] verifica-tion is defined as a process for assessing simulation numericaluncertainty 119880SN The simulation numerical error and uncer-tainty are composed of a grid convergence error (120575

119866) iterative

convergence error (120575119868) time step convergence error (120575TS)

and other parameters (120575119875) Therefore the numerical error is

the sum

120575SN = 120575119866

+ 120575119868+ 120575TS + 120575

119875 (1)

and the simulation numerical uncertainty is given by theformula

1198802

SN = 1198802

119866+ 1198802

119868+ 1198802

TS + 1198802

119875 (2)

where 119880119866 119880119868 119880TS and 119880

119875are the uncertainties arising

from the grid iterative time step and other parametersrespectively (see Stern et al [20])

The numerical uncertainty evaluation was performedusing two different methods the grid convergence index(GCI) method and the correction factor (CF) method Thegeneral form of the uncertainty evaluation based on thegeneralized Richardson extrapolation (RE) method can bewritten as follows

119880119896= 119865119878(

12057621119896

119903119901119896

119896minus 1

) (3)

where 12057621119896

is the solution changes for the 119896-input parameterbetween the solutions (fine (119878

1119896) to medium (119878

2119896) and coarse

(1198783119896)) 119903119896is the constant refinement ratio (recommended

6 International Journal of Rotating Machinery

values between radic2 and 2) 119901119896is the observed order of

accuracy and 119865119878is the safety factor Furthermore another

parameter is the convergence ratio (119877119896) which provides

information about the convergencedivergence of a solutionThe 119877

119896value was determined by the following ratio

119877119896=

12057621119896

12057632119896

(4)

The two different solution verification methods used in thisstudy differ in the choice of safety factor (119865

119878)

The GCI method proposed by Roache [21 22] is usedextensively and it is recommended for example by theAmerican Society of Mechanical Engineers (ASME) [23]and the American Institute of Aeronautics and Astronautics(AIAA) [24] Roache recommended for careful grid studies(three or more grids analyzed) 125 as the 119865

119878value

The other method used is the CF described in Stern et al[20] that uses a variable value of 119865

119878 In the CFmethod unlike

in the GCI method the uncertainty of the error dependson how close the solutions are to the asymptotic rangeThe expressions to assess the uncertainties were reported byWilson et al [25]

The verification study has been carried out for the criticalpoints of SR = 20 and SR = 25 in terms of 119862

119863estimation

errorThe iterative uncertainties are estimated by the fluctua-

tions of the time-history of the results in the last few periodsas indicated in Stern et al [20] Specifically as reported in (5)119880119868are estimated by half the difference of the maximum value

(119878119880) and the minimum value (119878

119871) of the final time-history of

the results

119880119868=

1003816100381610038161003816100381610038161003816

1

2(119878119880

minus 119878119871)

1003816100381610038161003816100381610038161003816 (5)

Then the grid uncertainty has been evaluated by the follow-ing expressions that is (6) for the GCI method and (7) forthe CF method

119880119896= 125 sdot

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

(6)

119880119896

=

[96 (1 minus 119862119896)2+ 11]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 lt 0125

[210038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 + 1]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 ge 0125

(7)

where 119865119878is equal to 125 and 119862

119896is the correction factor

Verification results using three systematically refined gridswith the refinement ratio (119903

119866) equal to radic2 are shown in

Table 5 The grid sizes range from 09M to 19M grid pointsand the three grids tested are shown in Table 4

Because 0 lt 119877119866

lt 1 monotonic convergence isachieved for 119862

119871and 119862

119863 where 119877

119866is convergence ratio for

the grid calculated according to (4) The uncertainty valuesare reported in Table 5

Table 4 The three grids tested

Grids CellsGrid A Coarse 0933 sdot 10

6

Grid B Medium 1320 sdot 106

Grid C Fine 1867 sdot 106

The values of simulation uncertainty reported in Table 5show that119880SN for 119862

119863is higher than119880SN for 119862

119871 due to much

larger errors in the estimation of 119862119863than of 119862

119871for SR = 20

and SR = 25Iterative convergence is achieved for all simulations and

119880119868is found to be negligible with respect to grid errors

similarly to what happens in other engineering applications(eg Wilson et al [26] and Xing et al [27])

Moreover the verification procedure cannot be com-pleted with the validation phase due to the lack of experi-mental uncertainty dataTherefore only the results related tosimulation numerical uncertainty are reported in Table 5

The numerical results of the verification study have beencompared with the experimental data as shown in Figure 7The comparison highlighted that no significant improvementin the 119862

119871and 119862

119863evaluation is detected between coarse

medium and fine mesh case However increasing the gridpoints increases the calculation effort as shown in Figure 8

For the reasons mentioned above the grid of Case B hasbeen assumed as the reference mesh This grid guarantees anacceptable solutionwithout an excessive computational effort(such as in Case C)

The comparison between experimental data and numer-ical results for SR in the range from 00 to 25 reportedin Figure 9 shows a good agreement in particular for 119862

119871

Regarding 119862119863 the CFD simulations give reliable results for

SR lt 15 and the error increases at higher values of SRlikewise highlighted in Thouault et al [13] and Da-Qing etal [5]

As shown in Table 5 it can be observed that for 119862119863the

comparison error (119864) is much greater than 119880SN Accordingto Oberkampf and Blottner [19] and Stern et al [20] it canbe said that when 119864 is much greater than the uncertaintyit is necessary to improve the simulations models It iswell known that one of the main sources of the modelingsimulation error is the turbulence models Nevertheless ashighlighted in Figure 9 comparing the different two-equationturbulence models that is 119896-120596 SST and Realizable 119896-120576 nosignificant differences are appreciableThe 119896-120596 SST is used asturbulencemodel for all the subsequent simulations howevera different simulation approach is required for an accurate119862

119863

evaluation at high SR

5 Results

The results of the simulations performed into the variableranges indicated in Table 2 are reported in terms of the so-called response curvesThese curves shown in Figure 10 rep-resent the values of 119862

119871and 119862

119863and aerodynamic efficiency

keeping constant 119889119890119889 of the FRThis representation is useful

because it permits us to clearly recognize the relationships

International Journal of Rotating Machinery 7

65 64 62

231213 199

Case A Case B Case C

SR 25SR 20

0

10

20

30

40

CL

erro

r

(a)

331 322 314

363 359 356

Case A Case B Case C0

10

20

30

40

C

Der

ror

SR 25SR 20

(b)

Figure 7 119862119871and 119862

119863percentage error between numerical (three mesh cases tested) and experimental data at SR = 20 and 25

Case A Case B Case C

CPU

tim

e per

tim

e ste

p (s

)

0

1000

2000

3000

Figure 8 Computational time required for the grids tested

Exp dataCFD k-εCFD k-120596 SST

minus1000102030405060708090

100

CL

05 10 15 20 2500SR

(a)

00

20

40

60

80

100

CD

05 10 15 20 2500SR

Exp dataCFD k-εCFD k-120596 SST

(b)

Figure 9 Comparison between CFD results and experimental data for lift (a) and drag (b) coefficient using mesh Case B and two differentturbulence models

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 International Journal of Rotating Machinery

Table 1 Geometric performance and structural related parameters collected from all-known rotor ships

Ship (year) Buckau (1924) Barbara (1926) E-Ship 1 (2010) Estraden (2014)Type Retrofit Newbuild Newbuild RetrofitHeight (m) 156 170 270 190Diameter (m) 28 40 40 30Aspect ratio 56 43 68 63End plate Yes Yes Yes YesMaterial Zinc coated steel Aluminum NA CompositeMax rpm 1350 1500 NA 2500

Table 2 Values of analyzed variables

Variables ValuesSR 10 15 20 30AR 20 40 60 80119889119890119889 10 20 30

investigations presented here It is observed that the angularrotor speeds have increased over the years thus allowinghigher SR However the SR values of interest for marineapplication remain in the range 10 to 30 For example SR =

25 is obtained for a typical relative wind velocity of 20 kn(10ms) a reasonable diameter of 30m and a rotation speedof 160 rpm

4 Numerical Experiments

Systematic variations of FR configurations have been inves-tigated by means of URANS simulations in incompressibleflow All the analyses have been performed using the com-mercially available computational fluid dynamics softwareCD adapco STAR-CCM+ v 906 The simulations were con-ducted using the same approach such as the oversetchimeragrid technique described in De Marco et al [17] and in DeMarco et al [11] Furthermore fairly wide ranges of the keyparameters that is AR SR and 119889

119890119889 have been examined

as detailed in the Table 2 and displayed in Figure 4 Thecharacteristics of FRs were evaluated in terms of lift anddrag coefficients and aerodynamic efficiencyThe simulationshave been launched on the computer cluster of the SCoPEsupercomputing centre at the University of Naples ldquoFedericoIIrdquo using up to 120 CPUs in parallel

41 Simulation Setup The rotating motion of the FR wassimulated using the oversetchimera mesh methodologywith distance-weighted interpolation method This methodwhich is especially suitable for rotational movements usesan interpolation factor inversely proportional to the distancefrom acceptor cell to donor cell as indicated in CD adapcoUserrsquos Guide [18]

Hybridmesh approach coupling unstructured and struc-tured mesh has been used for all the simulations Thecomputational domain contains two regions the backgroundnonrotating region and the overlapped rotating region(Figure 5) For the background and overlapped region an

AR

1 2 3

24

68

ded

Figure 4 Sketch of all geometry of FRs tested

unstructured grid approach was used while a structuredboundary layer mesh was created near the FR surface Thechoice of hybrid mesh approach is justified by the fact thatthis is a suitable compromise between accuracy and compu-tational effort compared with the Cartesian mesh as shownin the 2D preliminary study reported in De Marco et al [11]Furthermore the grid set up allowed a nondimensional walldistance (y+) value approximately equal to 10

The chosen URANS-solving algorithm uses a first-orderforward Euler scheme for the temporal discretization animplicit element-based finite volume method and a segre-gated flow approachwith second-order upwind discretizationof the convective terms A fully turbulent approach with 119896-120596Shear Stress-Transport (SST) turbulencemodel has been used(a comparison with other turbulence model is reported inFigure 9) All of the properties of the numerical solver aresummarized in Table 3

It has to be noted that the simulation time step is afunction of the angular speed Ω For the convergence of thenumerical scheme as a rule of thumb there is a limitationon themaximum cell-based Courant-Friedrichs-Lewy (CFL)number in a time stepTherefore the higher the angular speedthe lower the time step

42 Computational Domain and Boundary Conditions Abox-shaped domain has been created around the cylinder

International Journal of Rotating Machinery 5

Table 3 Summary of the numerical simulation setup

Pressure link Pressure Convectionterm

Temporaldiscretization Time step (s) Iteration per

time stepTurbulencemodel

Oversetinterpolation

scheme

Simple Standard 2nd order 1st orderFunction ofangular speed

(Ω)11 119896-120596 SST Distance

weighted

(a)

Overset region

Backgroundregion

Interface

(b)

Figure 5 Section of the computational grid (a) Close-up views of the hybrid mesh (b)

Inletvelocity

Inletvelocity

Inletvelocity

Symmetry plane

Pressure outlet

15d

5d275d

35H

Figure 6 Boundary conditions and domain dimensions in functionof the main dimensions of FR (119867 119889)

geometry as seen in Figure 6 In order to reduce the compu-tational effort only half the domain has been considered anda symmetry plane has been assumed containing the cylinderaxis and parallel to the free stream velocity A velocity inletboundary condition has been set on the front side of thedomain with a prescribed velocity this inlet velocity also hasbeen used to control the SR of the rotor keeping constantits angular speed Ω On the bottom and the top side of thedomain a symmetry boundary condition also is used On therear side of the domain surface a pressure outlet boundarycondition has been imposed with a relative pressure of value0 Pa An axial-symmetrical zone surrounding the rotor hadto be modeled overlapping the rotating mesh (fixed with therotor) and the underlying nonmoving mesh domain Thisturned out to be a necessary grid treatment for using theoverset mesh methodology

43 Numerical Uncertainty Analysis In order to assess thenumerical setup and to evaluate the simulation numericaluncertainty 119880SN a verification study has been performed

The benchmark experimental data are derived fromBadalamenti and Prince [8 12] and are related to an FR withAR = 51 (cylinder height 119867 = 045m) diameter of 119889 =

00889m and the Thom disk on the top of this FR with119889119890= 01778m (corresponding to 119889

119890119889 = 20)

According to the Oberkampf and Blottner [19] verifica-tion is defined as a process for assessing simulation numericaluncertainty 119880SN The simulation numerical error and uncer-tainty are composed of a grid convergence error (120575

119866) iterative

convergence error (120575119868) time step convergence error (120575TS)

and other parameters (120575119875) Therefore the numerical error is

the sum

120575SN = 120575119866

+ 120575119868+ 120575TS + 120575

119875 (1)

and the simulation numerical uncertainty is given by theformula

1198802

SN = 1198802

119866+ 1198802

119868+ 1198802

TS + 1198802

119875 (2)

where 119880119866 119880119868 119880TS and 119880

119875are the uncertainties arising

from the grid iterative time step and other parametersrespectively (see Stern et al [20])

The numerical uncertainty evaluation was performedusing two different methods the grid convergence index(GCI) method and the correction factor (CF) method Thegeneral form of the uncertainty evaluation based on thegeneralized Richardson extrapolation (RE) method can bewritten as follows

119880119896= 119865119878(

12057621119896

119903119901119896

119896minus 1

) (3)

where 12057621119896

is the solution changes for the 119896-input parameterbetween the solutions (fine (119878

1119896) to medium (119878

2119896) and coarse

(1198783119896)) 119903119896is the constant refinement ratio (recommended

6 International Journal of Rotating Machinery

values between radic2 and 2) 119901119896is the observed order of

accuracy and 119865119878is the safety factor Furthermore another

parameter is the convergence ratio (119877119896) which provides

information about the convergencedivergence of a solutionThe 119877

119896value was determined by the following ratio

119877119896=

12057621119896

12057632119896

(4)

The two different solution verification methods used in thisstudy differ in the choice of safety factor (119865

119878)

The GCI method proposed by Roache [21 22] is usedextensively and it is recommended for example by theAmerican Society of Mechanical Engineers (ASME) [23]and the American Institute of Aeronautics and Astronautics(AIAA) [24] Roache recommended for careful grid studies(three or more grids analyzed) 125 as the 119865

119878value

The other method used is the CF described in Stern et al[20] that uses a variable value of 119865

119878 In the CFmethod unlike

in the GCI method the uncertainty of the error dependson how close the solutions are to the asymptotic rangeThe expressions to assess the uncertainties were reported byWilson et al [25]

The verification study has been carried out for the criticalpoints of SR = 20 and SR = 25 in terms of 119862

119863estimation

errorThe iterative uncertainties are estimated by the fluctua-

tions of the time-history of the results in the last few periodsas indicated in Stern et al [20] Specifically as reported in (5)119880119868are estimated by half the difference of the maximum value

(119878119880) and the minimum value (119878

119871) of the final time-history of

the results

119880119868=

1003816100381610038161003816100381610038161003816

1

2(119878119880

minus 119878119871)

1003816100381610038161003816100381610038161003816 (5)

Then the grid uncertainty has been evaluated by the follow-ing expressions that is (6) for the GCI method and (7) forthe CF method

119880119896= 125 sdot

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

(6)

119880119896

=

[96 (1 minus 119862119896)2+ 11]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 lt 0125

[210038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 + 1]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 ge 0125

(7)

where 119865119878is equal to 125 and 119862

119896is the correction factor

Verification results using three systematically refined gridswith the refinement ratio (119903

119866) equal to radic2 are shown in

Table 5 The grid sizes range from 09M to 19M grid pointsand the three grids tested are shown in Table 4

Because 0 lt 119877119866

lt 1 monotonic convergence isachieved for 119862

119871and 119862

119863 where 119877

119866is convergence ratio for

the grid calculated according to (4) The uncertainty valuesare reported in Table 5

Table 4 The three grids tested

Grids CellsGrid A Coarse 0933 sdot 10

6

Grid B Medium 1320 sdot 106

Grid C Fine 1867 sdot 106

The values of simulation uncertainty reported in Table 5show that119880SN for 119862

119863is higher than119880SN for 119862

119871 due to much

larger errors in the estimation of 119862119863than of 119862

119871for SR = 20

and SR = 25Iterative convergence is achieved for all simulations and

119880119868is found to be negligible with respect to grid errors

similarly to what happens in other engineering applications(eg Wilson et al [26] and Xing et al [27])

Moreover the verification procedure cannot be com-pleted with the validation phase due to the lack of experi-mental uncertainty dataTherefore only the results related tosimulation numerical uncertainty are reported in Table 5

The numerical results of the verification study have beencompared with the experimental data as shown in Figure 7The comparison highlighted that no significant improvementin the 119862

119871and 119862

119863evaluation is detected between coarse

medium and fine mesh case However increasing the gridpoints increases the calculation effort as shown in Figure 8

For the reasons mentioned above the grid of Case B hasbeen assumed as the reference mesh This grid guarantees anacceptable solutionwithout an excessive computational effort(such as in Case C)

The comparison between experimental data and numer-ical results for SR in the range from 00 to 25 reportedin Figure 9 shows a good agreement in particular for 119862

119871

Regarding 119862119863 the CFD simulations give reliable results for

SR lt 15 and the error increases at higher values of SRlikewise highlighted in Thouault et al [13] and Da-Qing etal [5]

As shown in Table 5 it can be observed that for 119862119863the

comparison error (119864) is much greater than 119880SN Accordingto Oberkampf and Blottner [19] and Stern et al [20] it canbe said that when 119864 is much greater than the uncertaintyit is necessary to improve the simulations models It iswell known that one of the main sources of the modelingsimulation error is the turbulence models Nevertheless ashighlighted in Figure 9 comparing the different two-equationturbulence models that is 119896-120596 SST and Realizable 119896-120576 nosignificant differences are appreciableThe 119896-120596 SST is used asturbulencemodel for all the subsequent simulations howevera different simulation approach is required for an accurate119862

119863

evaluation at high SR

5 Results

The results of the simulations performed into the variableranges indicated in Table 2 are reported in terms of the so-called response curvesThese curves shown in Figure 10 rep-resent the values of 119862

119871and 119862

119863and aerodynamic efficiency

keeping constant 119889119890119889 of the FRThis representation is useful

because it permits us to clearly recognize the relationships

International Journal of Rotating Machinery 7

65 64 62

231213 199

Case A Case B Case C

SR 25SR 20

0

10

20

30

40

CL

erro

r

(a)

331 322 314

363 359 356

Case A Case B Case C0

10

20

30

40

C

Der

ror

SR 25SR 20

(b)

Figure 7 119862119871and 119862

119863percentage error between numerical (three mesh cases tested) and experimental data at SR = 20 and 25

Case A Case B Case C

CPU

tim

e per

tim

e ste

p (s

)

0

1000

2000

3000

Figure 8 Computational time required for the grids tested

Exp dataCFD k-εCFD k-120596 SST

minus1000102030405060708090

100

CL

05 10 15 20 2500SR

(a)

00

20

40

60

80

100

CD

05 10 15 20 2500SR

Exp dataCFD k-εCFD k-120596 SST

(b)

Figure 9 Comparison between CFD results and experimental data for lift (a) and drag (b) coefficient using mesh Case B and two differentturbulence models

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

International Journal of Rotating Machinery 5

Table 3 Summary of the numerical simulation setup

Pressure link Pressure Convectionterm

Temporaldiscretization Time step (s) Iteration per

time stepTurbulencemodel

Oversetinterpolation

scheme

Simple Standard 2nd order 1st orderFunction ofangular speed

(Ω)11 119896-120596 SST Distance

weighted

(a)

Overset region

Backgroundregion

Interface

(b)

Figure 5 Section of the computational grid (a) Close-up views of the hybrid mesh (b)

Inletvelocity

Inletvelocity

Inletvelocity

Symmetry plane

Pressure outlet

15d

5d275d

35H

Figure 6 Boundary conditions and domain dimensions in functionof the main dimensions of FR (119867 119889)

geometry as seen in Figure 6 In order to reduce the compu-tational effort only half the domain has been considered anda symmetry plane has been assumed containing the cylinderaxis and parallel to the free stream velocity A velocity inletboundary condition has been set on the front side of thedomain with a prescribed velocity this inlet velocity also hasbeen used to control the SR of the rotor keeping constantits angular speed Ω On the bottom and the top side of thedomain a symmetry boundary condition also is used On therear side of the domain surface a pressure outlet boundarycondition has been imposed with a relative pressure of value0 Pa An axial-symmetrical zone surrounding the rotor hadto be modeled overlapping the rotating mesh (fixed with therotor) and the underlying nonmoving mesh domain Thisturned out to be a necessary grid treatment for using theoverset mesh methodology

43 Numerical Uncertainty Analysis In order to assess thenumerical setup and to evaluate the simulation numericaluncertainty 119880SN a verification study has been performed

The benchmark experimental data are derived fromBadalamenti and Prince [8 12] and are related to an FR withAR = 51 (cylinder height 119867 = 045m) diameter of 119889 =

00889m and the Thom disk on the top of this FR with119889119890= 01778m (corresponding to 119889

119890119889 = 20)

According to the Oberkampf and Blottner [19] verifica-tion is defined as a process for assessing simulation numericaluncertainty 119880SN The simulation numerical error and uncer-tainty are composed of a grid convergence error (120575

119866) iterative

convergence error (120575119868) time step convergence error (120575TS)

and other parameters (120575119875) Therefore the numerical error is

the sum

120575SN = 120575119866

+ 120575119868+ 120575TS + 120575

119875 (1)

and the simulation numerical uncertainty is given by theformula

1198802

SN = 1198802

119866+ 1198802

119868+ 1198802

TS + 1198802

119875 (2)

where 119880119866 119880119868 119880TS and 119880

119875are the uncertainties arising

from the grid iterative time step and other parametersrespectively (see Stern et al [20])

The numerical uncertainty evaluation was performedusing two different methods the grid convergence index(GCI) method and the correction factor (CF) method Thegeneral form of the uncertainty evaluation based on thegeneralized Richardson extrapolation (RE) method can bewritten as follows

119880119896= 119865119878(

12057621119896

119903119901119896

119896minus 1

) (3)

where 12057621119896

is the solution changes for the 119896-input parameterbetween the solutions (fine (119878

1119896) to medium (119878

2119896) and coarse

(1198783119896)) 119903119896is the constant refinement ratio (recommended

6 International Journal of Rotating Machinery

values between radic2 and 2) 119901119896is the observed order of

accuracy and 119865119878is the safety factor Furthermore another

parameter is the convergence ratio (119877119896) which provides

information about the convergencedivergence of a solutionThe 119877

119896value was determined by the following ratio

119877119896=

12057621119896

12057632119896

(4)

The two different solution verification methods used in thisstudy differ in the choice of safety factor (119865

119878)

The GCI method proposed by Roache [21 22] is usedextensively and it is recommended for example by theAmerican Society of Mechanical Engineers (ASME) [23]and the American Institute of Aeronautics and Astronautics(AIAA) [24] Roache recommended for careful grid studies(three or more grids analyzed) 125 as the 119865

119878value

The other method used is the CF described in Stern et al[20] that uses a variable value of 119865

119878 In the CFmethod unlike

in the GCI method the uncertainty of the error dependson how close the solutions are to the asymptotic rangeThe expressions to assess the uncertainties were reported byWilson et al [25]

The verification study has been carried out for the criticalpoints of SR = 20 and SR = 25 in terms of 119862

119863estimation

errorThe iterative uncertainties are estimated by the fluctua-

tions of the time-history of the results in the last few periodsas indicated in Stern et al [20] Specifically as reported in (5)119880119868are estimated by half the difference of the maximum value

(119878119880) and the minimum value (119878

119871) of the final time-history of

the results

119880119868=

1003816100381610038161003816100381610038161003816

1

2(119878119880

minus 119878119871)

1003816100381610038161003816100381610038161003816 (5)

Then the grid uncertainty has been evaluated by the follow-ing expressions that is (6) for the GCI method and (7) forthe CF method

119880119896= 125 sdot

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

(6)

119880119896

=

[96 (1 minus 119862119896)2+ 11]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 lt 0125

[210038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 + 1]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 ge 0125

(7)

where 119865119878is equal to 125 and 119862

119896is the correction factor

Verification results using three systematically refined gridswith the refinement ratio (119903

119866) equal to radic2 are shown in

Table 5 The grid sizes range from 09M to 19M grid pointsand the three grids tested are shown in Table 4

Because 0 lt 119877119866

lt 1 monotonic convergence isachieved for 119862

119871and 119862

119863 where 119877

119866is convergence ratio for

the grid calculated according to (4) The uncertainty valuesare reported in Table 5

Table 4 The three grids tested

Grids CellsGrid A Coarse 0933 sdot 10

6

Grid B Medium 1320 sdot 106

Grid C Fine 1867 sdot 106

The values of simulation uncertainty reported in Table 5show that119880SN for 119862

119863is higher than119880SN for 119862

119871 due to much

larger errors in the estimation of 119862119863than of 119862

119871for SR = 20

and SR = 25Iterative convergence is achieved for all simulations and

119880119868is found to be negligible with respect to grid errors

similarly to what happens in other engineering applications(eg Wilson et al [26] and Xing et al [27])

Moreover the verification procedure cannot be com-pleted with the validation phase due to the lack of experi-mental uncertainty dataTherefore only the results related tosimulation numerical uncertainty are reported in Table 5

The numerical results of the verification study have beencompared with the experimental data as shown in Figure 7The comparison highlighted that no significant improvementin the 119862

119871and 119862

119863evaluation is detected between coarse

medium and fine mesh case However increasing the gridpoints increases the calculation effort as shown in Figure 8

For the reasons mentioned above the grid of Case B hasbeen assumed as the reference mesh This grid guarantees anacceptable solutionwithout an excessive computational effort(such as in Case C)

The comparison between experimental data and numer-ical results for SR in the range from 00 to 25 reportedin Figure 9 shows a good agreement in particular for 119862

119871

Regarding 119862119863 the CFD simulations give reliable results for

SR lt 15 and the error increases at higher values of SRlikewise highlighted in Thouault et al [13] and Da-Qing etal [5]

As shown in Table 5 it can be observed that for 119862119863the

comparison error (119864) is much greater than 119880SN Accordingto Oberkampf and Blottner [19] and Stern et al [20] it canbe said that when 119864 is much greater than the uncertaintyit is necessary to improve the simulations models It iswell known that one of the main sources of the modelingsimulation error is the turbulence models Nevertheless ashighlighted in Figure 9 comparing the different two-equationturbulence models that is 119896-120596 SST and Realizable 119896-120576 nosignificant differences are appreciableThe 119896-120596 SST is used asturbulencemodel for all the subsequent simulations howevera different simulation approach is required for an accurate119862

119863

evaluation at high SR

5 Results

The results of the simulations performed into the variableranges indicated in Table 2 are reported in terms of the so-called response curvesThese curves shown in Figure 10 rep-resent the values of 119862

119871and 119862

119863and aerodynamic efficiency

keeping constant 119889119890119889 of the FRThis representation is useful

because it permits us to clearly recognize the relationships

International Journal of Rotating Machinery 7

65 64 62

231213 199

Case A Case B Case C

SR 25SR 20

0

10

20

30

40

CL

erro

r

(a)

331 322 314

363 359 356

Case A Case B Case C0

10

20

30

40

C

Der

ror

SR 25SR 20

(b)

Figure 7 119862119871and 119862

119863percentage error between numerical (three mesh cases tested) and experimental data at SR = 20 and 25

Case A Case B Case C

CPU

tim

e per

tim

e ste

p (s

)

0

1000

2000

3000

Figure 8 Computational time required for the grids tested

Exp dataCFD k-εCFD k-120596 SST

minus1000102030405060708090

100

CL

05 10 15 20 2500SR

(a)

00

20

40

60

80

100

CD

05 10 15 20 2500SR

Exp dataCFD k-εCFD k-120596 SST

(b)

Figure 9 Comparison between CFD results and experimental data for lift (a) and drag (b) coefficient using mesh Case B and two differentturbulence models

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

6 International Journal of Rotating Machinery

values between radic2 and 2) 119901119896is the observed order of

accuracy and 119865119878is the safety factor Furthermore another

parameter is the convergence ratio (119877119896) which provides

information about the convergencedivergence of a solutionThe 119877

119896value was determined by the following ratio

119877119896=

12057621119896

12057632119896

(4)

The two different solution verification methods used in thisstudy differ in the choice of safety factor (119865

119878)

The GCI method proposed by Roache [21 22] is usedextensively and it is recommended for example by theAmerican Society of Mechanical Engineers (ASME) [23]and the American Institute of Aeronautics and Astronautics(AIAA) [24] Roache recommended for careful grid studies(three or more grids analyzed) 125 as the 119865

119878value

The other method used is the CF described in Stern et al[20] that uses a variable value of 119865

119878 In the CFmethod unlike

in the GCI method the uncertainty of the error dependson how close the solutions are to the asymptotic rangeThe expressions to assess the uncertainties were reported byWilson et al [25]

The verification study has been carried out for the criticalpoints of SR = 20 and SR = 25 in terms of 119862

119863estimation

errorThe iterative uncertainties are estimated by the fluctua-

tions of the time-history of the results in the last few periodsas indicated in Stern et al [20] Specifically as reported in (5)119880119868are estimated by half the difference of the maximum value

(119878119880) and the minimum value (119878

119871) of the final time-history of

the results

119880119868=

1003816100381610038161003816100381610038161003816

1

2(119878119880

minus 119878119871)

1003816100381610038161003816100381610038161003816 (5)

Then the grid uncertainty has been evaluated by the follow-ing expressions that is (6) for the GCI method and (7) forthe CF method

119880119896= 125 sdot

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

(6)

119880119896

=

[96 (1 minus 119862119896)2+ 11]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 lt 0125

[210038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 + 1]

1003816100381610038161003816100381610038161003816100381610038161003816

12057621119896

119903119901119896

119896minus 1

1003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161 minus 119862

119896

1003816100381610038161003816 ge 0125

(7)

where 119865119878is equal to 125 and 119862

119896is the correction factor

Verification results using three systematically refined gridswith the refinement ratio (119903

119866) equal to radic2 are shown in

Table 5 The grid sizes range from 09M to 19M grid pointsand the three grids tested are shown in Table 4

Because 0 lt 119877119866

lt 1 monotonic convergence isachieved for 119862

119871and 119862

119863 where 119877

119866is convergence ratio for

the grid calculated according to (4) The uncertainty valuesare reported in Table 5

Table 4 The three grids tested

Grids CellsGrid A Coarse 0933 sdot 10

6

Grid B Medium 1320 sdot 106

Grid C Fine 1867 sdot 106

The values of simulation uncertainty reported in Table 5show that119880SN for 119862

119863is higher than119880SN for 119862

119871 due to much

larger errors in the estimation of 119862119863than of 119862

119871for SR = 20

and SR = 25Iterative convergence is achieved for all simulations and

119880119868is found to be negligible with respect to grid errors

similarly to what happens in other engineering applications(eg Wilson et al [26] and Xing et al [27])

Moreover the verification procedure cannot be com-pleted with the validation phase due to the lack of experi-mental uncertainty dataTherefore only the results related tosimulation numerical uncertainty are reported in Table 5

The numerical results of the verification study have beencompared with the experimental data as shown in Figure 7The comparison highlighted that no significant improvementin the 119862

119871and 119862

119863evaluation is detected between coarse

medium and fine mesh case However increasing the gridpoints increases the calculation effort as shown in Figure 8

For the reasons mentioned above the grid of Case B hasbeen assumed as the reference mesh This grid guarantees anacceptable solutionwithout an excessive computational effort(such as in Case C)

The comparison between experimental data and numer-ical results for SR in the range from 00 to 25 reportedin Figure 9 shows a good agreement in particular for 119862

119871

Regarding 119862119863 the CFD simulations give reliable results for

SR lt 15 and the error increases at higher values of SRlikewise highlighted in Thouault et al [13] and Da-Qing etal [5]

As shown in Table 5 it can be observed that for 119862119863the

comparison error (119864) is much greater than 119880SN Accordingto Oberkampf and Blottner [19] and Stern et al [20] it canbe said that when 119864 is much greater than the uncertaintyit is necessary to improve the simulations models It iswell known that one of the main sources of the modelingsimulation error is the turbulence models Nevertheless ashighlighted in Figure 9 comparing the different two-equationturbulence models that is 119896-120596 SST and Realizable 119896-120576 nosignificant differences are appreciableThe 119896-120596 SST is used asturbulencemodel for all the subsequent simulations howevera different simulation approach is required for an accurate119862

119863

evaluation at high SR

5 Results

The results of the simulations performed into the variableranges indicated in Table 2 are reported in terms of the so-called response curvesThese curves shown in Figure 10 rep-resent the values of 119862

119871and 119862

119863and aerodynamic efficiency

keeping constant 119889119890119889 of the FRThis representation is useful

because it permits us to clearly recognize the relationships

International Journal of Rotating Machinery 7

65 64 62

231213 199

Case A Case B Case C

SR 25SR 20

0

10

20

30

40

CL

erro

r

(a)

331 322 314

363 359 356

Case A Case B Case C0

10

20

30

40

C

Der

ror

SR 25SR 20

(b)

Figure 7 119862119871and 119862

119863percentage error between numerical (three mesh cases tested) and experimental data at SR = 20 and 25

Case A Case B Case C

CPU

tim

e per

tim

e ste

p (s

)

0

1000

2000

3000

Figure 8 Computational time required for the grids tested

Exp dataCFD k-εCFD k-120596 SST

minus1000102030405060708090

100

CL

05 10 15 20 2500SR

(a)

00

20

40

60

80

100

CD

05 10 15 20 2500SR

Exp dataCFD k-εCFD k-120596 SST

(b)

Figure 9 Comparison between CFD results and experimental data for lift (a) and drag (b) coefficient using mesh Case B and two differentturbulence models

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Rotating Machinery 7

65 64 62

231213 199

Case A Case B Case C

SR 25SR 20

0

10

20

30

40

CL

erro

r

(a)

331 322 314

363 359 356

Case A Case B Case C0

10

20

30

40

C

Der

ror

SR 25SR 20

(b)

Figure 7 119862119871and 119862

119863percentage error between numerical (three mesh cases tested) and experimental data at SR = 20 and 25

Case A Case B Case C

CPU

tim

e per

tim

e ste

p (s

)

0

1000

2000

3000

Figure 8 Computational time required for the grids tested

Exp dataCFD k-εCFD k-120596 SST

minus1000102030405060708090

100

CL

05 10 15 20 2500SR

(a)

00

20

40

60

80

100

CD

05 10 15 20 2500SR

Exp dataCFD k-εCFD k-120596 SST

(b)

Figure 9 Comparison between CFD results and experimental data for lift (a) and drag (b) coefficient using mesh Case B and two differentturbulence models

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Rotating Machinery

Table 5 Grid and iterative uncertainty for 119862119871and 119862

119863at the two different SRs

SR Grids Grid ratio 119877119866

119875119866

1 minus 119862119866

119880119866

119880119866 119880

119868 119880SN |119864|

GCI CF

119862119871

20 A-B-C radic2 080 minus065 120 891 426 026 891 193025 A-B-C radic2 096 minus012 104 440 323 055 443 624

119862119863

20 A-B-C radic2 097 minus004 101 2006 1560 137 2011 362325 A-B-C radic2 096 minus013 104 1918 1402 215 1930 3136

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

E=

CLC

D

(a)

AR = 2AR = 4

AR = 6AR = 8

1 15 2 25 3 3505SR

0123456789

1011

CD

ded = 1

(b)

1 15 2 25 3 3505SR

ded = 1

0123456789

1011

CL

AR = 2AR = 4

AR = 6AR = 8

(c)

1 15 2 25 3 3505SR

ded = 2

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(d)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CD

ded = 2

(e)

1 15 2 25 3 3505SR

AR = 2AR = 4

AR = 6AR = 8

0123456789

1011

CL

ded = 2

(f)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

E=

CLC

D

AR = 2AR = 4

AR = 6AR = 8

(g)

1 15 2 25 3 3505SR

ded = 3

0123456789

1011

CD

AR = 2AR = 4

AR = 6AR = 8

(h)

1 15 2 25 3 3505SR

0123456789

1011

CL

ded = 3

AR = 2AR = 4

AR = 6AR = 8

(i)

Figure 10 Response curves for 119862119871 119862119863and aerodynamic efficiency (119864) at various SR AR and 119889

119890119889 for FR

between geometrical (AR 119889119890119889) and functional parameters

(SR) with FR performances (119862119871 119862119863 and aerodynamic

efficiency)The response curves in Figure 10 show that 119862

119871is mainly

influenced by the SR of the FR as expected high values of

SR cause large value of 119862119871due to higher circulation around

the cylinder Keeping constant the value of 119889119890119889 the amount

of 119862119871increases for high value of AR but this trend reduces

for high values of 119889119890119889 Also simulations confirm beneficial

effects of the FRrsquos end plate on its performance Referring to

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Rotating Machinery 9

119862119863the ability of larger end plates to reduce the induced drag

component is confirmed as shown in Figure 10 The reasonfor these improvements can be due to an effect similar toincreasing the AR values

About the variation of 119862119863with SR this has the same

behavior of 119862119871 while 119862

119863decreases as AR increases as for

a typical aircraft wing The maximum absolute value of theFR aerodynamic efficiency rises and translates to higher SRvalues when AR and 119889

119890119889 increase too

6 Surrogate Model for the Liftand Drag Coefficients

119862119871and 119862

119863equations in (8) summarize the results of the

extensive numerical analyses on the behavior of FR Theseequations represent a surrogate model which can be used topredict the performance of the FR in relation to SR AR and119889119890119889 This model is an effective mathematical tool for the

preliminary design of FRThe ratio of these two formulas allows evaluating the

aerodynamic efficiency of such devices In both equations thecoefficients 119886

119894119895119896and 119887119894119895119896

transform geometrical and functionalFRrsquos parameters into 119862

119871and 119862

119863 The values of 119886

119894119895119896and 119887119894119895119896

coefficients are presented in Table 6 The coefficients of thematrices 119886

119894119895119896and 119887119894119895119896

have been obtained by applying a least-squares root fit procedure to the numerical results similarto the optimization techniques used to find a set of designparameters as described in Balsamo et al [28]

119862119871=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119886119894119895119896SR119894AR119895 (

119889119890

119889)

119896

119862119863

=

4

sum

119894=1

4

sum

119895=1

3

sum

119896=1

119887119894119895119896SR119894AR119895 (

119889119890

119889)

119896

(8)

The validity of these equations is strictly related to the rangeof the variables analyzed 10 le SR le 30 20 le AR le 80and 10 le 119889

119890119889 le 30

A test of the reliability of the surrogate model has beenperformed using the experimental data available in Pearson[15] relevant to FR with AR = 50 and 119889

119890119889 = 15 These

values were used as input for (8) The comparison betweenexperimental data and the predicted results is shown inFigure 11 and it can be noted that 119862

119871is correctly estimated

while 119862119863is overestimated for values of SR which are greater

than 25 This discrepancy which is due to the higheruncertainty on the simulated drag results is less critical in theperspective of marine applications In fact as indicated abovethe SR values of interest in this field are not larger than 30often around 20

7 Flettner Rotor as Ship Propulsion Device

To evaluate the potentiality of the FRs as marine propulsiondevices it is important to consider that for FR on a ship theresulting wind speed is the vector sum of the environmentalwind and the ship speed If the resulting wind relative tothe ship coordinate system is coming from the bow quarter

05 10 15 20 25 30 35 40 45 5000SR

CL expCD exp

CL predictedCD predicted

0020406080

100120140

CLC

D

Figure 11 Comparison of experimental and predicted values of 119862119871

and 119862119863for FR with AR = 50 and 119889

119890119889 = 15

T

D

L

TF

VRW

120572

(a)

L

TF

T

D

VRW

120572

(b)

Figure 12 Total force and thrust delivered by FR at differentapparent wind directions from bow quarter (a) from stern quarter(b)

direction as illustrated in Figure 12(a) 119863 will have a negativecontribution to the resultant thrust (119879) In this case alower drag will of course be beneficial However if theresulting wind is from the stern quarter direction as depictedin Figure 12(b) then 119863 also contributes to 119879 under thiscircumstance a high drag is not disadvantage

In Figures 12(a) and 12(b) TF is the resultant of 119871 and 119863119881RW the relative wind velocity 119879 the effective thrust and 120572

the apparent wind angle Ultimately for a geometrically well-defined FR the resultant thrust depends on the relative windvelocity on the apparentwind angle and on the angular speedΩ of the FR Obviously the relation between 119881RW and Ω isquantified by SR

Figure 13 shows the values of119862119879and 119879 resulting from the

polynomials whose coefficients are shown in Table 6As strongly suggested by Figure 13 the thrust has

been evaluated at the maximum SR simulated in the study

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Rotating Machinery

Table 6 The values of 119886119894119895119896

and 119887119894119895119896

coefficients reported in (8)

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

0 0 0 46756 minus79919 1 0 0 minus89785 140718

0 0 1 minus78301 70071 1 0 1 140010 minus125048

0 0 2 20282 minus15268 1 0 2 minus35672 27377

0 1 0 minus37846 60030 1 1 0 77607 minus104703

0 1 1 60058 minus50611 1 1 1 minus112204 89137

0 1 2 minus15301 11013 1 1 2 27977 minus19292

0 2 0 8096 minus11649 1 2 0 minus16461 20215

0 2 1 minus11874 9810 1 2 1 22038 minus17098

0 2 2 2987 minus2141 1 2 2 minus5409 3698

0 3 0 minus0460 0669 1 3 0 0915 minus1155

0 3 1 0639 minus0558 1 3 1 minus1152 0964

0 3 2 minus0160 0121 1 3 2 0280 minus0207

119894 119895 119896 119886119894119895119896

119887119894119895119896

119894 119895 119896 119886119894119895119896

119887119894119895119896

2 0 0 38547 minus76506 2 0 0 minus4895 11799

2 0 1 minus62545 69271 2 0 1 8642 minus10539

2 0 2 16266 minus15189 2 0 2 minus2294 2290

2 1 0 minus37556 57951 2 1 0 5190 minus9412

2 1 1 54801 minus49793 2 1 1 minus7946 8065

2 1 2 minus13704 10709 2 1 2 2016 minus1716

2 2 0 8153 minus11180 2 2 0 minus1154 1831

2 2 1 minus10753 9493 2 2 1 1556 minus1547

2 2 2 2627 minus2034 2 2 2 minus0383 0327

2 3 0 minus0440 0636 2 3 0 0060 minus0104

2 3 1 0534 minus0531 2 3 1 minus0073 0086

2 3 2 minus0128 0113 2 3 2 0018 minus0018

minus4

minus2

0

24

6

810

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310320

330340 350

Thrust coefficient SR1SR2SR3

(a)

minus150

minus50

50

150

250

0 10 2030

40

50

60

70

80

90

100

110

120

130140

150160170180190200

210220

230

240

250

260

270

280

290

300

310

320330

340 350

Thrust (kN)

20ms15ms

10ms5ms

(b)

Figure 13 In (a)119862119879for a defined FR geometry (119867 = 280m 119889 = 40m) at different values of SR and apparent wind angle In (b) thrust values

delivered by the FR for different magnitude of relative wind velocity (fixed SR = 3)

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Rotating Machinery 11

(SR = 30) and referring to FR whose diameter and heightwere 40m and 280m respectively These dimensions areconsistent with the ship taken into consideration a producttanker 205m long at waterline and dislocating 74983 t Tow-ing tank tests of this ship indicate that the resistance at 10 knand 12 kn is 354 kN and 500 kN respectively

Therefore the comparison of resistance of a ship with thethrust data as shown in Figure 13 highlights that a coupleof FRs as few as 20 kn of 119881RW are able to give in a widerange of angles of apparent wind a thrust whose magnitudeis 03 and 02 times the resistance of a ship at 10 kn and 12 knrespectively

The aim of these considerations is a rough evaluationof the potentiality of the FR as a marine propulsion deviceFor a more comprehensive analysis of the FR effectivenessmore aspects have to be taken into account These includefor instance the asymmetric hydrodynamic flow conditionproduced by the transversal component of TF (heeling anddrift angle) extra rudder drag due to the aerodynamic yawmoment and the reduced efficiency of FR due to the shipmotions

8 Conclusions

In this paper a systematic approach to identify themost influ-encing parameters on FR performance and the applicabilityof such device for marine application has been presentedResults from the numerical simulations have been used toachieve a surrogate model useful for preliminary FR designs

Theuncertainty analysis shows that the highest numericaluncertainty and error are for 119862

119863(119880SN = 201 119864 = 362)

with respect to 119862119871(119880SN = 89 119864 = 193) Furthermore

it has been observed that the main source of numericaluncertainty is due to the grid The 119862

119863error and numerical

uncertainty trend seems to be related to the limits of theturbulence models used that is 119896-120596 SST and Realizable 119896-120576Reasonably the Large Eddy Simulation (LES) analysis shouldbe used for an accurate evaluation of119862

119863 in particular at high

SRRegarding the capability of FR to act as a propulsion

device it is confirmed that in terms of magnitude 119862119871and

aerodynamic efficiency of FR is much higher than the valuesgiven by a wing of comparable aspect ratio

Finally the potentiality of the FR as a marine propulsiondevice here evaluated on a tanker ship highlights that in awide range of wind angles a couple of FR can give a thrustwhose magnitude is up to 30 of the ship resistance inthe range of operational speed Also the assessment of theaerodynamic efficiency is less significant than the evaluationof each of the aerodynamic force components as the draggives a positive contribution to the thrust in a wide range ofapparent wind angles

Symbology and Abbreviations

120572 Apparent wind angle (deg)119860 Reference area (119867 lowast 119889) (m2)

AR = 119867119889 Aspect ratio119862119863

= 119863051205881198601198802 Drag coefficient

119862119871= 11987105120588119860119880

2 Lift coefficient119862119879

= 119879051205881198601198802 Thrust coefficient

CFL number Courant-Friedrichs-Lewynumber

119862119896 Correction factor

CF method Correction factor method119863 Drag (N)119889 Cylinder diameter (m)119889119890 End plate diameter (m)

120575119868 Iteration convergence error

120575119866 Grid convergence error

120575TS Time step convergence error120575RE Error evaluated by RE

methodDWT Dead weight tonnage (t)120576119896119894119895 Solution change

119864 Comparison error119891 Frequency (Hz)119865119878 Factor of safety

FR Flettner rotorGCI Grid convergence index119867 Cylinder length (m)119871 Lift (N)LES Large Eddy Simulation] Dynamic viscosity (Pa s)Ω Angular velocity (rads)120588 Air density (kgm3)119901119896 Estimated order of accuracy

Re = 119880119889] Reynolds numberRE Richardson extrapolation

method119903119896 Refinement ratio

SR = Ω1198892119880 Spin ratioSt = 119891119889119880 Strouhal number119879 Effective thrust (N)TF Total force (N)119880 Free stream or flux velocity

(ms)119880119866 Grid uncertainty

119880119868 Iteration uncertainty

119880SN Simulation uncertainty119880TS Time step uncertaintyURANS Unsteady Reynolds averaged

Navier-Stokes119910+ Nondimensional wall

distance

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Theauthors gratefully acknowledge the availability of theCal-culation Centre SCoPE of the University of Naples ldquoFederico

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 International Journal of Rotating Machinery

IIrdquo and thanks are due to SCoPE academic staff for the givensupport

References

[1] Enercon Wind Company ldquoEnercon E-ship 1 a wind-hybridcommercial cargo shiprdquo in Proceedings of the 4th Conference onShip Efficiency Hamburg Germany September 2013

[2] E G Reid ldquoTests of rotating cylindersrdquo Techinical Notes NACA209 1924

[3] A Thom ldquoEffects of discs on the air forces on a rotatingcylinderrdquo Reports amp Memoranda 1623 Aerospace ResearchCouncil 1934

[4] M W Swanson ldquoThe Magnus effect a summary of investiga-tions to daterdquo Journal of Basic Engineering vol 83 no 3 pp461ndash470 1961

[5] L Da-Qing M Leer-Andersen and B Allenstrom ldquoPerfor-mance and vortex formation of Flettner rotors at high Reynoldsnumbersrdquo in Proceedings of 29th Symposium on Naval Hydrody-namics Gothenburg Sweden August 2012

[6] J Seifert ldquoA review of theMagnus effect in aeronauticsrdquoProgressin Aerospace Sciences vol 55 pp 17ndash45 2012

[7] S Mittal and B Kumar ldquoFlow past a rotating cylinderrdquo Journalof Fluid Mechanics vol 476 pp 303ndash334 2003

[8] C Badalamenti and S A Prince ldquoVortex shedding forma rotating circular cylinder at moderate subcritical reynoldsnumbers and high velocity ratiordquo in Proceedings of the 26thCongress of International Council of the Aeronautical Sciences(ICAS rsquo08) Anchorage Alaska USA September 2008

[9] E R Gowree and S A Prince ldquoA computational study of theaerodynamics of a spinning cylinder in a crossflow of highReynolds numberrdquo in Proceedings of the 28th Congress of theInternational Council of the Aeronautical Sciences (ICAS rsquo12) pp1138ndash1147 Brisbane Australia September 2012

[10] L Prandtl ldquoThe Magnus effect and wind-powered shipsrdquoNaturwissenschaften vol 13 pp 1787ndash1806 1925

[11] A De Marco S Mancini and C Pensa ldquoPreliminary analysisfor marine application of Flettner rotorsrdquo in Proceedings ofthe 2nd International Symposium on Naval Architecture andMaritime (INT-NAM rsquo14) Istanbul Turkey October 2014

[12] C Badalamenti and S A Prince ldquoEffects of endplates on arotating cylinder in crossflowrdquo in Proceedings of the 26th AIAAApplied Aerodynamics Conference Honolulu Hawaii USAAugust 2008

[13] N Thouault C Breitsamter N A Adams J Seifert C Badala-menti and S A Prince ldquoNumerical analysis of a rotatingcylinder with spanwise disksrdquo AIAA Journal vol 50 no 2 pp271ndash283 2012

[14] K C Morisseau ldquoMarine application of magnus effect devicesrdquoNaval Engineers Journal vol 97 no 1 pp 51ndash57 1985

[15] D R Pearson ldquoThe use of flettner rotors in efficient shipdesignrdquo in Proceedings of the Influence of EEDI on Ship DesignConference London UK September 2014

[16] M Traut P Gilbert C Walsh et al ldquoPropulsive power contri-bution of a kite and a Flettner rotor on selected shipping routesrdquoApplied Energy vol 113 pp 362ndash372 2014

[17] A De Marco S Mancini C Pensa R Scognamiglio andL Vitiello ldquoMarine application of flettner rotors numericalstudy on a systematic variation of geometric factor by DOEapproachrdquo in Proceedings of the 6th International Conference on

Computational Methods in Marine Engineering (MARINE rsquo15)vol 1 Rome Italy June 2015

[18] CD-Adapco Star-CCM+ User Guide 2015[19] W L Oberkampf and F G Blottner ldquoIssues in computational

fluid dynamics code verification and validationrdquo AIAA Journalvol 36 no 5 pp 687ndash695 1998

[20] F Stern R V Wilson H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 1 methodology and proceduresrdquo Journal ofFluids Engineering vol 123 no 4 pp 793ndash802 2001

[21] P J Roache Verification and Validation in ComputationalScience and Engineering Hermosa New Mexico NM USA1998

[22] P J Roache ldquoCode verification by the method of manufacturedsolutionsrdquo Journal of Fluids Engineering vol 124 no 1 pp 4ndash102002

[23] I B Celik U Ghia P J Roache C J Freitas H Coleman and PE Raad ldquoProcedure for estimation and reporting of uncertaintydue to discretization in CFD applicationsrdquo Journal of FluidsEngineering vol 130 no 7 2008

[24] R Cosner W L Oberkampf C L Rumsey C Rahaim and TShih ldquoAIAA Committee on standards for computational fluiddynamics status and plansrdquo AIAA Paper 2006-889 AmericanInstitute of Aeronautics and Astronautics Reno Nev USA2006

[25] R Wilson J Shao and F Stern ldquoDiscussion criticism of thecorrection factorrdquo Journal of Fluids Engineering vol 126 no 4pp 704ndash706 2004

[26] R V Wilson F Stern H W Coleman and E G PatersonldquoComprehensive approach to verification and validation ofCFDsimulationsmdashpart 2 application for RANS simulation of acargocontainer shiprdquo Journal of Fluids Engineering vol 123 no4 pp 803ndash810 2001

[27] T Xing P Carrica and F Stern ldquoComputational towing tankprocedures for single run curves of resistance and propulsionrdquoJournal of Fluids Engineering vol 130 no 10 Article ID 10110214 pages 2008

[28] F Balsamo F De Luca and C Pensa ldquoA new logic forcontrollable pitch propeller managementrdquo in Proceedings ofthe 14th International Congress of the International MaritimeAssociation of the Mediterranean (IMAM rsquo11) vol 2 pp 639ndash647 Genoa Italy September 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of