proceedings

Tom 52 (66) Fascicola 3

ISSN 1224-6077

SCIENTIFIC BULLETIN of the POLITEHNICA University of Timioara, Romania

Transactions of Mechanics

Proceedings of the 3nd Workshop on

Vortex Dominated Flows

Achievements and Open Problems

Timioara, Romania, June 1-2, 2007

Edited by S. Bernad, S. Muntean, R. Susan-Resiga

Editor in chief Prof.dr.ing. Victor BLOIU

Editors

Dr.ing. Sandor BERNAD, Dr.ing. Sebastian MUNTEAN, Prof.dr.ing. Romeo SUSAN-RESIGA

Workshop Scientific Committee

Prof. R. RESIGA Charmain

Politehnica University of Timisoara

Dr. S. BERNAD Romanian Academy Timioara Branch

Dr. S. MUNTEAN Romanian Academy Timioara Branch

Prof. E.C. ISBOIU Politehnica University of Bucharest

Prof. C. BERBENTE Politehnica University of Bucharest

Prof. L. SANDU Technical University of Civil Engineering, Bucharest

Prof. A. LUNGU Dunrea de Jos University Galai

Prof. L.I. VAIDA Technical University, Cluj-Napoca

Prof. V. CMPIAN Eftimie Murgu University, Reia

Dr. Th. POPESCU Gheorghe Asachi Technical University, Iai

Editura ORIZONTURI UNIVERSITARE Typesetting: Digital data supplied by editors Cover-Design: Romeo SUSAN-RESIGA, Sandor BERNADA, Dan NIU Editorial adviser: tefan KILYENI Desktop publishing: Valentina TEF

Tiparul executat la Imprimeria MIRTON 300125 Timioara, Str. Samuil Micu nr. 7

Telefon: 0256-272926, 0256-225684 Fax: 0256-208924

FOREWORD

The Academic Consortium for Research and Development on Fluid Dynamics (ACCORD-FluiD), which brings together research teams from leading Romanian universities in a joint effort to address current challenges on vortex and swirling flows aero- and hydro-dynamics, has organized its third Workshop on Vortex Dominated Flows Achievements and Open Problems in Timioara June 1 2, 2007. This research consortium is supported by the Romanian National University Research Council grant No. 33 for the period 2005-2007, and it is aimed at: Fundamental research, focused on ellucidating the physics of vortex flows, and on developing

new mathematical models and numerical techniques for both inviscid as well as unsteady turbulent swirling flows;

Development of numerical techniques able to meet the special requirements for vortex flows, in particular swirling flows in adverse pressure gradient;

Development of experimental techniques for vortex flows; Applications for turbomachines, naval propellers, wind engineering, combustion systems.

The 2007 workshop brings together eight research teams from leading universities and research institutes in Romania: Politehnica University of Timioara; Romanian Academy Timioara Branch; Politehnica University from Bucharest; Aerospace Engineering School; Politehnica University from Bucharest; Power Engineering School; Technical Civil Engineering University; Bucharest; University Dunrea de Jos Galai; Technical University Cluj-Napoca; University Eftimie Murgu Reia; Technical University Gh. Asachi Iai.

The two-day meeting, June 1-2, 2007, in Timioara is aimed at evaluating the current

developments as well as at correlating the scientific efforts among the parteners. The 20 papers reviewed by the scientific committee, have been presented and discussed at the workshop then included in the present issue of the Scientific Bulletin of the Politehnica University of Timioara, Transactions on Mechanics.

Although the ongoing grant ends in 2007, the Academic Consortium for Research and Development on Fluid Dynamics ACCORD-Fluid will continue its activity as a national research network. Prof.dr.ing. Romeo SUSAN-RESIGA

TABEL OF CONTENTS

Romeo SUSAN-RESIGA, Sebastian MUNTEAN, Vlad HASMAUCHI, Sandor BERNAD ...............

Development of a Swirling Flow Control Technique for Francis Turbines Operated at Partial Discharge

Andrei-Mugur GEORGESCU, Sanda-Carmen GEORGESCU, Sandor BERNAD, Costin Ioan COOIU .............................

COMSOL MULTIPHYSICS Versus FLUENT: 2D Numerical simulation of the stationary flow around a blade of the Achard Turbine

Sandor BERNAD, Andrei-Mugur GEORGESCU, Carmen Sanda GEORGESCU, Danile BALINT, Romeo SUSAN-RESIGA ..

2D unsteady simulation of the flow in the Achard marine turbine

Corneliu BERBENTE, Sterian DNIL, Marius STOIA-DJESKA ..................................................... A semianalitical method for the wing aerodynamics

Marius STOIA-DJESKA, Sterian DANAILA, Corneliu BERBENTE ..................................................... A Physical And Theoretical Analysis of the Vortex breakdown on delta wings

Constantin Viorel CMPIAN, Dorian NEDELCU ................................................................................... Cavitation tip clearance. Numerical simulation and experimental results

Adrian STUPARU, Sebastian MUNTEAN, Daniel BALINT, Liviu ANTON, Alexandru BAYA ...... Numerical analysis of pump hydrodynamics at constant speed

Eugen Constantin ISBASOIU, Petrisor STANESCU, Marius STOIA-DJESKA, Carmen Anca SAFTA, Georgiana DUNCA, Diana Maria BUCUR, Calin GHERGU...

Swirling flows in the suction sumps. Experimental approach

Mircea DEGERATU, Andrei GEORGESCU, Liviu HAEGAN, Costin Ioan COOIU, Rzvan- Silviu TEFAN, Lucian SANDU .........................................................................................................................

Some aspects about a vortex building model placed upwind an aeroelastic model in the boundary layer wind tunnel

Adrian LUNGU . Free-surface turbulent flow around a lPg ship hull

Adrian LUNGU ......................................................................................................................................... Uncertainties in the free-surface potential flow code solution

Ana-Maria TOCU, Adrian LUNGU ......................................................................................................... Numerical flow investigation over a chemical tanker hull

Mihaela AMORARITEI ............................................................................................................................ Performances data of propulsion Systems for high speed ships

Dan OBREJA, Radoslav NABERGOJ, Liviu CRUDU, Sandita PACURARU ....................................... Simulation of the Ship Standard Manoeuvres

Florin PACURARU, Dan OBREJA ........................................................................................................... Numerical and Experimental Investigation on a Tractor Tug Resistance Performance

Corneliu BALAN, Diana BROBOANA, Catalin BALAN, Roland KADAR ........................................... On the stick slip boundary conditions at the wall of microchannels

Corneliu BALAN, Diana BROBOANA .................................................................................................... Pressure constrain in vicinity of the separation point in planar, steady and isochoric motion:

case inewtonian fluid

Florin BODE, Victor HODOR, Corina GIURGEA ................................................................................... Numerical investigation on a swirl burner with internal flue gas recirculation

Victor HODOR, Florin BODE, Paula UNGURESAN, Claudiu RATIU .. CFD first prediction in designing a 50kw swirling burner within its combustion chamber

Theodor POPESCU ................................................................................................................................... A foundation in distributions of Glauert theory

ScP

To

3`nVo

A SEMIANALITICAL METHOD FOR THE WING AERODYNAMICS

Department of University Politehnica of Bucharest

Department of University Politehnica of Bucharest

nt ohnica of Bucha

Tel.: (+

ABSTRACT The Prandtl lifting line model is able to consider the

the aerodynamic interaction between

Lifting line, wing, aerodynamics, collocation, sail

An = coefficient in series expansion of circulation

b = an C g coefficient

ate on wing

puters and large lable, there is a need for

sim

method for the analysis of the aerodynamics of different wing shapes and

ison of the performances of different wing geometries. The

the replacement of the lifting wing by a model

s which imparted to ilar to the actual

e still

ientific Bulletin of the olitehnica University of Timisoara

Transactions on Mechanics m 52(66), Fascicola 3, 2007

d Workshop on rtex Dominated Flows Timisoara, Romania

June 1 - 2, 2007

Corneliu BERBENTE, Prof.* Sterian DNIL, Prof. Aerospace Sciences E.Carafoli Aerospace Sciences E.Carafoli

Marius Stoia-Djeska, Assoc. Prof., DepartmePolite

f Aerospace Sciences E.Carafoli University rest

*Corresponding author: Polizu 1, 011061, Bucharest, Romania x: (+40) 21 3181007, Ema40) 21 023967, Fa il: [email protected]

main effects ofa parallel uniform flow and a wing of finite span with a sufficiently large aspect ratio. The differentialintegral equation for the vortex intensity can be reduced to an infinite system of linear equations for the coefficients of the Fourier series of circulation. However a collocation type method is not the most adequate one as it has to face chord or/and incidence jumps in several wing sections, starting with the wing ends. These jumps will cause instabilities altering the calculation results. In the following one presents a method able to avoid such jump instabilities by using a weighting integration over the wing span.

KEYWORDS

NOMENCLATURE

distribution = aspect ratio

semi-wing spD = induced dra

CL = lift coefficient c = local wing chord y = spanwise coordin

1. INTRODUCTION Even today, when supercom

computer codes are avaiplified models that allow for an easy grasp of

physical dominant effects. Lifting line theory is still useful because it provides a relatively simple

allows a relatively quick compar

primary results that may be obtained from the model are values of the induced drag coefficient and the lift-curve slope of a finite wing. The theory may be expanded to provide estimates of the change in the lift created by flaps and the rolling moment coefficient produced by an aileron deflection.

2. LIFTING LINE THEORY

2.1 The vortex system The lifting line model was essentially

consisting of a system of vorticethe surrounding fluid a motion simflow, and which sustained a force equivalent to the lift to be created. The vortex system can be divided into three main parts: the starting vortex; the trailing vortex system; and the bound vortex system. When a wing is accelerated from rest the circulation round it, and therefore the lift, is not produced instantaneously. Instead, at the instant of starting, at the sharp trailing edge the fluid is required to change direction suddenly whilmoving at high speed. This high speed calls for extremely high accelerations and produces very large viscous forces, and the fluid is unable to turn round the trailing edge to the stagnation point (on the upper surface). Instead it leaves the surface and produces a vortex just above the trailing edge. The stagnation point moves towards the trailing edge, the circulation round the wing, and therefore its lift, increasing progressively as the stagnation point moves back. When the stagnation point reaches the trailing edge the fluid is no longer required to flow round the trailing edge. Instead it decelerates gradually along the aerofoil surface, comes to rest at the trailing edge, and then accelerates from rest in a

different direction. The vortex is left behind at the point reached by the wing when the stagnation point reached the trailing edge. Its reaction, the circulation round the wing, has become stabilized at the value necessary to place the stagnation point at the trailing edge The vortex which has been left behind is equal in strength and opposite in-sense to the circulation); round the wing and is called the starting vortex or initial eddy (Figure. 1)

Figure1. The initial eddy

The pressure on the upper surface of a lifting wing is lower than that of the surrounding nvironment, while the pressure on the lower

r surface, and ay be greater than that of the surrounding

en

esurface is greater than that on the uppem

vironment. Thus, over the upper surface, the fluid will tend to flow inwards towards the root from the tips, being replaced by fluid which was originally outboard of the tips. Similarly, on the undersurface the fluid will either tend to flow inwards to a lesser extent, or may tend to flow outwards. Where these two streams combine at the trailing edge, the difference in spanwise velocity will cause the fluid to roll up into a number of small streamwise vortices, distributed along the whole span. These small vortices roll up into two large vortices just inboard of the wing-tips (Figure 2). The strength of each of these two vortices will equal the strength of the vortex replacing the wing itself.

Figure 2. Trailing vortices

Both the starting vortex and the trailing system of vortices are physical entities which can be explored and discerned and seen if conditions are right. The bound vortex system, on the other hand, is a hypothetical ich replace

th

T

x system. The hypothetical bo

arrangement of vortices wh

e real physical wing in every way except that of thickness. This is the essence of finite wing theory. It is largely concerned with developing the equivalent bound vortex system which simulates accurately, at least a little distance away, all the properties, effects, disturbances, force systems, etc., due to the real aerofoil.

he replacement bound vortex system must create the same disturbances, and this mathematical model must be sufficiently flexible to allow for the effects of the changed parameters. A real aerofoil produces a trailing vorte

und vortex must do the same.

Figure 3. Bound vortex system

A consequence of the tendency to equalize the pressures acting on the top and bottom surfaces of an aerofoil is for the lift force per unit span to fall off toward must produce th span. For co

the

s the tips. The bound vortex systeme same grading of lift along the

mplete equivalence, the bound vortex system should consist of a large number of spanwise vortex elements of differing spanwise lengths all turned backwards at each end to form a pair of the vortex elements in the trailing system. The varying span wise lengths accommodate the grading of the lift towards the wing-tips, the ends turned back produce the trailing system and the two physical attributes of a real wing are thus simulated (Figure 3).

2.2 Prandtl-Glauert formulation This model is an important example of using

vortices for the representation of solid-fluid interaction by vortex singularities, a representation directly related to the viscous action within boundary layer.

Lets consider an incompressible flow around a wing of finite span as sketched in Figure 4.

Figure 4. The wing geometry

The well known lifting line theory of Prandtl leads to the following differentialintegral equation:

= yyyd

yVcVky

b

b

2/

2/ dd

41)(

(1)

Here denotes the angle of attack, c(y) the wing chord, V the upstream undisturbed velocity and

the circulation [2]. Defining by: )( y

= cos2by , [ ] ,0 , (2)

Glauert assumed as a Fourier series:

=

=1

sin2p

p nAbV .

(3)

Now the problem consists in determination of the unknown coefficients Ap, p = 1,2,... . Introducing (3) in equation (1), one gets:

=

1 1 sinsin

sinppA

pA pp

, b

kc2

=

(4)

A certain number of points, called collocation points, are selected on the bounded vortex line (along the y axis). The equation is then imposed at each of these points and a set of linear algebraic equations, having Ap, p = 1,2,... as unknowns results. Under the form (4) the determination of the coefficients Ap, p = 1,2,3..., meets certain difficulties, both for the analytical and numerical calculations, due to instabilities at end stations

and . Thus, the term: 0= =

= 1 sinsin

)(ppA

S p .

(5)

at wing extremities

=1

2)0( pApS ,

(6)

=1

2)1()( pp ApS

has a slower convergence in terms of p2. In addition, at these points a chord discontinuity is present. In order to avoid the chord discontinuity at the wing ends, a first improvement was done by Carafoli, [1], by considering an approximate representation of the chord variation:

++= 4cos22cos2sin 4200cc

,

(7)

that smoothes the jump, but small modification in the wing planform appears.

3. PROPOSED FORMULATION Present improvement has several advantages: a)

it conserves the wing real chord variation, leading to simpler formulas; b) gives suggestions to accelerate the convergence of the infinite system of equations for the coefficients A p, p = 1,2,; c) is easier to be adapted for any kind of calculations (including numerical calculation).

A collocation method is equivalent to multiplying the equation (4) by a Dirac weight function centered on the collocation points, then integrating along the wing span. This approach has disadvantages at discontinuity points (in chord and/or angle of attack). There are many weight functions fitting the problem necessity. Will choose however functions of the same kind as appearing in the series (3). This corresponds to a Galerkin type selection what was proved to be very adequate in many other cases. By multiplying equation (4) with the weight functions

nsin n = 1,2,3... that vanish at the wing ends, then integrating over the wing span, one gets a stable rapid convergent system of equations for An :

= + 1 )1(2 pnpnpnnnn AHpIAnH ,K,2,1=n .

(8)

=0

sin nIn ,

==

dpnHH pnnp

0 sinsinsin .

(9)

etrical wing and incidence

np being the Kronecker symbol. The integrals In, Hnp, n, p = 1,2,3,...can be directly performed in many practical cases, for example for elliptical and polygonal wings. In case of symm ( ) one yields:

( ) ( )= , ( ) ( )= , (10), for n + p odd, (11

, for n = 2p = even. (12

A consequence (11), (12) is the vanishing of the r even values on:

m = 1,2,3...... (13

Then one nee for odd indicein the form [3]:

= ,

ere:

0=npH = )

) 0=nIof relations (10), coefficients An fo f

) 02 =mA , ds only the system (8) s

( )=

mp

pppmmmm AHpIAL

,11212,12121212 12 (14)

wh

nnn nHL 2= (15

Under assumption (subsequently confirmed) of

(four indices distance). On the other hand, the integrals H2m1,2p 1 are decreasing with the indices m, p (see relations (15)For these reasons one may truncate the infinite sumin (10), starting with p = m + 2.

can restrict ourselves to give only the coefficients A1 and A :

)

a rapid convergence of series (3) of the circulation, we neglect in (14) terms with respect to 32 +mA

12 mA

).

Thus we3

21331

133311 3

3HLLHILIA

= , ( )13133

31 AHIL

A = (16

the co aerodynamic forces ults:

)

For a better accuracy, one can start with three coefficients: A1, A3, A5, using three equations corresponding to m =1, 2, 3, respectively. Knowing

efficients A1, A3,, the can be evaluated. The lift coefficient res

1ACz = , Sb2= , (17)

where S and are the reference wing surface and the wing aspect ratio respectively. The coefficient of the induced drag , Cx , is:

=

+=

121

23

2

21

2231

n

znzxi A

ACAAnCC .

(18

4. TRAPEZOIDAL

)

WING For trapezoidal wings (Figure 4) the integrals

above introduced can be evaluated in closed form:

)1(2cos12

1221,1212

+==

mm

mmqm

HI mm , 000

K,2,1=m (19)

++

+=

20

220

32,1212.12

()1(coscos1)(1(

)1(4)12()12(4

pmpmmq

pmmHH pmpm

+

22

2

)1(coscos1(

)1

pmpmm

0) (2

12,1212.12 = mppm (21) where:

HH

01

ccq e= ,

bkc2

00 = . (22)

Taking into account that:

0)1()1(

coscos1)(1(lim 22 =

pmpmm

mp, K,3,2=p (23)

For the first coefficient A1, one gets:

)157264(16)57(4815)157264(16)2(30

2200

2

20

00

1

qqqqqq

A

+++++=

=

(24)

In this way one can calculate wings of various shapes, where the presence of engines and fuselage can also be considered.

MMETRIC WING NEAR WALL In the follow g one onsiders a wing not

necessarily symm b/2 at a distance /with respect to an infinite vertical plan. This circumstance could appear in a wind tunnel with

r a sail (Figure 5) fixed on from the deck of a vessel

(practically such rigid metal sails are used to maneuver big vessels near the shore).

In Figure 5 a hybrid combination between a sosail made of linen and a solid sail, provided with

. The angle of attack 0 is measured with respect to the zero lift axis, whereas the geometrical angle g is reported to the x axis. The positioning angles of slat and thesoft sail are

5. ASYin cetric of span 2

rectangular section and foa mast at a distance /2

ft a

slat, rigid connected to the mast and

v and , respectively.

Figure 5. The rectangular hybrid wing (VP) and the

trapezoidal hybrid wing (VT)

The system wingsolid infinite wall is equivalent from aerodynamic point of view with a wing in a mirror. As a consequence, the resulting motion takes place around a wing having a double span b. At / 2y = one have a new jump in the chord distribution. Once more the proposed method is recommended. By denoting with the angle, defined by:

b=sin ,

= 2,0arcsin b (25)

Integrals along the wing span [ ]( ) ,0 , are calculated by extracting the portion ( /2, /2 ) out of a complete wing with chord c0 at y = 0. We have calculated the required integrals for a trapezoidal wing, at constnt incidence, 0. Then one gets as particular cases the rectangular and the triangular wings. The simplest case corresponds to

param

elliptical wing. For the symmetrical wing the chord

eter variation, , defined by relation (4):

)cos1(2 0

== rb

kc ,b

kc2

00 = ,

01

ccq e= . (26)

Thus, one obtains for the integrals I2m-1, defined by relation (14):

=2

100

1 cos)sin1(2 rII r , (27)

( ) ( ) ++ cos= 22300 3 sin213sin132 rII r

the index r standing for reported. The other integrals are expressed as functions of I1r and I2r, as follows:

rIL 101 2+= , rHL 3303 32 +

= . (28)

+=

2

2

333

3sin4

sin55sin

562IH rr

2sin33r

(29)

Now one can calculate the first three coefficients ocirculation:

f

23

2031

23031

100

1 3 rrr

ILIAA = , 3 rILL

02 =A ,

( )rrr ALIAA 10

3

33

00

3 1 =

(30)

We have taken in consideration four cases: big slat

Comparisons of the analytical calculations with experiments are given in Tables 1 and 2. As a conclusion, the lifting line theory is applicablfor angle of attack 0 corresponding to interval (CZmin, CZmax). The angle 0 is measured with respect to the null lift axis of the hybrid wing system and depends on the curvature of the profile rofilemastsoft sailslat. Although this dependence is complicate, one can assume an almost constant slope of the curve C ()

6. CONCLUSIONS The good agreement between theory and

experimental data for the slope dCZ/d0, the four cases presented in Table 1, especially for larger values of the aspect ratio , suggest a linear variation of CZ with 0 - the angle of the relative speed V. The rigid mast was profiled as a wing. Therefore the assumption of a almost unmodified

firmed. cement

a) the square hybrid wing, both with (VP1a) and small slat (VP2a); b) the trapezoidal hybrid wing, with big slat (VT1a) and small slat (VT2a).

e

p d

zfor a fixed configuration.

direction of the null lift axis direction is conIn exchange, one may see a significant displa

of null lift axis with wing planform, but not with the slat chord. As well, the angle 0 at Czmax keeps

efficient,Cx, at Czmax, more

on effects. the integrals

REFERENC1. Carafoli, E., (1945), Theorie des ailes

monoplanes denvergure finie, Analele .R uc

2. fo ns u (1981), i fluid i resibile,

Ed.Acad. R.S.R. Bucureti. 3. (19 supr m

u aer ic piloergu finit n regim incompresibil,

In tehn ure XV37-49.

4. Maraloi, C., (2005) Experimental s for Determining the Propulsion

Parameters of the Hybrid-sail Ships, Revue

Roum echniques, Srie de 0. Berb , Mara oretical and mental SAe mics System, U. B. Scientific Bulletin, Series D, 68, pp.17 - 32

er ifting coefficient

The proposed method for solving the Prandtl equation, has the following advantages: it takes into account without problems the sudden chord variations or jumps (four jumps in case, of the wing in mirror); permits an exact calculations of

a value around 30 degree (Table 2). As regards the drag cothan a half (approx. 60%) is induced by the free vortex sheet, the rest belonging to frictiThe two times increases of the angle 0max in comparison to usual wings can be explained through the slat effect as well by flexible wing adaptation to flow (Table 2).

leading to simple analytical expressions; a convenient arrangement of the system of equations giving the coefficients A1 , A3 , eventually A5 (A2 = 0 , A4 = 0) with a good accuracy.

imental data for the slope of lTable 1. Comparisons analytical model with exp

ES

Acad Cara

omne, B ureti. tantinescli E., Co V. N.,

Dinam ca elor ncomp

Berbente, C., 73), A a unei etode pentr calcul odinam al ari r de anv rBul. st. Poli ic Buc ti, XX , pp.

Researche

aine des Sciences T Mcanique Applique, 5

5. ente C. Experi

loi C. (2006), Thetudy Regarding the

rodyna of a Ship Sail P.

0Z / ddC (deg-1) Model r 0 A1r

A3r theory exper.[3,4] (min error)

VP1.a. VP2a

0. 0.

0.4298 0.4030

3.689 3.920

0.707 0.72

8

08

0,0682 (9.94%)

)

0.1164 0.0614

0.1235

0.0627

0.682 (8.09%

VT1.a

0.7568

0.4670

5.834

0.50

VT2a 0.8000 0.4418 6.491

27

0.4941 0.0185 0.0769

0.0769 (0.0%)

0.0276

0.0751

0,0789 (4.82%)

Table 2. Comparisons analytical model with experimental data for Cx for Czmax

Cx for Czmax

(deg) Cz = 0

(

Czmax

id (Model

Czmax deg) max

( eg) theory

dus) in experiment[3,4]

VP1.a.

-23,5 -

3 3

2. 2.

0

0

,

.VP2.a 23.0

7.0 8.0

0.5

1.0

05 1

25 1

.41 0

.77 0

372

423

0,650 (57.2%) 0.750 (56.4%)

VT1.a VT2.a

- -

3 2

2. 2.

.

.

,

.

12.7

12.0

18.0 17.0

0.7

9.0

25 7

50 7

05 0

10 0

277

310

0,500 (55.4%) 0.500 (62.0%)

ScP

To

3`nVo

A PHYSICAL AND THEORETICAL ANALYSIS OF THE VORTEX BREAKDOWN ON

Marius STOIA-DJESKA, Assoc. Pro

DepaSterian DANAILA, Prof.

Department of

Department of

*Corre mania Tel.: (+ sa.ro

ientific Bulletin of the olitehnica University of Timisoara


d Workshop on rtex Dominated Flows Timisoara, Romania

June 1 - 2, 2007

DELTA WINGS

f.* rtment of Aerospace Sciences Elie Carafoli OLITEHNICA University from BucharesP t

Aerospace Sciences Elie Carafoli HNICA University from BuPOLITE charest

Corneliu BERBENTE, Prof.,

Aerospace Sciences Elie Carafoli EHNICA University from BucharesPOLIT t

sponding author: Polizu 1-6, 011061, Bucharest, Ro40) 21 4023967, Fax: (+40) 21 3181007, E-mail: marius.stoia@ro

ABSTRACT oncerns with the vortex breakdown irst, some experimental results are

pr

Vortex breakdown, vortex flow on delta wings

[m/s] radial velocity

The paper cphenomenon. F

esented in order to explain the vortex break down phenomenon. Further the Euler equations for axially symmetric flows are simplified using a number of assumptions based on the slenderness of the vortex core and on the conical flow structure inside the vortex. The resulting equations can be solved in closed form and the solutions obtained show two different features, resembling the jet-like stable region and the wake-like after breakdown region of the flow. These features are discussed in the paper.

KEYWORDS

NOMENCLATURE r

vv

[m/s] tangential velocity u [m/s] axial velocity [deg] angle of attack M [-] the Mach number Su a de r a

ics and not only vortex ant role. The low pressure

s intensively exploited in the design of modern civil and combat

ory by the Kutta condition.

enon. Fu

b tscrip s n Superscripts exte n l conditions

1. INTRODUCTION In aircraft aerodynamflows play an importinduced on the upper side of highly swept wings by the leading edge vortices results in an important increase of the lift capabilities of small aspect ratio

aircrafts [1, 4, 5]. The leading edge vortex occurs when the flow encounters a sufficiently highly swept sharp leading edge and can be explained within the framework of inviscid flow the

wings. This non-linear effect was and i

Increasing the angle of attack of the wing leads to an increase of the strength of the leading edge vortex. This is in fact a well-ordered vortical flow structure, steady and stable. Depending on the Mach number and geometrical parameters there is a critical angle of attack at which the internal structure of the vortex changes substantially and the vortex breakdown occurs. Vortex breakdown means a sudden increase of the cross section of the vortex core and the loss of the regularity of the flow. Further, vortex breakdown also marks the end of the favorable effects induced by the leading edge vortex. The phenomenon of vortex breakdown has been observed in wind tunnel experiments and real flights and can be investigated using computational simulations as well as theoretical approaches.

This paper concerns with the analysis of the stability of a narrow vortex core. First, some experimental results are presented in order to explain the vortex break down phenom

rther the Euler equations for axi-symmetric flows are simplified using a number of assumptions based on the slenderness of the vortex core and on the conical flow structure inside the vortex. The resulting equations subjected to rational boundary conditions can be solved in closed form and the solutions obtained show two different features, resembling the jet-like stable region and the wake-

like after breakdown region of the flow. These features are discussed in the paper.

2. FUNDAMENTALS OF DELTA WING AERODYNAMICS AND VORTEX

REAKDOWN The subsonic flow over a sharp edged delta wing

ck is aration. The

f the flow is the vortical structure th

B

at medium and large angles of attacharacterized by leading-edge sepdominant aspect o

at forms on the upper side of wings with leading edge sweep angles greater than 45 deg. The flow separates when encountering the sharp leading edge

and forms a free shear layer which contains vorticity. Due to this embedded vorticity the free shear layer rolls up in a spiral fashion and the result is a steady primary vortex. The vortex has a viscous core but the flow outside the core is essentially inviscid. The vorticity from the entire length of the leading edge is convected through the free shear layer to the vortex core which increases in strength and in cross-section in the downstream direction. There is also a second vortex sheet lying above the primary vortex. This secondary vortex is due to the flow separation due to strong adverse pressure gradients in the spanwise direction.

10deg. = b) 18 deg. = a)

c) Vortex breakdown is imminent d) Starboard vortex breakdown

at 18.3 deg. = , at 18.5 deg. = Figure 65LE =

Wind tunnhave proven that [

pressure and velocity

tion region gives t so called lift effect that represents an

1. The oil flow visualization of vortex breakdown at 0.85,M = 0el studies and numerical simulations

2, 3, 4, 5]: This suc hevortex

The presence of the stable primary vortex strongly affects the distributions on the wing upper side, the predominant and beneficial effect being a low-pressure region under the vortex core.

essential feature of highly swept delta wings; As the angle of attack increases over a limit value a large scale vortex breakdown occurs

above the wing and the flow becomes fully unsteady. e 1 shows some results of the oil flow Figur

visualization study of vortex breakdown on delta wi

approximately the low

It

nstream the trailing edge and does no

. MATHEMATICAL MODEL AND CLOSED FORM SOLUTIONS

w It is now clear that the vortex breakdown

Eu

ndrical coordinates are:

ngs at 00.85, 65LEM = = obtained at High Speed laboratory, TU Delft. The white region represents -pressure area and also delineates the position of the primary vortex. The vortex burst or breakdown mechanism is one of the unresolved problems in fluid mechanics. means a sudden increase of the cross section of the vortex core and the loss of the regularity of the flow. Further, bursting involves a sudden decrease in the magnitude of the axial and circumferential velocities of the core. Detailed measurements show that the axial component of the velocity is increasing up to the breakdown point location (axial velocities more than three times the freestream velocity were measured) where it decreases abruptly. Upstream the bursting point the core has a jet-like structure while downstream the core has a wake-like structure that expands in the radial direction. It was discovered that the vorticity vector is first oriented in the axial direction and after the vortex breakdown reorients itself along a transverse direction [4, 2].

At lower angles of attack the primary vortex burst point is dow

t affect the vortex lift. The interest is now to control the flow so that the bursting point to remain downstream the trailing edge for medium and high alpha. It is nowadays known that the breakdown can be postponed by axial air blowing or, in other words by increasing the jet like axial velocity. Unfortunately, for aeronautical applications this approach is inefficient. We consider therefore that a better understanding of the vortex breakdown mechanism represents the first step towards new solutions for the flow control.

3

3.1. Simplified equations of the vortical flo

mechanism is inviscid and thus the incompressible ler equations can be used as the starting point for

searching for rational but simplified flow models. Further, there are at least two completely different states of the vortex core that must be identified. In what follows we assume that the vortex core is isolated and its cross-sectional dimension is small relative to typical length scale along the axis of

vortex core. This assumption we made means that the vortex core is slender and slowly varying in axial direction.

For incompressible inviscid flow the Euler equations in cyli

2

1 1 0r rvvu v

x r r r

1 1 0

1 1 1 0

1 1 1 0

r

r r rr

r r

u u u pu vx r r xv v v pu v ux r r r ru u v pu v u ux r r r r

+ + + = + + + = + + + = + + + + =

(1)

Under the assumptions we made, in the slender, narrow region with rotational axially-symmetric flow the equations reduce to:

2

1rr

vu vx r r

0

1 0

1 1

1 0

r

r rr

r r

u u pu vx r xv v pu v ux r r ru uu v u ux r r

+ + =

+ + = + + = + + =

2)

The unknowns of these equations are the velocity components and the pressure. These can be

(

expressed as functions of x and the dimensionless radius ( )r r R x= where ( )R x denotes the radius of the cross-section of the core for x=const [3].. Then the pressure partial derivatives become:

1 1,p p d p d R p prr R r d x R d x r x

= = +

)

and the same rule applies for the velocity components. Introducing these partial derivatives in

(3

(2) one obtain a new system of partial differential equations that contains product terms like

,u uR Rux x

or

pRx

. For conical flows inside

ical v core the velocity and the

non-conical flows but for slender and narrow vortex cores terms like those above can be neglected. If we do so then the system (2) reduces to a system of ordinary differential equations with the only independent variable

the quasi-con ortexpressure do not depend on the axial direction. For

r . The solution of the equations gives a qualitative insight in what happens inside the vortex core.

3.2. Boundary conditions At the axis of the core the radial velocity vanishes, i.e. 0rv = for 0.r = At the exterior

of thboundary of the vortex core the axial and circumferential onents e velocity and the pressure match continuously the outer flow values, i.e. ( ) ( ) ( )

comp

, , for 1.e e eu U x v V x p P x r= = = = 3.3. Closed form solution The boundary conditions we assumed lead to the following closed solution

( )( )( )

( ) ( )(( ) (

22

1 2

12 2 2

r e

eVv SU H r H rS

p p V Ve V H r I rUe

= +

1eu U V H r

v V U G r

= =

= +

(4)

1)

where we denoted the functions:

(

( ) ( )1

2 2

r R 21 1r R

G r+ = ,

( ) ( ) ( )

( ) ( ) ( ) ( )

1 12 2 22 2

1 12 2 22 2

22 2 2

ln 1 1 1 1

1 1 1 1

H r r R r R

r R RI r H r

r R R

= + + + + = +

and

( )( )

11 2

'2 2'22

'21'2 2

1 11 4 1

2 1 1

RRV W= SR

R

+ + +

(5)

The swirl ratio of the flow outside the vortex core is denoted with e eS V U= and the parameter

be derived analytically too and is left to the reader.

1W = . The components of the vorticity vector can now

The behavior of the solution (4) depends on the values of the parameter W. For 1W = the velocity and vorticity vectors point in the same direction. A streamline coming from upstream rs the vortex core and continues downstream spiraling around the core axis with a slight reduction of the spiral radius. This is the jet-like part of the solution and it appears in the forward part of the wing. For 1W

ente

= the

velocity and vorticity vectors are pointing in opposite directions. The streamline starts at infinity downstream close to the axis and runs upstream with an increasing spiral radius. When the axial component of the velocity becomes positive the spiraling streamline starts to run downstream but with a sudden increase of the spiral radius. This is the wake-like part of the solution and this can be observed on the rear part of the wing. We consider that the vortex breakdown mechanism is in fact responsible for the switch in

S We have examined the physical behavior of the

a wing with sharp and highly

The present work has been supported from the arch Council Grant

1. Kuchemann, D., (1978) The Aerodynamic Aircraft, Pergamon Press

ects of

3. , Vol. 11, pp.

4. Vortical Flows to Improve the

5. ringer Verlag, New York

the solution state.

4. CONCLUSION

vortex flow on a deltswept leading edge. Further we derived an analytical solution for an isolated slender vortex core. The solution has two branches. The jet-like solution develops in the upstream of the bursting point while the wake-like solution develops downstream this point. However, the mechanism responsible for the switch in the flow state from one to the other is still unclear.

ACKNOWLEDGMENTS

National University Rese(CNCSIS) 33/2004. Oil flow visualization of vortex breakdown on delta wings at 00.85, 65LEM = = have been obtained from High Speed laboratory, Technical University Delft.

REFERENCES

Design of2. Ekaterinas, J.A., Sciff, L.B. (1990)

Numerical Simulation of the Effvariation of Angle of Attack and Sweep Angle on Vortex breakdown over delta Wings, AIAA -90-3000-CP Hall, M.G. (1961) A Theory for the Core of a Leading Edge Vortex, JFM209-227 Lamar, J.E. (2002) Understanding and ModelingTechnology Readiness Level for Military Aircraft terms of reference, NATO RTO AVT-E-10/RTG Rom, J. (1992) High Angle of Atack aerodynamics, Sp

SPolitehnica University of Timisoara

3Vortex Dominated Flows

ATION TIP CLEARANCE. NUMERICAL SIMULATION AND EXPERIMENTAL RESULTS

Constantin Viorel CAMPIAN, Prof.*

Faculty of Engineering Eftimie Murgu Univers

Dorian NEDELCU, Assoc. Prof. Faculty of Engineering

Tel.: (+40) 256 219134, Fax: (+40) 256 219134, Email: [email protected]

cientific Bulletin of the

Transactions on Mechanics Tom 52(66), Fascicola 3, 2007

`nd Workshop on

Timisoara, Romania June 1 - 2, 2007

CAVIT

ity of Resita Eftimie Murgu University of Resita *Corresponding author: P-ta Traian Vuia, No. 1-4, 320085, Resita, Romania

, [email protected]

ABSTRACT The pape and experimental clearancorrespond to the gap between runner blades and

r. Experimental results are obtained

inamics design of must generate a better control of

between rotating blade and

de model without and with anti vitation lip is done in the figure 1 and 2.

Figure 1. The 3D model of the blade without anti

cavitation lip

r presents a flow numerical simulationresults regarding cavitation tip

ce for Kaplan turbines. The analysed domain

runner chambeon the model and prototype.

KEYWORDS Kaplan turbine, cavitation tip clearance, vortex flow

1. INTRODUCTION Improvements in hydrodhydraulic turbinecavitation phenomenon. In this paper cavitation tip clearance is analyzed. Tip clearance cavitation appears inside the gapthe runner chamber. The flow through the clearance is the results of the intrados/extrados pressure difference. When the boundary layer separation occurs, the tip clearance cavitation appears. Supplementary, a vortex attached to the blade tip is generated in the channels between the blades, which is the source for the vortex cavitation. Numerical simulation of the clearance water flow was made by Navier-Stokes method.

The runner blades were manufactured with anti cavitation lips, in two geometrical solutions.

Experimental investigations were performed on the model in the laboratory and on the prototype in power station.

2. NUMERICAL SIMULATION RESULTS

2.1. Geometrical model The 3D bla

ca

Figure 2. The 3D model of the blade with anti

cavitation lip

For anti cavitation lip were analyzed two geometrical solutions, where the second solution correspond to a shorter length of the anti cavitation lip comparative with first solution, beginning from the leading edge.

2.2. Numerical simulation The numerical simulation were performed with

Navier-Stokes method [1] for blade without and with anti cavitation lip in two solutions.

The numerical results are graphically presented in figures no. 3 to 6 for solution 1 and 7 for solution 2. Figure no. 8 presents comparative results between the two solutions.

The pressure distributions are calculated at the same head for suction side of the blade where the anti cavitation lip is placed.

Figure 3 Pressure distribution on the blade

without anti cavitation lip top view

Figure 4 Pressure distribution on the blade without anti cavitation lip front view

Figure 5 Pressure distribution on the blade with

anti cavitation lip solution 1 top view


anti cavitation lip solution 1 cavitation bubles near blade surface


anti cavitation lip solution 2 top view

Figure 8 Comparative pressure distribution on the

blades with anti cavitation lips

The area close to the anti cavitation lip is the most important area for this study.

Figure 8 shows that solution 2 for anti cavitation lip (with shorter length) is better than solution 1, because the cavitation pitting area will be smaller.

3. EXPERIMENTAL RESULTS

3.1. Experimental results on the model Experimental results were performed on the Iron

Gates I turbine model [2]. The model has been installed on the test rig; the tests were performed, at the same operating conditions, for 3 blade configurations: blades without anti cavitation lips, figure 9, blades with long (solution 1) and short (solution 2) anti cavitation lips, figure 10 and 11.

Figure 9 Blade without anti cavitation lip

Figure 10 Blade with anti cavitation lip solution 1

Figure 11 Blade with anti cavitation lip solution 2

The efficiency and the cavitation picture on the model blade are the same without and with anti cavitation lips (solution 1 and 2).

3.2. Experimental results on the prototype

The experimental observations on the prototype runner blade were made after 8000 hours of operation. In the figures 12 and 13 are presented pictures with cavitation pitting areas and the long anticavition lip (solution 1). On the blade near the anti cavitation lip was observed a ationerosion area, which is not visible on the figures.

slightly cavit

Figure 12 Cavitation pitting on the anti cavitation lip solutia 1

Figure 13 Zoom on the cavitation pitting on

the anti cavitation lip solutia 1

h av

(so

In the figure 14 is presented a picture witc itation pitting areas and the short anticavition lip

lution 2). On the blades equiped with this solution of anticavitation lips, an area with depth cavitation pitting near the anticavitation lip appears.

Figure 14 The cavitation pitting on blade and the anti cavitation lip solutia 2

There are no significant cavitation differences between the blades with long, short and without anti cavitation lip, at the model tests.

On the prototype, solution 2 of the anticavitation lip induce on the lip and blade a significance cavitation erosion, comparative with solution 1. The modified geometry of the solution 2 (short length) determine the peripheral vortex attachment, which generate the cavitation erosion on the blade.

This cavitation behaviour was not possible to be observed on the model.

The tip clearance cavitation analysed in the study can not be numerical reproduced with

ee

e blade o

1. VA TECH CFD Cavitation Research, Result Presentation in Zurich, April, 2002.

2. VA TECH PdF1 Report of the Task Force Cavitation, June, 2003

4. CONCLUSIONS

accuracy. The very small gap (5 mm) between th with th

runner blade and runner chamber comparedunner diameter (9500 mm) and the sizr

c mpared with the small dimensions of the anticavitation lip limit the approximation of the phenomen by numerical simulation.

REFERENCES

Scientific Bulletin of the Politehnica University of Timisoara

Transactions on Mechanics Tom 52(66), Fascicola 3, 2007

3rd Workshop on Vortex Dominated Flows

Bucharest, Romania June 1 - 2, 2007

NUMERICAL ANALYSIS OF PUMP HYDRODYNAMICS AT CONSTANT SPEED

Adrian STUPARU, Assist. Prof.* Department of Hydraulic Machinery Politehnica University of Timisoara

Sebastian MUNTEAN, Senior Researcher Center of Advanced Research in Engineering

Sciences Romanian Academy - Timisoara Branch

Daniel BALINT, Assist. Prof. Department of Hydraulic Machinery Politehnica University of Timisoara

Liviu ANTON, Prof. Department of Hydraulic Machinery Politehnica University of Timisoara

Alexandru BAYA, Prof. Department of Hydraulic Machinery Politehnica University of Timisoara

*Corresponding author: Bv Mihai Viteazu 24, 300223, Timisoara, Romania Tel.: (+40) 256 403692, Fax: (+40) 256 403700, Email: [email protected]

ABSTRACT This paper presents the numerical investigation of the 3D flow in the impeller and the suction-elbow of a storage pump by using commercial code FLUENT 6.0. First the investigated centrifugal pump is described, then the equations that governs the flow and the boundary conditions imposed and in the end the results of the flow simulation.

KEYWORDS storage pump, numerical investigation, turbulent flow

NOMENCLATURE

gHpp

c INp = [-] pressure coefficient

g [m/s2] gravity k [m2/s2] turbulent kinetic energy

1. INTRODUCTION The progress in the field of Computational Fluid Dynamics (CFD) has made this technology an important tool in analysis and design of hydraulic turbomachinery. The turbomachinery flow is essentially unsteady due to the rotor-stator interaction. On the other hand, rigorously speaking, the geometrical periodicity of the rotor blade channels cannot be used since there are differences in the flow from one inter-blade channel to another. However, with carefully chosen and experimentally

validated assumptions, one can develop a methodology for computing the turbomachinery flow, so that very good and engineering useful results are obtained [5]. However, computing the real flow (unsteady and turbulent) through the whole storage pump requires large computer memory and CPU time even for our days computers. As a result, a simplified simulation technique must be employed to obtain useful results for pump analysis, using currently available computing resources.

2. COMPUTATIONAL DOMAIN, EQUATIONS AND BOUNDARY CONDITIONS The investigated storage pump has two stages with the impellers situated in opposition and a suction-elbow of complex geometry, Figure 1. Each impeller has five blades, Figure 2.

Figure 1. Cross section through the storage pump

Figure 2. Isometric view of the storage pump

impeller

The computational domain includes only the impeller of the centrifugal pump. For the numerical investigation only one inter-blade channel is used because of the symmetry of the geometry. Figure 3 shows the 3D computational domain with boundary conditions corresponding to an inter-blade channel of the impeller. The computational domain is bounded upstream by an annular section (wrapped on the same annular surface as the suction outlet section, but different in angular extension) and extends downstream up to cylindrical patch, in order to impose the boundary conditions on the outlet section.

Figure 3. Isometric view of the inter-blade channel

of the impeller

The inter-blade channel domain is discretized with 500k cells using a structured mesh coupled with a special boundary layer discretization on the blade faces, see Figure 4.

Figure 4. Mesh generated on the 3D computational

domain of the inter-blade channel

For the flow analysis presented in this paper we consider a 3D turbulent flow model. A steady relative 3D flow is computed,

0= V (1a)

( )Vg

V += ptd

d

(1b)

The numerical solution of flow equations (1a) and (1b) is obtained with the expert code FLUENT 6.0, [3], using a Reynolds-averaged Navier-Stokes (RANS) solver. As a result, the viscosity coefficient is written as a sum of molecular viscosity and turbulent viscosity T, and the last term in the right-hand-side of (1b) becomes ( )[ ]VT + . For the first case, when only the impeller domain is considered, we solve a relative flow, in a rotating frame of reference with angular speed

k = ( k being the unit vector of the pump axis direction). By introducing the relative velocity

rVW = (2) with r the position vector, the left hand side of (1b) becomes

( ) ( )( ) r

tr

WWWWt

++

+++

2

(3)

An important assumption used in the present computation is that the relative flow is steady. This

simplifies (3) by removing the first and last terms, and also allows the computation of impeller flow on a single inter-blade channel. The turbulent viscosity is computed using the RNG model. On the inlet surface of the impeller a constant velocity field was imposed normal on the surface. The velocity magnitude is computed using the flow rate of the operating point:

II S

Qv =

(4)

For the outlet section the outflow condition is imposed. That means both flow and turbulent quantities remain unchanged downstream to the outlet section. On the periodic surfaces of the impeller the periodicity of the velocity, pressure and turbulence parameters were imposed:

( )

+= z

nrvzrv

b,2,,, rr

,

( ) K ,,2,,,

+= z

nrpzrp

b

(5)

We investigated five operating points of the pump with the characteristics given in the table 1: Table 1: Operating points of the centrifugal pump

Operating point Parameter Symbol Value

Rotational speed

n [rot/min] 1500

Flow rate Q [m3/s] 1 Pumping head

H [m] 319 1

Hydraulic power

Pu=gQH[kW]

3128.273

Rotational speed

n [rot/min] 1500

Flow rate Q [m3/s] 1.1 Pumping head

H [m] 300 2

Hydraulic power

Pu=gQH[kW]

2941.95

Rotational speed

n [rot/min] 1500


H [m] 265.45 3

Hydraulic power

Pu=gQH[kW]

2603.135

Rotational speed

n [rot/min] 1500

Flow rate Q [m3/s] 0.9

4

Pumping H [m] 336

head Hydraulic power

Pu=gQH[kW]

3294.98

Rotational speed

n [rot/min] 1500


H [m] 350 5

Hydraulic power

Pu=gQH[kW]

3432.27

3. NUMERICAL RESULTS The pumping head is determined using the following equation:

( )( )

( )( )

++

++=

inlet

inlet

outlet

outlet

dSnv

dSnvg

vzg

p

dSnv

dSnvg

vzg

p

H

rr

rr

rr

rr

2

2

2

2

(6)

And the error is calculated with the equation (7):

100log

log =cata

catacalculat

HHH (7)

The results of the numerical simulation compared with the ones given by the pump producer are presented in table 2 and figure 5: Table 2: Pumping head values resulted from the numerical simulation and given by the pump producer

Q [m3/s]

HFLUENT [m]

Hcatalog [m]

[%]

0.8 184.59 175 5.48 0.9 177.7 168 5.46 1 167.62 159.5 5.09

1.1 155.42 150 3.61 1.2 143.57 132.725 8.17

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3Q [m3/s]

0

50

100

150

200

250

300H

[m]

H(FLUENT)H(catalog)

Figure 5. Pumping head vs. flow rate for the

investigated operating points

The efficiency of the impeller is determined using the equation: ( )

( )

=

M

dSnvvrM

dSnvvr

inlet u

outlet u

rr

rr

(8)

The results of the numerical simulation compared with the ones given by the pump producer are presented in table 3 and figure 6: Table 3: Efficiency values resulted from the numerical simulation and given by the pump producer

Q [m3/s]

HFLUENT [m]

catalog [%]

FLUENT [%]

0.8 184.59 83 88.75 0.9 177.7 86 91.12 1 167.62 87 90.65

1.1 155.42 85 92.30 1.2 143.57 80 93.08

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3Q [m3/s]

50

60

70

80

90

100

eta

[%]

eta(FLUENT)eta(catalog)

Figure 6. Efficiency vs. flow rate for the

investigated operating points

The pressure coefficient is calculated with the following relation:

gHppc Ip

N = (9

The distribution of the pressure coefficient along the pressure side and suction side of the blade for all five operating points are presented in figure 7 to 11

.

Figure 7. Pressure coefficient distribution along the blade for Q = 0.8 m3/s





From figure 7 to 11 one can observe that the minimum value of the pressure coefficient is located on the leading ege and this value is decreasing while the flow rate goes up. The NPSHr (Net Positive Suction Head required) is defined as:

gp

gV

gpNPSH iir

+= 22

(9)

where the variables with subscript (i) correspond to the averaged one on inlet section of the impeller.

In figure 12 the NPSHr distribution on the impeller blades is plotted for the five investigated operating points.

It is well known, the maximum risk of cavitation occurs where the largest NPSHr value (corresponding to minimum pressure) is obtained. Due to the sharpness of the leading edge, the maximum NPSHr value appears at the junction between blade suction side and the crown near to the leading edge (the red spots in Figure 12). The value of the NPSHr rises with the rise of the flow rate and so the risk of cavitation is higher.

Figure 12 NPSHr on the blades of the impeller for Q = 0.8 1.2 m3/s

4. CONCLUSIONS The paper presents a numerical study of the 3D

flow in the impeller of a storage pump. Comparison between numerical results and data given by the pump producer is presented.

A particular attention is paid to the analysis of the flow on the impeller blade. The numerical simulation predicts a minimum pressure on the suction side near the crown, in agreement with experimental observations.

The cavitation risk for the bigger flow rates is higher than for the smaller flow rates.

ACKNOWLEDGMENTS The authors acknowledge the support from the National University Research Council grants. All numerical computations have been performed at the Numerical Simulation and Parallel Computing Laboratory of the Politehnica University of Timisoara, National Centre for Engineering of Systems with Complex Fluids..

REFERENCES 1. Akhras, A., El Hajem, M., Morel, R.,

Champagne, J.Y., The Internal Flow Investigation of a Centrifugal Pump, Proceeding of Flucome, Sherbrooke, Canada, 2000

2. Fluent Inc., FLUENT 6. Users Guide, Fluent Incorporated, 2001.

3. Fluent Inc., Gambit 2. Users Guide, Fluent Incorporated, 2001.

4. Hofmann, M., Stoffel, B., Experimental And Numerical Studies On A Centrifugal Pump With 2d-Curved Blades In Cavitating Condition, Proceeding of Fourth International Symposium on Cavitation CAV2001, Pasadena, California, SUA

5. Muntean, S., Numerical methods for the analysis of the 3D flow in Francis turbine runners, PhD Thesis Politehnica University of Timisoara, Timisoara, 2002.

6. Sallaberger, M., Sebestyen, A., Mannschreck, E., Pinkas, W., Modern Pump Impeller Design With Consideration Of Non-Uniform Inlet Flow Fields, Proceedings of IAHR, Graz, 1999

7. Tamm, A., Ludwig, G., Stoffel, B., Numerical, Experimental And Theoretical Analysis Of The Individual Efficiencies of a Centrifugal Pump, Proceedings of ASME FEDSM01 2001 ASME Fluids Engineering Division Summer Meeting New Orleans, Louisiana, May 29 June 1, 2001

8. Tamm, A., Brten, A., Stoffel, B., Ludwig, G., Analysis Of A Standard Pump In Reverse Operation Using CFD, Hydraulic Machinery and Systems, 20th IAHR Symposyum, 2001.

9. Van Esch, B. P. M., Simulation of three-dimensional unsteady flow in hydraulic pumps, Thesis University of Twente, Enschede, 1997.

S

To

3V

SWIRLING FLOWS IN THE SUCTION SUMPS OF VERTICAL PUMPS. EXPERIMENTAL

Eugen Constantin ISBASOIU, Prof* Petrisor STANESCU, MEng.

Marius ST Department of

Carmen Anca

Politehnica University of Bucharest Politehnica University of Bucharest

Politehnica University of Bucharest *Corresponding author: 313 Splaiul Independentei, 060024, Bucuresti, Rom

ABSTRACT

working conditions in axial and

Vertical pump, swirling flow, suction sump, ults, numerical simulation, velocity

CTION hydro-mechanical equipments ons to receive water flowing

through the lve a large

physical model of the suction

a

[2], [3] or experimental using a hydraulic and

suction su

cientific Bulletin of the Politehnica University of Timisoara


`nd Workshop on ortex Dominated Flows Timisoara, Romania

June 1 - 2, 2007

APPROACH

Department of Hydraulic Machinery Politehnica University of Buch arest

, Assist. Prof.

S.C. AVERSA S.A. Bucuresti

OIA-DJESKAAerospace Sciences Elie Carafoli

Politehnica University of Bucharest

SAFTA, Assist. Prof Department of Hydraulic Machinery Politehnica University of Bucharest

Georgiana DUNCA, Assist. Department of Hydraulic Machinery

Diana Maria BUCUR, Assist Department of Hydraulic Machinery

Calin GHERGU, Prep. Department of Hydraulic Machinery

ania , Email: [email protected] Tel.: (+40) 21 4029 523, Fax: (+40) 21 4029 523

intake channel and the suction pump sump. So the flow could not invo

The experimental approach have the purpose to determine the mixed flow pumps operation if the water level in the intake channel lowers. It will be obtained the limit value of the suction head of installation pump so as the pumps could have safety conditions of working. The physical model of the suction sumps of the pumps is described for two types of vertical pumps: NMV 1000RA and NMV 2000RA. Experimental results combined with numerical simulations give us the behavior of the swirling flows in a suction sump of a vertical pump.

KEYWORDS

experimental resdistribution.

1. INTRODU Suction sumps are used in the pump statifrom the intake channel to the pumps suction aria. The pump functionality to the designed parameters is looking for a flow without swirls between the

quantity of air, [1]. The swirling flow is influenced by the geometry and the dimensions of the suction sump and, not at the least, by the working conditions of the pump. The study on the conditions of a vertical pump deals with the inferior limit of the water level in the sump pump if the level in the channel is fluctuating. Would be swirling flow at the lowest water level in the suction sump or not? To respond at this question two types of vertical pumps were proposed: NMV 1000RA and NMV 2000RA and their sumps suction. In [1] were mentioned the dimensions and the geometry of a suction sump for a vertical pump, the swirls types and the protection elements to have a flow without vortexes.

2. PHYSICAL MODEL OF THE SUMP The flow study in the suction sump could be

numerical scale model [4], [5]. Tests for NMV 1000RANMV 2000RA pumps were made. The

mp for NMV 1000RA pump was physical modeled on a scale of kl = 2.12, Figure 1 and a kl = 5 was used for NMV 2000RA, Figure 2. The scale

coefficients, kl, are the results of the hydraulic similitude, nq, for the particular case of equality between the speed triangle of the model pump and the real one. As a model pump was used a reference diameter of D = 400 mm.

Figure 1. The suction sump of the NMV 1000RA pump

(the dimensions of the prototype)

Figure 2. The suction sump of the NMV 2000RA pump

(the dimensions of the prototype)

3M

Classical m easure the working parameters, flow rate and pressure, of axial

ad or f the pump, H, is defined as the difference

be

. PARAMETERS MEASURED ON THE ODEL

ethods were used to m

or diagonal pumps, Figure 3. The pumping hethe head o

tween the discharge head of the pump, Hr, and the suction head of the pump, Ha. In the case of axial and mixed flow vertical pumps, if it is considered as

the origin the water level in the suction sump, the pumping head is done as

ag

Vg

pH rr ++= 2

2

(1)

where p is the pressure mr easured with the differential manometer placed on the out pipe of the pump, a is the difference of the level between the median manometer plane and the water level in the

Vsump, r is the medium velocity of water in the discharge pipe of the pump.

The flow rate, Q, was measured using the tighten section method by a diaphragm mounted on the discharge pipe of the pump. So:

= pmDQ 2

4

2

(2)

where D = 336 mm the discharg

e pipe of the pump; is the flow coefficient of the diaphragm;

2

Ddiameter; p is the pressure difference on the diaphragm; = 1000 kg/m3 water density at 200C

e.

= dm with d = 269 mm the diaphragm

temperatur

Figure 3 Measured parameters for axial and mixed flow

pumps

4 sump suction of NMV 1000RA pump and three for

pump. The working e in Table 1 with visual

directions of the suction sump. It could be seen in

. TESTS RESULTS Five sets of measurements were done: two for the

the sump of NMV 2000RAmeasured parameters arqualitative observations of the flow. During these tests the velocity components were measured in two perpendicular sections and

Figure 1 and Figure 2 the measure sections numbered with 1, 2, 3 and 4. The velocities were

Table 1 H Hsb

measured with a Pitot-Prandtl Tube and a differential manometer. Displaying the velocity components any disturbance of the velocity distribution from the turbulent profile indicates the presence of a parasite flow induced by a swirl flow. Figure 4 and Figure 5 indicates no significant deviations from the turbulent velocity distribution in the sump of NMV 1000RA pump. No submerged swirl [1] was formed at the entrance of the impeller.

Figure 6 and Figure 7 indicates a disturbance of the velocity components distribution and the swirling flows are imminent in these cases if the water level in the sump is changed (see Hsb in Table 1). The submerged head, Hsb, is the static pressure at the impeller entrance.

h p

r Q No.

The 3

pump mm MPa m /s m m

Observations

1 372 0.44 0.42 2.716 without vortex 7.8 333 0.25 0.62 5.24 1 w.946 ithout vortex 333 0.25 0.62 5.24 1.194 with vortex

2

N1000RA

MV

333 0.25 0.04 5.24 0.746 with vortex 3 850 1.9 0.628 24.31 1.546 without vortex 4 740 1.9 0.586 22.58 0.646 with vortex

850 1.4 0.629 17.87 0.446 with vortex 5 2000RA

NMV

850 1.4 0.625 17.87 1.996 without vortex

Figure 4. Velocity distribution on horizontal axis (1 and 2 measure section) and vertical axis (3 and 4 measure section),

NMV 1000RA, Hsb = 2.716 m, without vortexes.

Figure 5. Velocity distribution on horizontal axis and vertical axis, NMV 1000RA, Hsb = 2.716 m, without vortexes.

Figure 6. Velocity distribution on horizontal axis (1 and 2 measure section) and vertical axis (3 and 4 measure section),

NMV 2000RA, Hsb = 0.646 m, with vortexes.

Figure 7. Velocity distribution on horizontal axis and vertical axis, NMV 2000RA, Hsb = 0.646 m, with vortexes.

A numerical simulation of the flow in the suction sump was continuing [1] in both cases of the sumps of NMV 1000RA and NMV 2000RA vertical pumps. The FLUENT computer fluid dynamic code was using and the k- model in turbulent flow was applied. The NMV 1000RA pump was numerical modeled for the flow rates of 1 m3/s and 3 m3/s. In these cases the numerical results did not indicate a swirling flow that could generate problems in the

pump operation. The NMV 2000RA pump was numerical modeled for the flow rates of 10 m3/s and 15m3/s. At a lower water level in the suction sump of the pump a swirling flow was observed, Figure 8, Figure 9 and Figure 10.

Figure 8 Velocity distribution in the vertical and median planes, x-z axis with 10 m3/s flow rate for

NMV 2000RA pump

Figure 9 Velocity distribution in the horizontal plane, 10 m3/s flow rate, NMV 2000RA pump

Figure 10 Pathlines in the suction sump with 15 m3/s flow rate for NMV 2000RA pump

5. CONCLUSIONS The paper regarding the experimental study of

the swirling flows in the intake channel suction sump of vertical pumps. Influence of the level upstream in the suction pump and the development of the swirling flow in the suction sump pump are observed. The physical model and the results of the tests give us:

NMV 1000RA pump in the suction sump could work in good conditions without vortexes if the submerged head Hsb is more then 0.746 m. It is no recommended in pump operation at submerged heads less then 0.746 m to have a high flow rate.

NMV 2000RA pump in the suction sump could work without vortexes if the submerged head Hsb is lower then 1.146 m and the flow rate is between 0.586 m3/s and 0.617 m3/s.

REFERENCES 1. Isbasoiu, E.C., Munteanu T., Safta C.A.,

s.a, (2005), Swirling flows in the suction sumps of vertical pumps. Theoretical approach; Sci. Bul. Of University

Politehnica of Timisoara, Trans on Mechanics, pp 17-22.

2. Gustave A., s.a., (1996), Effects of approach flow condition on pump sump design, J. Hydr. Eng, ASCE, 122(9), pp 489-494.

3. Schafer F., Hellmann D.-H., (2005) Optimization of approach flow conditions of vertical pumping systems by physical model investigation, Proc. of FEDSM2005, Huston, TX, USA, FEDSM2005-77347.

4. Minisci E., Telib H., Cicatelli G., (2005) Hydraulic design validation of the suction intake of a vertical centrifugal pump station, by use of computational fluid dynamic (CFD) analysis, Proc. of FEDSM2005, Huston, TX, USA, FEDSM2005-77330.

5. Iwano R., Shibata T., (2002), Numerical prediction of the submerged vortex and its application to the flow in pump sumps with and without a baffle plate, 9th International Symposium on Transport Phenomena and dynamics of Rotating Machinery, Honolulu, Hawaii.

6. *** FLUENT 5 Users Guide, FLUENT Inc., 1998.

Scientific Bulletin of the Politehnica University of Timisoara

Transactions on Mechanics

3rd Workshop on Vortex Dominated Flows

Bucharest, Romania June 1 June 2, 2007

SOME ASPECTS ABOUT A VORTEX GENERATING BUILDING MODEL PLACED UPWIND AN AEROELASTIC MODEL IN THE BOUNDARY LAYER WIND TUNNEL

Mircea DEGERATU, Prof.*

Hydraulic and Environmental Protection Department, Technical University of Civil

Engineering Bucharest

Andrei GEORGESCU, Lecturer Hydraulic and Environmental Protection Department, Technical University of Civil

Engineering Bucharest Liviu HAEGAN, Senior Lecturer



Costin Ioan COOIU, Assistant Hydraulic and Environmental Protection Department, Technical University of Civil

Engineering Bucharest Rzvan- Silviu tefan, Assistant



Lucian SANDU, Prof. Hydraulic and Environmental Protection Department, Technical University of Civil

Engineering Bucharest *Corresponding author: Blvd. Lacul Tei 124, sect. 2, 020396 Bucharest, Romania. Tel.: +40 21 243 3660, Fax: +40 21 243 3660, E-mail: [email protected]

ABSTRACT Using as reference the assumptions synthesized

in the paper Dynamic wind tunnel tests for the Bucharest Tower Centre we have tried to evaluate the influence of a vortex generating building model placed upwind of the aero elastic model of the tower. Considering the actual construction development in Bucharest each aerodynamic study has to consider the influence of the built area that surrounds the studied building. Assuming different values of the free distance between the obstacle building and the studied one we tried to evaluate the structural influence of a building that is part of an urban agglomeration.

KEYWORDS Wind engineering, Dynamic wind loads, Dynamic structural response

NOMENCLATURE ax [m/s2] x- axis acceleration ay [m/s2] y- axis acceleration Ax [m] x- axis dynamic amplitude Ay [m] y- axis dynamic amplitude fx [Hz] x-axis frequency fy [Hz] y-axis frequency Tx [s] x- axis period Ty [s] y- axis period

Ud,x [m/s] x-axis dynamic displacement velocity Ud,y [m/s] y-axis dynamic displacement velocity g [m/s2] gravity

1. INTRODUCTION The experimental studies performed, synthesized in this paper, followed the determination of the vibration behavior of a tall structure with dynamic response exposed to the atmospheric boundary layer and include the influence of vortices generated by another upwind positioned building. These experimental researches continue the topics of the paper Dynamic wind tunnel tests for the Bucharest Tower Center published in the Scientific Bulletin of the Politehnica University of Timisoara- Transactions on Mechanics. The simulated atmospheric boundary layer is the same as the one used in the above mentioned paper- i.e. a general power law profile with =0.23. The former paper presented the experimental tests performed in the boundary layer wind tunnel called TASL-1 from the Wind Engineering Laboratory- Technical University of Civil Engineering Bucharest for a 107 m tall building. We presented the following results: a). the building structure; b). the similitude criteria; c). the concept, design and experimental implementation of the

aero-elastic model of the building; d). the experimental conditions including atmospheric boundary layer simulation; e). the measurement methodology; f). the results obtained for the acceleration, frequency and dynamic amplitude both along wind and cross wind using as reference the building axis, for eight different wind directions.

2. EXPERIMENTAL RESULTS OBTAINED USING THE MODEL The measurements were performed for two different values of the wind/ building incidence angle using a 1:100 scaled model (first campaign: =95 - S-E wind- and the second campaign =5- S-W wind) using Reynolds numbers of the order of 105. We analyzed the influence of the vortices generated by the structure situated upwind of the studied model. The model of the structure situated upwind is 80 cm long, 15 cm wide and 30 cm tall facing the incident air stream with the larger face crossing the wind direction in the experimental zone of the tunnel. This obstacle building was positioned in front of the model at three different distances: 90 cm, 180 cm and infinite value (the reference value, with no building upwards as shown in fig. 1a,b,c).

Fig. 1a

Fig. 1b

Fig. 1c We determined the vibration response characteristics of the aero-elastic 1:100 scale model using both x and y directions with accelerometers as accelerations (ax,ay), dynamic amplitudes of vibrations (Ax, Ay), frequencies (fx,fy), periods (Tx,Ty) and dynamic displacement velocities (Ud,x,Ud,y). These experiments were performed in order to observe the differences induced by the distance between the buildings as well as the wind simulated velocity profile. The results are divided into two groups with respect to the wind/ building incidence angle (SE-95 and SW-5) each divided into three subgroups with respect to the position of the building situated upwind the model (90 cm, 180 cm, and ), so weve indexed our results with two arguments (SE 95-90, SE 95-180, SE 95- and SW 5-90, SW 5- 180, SW 5-).

3. EXPERIMENTAL RESULTS TRANSPOSED TO THE REAL BUILDING The vibration characteristics obtained by the measurements performed on the 1:100 scale model for the six different situations were transposed at the real scale using the proper similitude scales for each parameter. These scales were obtained using certain limitations for the wind action on aero elastic structures (just as the studied building is in our case). The transposed results at the natural scale represent the vibration characteristics along the x and y axis of the structure at a reference height of 100 m above ground. - The first ten diagrams present the vibration characteristics of the model due to loads induced by SE wind (SE 95-90, SE 95-180, SE 95-); - The last ten diagrams present the vibration characteristics of the model due to loads induced by SW wind (SW 5-90, SW 5- 180, SW 5-).

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/s2 ]

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el

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z] M

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z] P

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tip

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m] M

odel

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odel

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tipSV 5 - ? SV 5 - 90 SV 5 - 180

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] Mod

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m/s

] Mod

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m/s

] Pro

totip

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/s2 ]

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el

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/s2 ]

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totip

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] Mod

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] Pro

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z] M

odel

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z] P

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odel

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] Mod

el

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] Pro

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] Mod

el

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[m/s

] Pro

totip

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4. CONCLUSIONS The experimental studies were performed for Reynolds numbers in the range [2.5 .... 7.5]* 107. These numbers are big enough to insure the self simillarity of the longitudinal velocity profile for the inertial domain which includes the fluctuating components of the velocity that induce the resonance excitement for this tall building category. The assumptions that will follow were made for Reynolds numbers in the range [6.5 .... 7.5]* 107 because this domain offers significant values for the aeroelastic behavior of the analyzed structure. Regarding the acceleration parameters, the vortices created upwind induce significant growth of the values referring to the x- axis for SE wind load and the y- axis for the SW wind load and decrease the acceleration values on the y- axis for SE wind load and the x- axis for SW wind load. Regarding the dynamic amplitudes, the vortices created upwards induce decreasing values reffering to both axis directions and both wind directions. As the distance between the obstacle building decreases, the amplitude values decrease is stronger. The present research confirms, once again, the necesity of performing this type of studies in order to get a good idea of the interaction between the

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] Mod

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SE 95 - SE 95 - 90 SE 95 - 180 Series4

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] Pro

totip

SE 95 - ? SE 95 - 90 SE 95 - 180 atmospheric boundary layer and the slender structures. The final caption presents the model placed in the experimental vein of the aerodynamic wind tunnel (Fig.2).

Fig. 2

REFERENCES 1. Degeratu, M., Georgescu, A., Hasegan, L.,

Cosoiu, C., Pascu, R., Sandu, L. 2006 Dynamic wind tunnel tests for the Bucharest tower center., Trans. on Mechanics, Sci. Bull. Politehnica University of Timisoara, Romania, Tom 51(65), Fasc. 3.

2. Davenport, A.G. 1968. The application of the boundary layer wind tunnel to the prediction of wind loading. Proc. of International Research Seminar of Wind Effect on Buildings and Structures, Toronto.

3. Degeratu, M. 2002. Atmospheric boundary layer (in Romanian), Timioara: Orizonturi Universita

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