guide for power prediction

TMR7 Experimental Methods in Marine Hydrodynamics

Guide to scaling of resistance and prediction of full scale power Ship data are found later in this document. Values of some coefficients used in the resistance and power prediction are given here. There is also an enclosure with formulas used in the resistance and power prediction. What you find here is a guide on how to use those formulas. In this analysis it is recommended to use Excel or a similar tool. For all speeds tested do as follows: Calculate total resistance coefficient CTm

Calculate residual resistance coefficient CR, using CBDm=0, 1+ko=1.0699, νm=1.075•10-6 m2/s Calculate full scale total resistance coefficient CTs, using CA=-0.228E-03. CBDs=0, νs=1.187•10-6 m2/s Calculate full scale resistance RTs – now you are done calculating full scale resistance! The open water test has been given to you as part of the model data. You will need to interpolate in the open water diagram as part of the analysis of the propulsion test. This can be done manually on a printed diagram, or it can be done by in a spreadsheet or Matlab. A description of how to do this in Excel follows. Import the open water curve into Excel (or similar). Create third-order polynomials of J as function of KT, and KQ as function of J. You can do this by creating a graph with the curve, add a trend line, select polynomial as type of trend line, and select “display equation on graph”. Make sure you show enough numbers for the parameters in the equation, for instance by right-clicking the equation and selecting scientific with four digits as number format. For each speed in the propulsion test do as follows: Calculate J, KT, and KQ. from the propulsion test results. Enter the open water diagram with KT found from the propulsion test, and read off the corresponding J-value. This J-value is called J0. This can be done with KT-J regression Read off the KQ-value corresponding to J0. It is called KQ0. This can be done with a J-KQ regression. Calculate thrust deduction t, wake fraction w and relative rotative efficiency ηR. Find J* from the open water diagram by entering the open water diagram with the following

2 2 2(1 ) (1 )TsT

s s

RKJ nprop t D V wρ

=⋅ ⋅ − ⋅ ⋅ ⋅ − 2 (you can make a KT/J2-J regression to make this

simpler). Find KQ for J* from the open water diagram (by using the regression for KQ as function of J). Calculate RPM from J* Calculate PD and PB from KQ. Use a mechanical efficiency ηm=0.97 for calculating PB.

2

ENCL. APPENDIX 1 REPORT 601622.00.01 DATE 2003-04-10

TOWING TESTS

SHIP RESISTANCE

REF M2375J The hull model is towed by the carriage at which the total resistance is measured at different speeds. The hull model is equipped with a rudder and a trip-wire at station 9 ½ (19). The conversion from hull model (m) into ship (s) is made by using the form factor method. In this method it is assumed that the total resistance can be divided into two parts, represented by the viscous resistance and the residuary (due to vorticity, wave making and wave breaking) resistance (CR). The viscous resistance is determined by multiplying the frictional resistance (CF) with a constant form factor (ko), which is identical for model and ship. Further, it is assumed that the residuary resistance (CR) is identical for model and ship. MODEL (m):

Total resistance coefficient: BDmAAmRmoFm

mmm

TmTm CCCkC

SV

RC ++++⋅=

⋅⋅= )1(

22ρ

Frictional resistance coefficient: 2)2(log075.0−

=nm

Fm RC (ITTC – 57 correlation line)

Residuary resistance coefficient: BDmAAmFmoTmRm CCCkCC −−⋅+−= )1( SHIP (s):Total resistance coefficient: BDsAAsAoFFsRmTs CCCkCCCC ++++⋅∆++= )1()(

Frictional resistance coefficient: 2)2(log075.0−

=ns

Fs RC

Total resistance: sss

TsTs SVCR ⋅⋅⋅= 2

2ρ

Effective power: 1000

sTsE

VRP

⋅=

Form factor: 30.6 75ok ϕ ϕ= + where BTTLC

FPAPWL

B ⋅+= )(ϕ

Air resistance coefficient: SACAA

T001.0 ⋅=

Transom stern resistance coefficient: 2/1

2/3

)()/(029.0

F

BBD C

SSC ⋅=

Roughness allowance: [ ] 221.0 33.403)(31.110 FssF CVHC ⋅−⋅⋅=∆ Where H = hull surface roughness in µ(10-3 mm). H=150 µ. and Vs = ship speed in m/s Only ∆CF values > 0 are used


PROPULSION TESTS

REF M2375J The hull model is supplied with a propelling machinery and a driving propeller. The rate of revolution is regulated until the model is free relatively to the attached towing carriage. In order to obtain turbulent flow around the model, a trip wire is placed at station 9½ (19). To compensate the difference between the frictional resistance of the model and the frictional resistance of the ship, converted to model scale, the model is unloaded with a towing force in the direction of motion. The towing force (FD) is calculated by the formula:

mmm

SD SVCF ⋅⋅⋅= 2

2ρ

[ ] )()1()( BDsBDmAoFFsFms CCCkCCCC −+−+⋅∆+−=

During the tests, the following parameters are recorded: Propeller thrust T Propeller torque Q Rate of revolution n Model speed V Thrust and torque measured during propulsion and open water tests are expressed non-dimensionally as:

42 DnTKT ⋅⋅

=ρ

and 52 DnQKQ ⋅⋅

=ρ

In the open water diagram KT and KQ are presented as functions of the advance coefficient (J). By entering the open water diagram with the thrust coefficient (KT) measured during the propulsion test, corresponding JO and KQO-values are obtained which are used to estimate wake fraction, relative rotative efficiency, hull efficiency and quasi-propulsive coefficient.

Wake fraction:

DnVJ

w O

⋅

−= 1

Relative rotative efficiency: Q

QOR K

K=η

Hull efficiency: wt

H −−

=11η

Quasi-propulsive coefficient: RHOD ηηηη ⋅⋅= (ηO = propeller efficiency in open water)

Thrust deduction fraction: T

FRt DT −−= 1 (note: T is total thrust – sum of all props.)


OPEN WATER TESTS

REF M2375J The propeller model is driven by a dynamometer at which thrust, torque and rate of revolution are recorded. The immersion of the propeller shaft is ≥ propeller diameter. Test procedure: The rate of revolution is kept constant and by varying the speed, we get the variation of the advance coefficient (J). At each advance coefficient exact rate of revolution, (n), propeller thrust, (T), and torque, (Q), are recorded. The results are presented dimensionless as:

Dn

VJ A

⋅= , advance coefficient

42 DnTKT ⋅⋅

=ρ

, thrust coefficient

52 DnQKQ ⋅⋅

=ρ

, torque coefficient

π

η2⋅⋅

=Q

TO K

JK , propeller efficiency in open water


PERFORMANCE PREDICTION

REF M2375J The performance prediction is based on the assumption that the thrust deduction fraction, t, the wake fraction w and the relative rotative efficiency, ηR, are free from scale effects. From the total resistance of the ship, RTs, and the thrust deduction fraction, t, the following relation is established:

2 2 2(1 ) (1 )TsT

s s2

RKJ nprop t D V wρ

=⋅ ⋅ − ⋅ ⋅ ⋅ −

(nprop is number of propellers)

For each speed, the intersection point of the KT – J2 curve given above with the open water diagram is found. The advance coefficient J* at this point gives the rate of revolution:

*

)1(60JV

Dw

RPM ss ⋅−⋅

=

The corresponding torque coefficient KQ, and the relative rotative efficiency, ηR, gives the delivered power:

5 32( ) ( )1000 60Q

DR

KRPMP kW nprop Dπ ρη

= ⋅ ⋅ ⋅ ⋅ ⋅

The calculation is repeated for different speeds giving the speed/power curve for the actual pitch ratio. An extrapolation of the open water diagram gives speed/power curves for different pitch ratios. The final pitch ratio and speed/power curve is found by interpolation for the actual RPM and power. Finally the brake power and merit coefficient are calculated:

M

DB

PkWPη

=)(

B

sADM P

VC

33/2 ⋅∇= (VS in m/sec.)


LIST OF SYMBOLS

REF M2375J Symbol

Title Dimensions

AEAOATB c CACAACADMCADXCBCBDCDCF

∆CFCLCMCPCRCSCTCTACVd D FDFng J K0KQKTKTDKTPLOALPPLWLn nprop P PBPDPEPS

Expanded blade area Disc area Transverse projected area of ship/model above the waterline Breadth moulded Chord length Empirical correlation coefficient determined from trial analyses Air resistance coefficient Merit coefficient Admirality coefficient Block coefficient Transom stern resistance coefficient Drag coefficient Frictional resistance coefficient Roughness allowance Lift coefficient Midship section coefficient Prismatic coefficient Residuary resistance coefficient Towing force coefficient Total resistance coefficient Appendage resistance coefficient Viscous resistance coefficient Hub diameter Propeller diameter Towing force Froude number Acceleration due to gravity Advance coefficient Form factor Torque coefficient Thrust coefficient Duct thrust coefficient Propeller thrust coefficient Length overall Length between perpendiculars Length of waterline Rate of revolution Number of propellers Propeller pitch Brake power Delivered power at propeller Effective power Shaft power

L2

L2

L2

L L - - - - - - - - - - - - - - - - - L L LMT-2

- LT-2

- - - - - - L L L REVS.T-1

- L L2MT-3

L2MT-3

L2MT-3

L2MT-3

ENCL. APP. 5 cont. REPORT 601622.00.01 DATE 2003-04-10

LIST OF SYMBOLS

REF M2375J Symbol

Title Dimensions

Q R RnRTS SBt t T T TDTPV VAw Z α ηD

Torque Propeller radius Reynolds number Total resistance Wetted surface Area of transom stern below the waterline Max. thickness of a propeller section Thrust deduction fraction Draught moulded Thrust Duct thrust Propeller thrust Speed of ship or model Speed of advance of propeller Wake fraction Number of blades of a propeller Angle of attack Propulsive efficiency or quasi-propulsive coefficient

L2MT-2

L - LMT-2

L2

L2

L - L LMT-2

LMT-2

LMT-2

LT-1

LT-1

- - - -

ηH Hull efficiency - ηM Mechanical efficiency - η0 Propeller efficiency in open water - ηR Relative rotative efficiency - λ ν ρ ∇ ∆

Linear scale ratio Kinematic viscosity Mass density of water Displacement volume Displacement mass

- L2T-1

ML-3

L3

M

ENCL. i) REPORT 846001.20.01 DATE 2004-06-21

PRINCIPAL HULL DATA

REF M2375J HULL MODEL NO.: M2375J Model Scale: 25.676 Loading condition: Design WL Draught AP/FP: 6.500 / 6.500 [m] Setup: m2375j0s10 Symbol Unit SHIP MODEL —————————————————————————————————————————————————————————————— Length overall LOA [m] 140.019 5.453 Length on designed waterline LWL [m] 134.600 5.242 Length betw. perp. LPP [m] 131.300 5.114 Breadth moulded B [m] 22.700 0.884 Breadth waterline B [m] 22.700 0.884 WL

Depth to 1st deck D [m] 26.002 1.013 Draught at LPP/2 T [m] 6.500 0.253 Draught at FP TFP [m] 6.500 0.253 Draught at AP TAP [m] 6.500 0.253 Trim (pos. aft) t [m] 0.000 0.000 Rake of keel [m] 0.000 0.000 Rise of floor [m] 0.000 0.000 Bilge radius [m] 3.000 0.117 —————————————————————————————————————————————————————————————— Water density ρs [kg/m3] 1025.87 998.62 Shell plating thickness [mm] 0.00 0 Shell plating in % of displ. [%] 0.50 0.00 —————————————————————————————————————————————————————————————— Volume displacement ∇ [m3] 11094.3 0.655 Displacement ∆ [t] 11438.2 0.655 Prismatic coefficient* CP [-] 0.5887 0.5887 Block coefficient* C [-] 0.5727 0.5727 B

Block coefficient based on LWL CBLW [-] 0.5583 0.5583 Midship section coefficient CM [-] 0.9727 0.9727 Longitudinal C.B. from LPP/2 LCB [m] -5.833 -0.227 Longitudinal C.B. from LPP/2* LCB [% LPP] -4.442 -4.442 Longitudinal C.B. from AP LCB [m] 59.817 2.330 Wetted surface S [m2] 3826.45 5.804 Wetted surf. of transom stern AT [m2] 10.38 0.016 Transverse area above water AV [m2] 692.00 0.233 —————————————————————————————————————————————————————————————— Remarks: *Refers to LPP Hydrostatic corrections included CBLW, is based on naked hull displacement Appendages: Twin propeller shaft with V -bracket,twin spade rudders, one bow tunnel thruster with pressure relief opening. Turbulence stimulator: Sand strip at station 19.5

ShipX (RepGen version 2.0.15) 28-Sep-04 13:48:27

ENCL. ii) REPORT 846001.20.01 DATE 2005-10-06

OPEN WATER TEST

REF M2375J PROPELLER MODEL No.: P1284 Model Scale: 25.676 Symbol Unit SHIP MODEL —————————————————————————————————————————————————————————————— Propeller diameter D [mm] 4500 175.26 Pitch ratio at r/R = 0.7 P/D0.7 [-] 1.220 1.220 Blade area ratio AE/A0 [-] 0.525 0.525 Number of blades Z [-] 4 4 Chord/Diameter ratio c/D0.7R [-] 0.3549 0.3549 Thickness/Chord ratio t/C0.7R [-] 0.0574 0.0574 Hub diameter ratio d/D [-] 0.298 0.298 —————————————————————————————————————————————————————————————— TEST CONDITIONS Propeller revolutions n [Hz] 12.48 Water temperature T [°C] 17.80 Average Reynolds no. at 0.75R R [-] 0.79·10n

——————————————————————————————————————————————————————————————

6

No scaling is applied to the results J K K η K /JT Q 0 T

(-) (-) (-) (-) (-)

2

———————————————————————————————————————————————————————————————— 0.000 0.619 0.0996 0.000 -1.000 0.090 0.578 0.0928 0.089 70.891 0.182 0.533 0.0858 0.180 16.137 0.274 0.488 0.0790 0.269 6.519 0.365 0.447 0.0731 0.354 3.359 0.454 0.404 0.0673 0.434 1.960 0.546 0.359 0.0613 0.509 1.204 0.637 0.316 0.0556 0.576 0.777 0.729 0.275 0.0503 0.635 0.517 0.821 0.230 0.0440 0.684 0.342 0.911 0.187 0.0376 0.723 0.226 1.002 0.142 0.0306 0.738 0.141 1.096 0.092 0.0227 0.702 0.076 1.189 0.035 0.0133 0.503 0.025 ———————————————————————————————————————————————————————————————— Setup: Open water test file: p1284s1 p1284c1_frip_1 (Cs)

ShipX (RepGen version 2.0.16) Sep 26, 2005 3:47:48 PM

ENCL. iii) REPORT 846001.20.01 DATE 2005-10-06

OPEN WATER DIAGRAM

REF M2375J

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Kt,1

0·K

q,ηo

J

PROPELLER MODEL No.: P1284 NO SCALING APPLIED

Pitch ratio = 1.220 Setup: p1284s1

Thrust coefficient Kt - datapointsTorque coefficient 10·Kq - datapointsOpen Water Efficiency ηo - datapoints

ShipX (RepGen version 2.0.16) Sep 26, 2005 3:47:49 PM

guide for power prediction

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