8.7.1 Introduction
The components of propulsive efficiency (wake, thrust deduction and relative rota- tive efficiency) can be determined from a set of propulsion experiments with mod- els. A partial analysis can also be made from an analysis of ship trial performance,
provided the trial takes place in good weather on a deep course and the ship is ade- quately instrumented.
A complete set of performance experiments would comprise the following:
(i) A set of model resistance experiments: to determineCTM as a function ofFr, from which shipCTScan be found by applying appropriate scaling methods, see Chapter 4.
(ii) A propeller open water test: to determine the performance of the model propeller. This may possibly be backed by tests in a cavitation tunnel, see Chapter 12.
(iii) A self-propulsion test with the model, or a trial result corrected for tide, wind, weather, shallow water etc.
The ITTC recommended procedure for the standard propulsion test is described in ITTC2002 [8.11]
8.7.2 Resistance Tests
The model total resistance is measured at various speeds, as described in Section 3.1.4.
8.7.3 Propeller Open Water Tests
Open water tests may be made either in a towing tank under cavitation conditions appropriate to the model, or in a cavitation tunnel at cavitation conditions appropri- ate to the ship. These are described in Chapter 12. Thrust and torque are measured at variousJvalues, usually at constant speed of advance, unless bollard conditions (J=0) are required, such as for a tug.
8.7.4 Model Self-Propulsion Tests
The model is towed at various speeds andat each speeda number of tests are made at differing propeller revolutions, spanning the self-propulsion condition for the ship.
For each test, propeller revolutions, thrust and torque are measured, together with resistance dynamometer balance load and model speed. The measurements made, as described in [8.11], are summarised in Figure 8.8.
8.7.4.1 Analysis of Self-Propulsion Tests
In theory, the case is required when thrust=resistance,R=TorR−T=0.
In practice, it is difficult to obtain this condition in one run. Common practice is to carry out a series of runs at constant speed with different revolutions, hence, different values ofR−Tpassing through zero. In the case of the model, the model self-propulsion point is as shown in Figure 8.9.
8.7.4.2 Analysis for Ship
If thetotalresistance obeyed Froude’s law, then the ship self-propulsion point would be the same as that for the model. However,CTM>CTS, Figure 8.10, whereCTSis
Carriage Hull model Duct/pod Environmental conditions
Speed measurement, tachometer/probe
Resistance dynamometer
Propeller
dynamometer Dynamometer
Temperature measurement, thermometer
Propeller
Sinkage and trim, measurement
devices
Model speed Resistance / external tow force
Sinkage and trim
Thrust, torque, rate of revolution
Duct / pod thrust
Tank water temperature
Signal conditioning and data acquisition
Data analysis
Figure 8.8. Propulsion test measurements.
the ship prediction (which may include allowances forCVscaling of hull, appendages, hull roughness and fouling, temperature and blockage correction to tank resistance, shallow water effects and weather allowance full scale). This difference (CTM–CTS) has to be offset on the resistance dynamometer balance load, or on the diagram, Figure 8.9, in order to determine the ship self-propulsion point. IfRTmis the model resistance corresponding toCTMandRTmsis the model resistance corresponding to CTS, then the ship self-propulsion point is at (R−T)=(RTm −RTms). This then allows the revolutionsn, behind thrustTband behind torqueQbto be obtained for the ship self-propulsion point.
In order to determine the wake fraction and thrust deduction factor an equiv- alent propeller open water condition must be assumed. The equivalent condition is usually taken to be that at which the screw produces either
(i) the same thrust as at the self-propulsion test revolutions per minute (rpm), known asthrust identityor
(ii) the same torque as at the self-propulsion test rpm, known astorque identity.
The difference between the analysed wake and thrust deduction values from these two analyses is usually quite small. The difference depends on the relative rota- tive efficiencyηRand disappears forηR=1.0.
Q T
0
n
Qb
Tb
Model self-propulsion point Ship self-propulsion point
(RTm− RTms) R −T R −T
Figure 8.9. Model and ship self-propulsion points.
8.7.4.3 Procedure: Thrust Identity
(a) From the resistance curves, Figure 8.10, (CTm–CTs) can be calculated to allow for differences between the model- and ship-predictedCTvalues. (Various loadings can be investigated to allow for the effects of fouling and weather etc.)
(b) nandJb(= nV s.D) can be determined for the self-propulsion point andTbandQb; hence,KTbandKQbcan be obtained from the self-propulsion data, Figure 8.9.
(c) Thrust identity analysis assumes KTo = KTb. The open water curve, Figure 8.11(a), is entered with KTb to determine the corresponding Jo,KQo
andηo.
The suffix ‘b’ indicates values behind the model and suffix ‘o’ values in the open water test.
The wake fraction is given by the following:
wT = (VS−VO)
VS =1−VO
VS =1−nDJo
nDJb =1−Jo
Jb, (8.9)
whereJb = nDVS andVSis ship speed.
CT
Fr
CTm
CTs (CTm − CTs)
Figure 8.10. Model and shipCTvalues.
J KT
KQ
η
10KQ
KT η
J0
KQb
KT0
η0
(b)
J KT
KQ
η
10KQ
KT η
J0
KTb
KQ0
η0
(a)
Figure 8.11. Open water curve, (a) showing thrust identity, (b) showing torque identity.
The thrust deduction is given by the following:
t = (Tb−R)
Tb =1− R
Tb =1−0.5ρSV2CT S
ρn2D4KT b =1−0.5Jb2SCT S
D2KT b . (8.10) The relative rotative efficiency is given by the following:
ηR=ηb
ηo
= JoKT b
2πKQb.2πKQo JoKTo =KT b
KTo.KQo
KQb. (8.11)
For thrust identity,
KTo=KT b and ηR= KQo
KQb. (8.12)
For torque identity,Jo=Jfor whichKQo=KQbandηR=KT b/KTo. Most commercial test tanks employ the thrust identity method.
Finally, all the components of the quasi-propulsive coefficient (QPC)ηDare now known andηDcan be assembled as
ηD=ηoηHηR=ηo
(1−t)
(1−wT)ηR. (8.13)
8.7.5 Trials Analysis
Ship trials and trials analysis are discussed in Chapter 5. Usually only torque, revolu- tions and speed are available on trials so that ship analysis wake fractionwTvalues are obtained on a torque identity basis. Thrust deductiontcan only be estimated on the basis of scaled model information (e.g. [8.12]), andηRcan only be obtained using estimated thrust from effective power (PE), see worked example application 3, Chapter 18.
8.7.6 Wake Scale Effects
The model boundary layer when scaled (see Figure 3.21) is thicker than the ship boundary layer. Hence, the wake fraction wT tends to be smaller for the ship, although extra ship roughness compensates to a certain extent. Equation (5.22) was adopted by the ITTC in its 1978 Performance Prediction Method to allow for wake scale effect. Detailed full-scale measurements of wake are relatively sparse. Work, such as by Lübke [8.13], is helping to shed some light on scale effects, as are the
increasing abilities of CFD analyses to predict aft end flows at higher Reynolds num- bers [8.9, 8.10]. Lübke describes an investigation into the estimation of wake at model and full scale. At model scale the agreement between computational fluid dynamics (CFD) and experiment was good. The comparisons of CFD with experiment at full scale indicated that further validation was required.