6 Propeller performance characteristics
6.3 Propeller scale effects
Open water characteristics are frequently determined from model experiments on propellers run at high speed and having diameters of the order of 200 to 300 mm. It is, therefore, reasonable to pose the question of how the reduction in propeller speed and increase in diameter at full scale will affect the propeller performance charac- teristics. Figure 6.5 shows the principal features of scale effect, from which it can be seen that whilst the thrust characteristic is largely unaffected the torque coefficient is somewhat reduced for a given advance coefficient.
The scale effects affecting performance characteris- tics are essentially viscous in nature, and as such are primarily due to boundary layer phenomena dependent on Reynolds number. Due to the methods of test- ing model propellers and the consequent changes in Reynolds number between model and full scale, or indeed a smaller model and a larger model, there can arise a different boundary layer structure to the flow over the blades. Whilst it is generally recognized that most full-scale propellers will have a primarily turbulent flow over the blade surface this need not be the case for the model where characteristics related to laminar flow can prevail over significant parts of the blade.
In order to quantify the effect of scale on the per- formance characteristics of a propeller an analytical procedure is clearly required. There is, however, no
common agreement as to which is the best procedure.
In a survey conducted by the 1987 ITTC it was shown that from a sample of 22 organizations, 41 per cent used the ITTC 1978 procedure; 23 per cent made cor- rections based on correlation factors developed from experience; 13 per cent, who dealt with vessels having open shafts and struts, made no correction at all; a fur- ther 13 per cent endeavoured to scale each propulsion coefficient whilst the final 10 per cent scaled the open water test data and then used the estimated full-scale advance coefficient. It is clear, therefore, that research is needed in this area in order to bring a measure of unification between organizations.
At present the principal analytical tool available is the 1978 ITTC performance prediction method, which is based on a simplification of Lerbs’ equivalent pro- file procedure. Lerbs showed that a propeller can be represented by the characteristics of an equivalent sec- tion at a non-dimensional radius of around 0.70R or 0.75R, these being the two sections normally cho- sen. The method calculates the change in propeller performance characteristics as follows.
The revised thrust and torque characteristics are given by
KTs=KTm−KT
KQs =KQm−KQ
(6.11) where the scale correctionsKTandKQare given by
KT= −0.3CD
P D
cZ D
KQ=0.25CD cZ
D
and in equation (6.11) the suffixes s and m denote the full-scale ship and model test values respectively.
The termCDrelates to the change in drag coefficient introduced by the differing flow regimes at model and full scale, and is formally written as
CD=CDM−CDS
where CDM=2
1+2t
C
0.044
(Rnx)1/6 − 5 (Rnx)2/3
and CDS=2
1+2t
c 1.89+1.62 log10 c
Kp
−2.5
In these relationships t/c is the section thickness to chord ratio;P/Dis the pitch ratio;cis the section chord length andRnxis the local Reynolds number, all relat- ing to the section located 0.75R. The blade roughness Kpis taken as 30×10−6m.
In this method it is assumed that the full-scale pro- peller blade surface is hydrodynamically rough and the scaling procedure considers only the effect of Reynolds number on the drag coefficient.
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96 Marine propellers and propulsion
Figure 6.4 Curves of KT, KQandηand cavitation sketches for KCD 4 (Reproduced from Reference 15)
Propeller performance characteristics 97
Figure 6.5 Principal features of scale effect
An alternative approach to the use of equation (6.11) has been proposed by Vasamarov (Reference 1) in which the correction for the Reynolds effect on propeller open water efficiency is given by
ηos=ηom−F(J) 1
Rnm
0.2
− 1
Rns
0.2 (6.12) where
F(J)= J
J0
α
From the analysis of the functionF(J) from open water propeller data, it has been shown thatJ0can be taken as the zero thrust advance coefficient for the pro- peller. Consequently, if model tests are undertaken at two Reynolds numbers and the results analysed accord- ing to equation (6.12); then the functionF(J) can be uniquely determined.
Yet another approach has recently been proposed (Reference 2) in which the scale effect is estimated using open water performance calculations for propellers hav- ing similar geometric characteristics to the Wageningen B-series.
The results of the analysis are presented in such a way as
1− KT
KTI =f(Rn,KT) 1− η0
η0I =g(Rn,KT)
⎫⎪
⎪⎬
⎪⎪
⎭ (6.13)
where the suffix I represents the values ofKT andη0
for an ideal fluid. Consequently, if model values of the thrust and torque at the appropriate advance coefficient
are known, that isKTm,KQm, together with the model Reynolds number, then from equation (6.13) we have
KTm
KTI =1−f(Rnm,KTm)
⇒KTI= KTm
(1−f(Rnm, KTm) = KTm 1−
1−KKTm
TI
Rnm
Similarly
η0I= η0m
1− 1−ηη0m
0I
Rnm
From which the ideal values ofKTIandη0Ican be deter- mined for the propeller in the ideal fluid. Since the effect of scale on the thrust coefficient is usually small and the full-scale thrust coefficient will lie between the model and ideal values the assumption is made that
KTS
KTM+KTI
2
that is the mean value, and since the full-scale Reynolds numberRnsis known, the functions
f(Rns,KTs) and g(Rns,KTs)
can be determined from which the full-scale values of KTsandη0scan be determined from equation (6.13):
KTs =KTI[1−f(Rns,KTs)]
η0s=η0I[1−g(Rns,KTs)]
from which the full-scale torque coefficient can be derived as follows:
KQs= J 2π
KTs
η0s
The essential difference between these latter two approaches is that the scale effect is assumed to be a function of both Reynolds number and propeller load- ing rather than just Reynolds number alone as in the case of the present ITTC procedure. It has been shown that significant differences can arise between the results of the various procedures. Scale effect correction of model propeller characteristics is not a simple procedure and much attention needs to be paid to the effects of the flow structure in the boundary layer and the variations of the lift and drag characteristics within the flow regime.
With regard to the general question of scaling, the above methods were primarily intended for non-ducted pro- pellers operating on their own. Nevertheless, the subject of scaling is still not fully understood. Although the problem is complicated by the differences in friction and lift coefficient, the scale effect is less predictable due to the quantity of both laminar flow in the boundary layer and the separation over the blade surfaces. Con- sequently, there is the potential for the extrapolation
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98 Marine propellers and propulsion
process from model to full scale to become unreliable since only averaged amounts of laminar flow are taken into account in the present estimation procedures.
To try and overcome this difficulty a number of tech- niques have been proposed, particularly those involving leading edge roughness and the use of trip wires, but these procedures still lack rigour in their application to extrapolation. Bazilevski (Reference 41), in a range of experimental conditions using trip wires of 0.1 mm diameter located at 10 per cent of the chord length from the leading edge showed that the experimental scatter on the measured efficiency could be reduced from 13.6 to 1.5 per cent with the use of turbulence stimulation. It was found that trip wires placed on the suction surface of the blades were more effective than those placed on the pressure face and that the effectiveness of the trip wire was dependent upon the ratio of wire diameter to the boundary layer thickness. Boorsma in Reference 42 considered an alternative method of turbulence tripping by the use of sand grain roughness on the leading edge based on the correlation of a sample of five propellers.
In his work he showed that the rotation rate correlation factor at constant power could be reduced from 2.4 to 1.7 per cent and, furthermore, concluded that turbulence tripping was not always effective at the inner blade radii.
It is often considered convenient in model experi- ments to perform model tests at a higher rotational speed than would be required by strictly adhering to the Froude identity. If this is done this then tends to minimize any flow separation on the trailing edge or laminar flow on the suction side of the blade. Such a procedure is particularly important when the propeller is operating in situations where relatively low turbulence levels are encountered in the inflow and where stable laminar flow is likely to be present. Such a situation may be found in cases where tractor thrusters or podded propulsors are being investigated. Ball and Carlton in Reference 43 show examples of this type of behaviour relating to model experiments with podded propulsors.
Clearly compound propellers such as contra-rotating screws and ducted propellers will present particular problems in scaling. In the case of the ducted pro- peller the interactions between the propeller, the duct and the hull are of particular concern and importance.
In addition there is also some evidence to suggest that vane wheels are particularly sensitive to Reynolds num- ber effects since both the section chord lengths and the wheel rotational speed are low, which can cause difficulty in interpreting model test data.
Holtrop (Reference 44) proposed that the scaling of structures like ducts can be addressed by considering the interior of the duct as a curved plate. In this analysis an assumed axial velocity ofnPtipis used to determine a correction to the longitudinal towing forceFgiven by
F=0.5ρm(nPtip)2(CFm−CFs)cmDm
wheren,Ptip,candDare the rotational speed, pitch at the blade tip, duct chord and diameter, respectively.
In the case of podded propulsor housings the problem is rather more complicated in that there is a dependence upon a number of factors. For example, the shape of the housing and its orientation with respect to the local flow, the interaction with the propeller wake and the scale effects of the incident flow all have an influence on the scaling problem.