Date. Author Address
October 2006
TJ.C. van Terwisga, J. Hoitrop and M.B. Flukkema
Deift University of Technology Ship Hydromechanics Laboratory Mekelweg 2, 26282 CD Deift
A parametric power prediction model for tractor pods
by
T.3.C. van Terwisga, J. Holtrop and M.B. Flikkema
Report No. 1545-P 2006
Presented at the 2" T-POD Conference be held in Brest, France, 3rd 5th October 2006
TU Deift
DeIft University of Technology
http://www.univ-brest.fr/tpodO6/
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with Pôle Mécanique Brestois
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PÔLEMECANIQUE BRESTOiSGeneral information
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9/10/2007 Home
GENERAL INFORMATION
Following the success of the ist T-POD conference held at the University of Newcastle in 2004,
there have been some landmark developments in the field of podded propulsion and emerging motor technologies.
These developments have been complimented by the activities of several high European Union (EU) projects such FASTPOD and the recent report of the 24t1 Azimuthing Podded Propulsiion Committee as well as several other projects worldwide.
T-POD 2006 will address all key aspects associated with podded propulsion inc Naval applications, as listed below in the Topics of Interest.
T-POD 2006 will also be supported by strong industrial participation to encomp technological challenges encountered in the current and future applications. T-POD 2006 will be held in Brest, France, 3rd - 5th October 2006
T-POD 2006 will be the occasion for one-to-one meetings. At the registration th attendees will be provided and during the second and third days time and spac be provided as requested for one-to-one meetings.
Home
http://www.univ-brest.fr/tpod06/general.html 4/10/2007
Organizalion
ORGANIZATiON
T-POD 2006 is managed by three committees:
Chair committee:
Jean-Yves BILLARD Mehmet ATLAR Christian LAINE
Scientific committee:
André Astolfi (IRENAV) France Français Besnier (Principia) France Neil Bose (MU) Canada
Jon Eaton (ARL) USA
Jean-Paul Hautier (L2EP) France Seu-Eun Kim (Samsung) S Korea Leszek Konieczny (CTO) Poland
Kazimierz Lapinski (Gydinia Shipyard) Poland Pascal Lemesle (BE MAURIC) France Paul Letelier (AR EVA) France
Francisco Pereira (INSEAN) Italy Ted Rosendahl (SSPA) Sweden
Kadir Sarioz (ITU) Turkey Mario Felefakis (RCC) USA Osman Turan (UG&S) UK Michael Woodward (UNEW) UK
Local committee:
André Astolfi Jean-Yves Cognard Henda Djendi Magalie Lamande Jean-Yves Billard Marie Coz Claude Goineau Jean-Marc Laurens Page 1 of3David Bellevre (BEC) France Pierre Besse (BV) France John Canton (LR) UK
Jürgen Fnesch (HSVA) Germany Stuart Jessup (Carderock) USA Spyros Kinnas (UT) USA
Gent Kuiper (MARIN) Netherlands Jean-Marc Laurens (ENSIETA) France Jean-Emile Le Soudeer (Wrtsila) Finlai Carole Pavaut (CAT) France
Alexander Pustoshniy (Krylov) Russia Antonio Sanchez-Caja (VTT) Finland Noniyuki Sasaki (Sumitomo) Japan Jean-Français Signst (DCN) France Yang Ying Wang (DTU) China
Jean-Frédénc CharpentiE François Deniset Christian Lainé
Blaise Nsom
http://www.univ-brest.fr/tpodo6/conferencehtm
MAIN EVENTS
Opening ceremony : The opening ceremony will be chaired by thepresident of the University of B Claude Bodéré. Photos.
Opening Session : Two general papers will be presented, the firstone deals with the achievments FASTOD project and the second aims at an overview of theevolution and recent advances of numen applied to propulsion.
Panel session : On Tuesday a special session is organized witha panel of main actors in the doma is aimed at the following topic: What are the future trends in podded propulsion. Photos.
Invited lectures: Two general invited lectures will be presented, on Wednesday and Thursday mori be pronounced by J. Carlton and N. Sasaki.
Cocktail reception :Following the panel session held on Tuesdaya cocktail will be served in front ol lighthouse just in the vicinity of the congress centre giving opportunity to pursue the discussions. Phot Conference banquet: On Wenesday evening a banquet will be organized in therestaurant at the s the conference center. Britton animations will be presented during the dinner. Photos.
ITTC: A conference of the POD panel of the hIC will be held independently in Brest after the meeti
Posters: During the conference space will be provided topresent posters or advertisments either f or industrial attendees. Please contact the chair committee.
4/10/2007
Conference program
Submission of abstracts
http://www.univ-brest.fr/tpoclø6/subnijssjon.htm
LATE SUBMISSION OF CONTRIBUTIONS
Receiption of new papers is closed but, as the aim of the conference is a large exchange of exr between scientists, ship owners and ship yards a large place is preserved both for indMdualco and for unformal presentations.
If you wish to attend the conference and time to present some aspects of your activities or som problems you face or you have solved, feel free to contact one of the chairmen of the congress All abstracts must be submitted in Word (doc), PostScript (ps)
or Portable Document Format (pdn to:
tpodO6ecole-navaIe dot fr
ABSTRACTS
More than 30 abstracts have been retained for presentation: They concern the following topics.
Page 1 of3
Posters
4/10/2007 Hydrodynamic #1
Hydrodynamic # 2
Hydrodynamic # 3 Cavitation Operation
Design #1
http://www.uriiv-brest.fr/tpodo6/sessjon3 .html
Wednesday 10h45 - 12h25
Session 3
Numerical hydrodynamics (1)
Chair : A. Sanchez - Caja
10h45: Hydrodynamic study of podded propulsors with systematically varied geometry
M. F. Islam S. Molloy
He B. Veitch
Bose P. Liu
Memorial University of Newfoundland, Canada Institute of Ocean Technology, Canada
11h10: Discussion on hydrodynamic performance for podded propeller by using surface panel method
Z. Lijun W. Yanying
Da/lan University of Technology, China
11h35 : A parametric power prediction model for tractor pods
M. B. Flikkema J. Holtrop
T. J. C. Van Terwisga Marin, The Netherlands
12h00: Numerical prediction of unsteady performance of podded propellers
C. Ma z. Qian
J. Yang x. Zhang
Du S. Huang
NA val Academy of Armament, Beying, China Shanghai Jiao Tong University, China
9/10/2007
Opening session Invited lectures
A PARAMETRIC POWER PREDICTION MODEL FOR TRACTOR PODS
M.B. Flikkema, MARIN, The Netherlands J. Holtrop, MARIN, The Nether1ands T.J.C. Van Terwisga, MARIN, The Netherlands
This paper presents a parametric computational model for power prediction of ships propelled by
tractor pods. The effect of the pod housing on the propeller performance is determined by a coefficient similar to the wake fraction and the relative rotati.ve effieiency. The pod resistance ¡s determined using
a form factor and an additional constant for the pressure resistance. Subtracting the pod resistance from the propeller thrust gives the unit thrust. The pod unit - shzo interaction can be described by propulsión factors. The uncertainty of 'the calculation model is estimated to be' 9% for the power predicted for a given combination; of speed'and resistance and 5% for the rotation rate prediction at 'equal' power. The uncertainty of the local velocity behind the pod ;ropeiler contributes most to the
uncertainty of the results. Therefore, it is recommended to focus further on the flow field behind the
pod propeller.
This will alsó give more insight into the extrapolation of model
test results.Furthermore, propeller hub effects are discussed. A: comparison ofCFD calculation results of the gap effect with measurements of the gap effect shows that still some work has to be done to get a better
understanding of the gap effect.
Keywords: Jod, Power prediction, Gap effect, Uncertainty, Propulsion
i
IntroductionAn early stage power prediction is important for an assessment ofthe investment and lifetimecosts of the propulsion system. Methods thereto for conventional propellers exist in abundance but not however
for podded propulsion systems This paper describes a computational model for power prediction of ships fitted with pods whiç was derived by Fhkkema [2] This computational modelserves a purpose
in the selection of propulsibns systems at the early ship design stage.
The presented computational; model is only applicable to tractor pods in free-sailing conditions. The interaction between the pod 'housing and the propeller' becomes less well predictable 'in the overloaded low-speed conditions. The formulátións are based on a sample of results of model tests performed at
MARIN in Wageningen. Tractor pods are the most common pod type and these are also tested more often than pushing pods and pods with co-rotating, propellers. Of the latter two pod types, not enough
experimental data are available. Of tractor pods however, MARIN has an extensive database from
which a subset of 59 model tests has been used in the present study.
Propeller hub effects for pod propellers play a larger role than for conventiönal shaft propellers due to
larger and conical hubs on pod propellers These effects influence measurements of the pod propeller
shaft thrust. It is important for a propeller designeù that these hub effects are corrected for in the
measurement results, either: by measurement of the hub effects or by estimating these effects. In 'both
Section 2 of this paper discusses model measurements with pods where it focuses on the issue of the propeller hub effects. Sections 3 and 4 discuss the numerical model and the uncertainty respectively.
Some outstanding issues will be discussed in section 5. Finally, section 6 lists the conclusions and
recommendations.
2 Model Measurements
Open water tests on scaled models of the entire pod unit areusually the basis of most power predictions in combination with a propulsion test, or a resistance test if propulsion experiments are not feasible for some reason. In these experiments the propeller rotation rate, the propeller shaft thrust, the propeller shaft torque and the. thrust exerted by the whole pod unit are measured. From the comparison of'the results of the propulsion tests and the open water test, the classical propulsion factors for the pod unit
(t, w, ??r can 'be determined.
For the designer of the propeller, the propeller bladé thrust and the local velocity field in the propeller
disk are important design input data. In the model tests, the propeller shaft thrust is measured. This
propeller shaft thrust deviates from the propeller blade thrust because of propeller hub effects These hub effects, which are generally larger here than in conventional propellers, are twofold:
e Hub resistance;
s Effect ofthe gap between pod housing and hub.
The propeller hub resistance is determined iñ'a similar way as the hub resistance for conventionalL shaft
propulsion. However, the hub of a pod propeller is much larger than the hub of a conventionalshaft propeller. Moreover, it usually has a pronounced conical shape. The drag coefficient for the hub
resistance is therefore much larger for a pod propeller than for a more traditional one.
In the model experiment the water in the gap between the propeller hub and the pod unit rotates due to
the rotation of the propeller hub A Couette type of flow is found in the gap which causes a pressure distribution over the rear end of the propeller hub. Integration of this pressureover the area of the rear end of the hub gives an extra thrust component which is only included in the measured prOpeller shaft thrust. Fortunately, the pressure difference over the gap width is small. Moreover, no differencein unit
thrust is found in the measurements for different .gap widths Furthermore, the gap effect does not
appear to influence the torque measured in the propeller shaft.
The gap effect has been studied extensively by Van Rijsbergen [8]. Measurements have been made for four different gap widths, and results of the shaft thrust were compared. This study assumed that the
entire variation in shaft thrust can be attributed to gap effects The changing interaction with the pod
strut is, however, not taken into account. Results of the measurements show an increasing gap effect for decreasing gap width. Fig. .1 shows the difference in measured shaft thrust for different gap widths in a
non-dimensional manner in comparison with a gap width of 2.2 mm. A theoretical backup for this
variation is found in the theory on the flow between a rotating. and a stationary disk as described by
Batchelor [1]. As could be expected, the measurements of Van Rijsbergen did not show significant
0.008 0.006 0.004 0.002 4) O -0.002 -0.004 -0.006
Fig. i Difference in propeller thrust fúr different gap widths with reference to a gap width of
2.2 mm
Computational Fluid Dynamic (CFD) calculations on the gap effect have been made by Flikkema [2]. The pod has been modeled as a two dimensknal axisymmetric body with the propeller modeled as an actuator disk. The form of pod house was the same as the one which was tested by Van Rijsbergen [8]. Calculations have been made for two gap widths.
Results of the CFD calculations are shown in Fig. 2. This figure shows the difference in integrated
pressure over the rear side of the propeller hub for a 4 mm gap width in comparison with a 2 mm gap width. The gap effect for the larger gap is larger than for: the smaller gap. This is in contradiction with; the measurements shown in Fig. I. The difference in gap effect is also smaller for the CFD calculated results than for the measurement results.
o 2 04 0 6 0
J E-1
2 4
Fig. 2 D(fference in calculated shaft thrust between 2 mm and 4 mm gap
The differences between calculated and measured results can be prescribed to simplifications and assumptions done for both the measurement as for the CFD calculations. Further studies of thegap effect should contain a validity check of the aforementioned CFD code. This should be done by
comparison with measured the gap effect.
Two techniques are available for determining thç gap effècts in modél measurements:
Measurement of the gap pressure at different radii of the propeller hub. Integrating this
pressure over the aft side of the propeller hub gives the axial component of the gap effect.
Measuring the propeller blade thrust for each blade separately at the root of the blade iñ
combination with the propeller shaft thrust. The difference between these values is the sum
of the propeller hub effects and the hub resistance.
Measurement of the propeller gap pressure or the blade thrust should become common practice in
model tests on pods. 'Eventually, this will improve the accuracy of'the power prediction and it will also improve' the understanding of the flow over pods.
The CFD calculàtiöns were performed using a twodimensional model. It is possible that three
dimensional effects are present in the gap pressure Calculations of the pressure in the propeller gap should' be validated by comparison with measurements of this pressure. In this way, an analysis can besetup of the gap effect and possible correction formulations can be derived which should make it
possible to correct the measured shaft thrust for the gap effect. The flow pattern in the gap has a similar form as that which was' found in theory like Batchelor ['1]. A Couette type of flow was fotind in thegap,
which is similar to the flow' between a stationary and rotating disk. This is considered only a first step to the validation of the calculated results.
3 Computational model
Power predictions for shaft driven propellers are usually made using propulsion factors as thewake fractión (w), the thrust deduction (t and the relative rotative efficiency ('ir). These three coefficients
account for the interaction between a' ship-like body and the nearby propeller. A Similar approach can be followed for the determination of the effect of the presence of a pod on the performance of a single
propeller.
The wake fraction (w) accounts for the effect of the ship on the propeller inflow' velocity and it is
defined as:
W=;-A ..1'O
Vs Js
In whiòh V is the ship speed, VA is the advance velocity, Jo is the open water advance coefficient and J3
is the ship advance coefficient. The thrust deduction (t) accounts for the increase in resistance due to the propeller action and it is' defined as:
TR
T (2)
The relative-rotative efficiency (17r) accounts for the difference in propeller effkiency between open water and behind-ship condition. The i7,. is defined as:
Q0T
QT
For thrust identity, this reduces to the ratio of the torque in uniform flow, Qo, to that measured behind the ship or its model, Q.
In a similar way we describe the interaction between the pod housing and the propeller. 3.1. Propeller - Pod interaction
The propeller - pod interaction consist of pod - propellereffects and propeller - pod effects. The effect of the pod on the propeller is twofold:
I. The inflow velocity is disturbed by the pod body;
2. The pod strut has an effect on the propeller torque and thrust.
These two effects combined should be the key factors in transferring
the propeller open watercharacteristics to characteristics of the propeller attached toa pod.
Ideally, the change in inflow of the propeller due to the presence of the pod is determined from model tests. The ratio of the advance coefficient of the single propeller in open water (J0) over the advance coefficient of the propeller in the behind condition (Js) for thrust identity leads to a wake fraction for
the presence of the pod similar to (1). Assuming that the relation between thrust and torque of the
propeller mounted on the pod is the same as in open propeller situation, a torque of the propeller on the
pod (Qo) can be determined This torque does not yet contain the effect of the pod
strut on the propeller. Using a fàctor similar to the relative-rotative efficiency, (3), the effect of the strut on thepropellertorque can be determined.
As noted in section 2, model measurements on pods should be interpreted with caution. The
determination of the propeller thrust is not always accurate enough to determine a reliable wakefraction and the relative-rotative efficiency separately for pods On the other hand, the measurement of
the torque gives the desired result because this is not influenced by propeller hubeffects. Hence, the wake fraction for the effect of the presence of the pod on the propeller is therefore not defined for
thrust identity but for toIque identity. The ratió of the advance coefficient of the propeller on the pod
(J1) over the advance coefficient of the single propeller in open water (Jopen) gives the pod wake fraction:
(l_w)=
pThe pod wake fraction includes the effect of the pod on the 'inflów velocity and the effect of the strut on the torque. The pod wake fraction thus represents a combined effect of w and'ir as defined in (I) and (3).. Fig. 3 shows some characteristic results of the pod wake fraction determined from model tests.
This shows that, for free-sailing conditións, the pod wake fractión is almost constant for tested pods. For bollard pull conditions, the pod wake fraction becomes undefined and goes to infinity or to zero. This depends on the difference in the slope of the KQ line for open propeller and pod propeller. This pod wake fraction approach is thus only valid for free-sailing conditions.
2.5 3 0o n. .0.5 O Advance coefficient (-)
Fig. 3 Pod wake fraction for 3 cases determinedfrom model tests
Obviously, the pod wake fraction is function of the pod house geometry and, to a much smaller extent,, of the propeller geometry. Regression analysis of the pod wake fraction, determined from a set of 44 experimental results, shows that the .pod wake fraction is a function of the following pod and propeller parameters:
Propellçr pitch over diameter ratio (P/D);
Pod length over house diàmeter ratio (L0th'D0d);. POd front taper angle (B);
Pod house diameter over propeller diameter ratio (D0/D).
For increasing L,dD0d the influence of the pod housing on the propeller is expected to decrease.
Whenthis ratiotends togo to infinity, the propeller performance will be the same on the pod as in open water conditions. Increasiñg ß will lead to an increasing effect of the pod on the propeller. The same holds for increasing DOID. For lager pitch diameter ratios, the leading edge of the propeller blades is
further away from the pod which will make the influence on the inflow less strong. Ranges of pod
wake fractions determined from model measurements are shown in Table I.
In analogy With the propulsion coefficients,. the relative rotative efficiency is determined for a change
Due to difficulties in the
measurement of propeller thrust for pods, 7rT can not be determined. Therefore, 7/rT is assumed to be 1, acknowledging that there could well be a systematic error in this parameter.Table ¡ Pod characteristics used in measurements for dtprmini
3.2. Pod house resistance
The resistance of the pod, including effects of the action of the propeller,
is obtained from thedifference between measured propeller shaft thrust and the measured pod unit thrust. Propeller induced effects on the resistance are:
Increase of flow velocity over the pod;
Propeller-induced pressure gradient over the pod; Stator - pod interaction effects.
The pod unit thrust cannot be determined extremely accurate from model tests This is caused by uncertainty ¡n the determination of the propeller shaft thrust and the stochastic variation iñ the
measured unit thrust. Thus, the relatively small difference of two large numbers, each measured with a limited degree of accuracy, becomes less accurate. Essentially, the pod-house drag is composed of both a Reynolds number dependent part and a Reynolds number independent part. The part that is dependent on the Reynolds number is described y the form factor concept. The pod resistance is then obtained by the following expression:
RPOd =pV2SCF (1+k)+_7TDPOdPV2CD (6)
Where CF is the frictional resistance of. an equivalent flat plate and the factor (1+k) accounts for the effect of the form, both on the Reynolds number dependent part of the pressure drag and the frictional resistance of the pod housing. The coefficient CDp accounts for the additional drag andDp0d is the pod
diameter. CFD calculations have -been made by Hoekstra and Windt [3] to determine the form factor
a+k,) and the pressure coefficient CDp for different pod types. Table 2 gives the
range of thecoefficients found from these calculations.
Table 2 Range of-(i±k) and CO3, determined by CFD
Coefficient Minimum Maximum Average
No suitable, stable and consistent parametric model could yet be derived for the combinmed parameters
,(1+k) and CDp. Instead a more simple formulation which uses only a form factor could be determined,
ignoring the contribution of the Reynolds number independent portion of the pod house drag, This
formulation, due to Rains et al [7] is:
(D
'
"D
(i±k)=l+L51
Ld)
podThis seems to. be a reasonable assumption when CDp is taken as 0. The consequence of this approach is that the prediction of the pod house drag now becomes valid for one typical dimension, as the ratio of the Reynolds number dependent and independent parts as determined by CFD calculations do no longer apply. In this parametric model the prediction applies to the model scale only.
The velocity (V) in equation (6) is the lôcai axial velocity behind the working propeller. This local
velocity can be obtained either using the classical actuator disc model or from the assumption that the flow in the slipstream satisfies the propeller no-slip condition as discussed by Holtrop and Mennen [5]. From the analyzed data, no preference for one or the other formulâtion is apparent, taking into account
the uncertainty of several parameters involved. In this numerical model a combination of the local velocity calculated by the actuator disk model, V2, and the velocity calculated using the no-slip
condition, V1,, is used. The lOcal velocity, Vcai, is used as a weighted average of these two velocities:
'Ioca! gV. +(l
-
g) ';
Where V1 is the velocity calculated with the no-slipcondition:V1 =anP+(la)VA
And V2 is the velocity calculated with the actuator disk theory:
(I
8 TI fl+
i I+V
A
if
pVD2
AIn model experiments on pod-driven ships, the coefficient a is determined from a load-variation test, either carried out as an open water test, or as part of the model propulsion experiment. In the MARThI
experiments on tractor pods, a is always found to be between 0.9 and 1.6. Holtrop and Mennen [5]
suggest that a can generally be taken as 1.3. There is no reason to believe that a value of the coefficient
g different from Y2 leads to distinctly different results In this way the average of both calculation
models, equations (9) and(10), is used as the local velocity..
This approach to the velocity calcülation can be improved When more knowledge of the mutual
interference between pod and propeller is available. The pod wake fraction accounts for a variation in propeller inflow speed due to the presence of the pod housing. One would expect that the flow velocity
behind the propeller is a functiOn of the pod wake fraction. Due to the fact 'that the propeller blade
(7)
thrust cannot be measured, the pod wake fraction also contàins a part that accounts for the
relative-rotative efficiency imposed by the strut This makes the pod wake fraction less suitable for use in the calculation of the local flow velocity.
ideally, the propeller blade thrust can be measured from which the pod wake fraction for thrust identity is determined. In that case the local velocity can be determined by:
Ioca!
=(1p):V4 f(n,P,T,V4,D,X)
X, is the distance between the propeller and the pod. The second term should be a fUnction to be determined by the actuator disk theory and the no-slip condition as described in equations (8), (9) and (10). This approach will give more insight in the effect, of the propeller on the flow, the coefficients a
andg.
U sing the definitiOn of equation (2), the resistance can be described in the form of thrust deductión
factor., This would then be:
--
T (12)p
In which T is the propeller thrust and T is the unit thrust corrected for scale effects. 'This is always
positive and clôse to zero.
Combining all of the pod propulsión' factors discussed above, pod propulsion factors, the open water efficiency can de determined from the propeller open-water efficiency by:
iepod = 7lOopen.
-
7lrT (13)Where Oôpenis the open-water efficiency of a single propeller.
3.3.. Hull - Pod propulsion coefficients
The propulsion coefficients are calculated for the pod unit. The propulsion coefficients have been deterniined by regression. analysis of model test results The thrust deduction factor for pods.(t) is
calculated by:
t =0.21593+0.099768cß 0.56056 (14)
The block coefficiènt is a factor which accounts for the bùttock slope in the aft ship. Since the tilt angle
of the pod is not taken into consideration, Cß. is an important factor. The last term accounts for the
as those used for conventional shaft propulsion as given by Holtrop and Mennen [4']. Thewake fraction
for pods(Wa) is calculated by:
w,
O.21035O..18053C8 ±56.724CC 0.18566
±0 O90198-
(15)The product of CB and C accounts for the boundary làyer on the hull. In this formula, the relative tip
clearance (C,11/D) is added as parameters to. the parameters described by Holtrop and Mennen. [4]. This
coefficient accounts for the degree in which the pod unit is embedded in the hull boundary layer. Thus it reflects effects of the influences in propeller inflow as. a function of the tip-hull clearanceas a non-dimensional distance of the propeller from the body. The relative-rotative efficiency for pods (,,). is. calculated by:
=1.493-0. 18425C 0.4278LCB_ø.338o4P/ (16)
The longitudinal, prismatic coefficient (Ge) expresses the fullness of the ship. The longitudinal position
of the center of buoyancy (LCB) expresses the distributión of this fullness. The pitch over diameter ratio (P/D) accounts for the propeller torque. The range covered by the regressión analysis for the
propulsion coefficients is given in Table 3.
Table 3 RanMe of propulsion coe
3.4. Validity of model
The range covered by the test results on which the calculation model is based is indiéated: bythe ranges'
of the various parameters used in the mathematical model. Table 4 shows the range of the input
parameters.
Table 4 Ran2e of invut narameters
Minimum value Maximum value
tu. 0.01 0.18
w '0.00 0.16
0.96 1.09
Minimum value Maximum value Average value (Av) Maximum
The validity range of the computational model is given as a 9-dimensional space of which the ordinates
are defined by the 9 input parameters. Ali combinations of parameters should be within the
9-dimensional space, the body encloses the ranges of these parameters. This body is transformed to be "spherical" with a radius R and a radius for each separate parameter ri which is calculated by:
X' Av,
r=
mdev,
Ay1 and mdev are the average and maximum deviation respectively as given in Table 4. The total
radius of the domain is thencalculated from:
R='
1.615
The figure of 1615 is the maximum of the summation of separate radii (re). This radius (R), and the separate radii (r1), should be lOwer than 1 for the input to be inside the calculatión domain. It is
expected for a more extreme eccentricity that the quality of the predictions drops progressively.
4 Uncertainty
The uncertainty of a computational model is important in guiding the user in the interpretation of the calculated prediction. This section discusses the uncertainty at different stages of the design and looks for the sources of the uncertainty.
Uncertainty originates from assumptions and simplifications in the attempt to simulate the true situation by 'calculations. These assumptions lead to errors in the results, in comparison to the true
value. One can argue that the true value of a quantity is never known, and: that all measurement and computations are an approximation of this value. Forthe computational model the uncertainty lies both
in the assumptions and in the uncertainty of model measurements on which the numerical model is
based.
These assumptions are necessary to simplify the computational model' but have consequences on the accuracy of the calculated result. Major assumptions made are:
The relative rotative efficiency that accounts for the difference in thrust, 7/rr, is assumed to be 1.
This assumption has to be made because the propeller blade thrust cannot be measured
accurately :fl modèl tests. The consequence of this is that the pod resistance cannot be
determined from model scale and' the calculated propeller shaft thrust is not accurate. To bypass this problèm, the resistance is fitted with an equation for the difference between unit thrust and
propeller thrust In this relation the propeller thrust is also determined with the assumption
In the determinatión, of the local flow velocity, the coefficient a is taken as 1 .3 while the experimentally determined range is from 0.9 to 1.6. The value of a can be determined from
open Water measurements. The effect of this assumption is that the slòpe of the calculated K
line is not the same as the slope from the measurement. This will have an effect on the pod
resistance.
The numerical model works with B-series propellers. The open water characteristics of the
design propellers for pods are different from the B-seriesopen water characteristic& This causes an error in the determination of the pod thrust and torque and thus on the working point of the
propeller This assumption can be cured when the propeller open water characteristics of the
used propeller are known. In this case, the uncertainty of the calculation model is decreased as shown in chapter 4.
The resistance of the pod is calculated on model scale and then extrapolated to full scale. An extrapolation model of pod resistance cannot be checked because the unit resistance can not be
determined from full scale tcsts This leads to an additional uncertainty in the extrapolation of the calculáted results.
The computational model can be improved. The method of measuring the pod propeller thrust should contain a correction of the propeller hub effects. Thiswill lead to separatión of the effectof the pod on
the propeller and the mutual effect of the strut and the propeller. This will also lead
to a betterunderstanding of the flow velocity over the pod.
The uncertainty is calculated using equation (7) for ('l+k,)and taking Dp as 0. This is done beôause no
parametric formulations forthe combination of these parameters were found. 4 1. Computational model
The uncertainty estimate is based on the difference between the calculated results andthe performance
predicted from tank tests. This is evaluated for the shaft power at equal ship resistance and ship speed and for the propeller rotatión rate at equal power and ship speed. The difference is given in percentage
of the tank prediction result. The uncertainty is split into two parts:' The bias error (B) and the precision
limit (P). An estimation of the bias error is obtained from the average errcr and the precision limit is obtained from the standard deviation of the results. The uncertainty is then calculated using:
U=JB2P2
(19)The uncertainty analysis is performed for 3 situations. The programmed computational model applies open water characteristics of Wageningen B-series propellers. This already makes a substantial error because most tested pod propellers are especiàlly designed for the pod. Comparing these results with experimental results, an average bias error of 08% for the shaft power and -0.6% for the rotation rate is
found. The standard deviation is 7.3% and 4.4% for the shaft power and propeller rotation rate
respectively. The resulting uncertainty is shown 'in Table 5 and the distribution of the error is shown in
Fig. 4.
When comparing the' results of the numerical model for the few test results of which the error in
propeller rotation rate this is -2.6%. The standard deviation of the shaft power and propeller rotation
rate is 4 2% and 1 7% respectively which comes to an uncertainty as given in Table 5 The larger average bias error is because some parameters were tuned in the computational model to come to a
small bias error for all measurements In this way, a small correction for the propeller not being a B-series propeller is included.
Täble 5 Results of Uncertainty calculation
The results of the uncertainty calculations can be used for validation of the computational model. If the computational model is used in an early design stage, the uncertainty of the B-series propellers can be used. If the numerical model is used in a later design stage for a first power estimation, the uncertainty for the design propellers should be used.
a
4.2. Sensitivity
The relative sensitivity of the computational model is the change in result due to a distortion in one input parameter. This is defined as:
dY/
en- (20)
/X
A large value of sensitivity denotes a large dependency of the output on input parameter i. A study of the sensitivity of this computational model shows that the calculation of the power is most sensitiveto
variations in propeller pitch over diameter ratio, ship speed and resistance, ship length and propeller diameter. The rotation rate is most sensitive to the same parameters with exception of the ship length.
Power Rotation rate
Error 1%)
Fig. 4 Uncertainty of PD and ncalculations for three situations
The open water characteristics of these propellers are represented by Wageningen Bseries propellers in which a
substantial error ispresent.
2
The open water characteristics of these propellers have a small (<2%) error when represented by Wageningen B series propellers
Description Uncertainty PD [%] Unce;tainty n I%1 Number of samples
From this analysis it is apparent that the sensitivity of the calculation result of the rotation rate is much
less than the sensitivity of calculated power. This rule holds for every input parameter with the
exception of the propeller diameter. The propellerdiameter has a large effect on the advance coeffiòient and thus on the rotation rate for a constant ship speed and resistance.
The factor that contributes most to the uncertainty is' the determination of the localvelocity over' the pod and' strut. The coefficient a is taken in the calculation method as 1.3 which is an assumption based on experience. This 'coefficient can be determined from open water tests with the pod, however these arenot available in the numerical model. This makes the uncertainty in the velocity determination large and the relatively large sensitivity also causes a large effect on the total uncertainty.
5 Outstanding issues
Model measurement results have to be extrapolated to full scale to account for scale effects due to deviating Reynolds numbers. Also the pod resistance is liable to Reynolds' scaling effects. The pod resistance, defined as the difference between the propeller shaft thrust and the unit thrust, consists of:
Propeller hub effects; Pod' pressure resistance; Pod frictional resistance; Strut stator effect.
The propeller hub effects have been discussed earlier in this paper.
The strut stator effect is caused by the rotation in the flow field behind' the propeller. This gives the
strut profile an angle of attack with the inflow. The strut will prodUce a lift of whiôh a substantial part is in longitudinal direction. The angle of attack of the strut (a) can be approximated as the swirl angle
'behind a propeller (fi):
ß =arctan (21)
In which km denotes a factor accounting for the variation of the slipstream velocity with respect to the distance from the propeller. Using this angle, the lift produced by the strut can be calculated and the longitudinal component of this lift force can be used as a resistance component to determine the pod resistance from the difference between the propeller and the pod thrust.
At present, MARIN uses the PodU method for extrapolation of model test results. There still isa large
actually simplifies the problem by stating that (1 +k) would be 1. The documentation of the attempt of the I1TC Specialist Committee [6]: seems to overlook the importance of a correct determination of the local flow velocity. The main attention of [6] is directed on the discussion of the form factor while the local flow calculation has not been discussed. The discussion on the issue of the form factor of a pod is unsatisfactory as it touches only one single issue Instead, it should be integrated jn a better modeling of the flow and drag and lead to a correct and reliable method for the determination of the local flow speed. Therefore, more research should be done to the flow velocity behind a pod propeller.
6 Conclusions and Recommendations
The computational model is restricted to free-sailing ships fitted with tractor pods. This limitation is
dUe to the assumption that the pod wake fraction is constant for moderately and lightly loaded
propellers. Due to the difficulty in very accurate measurements of the propeller thrust in a pod (because of gap'effect), the propeller - pod interaction coefficients are based on torque identity since torque does notappear to be significantly affected by the hub - 'pod gap geometry. The uncertainty of the numerical model for an early design stage prediction of propulsive power is 9% based on a given thrustspeed relation and 4% for the rotation rate prediction.
A better understanding of axial forces on a pod during model tests should be' acquired by conducting more research into the gap effect. Measurement of the pressure in the gap at different radii should be
used to validate CFD results obtained by Flikkema f2]. This can lead' to a better insight in the flow velocity over the pod house and the separate influences of the pod and the strut on the propeller
performance.
Extrapolation of model test results of pods is stili a difficult issue due to scale effects and propeller pod
interaction. The ITTC Specialist Committee on pods (2005) has attempted to come to a unanimous
opinion on the best approach for correcting for scale effects due to differences in Reynolds number. Unfortunately, this attempt has not led to a unanimous standpoint. The Committee did not explicitly mention the importance of the velocity determination behind the propeller and its effects on the pod
resistance, a feature which plays a substantial role in scale effects and' interaction. It is therefore
recommended that more research be dedicated to flow fields behind pod propellers.
References
I Batchelor O.K., (1950),
"Note on a class of solutions of the Navier-Stokes equations
representing steady r tationally=symmetric flow ", Trinity 'College Cambridge, July 1950
2
Flikkema M.B., (2005), "Pod power and rotation rate prediction - Delfi University of
Technology Master Thesis", MARIN Report No 1991'O- lCP, Wageningen, The Netherlands, December 2005 (restricted availability).
3 Hoekstra M., Windt J., (2005), "Numerical studies of scale effects on the flow around pods ",
MARIN Report No. 19909-l-RD, Wageningen, The Netherlands, 2005 (restricted availability).
5 Hôltrop J., Mennen G.G.J., (2003), "Scale Effects in Complex Propulsors
- a simpl/ìed
method', MARiN Report No. 17691-1-SP, Wageningen, The Netherlands, December 2003
(restricted availability).
6 ITTC Specialist Committee, (2005), " Propulsions, Performance, Podded Propulsor Tests and
Extrapolations - interim Precedures For Podded Propulsor Tests and Extrapolations", ITTC
Recommendation 7.5-02-03-01.3, 2005
7
Rains D.A., Van Ladingham D.J., Schiappi ftC., Hsiung C.C., Kirkman K.L., (1981),
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18-24.
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161 15-1-DT, Wageningen, The Netherlands, October 2004 (In Dutch) (restricted avai1abiIity) 9 Simonsen C.D., (2000), "Rudder, Propeller and Hull Interactions by RANS", Technical
