LiShancheng XiongYing WangZhanzhi

Received：2018 - 04 - 16Supported by: National Natural Science Foundation of China (51479207); Research Fund of State Key Laboratory of Ocean Engi⁃

neering, Shanghai Jiao Tong University (1514)Author(s): Li Shancheng, male, born in 1993, master degree candidate. Research interest: ship fluid mechanics. E-mail: lis⁃

[email protected] Ying, male, born in 1958, Ph.D., professor, doctoral supervisor. Research interest: Ship fluid mechanics. E-mail:[email protected]

*Corresponding author：Xiong Ying

To cite this article：Li S C, Xiong Y, Wang Z Z. Hydrodynamic and cavitation performance of podded propulsor under steeringconditions[J/OL]. Chinese Journal of Ship Research, 2019, 14(1). http://www.ship-research.com/EN/Y2019/V14/I1/33.

DOI：10.19693/j.issn.1673-3185. 01256

Hydrodynamic and cavitationperformance of podded propulsor

under steering conditions

Li Shancheng，Xiong Ying*，Wang ZhanzhiCollege of Naval Architecture and Ocean Engineering，Naval University of Engineering，Wuhan 430033，China

Abstract：［Objectives］The interaction between the body of pod propulsor and the propeller is great，leading tocomplex flow phenomena. As a consequence，under steering condition which is away from design point，loads ofblades change sharply and the cavity characteristics deteriorate. In order to analyze the hydrodynamic characteristics ofthe pod propulsor，［Methods］ the full structural grid based on the Reynolds Averaged Navier-Stokes （RANS）approach is adopted. Besides，the cavity structures are predicted by the Sauer model. Finally，the model experiment ofthe pod propeller is carried out in the cavity channel.［Results］The results show that the numerical data are in greatagreement with the experiment counterparts which presents the correspondingly high accuracy of this numerical model.Under steering condition，the thrust and torque of pod propulsor are greater than the counterparts under straightcondition. After the propulsor deflects，the pressure at different circumferential positions fluctuates with the change ofcircumferential angle. What's more，cavity contours show different structures and the cavitation intensifies as thedeflection angle rises.［Conclusions］The research results can provide reference for the design of pod propeller.Keywords：podded propulsion；steering condition；hydrodynamic performance；cavitation performance；blade loadCLC number: U661.3

0 Introduction

Podded propulsor combines the functions of steer⁃ing and propulsion to complete the operation of shipturning. When the podded propulsor is deflected, theload it bears will increase, and the hydrodynamicand cavitation performance will deteriorate. There⁃fore, it is important to study the hydrodynamic andcavitation performance of the podded propulsor un⁃der steering conditions. At present, scholars in Chinaand abroad have carried out a lot of work in open wa⁃ter performance experiments and numerical predic⁃tions, and have accomplished many achievements [1-4].Szantyr [5] carried out experimental research on thehydrodynamic performance of the podded propulsorunder oblique flow conditions based on the cavita⁃tion tunnel, and measured the thrust and lateral

force of the propulsor. Liu et al. [6] studied the hydro⁃dynamic performance of the podded propulsor understeering conditions, and analyzed the thrust andtorque changes of the propeller in detail. Amini et al. [7]

used the method of potential flow and viscous flow tocalculate the bearing force of the podded propulsorat different deflection angles. Xiong et al. [8], Wang etal. [9] and Shen et al. [10] analyzed the hydrodynamicperformance of podded propulsor under different rud⁃der angle conditions based on the Reynolds AverageNavier-Stokes (RANS) numerical simulation meth⁃od. The experimental comparison results show thatthe hydrodynamic performance of the podded propul⁃sor can be accurately predicted by using the RANSmethod combined with the structured meshes. Interms of cavitation, Friesch [11] carried out a cavita⁃tion experiment on a typical towed podded propulsor.

CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019 31

downloaded from www.ship-research.com

CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019The results show that when the propeller load is in⁃creased at a certain angle, the cavitation perfor⁃mance will change significantly; and different direc⁃tions of deflection will lead to different densities ofcavitation. Yang[12] summarized the reports of the25th ITTC pod propulsion expert committee, and pro⁃posed to attach great importance on the open watercharacteristics under non-design conditions in thepodded propulsor experiments, especially the loss ofpropulsive efficiency caused by the small rudder an⁃gles. In summary, the current research results mainlyfocus on the observational experiments on the hydro⁃dynamic performance and cavitation change of thepodded propulsor under steering conditions. Theload changes of blade and the cavitation performanceof podded propeller after the deflection of the pod⁃ded propulsor have not been studied deeply. Howev⁃er, under steering conditions, the blade load of thepodded propulsor changes significantly, and its cavi⁃tation performance will deteriorate. The intense cavi⁃tation will lead to the decrease of the propulsor effi⁃ciency and the denudation of blade materials. There⁃fore, studies of the hydrodynamic and cavitation per⁃formance of the podded propulsor under steering con⁃ditions do have certain engineering application values.

Based on the hydrodynamic performance predic⁃tion results of the podded propulsor, this paper ana⁃lyzes the change of the blade pressure distribution ofthe podded propulsor under steering conditions, anduses the Sauer cavitation model to predict the cavitationperformance of the podded propulsor. Finally, theopen water and cavitation experiments of the poddedpropulsor under steering conditions are carried outin the cavitation water tunnel, for the purpose of veri⁃fying the accuracy of the numerical prediction method.1 Research object

In this paper, the experimental propulsor modelwith the scale ratio of 1∶25 is taken as the researchobject. Fig. 1 shows the model of the pod body, andFig. 2 is the geometric diagram of the pod body. Ta⁃ble 1 and Table 2 manifest the main parameters ofthe propeller and the pod body, respectively.

2 Numerical methods

2.1 Control equation

The RANS equation is¶ρm

¶t+¶(ρui)¶xi

= 0 （1）¶(ρmui)

¶t+¶(ρmuiuj)

¶xj

= -¶p¶xi

+ ¶¶xj

é

ëêê

ù

ûúú( )μ + μ t

æ

èçç

ö

ø÷÷

¶ui

¶xj

+¶uj

¶xi

（2）Where ρm is the mixed-phase density, wherein themixed phase consists of the liquid phase and the va⁃por phase of water, and the speeds of the two mixedphases are assumed to be the same; t refers to time;ρ means the fluid density; xi and xj (i, j = 1, 2, 3)are the direction coordinates in the three-dimension⁃al Cartesian coordinate system; ui and uj are thecomponents of the fluid velocity in the xi and xj di⁃rections; p refers to the pressure on the fluid mi⁃cro-unit; μ means the mixed-phase viscosity; μ tFig.1 Model of pod body

Fig.2 Geometric diagram of the pod body

Strut length

Strutheight

StrutdistanceTaper length

Length

Poddiameter Hub

diameter Fore taper angleAft taper angle

ParameterPropeller diameter D / mm

Designed pitch ratioSide rake/（°）

Expanded area ratioPropeller turning direction

Blade number

Value and definition2241.1250.6Left

5

Table 1 Main parameters of propeller

ParameterPod diamete/DPod length/DStrut height/DStrut length/D

Strut distance/DMaximum strut width/D

Aft taper length/DFore taper angle/（°）Aft taper angle/（°）

Numberical value0.446 41.732 1

1.250.714 30.321 40.222 7

0.52932

Table 2 Main parameters of pod body

32


is the mixed-phase turbulent viscosity.Hydrodynamic performance is also the liquid

phase property. For the convenience of calculation,the SST k-ω two-equation model [13] will be used asthe turbulence model. The model introduces mixedfunction to solve the Standard k-ω model flowing innear wall regions and the Standard k-e model flow⁃ing in far fields.2.2 Cavitation model

When the cavitation performance is calculated, ρm

is the mixed-phase density of vapor and liquid, thevalue of which is determined by the vapor-phase vol⁃ume fraction v :

ρm = vρv + (1 - v)ρ l （3）Where ρ l and ρv are the densities of the liquidphase and the vapor phase, respectively.

Assuming that the vapor phase exists in the formof bubbles in the liquid phase, its transport equationwill be

¶(νρv)¶t

+¶(νρvui)¶xi

= m+ - m- （4）Where m+ is the evaporation rate of the liquidphase to the vapor phase; m- is the condensationrate of the vapor phase to the liquid phase.

Sauer established the expressions of m+ and m- [14]:When p < pv ,

m+ = 3ρ l ρv

ρm

1R0

ν (1 - ν ) 23

pv - pρ l

（5）When p > pv ,

m- = -3ρ l ρv

ρm

1R0

ν (1 - ν ) 23

p - pv

ρ l

（6）Where R0 refers to the radius of a bubble; pv refersto the saturated vapor pressure.2.3 Computational domain and mesh

division

The computational domain of uniform flow fieldsconsists of the far field and the propeller rotationfield, as shown in Fig. 3. The front and the peripheryareas are velocity inlets; the front inlet is 5D fromthe center of the propeller; the cross-sectional areacovers an area of 6D × 6D; and the pressure outlet is12D from the propeller disk. When hydrodynamicperformance is calculated, the mesh generation soft⁃ware ICEM will be used to divide the global hexahe⁃dral meshes, and the total number of meshes is about3.5 × 106. In this paper, the software STAR-CCM +

for commercial numerical calculation will be used.Firstly, steady calculation for podded propulsor is

performed through the application of the dynamic ref⁃erence system. After convergence, unsteady methodswill be used to accelerate the convergence process.The time for simulation corresponds to the time forthe rotation of the propeller by 1° , and the hydrody⁃namic calculation uses the combination of RANSand SST k-ω model. The incoming flow velocity is3 m/s, and the advance coefficient can be changedby changing the rotation speeds.

During the calculation of the cavitation perfor⁃mance, the pod and the blade (especially the bladetip) meshes need to be refined, and the total numbersof meshes are 6 × 106. Firstly, steady calculation isperformed by the application of dynamic referencesystem method, and then the unsteady calculation iscarried out. The environmental pressure is graduallyreduced in order to reach the requirement for thenumbers of cavitations. After the convergence, thecavitation model will be used for calculation. Thetime corresponds to the time for the rotation of thepropeller by 1°, and the cavitation model selects theSchnerr-Sauer model. The incoming flow velocity is3.3 m/s, and the outlet pressure is consistent withthe experimental environment.

The deflection angle of the pod, the thrust T andthe torque Q of the propeller are defined in Fig. 4.When looking from the stern to the bow, the pod de⁃flection angle is β . The leftward deflection is nega⁃tive, and the rightward deflection is positive. Whenthe blade is facing the pod strut, the circumferentialangle of blade is θ = 0°.

（a）Computational domain division

Pressure outlet

Velocity inlet

Velocity inlet

x

y

z

o

（b）Blade mesh （c）Pod meshFig.3 Computational domain and mesh generation

Li S C, et al. Hydrodynamic and cavitation performance of podded propulsor under steering conditions 33


CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019

During the calculation process, the pod deflectioncan be achieved by changing the direction of the in⁃coming flow, and the flow at the velocity inlet is

Vx = U cos β

Vy = U sin β

J = U/nD （7）Where Vx refers to the axial velocity of the incomingflow at the blade section; Vy is the lateral velocity ofthe incoming flow at the blade section; U means theincoming flow velocity; J is the advance coefficient;n is the propeller rotation speed.3 Experimental methods

The experimental arrangement is shown in Fig. 5,wherein the sizes of the cavitation tunnel are 2.6 min length, 0.6 m in width and 0.6 m in height. TheCASSIONS-produced H101 dynamometer with athrust range of ± 600 N, torque range of ± 30 N·m,and maximum rotation speed of 3 000 r/min is usedin this experiment. During the experimental process,the rudder angle deflection of the podded propulsorcan be achieved by deflecting the pod dynamometer.

3.1 Open water experiment

In order to ensure that the Reynolds numbermeets the requirements of the open water experi⁃ment, the incoming flow velocity is set as 3 m/s. Dur⁃ing the experimental process, the advance coefficientcan be changed by changing the propeller rotationspeed. The condition for Reynolds number that cansatisfy the experiment of cavitation tunnel is

Rn(0.75R) =b0.75R U 2 + (0.75πnD)2

ν′> 3 ´ 105 （8）

Where Rn(0.75R) is the Reynolds number at 0.75R ofthe propeller, and R means the radius of propeller;b0.75R is the chord length of the blade section at0.75R; ν′ refers to the kinematic viscosity coeffi⁃cient of water.

The equations for calculating the thrust coefficientKT and the torque coefficient KQ are

KT =T

ρn2 D4

KQ =Q

ρn2 D5 （9）3.2 Cavitation observation experiment

In the cavitation observation experiment, the in⁃coming flow velocity is set as 3.3 m/s; the propellerrotation speed is 1 254 r/min; and the number of cav⁃itations is σn = 1.44.

The expression for the number of cavitation isσn =

p0 - ρghp - pv

0.5ρ( )nD2

（10）Where p0 is the pressure at the center of the work⁃ing section of the circulating tunnel, and its value isset as 0.22 standard atmospheric pressure; g refersto the gravity acceleration; hp = 0.3 m, meaning thevertical distance between the center of the propellermodel and the center line of the working section ofthe podded propulsor; pv = 2.338 × 103 Pa.4 Result analyses

4.1 Analysis of hydrodynamic perfor-mance

4.1.1 Analysis of the hydrodynamic perfor-mance in podded propeller

1) Mesh independence analysis.On the basis of hydrodynamic calculation, J =

0.64 is selected, and mesh independence analysis isperformed under straight conditions and +10° deflec⁃tion conditions. In the three mesh cases shown in Ta⁃

Fig.4 The hydrodynamic performance parameters，deflectionangle，circumferential angle and coordinate system ofpodded propulsion

x

y

z

θ =0°Q

Tβ

Fig.5 The arrangement of model test

Pod dynamometer

34


ble 3, the methods of dividing the near-wall meshesalong the normal direction of the wall surface are thesame, while the mesh numbers in the rotation field ofthe propeller are different. The calculation results ofthe thrust coefficient and the torque coefficient areshown in Table 4.

It can be seen from Table 4 that the calculation re⁃sults of the three mesh cases are relatively close toeach other. In view of the requirements for the com⁃putational efficiency and the time, this paper will se⁃lect mesh 2 for subsequent calculations.

2) Straight conditions.Under straight conditions, the comparisons be⁃

tween the experimental values and the calculated val⁃ues of thrust coefficients and torque coefficients ofthe podded propulsor are shown in Table 5. Whenthe advance coefficient is J < 1, the errors are within5%, and the goodness of fit is high.

3) Steering conditions.Under steering conditions, the advance coefficient

J = 0.64 is selected to calculate the hydrodynamicperformance of the podded propulsor at rudder an⁃gles of 0° , ± 5° and ± 10° . The average value of thepropeller in one rotation period is selected as theCFD calculation result, as shown in Fig. 6. It can beseen from the figure that the calculation results arein good agreement with the experimental results, thechange trend is consistent, and the errors are within3% ; the blade thrust increases with the increase of

the deflection angle β of the pod. The advance ve⁃locity of the propeller is small under steering condi⁃tions compared with that under straight conditions,and the increase of deflection angle will lead to thefurther decrease of the advance velocity and the sub⁃sequent increase of the thrust and torque.

4.1.2 Analysis of blade load under open waterconditions

1) Analysis of blade force of a single propeller un⁃der oblique flow conditions.

In order to analyze the pressure distribution afterthe deflection of the podded propeller, the sin⁃gle-propeller steering condition will be consideredfirstly. As shown in Fig. 7, taking the right obliqueflow as an example, the blade facing the pod bodystrut is defined as the main blade, and the circumfer⁃ential angle of blade is θ = 0°. When the blade ro⁃tates to the right, the direction is positive and the cir⁃cumferential angle increases. The incoming flow atthe blade section is defined as

V tangential =Ωr - U sin β cos θ （11）Where V tangential refers to the circumferential velocityof the incoming flow at the blade section; Ω meansangular velocity of the propeller rotation; r is the radi⁃us of the blade section.

Under a fixed oblique flow, the axial velocity Vx

is not affected by the change of the circumferential

Mesh case123

Mesh number7×105

1.6×106

4×106

Table 3 Three mesh cases of propeller

Mesh case123

Straight conditionsKT

0.3710.3600.358

10KQ

0.7600.7450.744

Rightward deflection of 10°KT

0.3820.3750.373

10KQ

0.7810.7630.762

Table 4 Comparison of KT and KQ of three mesh cases

J

0.640.740.850.961.07

Experimental valueKT

0.3510.3000.2470.1920.138

10KQ

0.7350.630.540.440.34

Calculated valueKT

0.3600.3100.2570.2000.147

10KQ

0.7450.620.550.460.34

Error / %KT

2.563.334.054.176.52

10KQ

1.36-1.591.854.550.00

Table 5 Comparison of thrust coefficient and torquecoefficient of podded propulsion in straight forward

（a）Thrust coefficient

（b）Torque coefficientFig 6 Thrust coefficient and torque coefficient of podded

propeller of different deflection angles

-10 -5 0 5 10β /（°）

-10 -5 0 5 10β /（°）

ExperimentCFD0.480.440.400.360.320.280.240.20

K T

1.00.90.80.70.60.5

10KQ

ExperimentCFD



CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019angle of the propeller, but the circumferential veloci⁃ty V tangential is affected, which will lead to the changeof the attack angle α of the blade section at differ⁃ent positions:

α = ϕ - arctan(Vx

V tangential) （12）

Where ϕ is the pitch angle of the blade section. Itcan be seen from Eq. (12) that as the pitch anglechanges, the attack angle also changes continuously.

Fig. 7 shows the comparisons between the attackangle of the blade section and the pure axial flow( β = 0° ) at different circumferential angles. The at⁃tack angle in the blade section of blade 1 is smallerthan the pure axial flow, and the correspondingblade thrust is also smaller; the attack angle in bladesection of the blade 2 is larger than the pure axialflow, and the corresponding blade thrust is also larg⁃er. According to the characteristics of the cosinefunction, Eq. (11) and Eq. (12), the attack angle andthe thrust are the minimum when θ = 0° ; and theyare the maximum when θ = 180° . Similarly, for theleft oblique flow, the blade has the largest thrustwhen θ = 0, and the smallest thrust when θ = 180°.

2) Force analysis of podded propeller.The thrust of the podded propulsor at each deflec⁃

tion angle in one rotation period of the main blade isshown in Fig. 8.

It can be obtained from the figure that(1) Under straight conditions, due to the blocking

action of the pod struts, the thrust of the podded pro⁃pulsor is the largest when θ = 0°.

(2) When the blade is deflected to the right, theo⁃retically, the blade pressure is the smallest whenθ = 0°, but the minimum of the blade pressure is de⁃layed to θ = 50° due to the blocking action of thepod strut; similarly, the maximum of the pressure ex⁃ists at around θ = 240°.

(3) When the blade is deflected to the left, theblade pressure is the largest when θ = 0° , which isdue to the blocking action of the pod strut on the onehand, and on the other hand, from the effect of theoblique flow. Due to the interference of the blockingaction of the pod on the blade, the minimum of theblade pressure is delayed to around θ = 225° . Theblade pressure distributions shown in Fig. 9 also vi⁃sually reflect the fluctuation law of the blade thrustcoefficient.

(4) As the deflection angle increases, the peak/trough circumferential position of the main blade

（a）Diagram for blade angle and lateral incoming flow

（b）Section velocity triangle of blade 1

（c）Section velocity triangle of blade 2

θ =180°

θ =270°

Blade 2

θ =90°θ =90°

θ =0°

Blade 1 Ωr

Usi

nβ

cos θ

xy

z

Vy = U sin β

U sin β cos θ

U cos β

Ωr

U sin β cos θ

U cos β

U β =0°

U

αβ =

0°

α

U β =0°

U

αβ =

0°

α

Ωr

Fig.7 Hydrodynamic analysis of blade section

（a）Thrust coefficient

（b）Torque coefficientFig.8 Curves of thrust and torque coefficient of the main blade

in one rotation period

β =-10°β =-5°β =0°β =5°β =10°

0.100.090.080.070.060.05

K T

0 50 100 150 200 250 300 350θ /（°）

0 50 100 150 200 250 300 350θ /（°）

0.18

0.16

0.14

0.12

0.10

0.08

10KQ

β =-10°β =-5°β =0°β =5°β =10°

36


thrust and torque does not change; the pulsation am⁃plitude of the blade thrust increases; and the excit⁃ing force of the podded propulsor also increases.

The pressure distributions of the blade at differentdeflection angles are shown in Fig. 9, wherein theleft figure manifests the suction surface and the rightone manifests the pressure surface. It can be ob⁃tained from the figure that

(1) Under straight conditions, the negative pres⁃sure on the blade tip of the suction surface directlyin front of the strut is relatively small; due to theblocking action of the pod, the positive pressure onthe pressure surface of the blade directly in front ofthe strut is relatively large.

(2) Under steering conditions, the pressures ofeach blade in different circumferential positions aredifferent, and they are asymmetric in the vertical andhorizontal directions, which will increase the bearingforce and exciting force of the podded propeller.With the increase of the deflection angle of the pod,the asymmetry of the pressures will continue to dete⁃riorate.

(3) When the blade is deflected to the left, the neg⁃ative pressure of the blade tip on the right side andthe upper side of the suction surface increases, andthe positive pressure of the pressure surface increas⁃es accordingly; when the blade is deflected to theright, the negative pressure of the blade tip on theright side and the lower side of the suction surface in⁃creases, indicating that steering conditions adverselyaffect the cavitation performance of the propeller.

The equation for calculating the pressure coeffi⁃cient CP is

CP =P

0.5ρn2 D2（13）

Where P refers to the pressure on the blade.The pressure coefficient distribution curves of the

blade section at r = 0.8R shown in Fig. 10 can betterdescribe the pressure field distribution at differentdeflection angles. If the opening of the leading edgeis larger, the attack angle of the corresponding bladesection is larger, and the corresponding blade load islarger [13-15].

Pressure/ Pa-100 000 -68 000 -36 000 -4 000 28 000 60 000 Pressure/ Pa-100 000 -68 000 -36 000 -4 000 28 000 60 000





（a） β = -10°

（b）β = -5°

（c）β = 0°

（d）β = 5°

（e）β =10°Fig.9 Blade pressure distribution contours

CP

（a） θ =0°

0.0 0.2 0.4 0.6 0.8 1.0x/c

3210

-1-2-3-4

β =-10°β =0°β =10°




Fig. 10(a)-Fig. 10(e) show pressure coefficient dis⁃tribution curves at different circumferential angles( β = -10°, 0° , 10°). It can be seen from the figuresthat when x/c < 0. 2 ( c refers to the chord length,and x means a certain position of the chord length),the pressure coefficient curve of the suction surfacewill first drop to the lowest point, and then rise,which is related to the attack angle of the blade it⁃self. This can also be seen from Fig. 9. When θ = 0°,72°, the load of the blade deflected to the left is high⁃er than that deflected to the right, and when θ =144° , 216° , 288° , the load of the blade deflected tothe right is higher than that deflected to the left.When the circumferential angle is θ = 0°, 216°, thedifferences of the pressure coefficient distributioncurves under each steering condition are more obvi⁃ous.

Fig. 10(f)-Fig. 10(h) show the pressure coefficientdistribution curves at different deflection angles ( θ =0° , 72° , 144° , 216° , 288° ). It can be seen from thefigures that under straight conditions, and when β =0° , θ = 0° , the opening of the pressure coefficientcurve near the strut is the largest and the blade loadis larger; the pressure curve distributions when theblade is deflected to the left ( β = -10° ) show thatwhen θ = 0° , the leading edge opening of the pres⁃sure curve is the largest, indicating that the bladeload is greater than that at other circumferential an⁃

Cp

CP

（b） θ =72°0.0 0.2 0.4 0.6 0.8 1.0

x/c

3210

-1-2-3-4

β =-10°β =0°β =10°

（c） θ =144°0.0 0.2 0.4 0.6 0.8 1.0

x/c

CP

3210

-1-2-3

β =-10°β =0°β =10°

（d） θ =216°0.0 0.2 0.4 0.6 0.8 1.0

x/c

CP

3210

-1-2-3-4

β =-10°β =0°β =10°

（e） θ =288°0.0 0.2 0.4 0.6 0.8 1.0

x/c

CP

3210

-1-2-3

β =-10°β =0°β =10°

（f） β =0°0.0 0.2 0.4 0.6 0.8 1.0

x/c

3210

-1-2-3-4

θ =0°θ =72°θ =144°θ =216°θ =288°

Fig.10 Blade section pressure coefficient distribution at r=0.8R

（g） β =-10°0.0 0.2 0.4 0.6 0.8 1.0

x/c

CP

3210

-1-2-3-4

θ =0°θ =72°θ =144°θ =216°θ =288°

（h） β =10°0.0 0.2 0.4 0.6 0.8 1.0

x/cC

p

3210

-1-2-3-4

θ =0°θ =72°θ =144°θ =216°θ =288°

38


gles at this time; when θ = 216° , the leading edgeopening and the blade load of the pressure curve arethe smallest; the pressure curve distributions whenthe blade is deflected to the right ( β = 10° ) showthat when θ = 216°, the leading edge opening of thepressure curve is the largest, indicating that theblade load is greater than that at other circumferen⁃tial angles at this time, and when θ = 72°, the lead⁃ing edge opening and the blade load of the pressurecurve are the smallest.4.2 Analysis of cavitation performance

In order to analyze the blade cavitation perfor⁃mance of the podded propulsor under steering condi⁃tions, the cavitation experiment and numerical simu⁃lation are carried out in this paper. The results areshown in Fig. 11, where, the left figure is the experi⁃mental one, the middle one is the numerical simula⁃tion, and the right one is a partial view of the numeri⁃cal simulation. The figures show

1) At different deflection angles, the goodness offit between the cavitation experiment and the numeri⁃cal simulation results is high.

2) When the pod is under straight conditions, thecavitation areas of each blade are basically the same,and the cavitation is relatively stable. Due to theblocking action of the struts, the cavitation areas ofblade near the strut are slightly larger.

3) When the pod is deflected, the cavitation areasof different blades are different, which will increasewith the increase of deflection angles. Under steeringconditions, the cavitation degree of the blade is moresevere than that under straight conditions.

4) When the pod is deflected to the port side, thecavitation areas are significantly larger than those inother positions if the blade is turned to the upperside and the right side of the propeller disk; whenthe pod is deflected to the starboard side, the cavita⁃tion areas are significantly larger than those in otherpositions if the blade is turned to the lower side andthe left side of the propeller disk. This is because thedeflection changes the direction of the incomingflow, thus leading to different incoming flow and at⁃tack angles of the blades at different circumferentialangles. Due to the blocking action of the pod whichwill cause severe cavitation of the blades near the

（a）β =-10°

（b）β =-5°

（c）β =0°




strut, differences of the blade cavitation areas areproduced in different deflection directions.

5) Under oblique flow conditions, the cavitation ar⁃eas of the blade change with the circumferential an⁃gles. The generation and collapse of the cavitationswill lead to intense pulsation on the ship hull. At thesame time, intense cavitation will severely ablate theblade materials.5 Conclusions

In this paper, the hydrodynamic performance andcavitation performance of the podded propulsor un⁃der steering conditions are analyzed, and the conclu⁃sions are as follows:

1) Combining the RANS method, the Schnerr-Sau⁃er cavitation model and the full structured meshes,the hydrodynamic performance and cavitation perfor⁃mance of the podded propulsor under steering condi⁃tions can be accurately predicted.

2) Under straight conditions, the pressure surfaceof the blade near the strut has a large positive pres⁃sure and the suction surface has a large negativepressure. After the deflection of the pod, the blade at⁃tack angle and the blade force are constantly chang⁃ing. However, due to the blocking action of the pod,the peak/trough of the blade pressure does not occurat 0° or 180° , but a certain angular deflection ap⁃pears. As the deflection angle increases, the peak/trough circumferential position of the blade pressurepulsation does not change, but the pulsation ampli⁃tude increases, which will adversely affect the excit⁃

ing force of the podded propeller.3) The pressure distributions of the pod blades

change continuously along the circumferential an⁃gles, and the lateral and vertical pressure distribu⁃tions are asymmetric. This asymmetry deteriorateswith the increase of the deflection angles.

4) Under steering conditions, the cavitation sizesof the podded propulsor blades in each circumferen⁃tial position are different. When the blade is deflect⁃ed to the right, the left and lower sides have largercavitations, and the cavitations at the upper andright sides are smaller; when the blade is deflectedto the left, the right and upper sides have larger cavi⁃tations, and the cavitations at left and lower sides aresmaller. The pulsation changes in the propeller cavi⁃tation will cause intense pulsation on the ship hull,which will seriously ablate the materials of the hulland the propeller.References［1］ Wang Z H. Podded electric propulsion system［J］. Ma⁃

rine Electric & Electronic Engineering，1999（4）：

30-32，37（in Chinese）.［2］ Islam M F，Veitch B，Akinturk A，et al. Experiments

with podded propulsors in static azimuthing conditions［C］//Proceedings of the 8th Canadian Marine Hydro⁃mechanics and Structures Conference. St Jone's，NL，Canada：NRC Institute for Ocean Technology，2007.

［3］ Guo C Y. The performance of podded propulsor instraight forward motion and at helm angles［D］. Shang⁃hai：Shanghai Jiaotong University，2009（in Chinese）.

［4］ Yang C J，Qian Z F，Ma C. Influences of pod on thepropeller performance［J］. Journal of Shanghai Jiao⁃

（d）β =5°

（e）β =10°Fig.11 The cavity of pod propeller in experiment and simulation

40


tong University，2003，37（8）：1229-1233（in Chi⁃nese）.

［5］ Szantyr J A. Hydrodynamic model experiments withpod propulsor［J］. Oceanic Engineering International，2001，5（2）：95-103.

［6］ Liu P F，Islam M，Veitch B. Unsteady hydromechan⁃ics of a steering podded propeller unit［J］. Ocean Engi⁃neering，2009，36（12/13）：1003-1014.

［7］ Amini H，Sileo L，Steen S. Numerical calculations ofpropeller shaft loads on azimuth propulsors in obliqueinflow［J］. Journal of Marine Science and Technology，2012，17（4）：403-421.

［8］ Xiong Y，Sheng L，Yang Y. Hydrodynamics perfor⁃mance of podded propulsion at declination angles［J］.Journal of Shanghai Jiaotong University， 2013， 47（6）：956-961（in Chinese）.

［9］ Wang Z Z，Xiong Y，Sun H T，et al. Numerical studyon hydrodynamic performance of podded propulsor instraight forward and steering conditions［J］. Journal ofPropulsion Technology，2016，37（3）：593-600（inChinese）.

［10］ Shen X R，Fan S M，Cai Y J，et al. Experimental in⁃vestigation on cavitation performance of podded pro⁃pulsor under small helm-angle condition［J］. Ship⁃

building of China，2012，53（1）：1-8（in Chinese）.［11］ Friesch J. Cavitation and vibration investigations for

podded drives［C］//Proceedings of the first Interna⁃tional Conference on Technological Advances in Pod⁃ded Propulsion. Newcastle，UK：University of New⁃castle，2004：387-399.

［12］ Yang C J. Work introduction of the 25th ITTC podpropulsion expert committee［C］// Proceedings of the2008 Conference on Ship Hydrodynamics and the Chi⁃nese Shipping Academia entered the ITTC 30th Anni⁃versary. Hangzhou：Chinese Society of Naval Archi⁃tects and Marine Engineer，2008：365-368（in Chi⁃nese）.

［13］ Menter F R. Two-equation eddy-viscosity turbulencemodels for engineering applications［J］. AIAA Jour⁃nal，1994，32（8）：1598-1605.

［14］ Chang X，Liang N，Wang C，et al. Numerical analy⁃sis of unsteady hydrodynamic performance of propel⁃ler in oblique flow［J］. Journal of Harbin EngineeringUniversity，2017，38（3）：1048-1055（in Chinese）.

［15］ Dubbioso G，Muscari R，Mascio D A. Analysis of theperformances of a marine propeller operating inoblique flow［J］. Computers & Fluids，2013，75：86-102.

偏转工况下吊舱推进器的水动力和空泡性能

李善成，熊鹰*，王展智海军工程大学舰船与海洋学院，湖北武汉 430033

摘要：［目的目的］吊舱推进器与螺旋桨之间干扰强烈，流动现象复杂。在操舵工况下远离设计点条件工作时，桨

叶载荷会出现剧烈变化，且空泡性能也将同步恶化。为了分析吊舱推进器在偏转工况下的水动力和空泡性能，

［方法方法］首先，采用全结构网格，基于雷诺平均（RANS）数值模拟方法对吊舱推进器的水动力性能开展研究；然

后，采用 Sauer模型预报吊舱推进器偏转工况下的空泡性能；最后，在空泡水筒中开展吊舱推进器的模型实验。

［结果结果］结果表明：数值计算结果与实验结果的吻合度较高，验证了数值预报方法的准确性；偏转工况下，吊舱桨

的推力和扭矩均高于直航工况；吊舱偏转后，随着周向角的变化，不同周向位置的压力将呈脉动变化趋势；桨叶

的空泡形态存在差异性，且随吊舱偏转角度的增加而恶化。［结论结论］研究成果可以为吊舱推进器设计提供参考。

关键词：吊舱推进器；偏转工况；水动力性能；空泡性能；桨叶载荷



Documents

LiShancheng XiongYing WangZhanzhi