船后螺旋桨空泡数值预报及试验对比.pdf

Numerical Predictions of the Propeller Cavitation behind Shipand Comparison with ExperimentLIU Deng-chenga, b, ZHOU Wei-xina, b(a. National Key Laboratory on Ship Vibration & Noise; b. Jiangsu Key Laboratory of Green Ship Technology,China Ship Scientific Research Center, Wuxi 214082, China)Abstract: The effects of turbulence model on propeller cavitation simulation results are presented. Itshows that the common turbulence model can deal well with the propeller cavitaion shapes. And thenthe propeller cavitation performance behind ship was numerically simulated using a hextetrahedralmesh based on RANS solver, the Suaers cavitation model based on transport equation and a SSTk- turbulence model were coupled in the RANS solver. A symmetry boundary condition is appliedon the top of computational domain instead of the free surface, which is similar to a tunnels wall.To observe the cavitation pattern during the revolution of propeller, the propeller is rotated with a con鄄stant rotation angle of 1.0 degree using a sliding mesh technique. Cavitation patterns of the simula鄄tions are compared with the experimental results carried out in Large Cavitation Channel of CSSRC(LCC). Although the predicted propeller tip vortex cavity is missing because of the mesh resolution, thepredicted dynamic cavitation behaviors generally well agree with experimental observation.Key words: cavitation; propeller; ship; numerical predictionCLC number: U661.73Document code: Adoi: 10.3969/j.issn.1007-7294.2016.03.0010 IntroductionThe propeller cavitation can rise up the vibration, the noise and the erosion. Therefore,the predicted propeller dynamic cavitation behavior is of great interest for propeller designer.Cavitation presents complex unsteady, turbulent and multi-phase flow phenomena with alarge density difference and mass transfer. These features result in a unique challenge for thesimulation of cavitating flows.The simulations of cavitating flow using viscous CFD method were performed actively inthe last decade because cavitation models and computation power have been rapidly devel鄄oped. Many researchers did some simulations of foil and propeller cavitating flow. For ex鄄ample, Rhee and Kawamura1studied the cavitating flow around a marine propeller using anunstructured mesh. Liu2-4simulated the cavitation performance of marine propeller using ahybrid mesh based on RANS solver using singhal model. Coutier-Delgosha et al5computedReceived date：2015-12-03Foundation item: Supported by the National Natural Science Foundation of China (Grant No.11332009)Biography：Liu Deng-cheng(1982-), male, senior engineer, E-mail: edon_;ZHOU Wei-xin(1970-), male, researcher.Article ID：1007-7294（2016）03-0233-10第20卷第3期船舶力学Vol.20 No.32016年3月Journal of Ship MechanicsMar. 2016234船舶力学第20卷第3期cavitating flows around 2D foil by modifying turbulence model, and the sheet cavity length andthe dynamic shedding behaviour were very similar to those observed in the experiment. Li6-7predicted unsteady cavitating flows of 2D NACA0015 foil and 3D twisted foil using the sameidea. Shin et al8carried out cavitation simulation on conventional and high-skewed propellersin the Behind-Hull Condition. Paik et al9simulated the cavitation and hull pressure fluctua鄄tion for propeller with hull interaction, and so on.In this paper, the effects of turbulence model on propeller cavitation simulation results areresearched. And then the propeller cavitation performance behind ship was numerically simu鄄lated using a hextetrahedral mesh based on RANS solver, the Suaers cavitation model basedon transport equation and a SST k- turbulence model were coupled in the RANS solver.1 Numerical method1.1 Governing equationsFor the multi-phase flow solutions, the single-fluid mixture model is employed. The gov鄄erning equations are written for the mass and momentum conservation of mixed fluid as fol鄄lows:坠 籽m! 坠t+坠 籽mui!坠xi=0(1)坠 籽mui!坠t+坠 籽muiuj!坠xj=-坠p坠xi+坠坠xj滋+滋t!坠ui坠xj+坠uj坠xi!#$(2)where 籽mis the mixed density, 滋 is the mixed viscosity, 滋tis the mixed eddy viscosity whichis calculated by turbulence model.Convection terms are discretized using a second order accurate upwind scheme, while dif鄄fusion terms are discretized using a second order accurate central differencing scheme. A seg鄄regated solver with SIMPLE as the velocity-pressure coupling algorithm was selected. The dis鄄crete equations are solved using Gauss-Seidel iterations, and algebraic multi-grid method ac鄄celerates the solution convergence. The effect of gravity is neglected. The double model is usedfor dealing with free-surface.1.2 Sauer cavitation modelThe mixed density is controlled by vapor fraction 琢:籽m=琢籽v+ 1-!琢 籽l(3)The vapor transport equation is written as:坠 琢籽v!坠t+琢 琢籽vui!坠xi=m觶+-m觶-(4)where 籽vand 籽lare the density of vapor and liquid, respectively. m觶+and m觶-are the rates ofvapor generation and condensation, respectively. Sauer derived the expressions of m觶+and m觶-.第3期LIU Deng-cheng et al: Numerical Predictions of the Propeller235If ppvm觶+=3籽l籽v籽m4仔n33姨琢2/31-姨姨琢4/323pv-p籽l姨(5)If ppvm觶-=-3籽l籽v籽m4仔n33姨琢2/31-姨姨琢4/323p-pv籽l姨(6)where 籽vis saturated vapor pressure.2 The effect of turbulence modelFor research the effect of different turbulence model, three different turbulence models areemployed to research the effect of different turbulence model which include k-, SST k- andReynolds stress turbulence model (RSM). The PPTC propeller cavitation in uniform flow is car鄄ried out. PPTC propeller is an international standard model which is proposed on the first work鄄shop on cavitation and propeller performance. There are abundant experimental data.Tab.1 presents the case of computational. The expressions of advance ratio and cavitationnumber are written as follows:J=VND,滓n=p-pv0.5籽 N姨姨D2(7)Tab.1 The case2-1 of cavitation computationalFor tip vortex region grid refinement, a block was created according to the helix line, andthe pitch is equal to the propeller pitch at the 1.0 time radius (see Fig.1). The textetrahedralmesh is used (see Fig.2).Advanced coefficientCavitation numberRate of revolutions (1/s)Velocity (m/s)1.0192.024153.821Fig.1 The block for tip vortex region grid refinementFig.2 The grid typesFig.3 presents the comparison of the computed cavity shapes with the experimental re鄄sults which come from Potsdam Model Basin at the first workshop on cavitation and propellerperformance. The computed cavity shapes can be confirmed by the iso-surface of vapor volumefraction of 0.1. From the experimental results we clearly see that the cavitation is to occur in thetip, root and leading edge of suction side of propeller. Fig.4 shows that the all computationalcases catch the cavity in the tip, root and leading edge, but the sheet cavitation at leadingedge is a little unpredicted. The computational results indicated that the common turbulencemodel can deal well with cavitating flow, and the SST k- turbulence model is chosen for sim鄄ulating the propeller cavitation behind ship because this turbulence model is often imposed inpropeller performance simulation.3 Propeller cavitations behind ship3.1 Geometry and computational domainAn 82000DWT bulk carrier with five blades propeller was chosen for the cavitation sim鄄ulation which has experimental data of cavitation observation come from LCC of CSSRC. Pro鄄peller model is a five bladed propeller with diameter D=0.237 m and area ratio of 0.52.The computational domain was created: The inlet of the domain is at 1.5L upstream of theship hull; exit at 2.5L downstream; outer boundary at 1.5L from the center of symmetrical plane;L is the length of ship.3.2 Computation mesh and conditionsThe entire domain is filled with hextetrahedral mesh. The minimum size of grid is 1.8 mmin the ship stern region and 0.5 mm in the propeller tip region (see Fig.4), there are only about24 grids in the propeller tip vortex region because of the size of propeller model tip vortexcavitation is about 12 mm, so the propeller tip vortex cavitation will be missing. The grid cellsnumber was about 3.2 million in static region and 0.8 million in rotating region.Boundary conditions were set to simulate the flow around ship with propeller: on the inletboundary and the outer boundary, velocity components of uniform stream with the given in鄄flow speeds were imposed; on wall surface, the no slip condition was imposed; and on thek-SST k-RSMEXP.Fig.3 The computational cavity shapes and compared with experimental236船舶力学第20卷第3期symmetrical plane boundaries of free-surface, symmetry was ensured; on the exit boundary,the static pressure was set to a constant value according to the cavitation index. The unsteadywetted computation results are used as the initial value of unsteady cavitation simulation. Thepropeller is rotated with a constant rotation angle of 1.0 using a sliding mesh technique. Theconditions are described in Tab.2. The expression of cavitation index is written as follows:n 0.8!R=P0.8R-Pv0.5籽 0.8仔n!D2(8)Tab.2 The computational conditionsFig.4 The mesh of ship stern surface3.2 Results and comparison with experimentThe simulations of propeller cavitating flow with ship are calculated at two conditions.The computed results of thrust coefficient are summarized in Tab.3. The results of model testare also presented at wetted condition. For the wetted simulation, the comparison shows quitegood agreement, and the thrust coefficients are over predicted 4.34% and 1.73% at design andballast condition, respectively. The simulated results show that the thrust coefficient will beslightly increased less than 1% when propeller comes into cavitation at design and ballastcondition.Cavitation patterns at some propeller blade angle at the design and ballast draught con鄄ditions are compared with the experimental results in Figs.5 and 6, respectively. The iso-sur鄄face of vapor volume fraction at value 0.1 shows the interface of cavity. The tip vortex cavita鄄tion in simulation results is missing which is consistent with expected, but the cavity patternsgenerally well agree with the experiments. At the design and ballast draught condition, the lead鄄ing edge cavitation from 0.7R to 0.95R of the propeller blade at propeller blade angle of 350is appeared in the numerical simulation, while the patch cavitation is observed in model test.Design draught(CSR with 15% S.M.)Ballast draught(CSR with 15% S.M.)Vs (kn)ns(rpm)0.8nRKTVm (m/s)nm(1/s)14.2585.00.504 40.191 35.2943014.0784.60.353 90.196 85.25130第3期LIU Deng-cheng et al: Numerical Predictions of the Propeller237Tab.3 The thrust coefficient at two conditionsConditionWetted, expWetted, cal.ErrorCavity, cal.ChangeKt_expKt(Kt-Kt_exp)/Kt_expKt_c(Kt_c-Kt)/KtDesignBallast0.191 30.196 80.199 60.200 54.34%1.73%0.201 50.202 20.95%0.85%35001020350010203040506030405060Fig.5 The comparison of cavitation patterns at design draught condition238船舶力学第20卷第3期Fig.7 and Fig.8 show the cavitation photos at design and ballast draught condition. At thetwo draught conditions, the cavitation presents unstable behavior at some propeller blade angleof 20 and 30, especially at the ballast draught condition, but the simulation results are sta鄄ble at all blade angles. The simulations results can present the cavitation dynamic behavior with35001020350010203040506030405060Fig.6 The comparison of cavitation patterns at ballast draught condition第3期LIU Deng-cheng et al: Numerical Predictions of the Propeller239blade angles, not present the cavitation dynamic behavior with time at the same blade angle.4 ConclusionsFirstly, the effects of turbulence model on propeller cavitation simulation results are pre鄄01020304050Fig.7 Cavtation photos at design draught condition01020304050Fig.8 Cavtation photos at ballast draught condition240船舶力学第20卷第3期sented. It shows that the common turbulence model can deal well with the propeller cavitaionshapes. And then the propeller cavitation performance behind ship was numerically simulatedusing a hextetrahedral mesh based on RANS solver, the Suaers cavitation model based ontransport equation and a SST k- turbulence model were coupled in the RANS solver. And thesimulation results were compared with the experimental results performed in the large cavita鄄tion channel.The simulated results show that the thrust coefficient will be slightly increased less than1% when propeller comes into cavitation at design and ballast condition. The cavitation pat鄄terns of simulations results can present the cavitation dynamic behavior with blade angles, notpresent the cavitation dynamic behavior with time at the same blade angle. Although the pre鄄dicted propeller tip vortex cavity is missing because of the mesh resolution, the predicted dy鄄namic cavitation behaviors generally well agree with experimental observation. We believe thatnumerical assessment cavitation pressure fluctuation is tangible in the near future.For the further work, simulations of hull pressure fluctuation for a marine propeller op鄄erating behind a hull will be simulated.References1 Shin Hyung Rhee, Takarumi Kawamura. A study of propeller cavitation using a RANS CFD methodC/ The 8th Interna鄄tional Conference on Numerical Ship Hydrodynamics, September 22-25, 2003. Busan, Korea, 2003.2 Liu Dengcheng, Hong Fangwen, Zhao Feng, Zhang Zhirong. The CFD analysis of propeller sheet cavitationC/ Proceed鄄ings of the 8th International Conference on Hydrodynamics, September 30-October 3, 2008. Nantes France, 2008.3 Liu Dengcheng, Hong Fangwen. The Numerical Predicted of SMP11 propeller performance with and without cavitationC/Second International Symposium on Marine Propulsors, SMP11, June, 2011. Hamburg, Germany, 2011.4 Liu Dengcheng. The numerical predicted of VP1304 propeller cavitation performance in oblique flowC/ Fourth Interna鄄tional Symposium on Marine Propulsors. smp15, May 31-June 4, 2015. Workshop: Propeller performance. Austin, USA,2015.5 Coutier-Delgosha O, Fortes-Patella R, Reboud L. Evaluation of the turbulence model influence on the n