Numerical Study of Pressure Fluctuation Induced by Propeller Cavitation with Pre-shrouded Vanes

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(1.China Ship Scientific Research Center,Wuxi 214082,China;2.Jiangsu Key Laboratory of Green Ship Technology,Wuxi 214082,China;3.CSIC Shanghai Marine Energy Saving Technology Development Co.,Ltd.,Shanghai 200011,China)

Abstract:A numerical method to predict the propeller cavitation and hull pressure fluctuation in the ship stern is set up in this paper by using unsteady viscous RANS approach and Schnerr-Sauer cavitation model.The numerical error or uncertainty is estimated with verification and validation method before evaluation of the energy-saving performance at self-propulsion condition by using the revised ITTC’78 method.Then the hull pressure fluctuation induced by propeller cavitation is predicted without Pre-Shrouded Vanes(PSV,CMES-PSV).The numerical method is used to study the hull pressure fluctuation with PSV,which has five fins and a half duct.The cavity patterns and the amplitudes of the first and second blade frequencies(BF)of hull pressure fluctuation are compared.When PSV energysaving device is used,the 1BF and 2BF pressure fluctuations decrease about 33% and 20% respectively,and the cavitation shape areas also decrease.

Key words:propeller cavitation;CFD;pressure fluctuation;energy-saving device

0 Introduction

In recent years,ship energy saving has become an important topic in shipbuilding and shipping industry all over the world.An energy-saving device between the ship stern and propeller is one of the effective measures to realize energy saving of a ship.We know that when cavitation occurs on a propeller,the pressure fluctuation will be drastically increased.In some serious conditions,the hull structure at stern could be destroyed by the pressure fluctuation,which will also reduce the comfort of crew accommodation.So,the cavitation performance when an energy saving device is installed at the ship stern should be investigated.

With the development of the hardware technology,high performance computing could be used in computational fluid dynamics(CFD).The RANS approach,one of CFD methods,has been used to simulate the cavitation of a ship and propellers widely since 1980s[1-2].Watanabe et al[3]used RANS method to simulate the propeller cavitation in uniform and non-uniform flows.The pressure distribution on the propeller showed a good agreement with experiments and the steady cavity simulations were basically consistent with test results.Paik et al[4]simulated the unsteady cavitation induced pressure fluctuation as the blades passed through the high wake flow of ship stern.The results from spectrum analysis showed there were three high amplitudes with the frequency the same as the 1st,2nd and 3rd blade rotating frequency,and results showed good agreement with those of experiments.Li et al[5]predicted the E779A propeller cavitation in non-uniform wakes and verified the accuracy of its CFD method.Yang et al[6]used RANS method to simulate the cavitation on propeller and monitored the pressure fluctuation on a double-stern ship.Detailed analysis was presented for the distribution and amplitude of pressure fluctuations.Paik et al[7]compared the cavitation patterns on two propellers with slightly different geometries by the commercial software FLUENT.Some researchers tried to use an open source CFD code to simulate the propeller cavitation performance behind the ship hull,such as Asnaghi[8]and Zheng[9],and the simulations showed a good agreement with experiments.Bensow[10]simulated the hull-propeller interaction with a pre-swirlstator installation in model scale,and the hydrodynamic performance of cavitation flow of the propeller was shown.With more and more energy-saving devices installed in ship stern,the propeller cavitation and hull vibration risk increase.Therefore,the hull pressure fluctuation and cavitation performance should be evaluated when an energy-saving device is installed.

This paper is dedicated to comparison of the unsteady cavitation generated on a propeller in the stern region with and without PSV,and analysis of the hull pressure fluctuations induced by the unsteady cavitation.

1 Methods

1.1 Governing equations

The solution of the flow field is based on the continuity equation and momentum equations.Here the RANS equations were adopted,which has a lower computational effort and enough accuracy for ship engineering.

whereUis the velocity,pis the mixture pressure,Fsis the body force,ρis the mixture density,μis the laminar viscosity,andμtis the turbulent viscosity.The SSTκ-ωturbulence model is used to simulate the turbulent viscosityμt,this model is widely studied in ship hydrodynamics.

The interface of liquid and vapor is captured by VOF approach,the fluid is scaled by the liquid volume fractionγ,γ=1 means the physical properties of the pure water.

The density and dynamic viscosity are shown below:

where the subscripts v and l refer to the vapor and liquid components.

The mass transfer equation of the liquid volume fractionγis:

We should model the mass transfer ratem˙.

Combining the transport Eq.(1),Eq.(3)and Eq.(5),we can get

1.2 Cavitation model

When the local pressure becomes lower than the vapour pressure,a phenomenon of the transition of water into vapor will be generated because of the small gas nuclei in the water.This phase change processing could be solved by some cavitation mass transfer model,such as Schnerr-Sauer.This model is widely used to predict propeller cavitation.

wheren0is the number density of micro bubbles per liquid volume,Ris the initial nuclei radius.Schnerr-Sauer’s cavity model could consider the motion of a single bubble of radiusR,which is based on bubble dynamics.

1.3 Solution procedure

We use the finite volume method to discretize the fluid governing equations,and the cell-center positions of computational grid are used to store the unsolved flow variables.The time items are in Euler format,and the momentum equation is in second order form.

The commercial solver Fluent used in this study is a multiphase flow solver,taking two fluids into account using the VOF method.

We use quasi-stable MRF method to simulate the rotation of a propeller for quasi-steady flow as an initial input,a sliding mesh method as well as interface between ship static region and propeller moving region is then applied to simulate the unsteady flow field.The SIMPLE algorithm is used for solving the velocity and the pressure fields.This simulation processing could reduce the computational time.

1.4 Boundary conditions and mesh generation

The investigated model in this paper is a tanker.A four-bladed fixed pitch propeller is installed at the stern of this ship.The main parameters of the model propeller are shown in Tab.1,and the hull and propeller geometry are shown in Fig.1.

Fig.1 Tanker hull and propeller geometry

Tab.1 Main parameters of ship model

The simulation region consists of inlet,pressure outlet and no-slip boundaries.At the inlet boundary,a fixed value of velocity is given,and the pressure value calculated by cavitation numberσnis constant at the pressure outlet boundary.The hull,propeller,PSV,rudder and hub boundary are no-slip wall conditions respectively.

The commercial software HEXPRESS is used to generate the mesh.The computational domain is divided into two parts.One part named ship region contains the flow region that includes the inlet,outlet,ship,PSV and rudder,and the other part named propeller region contains propeller rotational cylinder.The unstructured hexahedral cell is used to generate the whole region grid.On the wall boundary such as ship wall,5 boundary layer cells with 1.3 stretching factor are inserted,which could meet the requirements of wall function condition.The overview of the surface mesh is shown in Fig.2.

Fig.2 Surface mesh of the stern region

2 Results

2.1 Simulation uncertainty assessment

The grid and iterative convergence are studied by the reference of ITTC revised procedure[11]and CFD uncertainty analysis method suggested by Xing and Stern[12].The simulation uncertainty of the ship model resistance is evaluated by verification and validation method.

A cut-cell unstructured grid type is used to generate the cell around the complex surface of this ship.The surface grid size increases bywith a constant ratio of growth which insures the similarity of these three grid systems(GS1,GS2,GS3).GS1,GS2 and GS3 are the fine,medium and coarse grid systems respectively,as shown in Tab.2.They+is the first cell dimension measured normal to the wall.

Tab.2 Grid systems

The error and the uncertainties of the viscous resistance coefficientCVMare shown in Tab.3.The subscript M refers to the model,V refers to viscous.The grid uncertainty(UG,the subscript G refers to grid)is about 1.72%ofSC(SCis the numerical reference value,the subscript C refers to correction),and decreases to 0.29% with correction.In Tab.3,RGis the convergence ratio,pGis the order of accuracy,CGis the correction factor,δ*Gis the numerical error,andUGCis the correction ofUG.

Tab.3 Verification of CVM

The validation process ofCVMis utilizing benchmark model test value to estimate the uncertainty of the numerical model.The comparison error(E),validation uncertainty(UV)and numerical uncertainty(USN,the subscript S refers to simulation,N refers to numerical)are defined as following:

where the other numerical parameter uncertainty(UP,the subscript P refers to numerical parameter)due to time step is zero in the present problem.Tab.4 shows the validation ofCVM.It is assumed that the test uncertainty(Uexp)is 2.0%.||E＜UVmeans the validation of numerical simulation is achieved.

Tab.4 Validation of CVM

2.2 Evaluation of energy saving

The model simulations to estimate the self-propulsion performance with and without PSV were carried out.Fig.3 presents the results of experiments and simulations of thrust coefficient(KT),torque coefficient(KQ)and open water efficiency coefficient(η0).At the advance ratioJ=0.6,the errors ofKT,KQandη0are about 2.07%,5.71%,and-3.04%,respectively.Tab.5 presents the results of simulations of the self-propulsion.For the three given model speeds(VM),the propeller torque(QM)decreases when the energy-saving device is installed.The delivered powers(PDM)with PSV reduce by 4.1%,3.3%and 4.2%at three different model speeds,respectively.

Fig.3 Comparison of propeller open water performances

Tab.5 Simulation data of self-propulsion

The self-propulsion performance is calculated using the revised ITTC’78 method[13-14].Tab.6 shows the self-propulsion factors and delivered power reduction for PSV.The PSV significantly improves the wake fraction(wS,the subscript denotes the full scale ship)and little changes in thrust reduction(tS),so the hull efficiency(ηHS)increases.The rotative efficiency(ηRS)increases a little and the propeller open water efficiency(η0S)decreases.Due to these the propulsive efficiency(ηDS)increases with PSV.Accordingly,the PSV reduces the delivered power by 2.2%,1.7% and 2.2% at the ship speeds of 13 kn,14 kn and 15 kn respectively.

Tab.6 Results of self-propulsion analysis with and without PSV of full scale ship

2.3 Flow field comparison

The cavitation simulation input parameters in this study are listed in Tab.7.Wherenis the propeller rotational speed,σn0.8Ris cavity number at 0.8Rof propeller,andKTis the thrust coefficient of the propeller after the ship hull from self-propulsion prediction.

Tab.7 Test conditions(Ballast draft)

In model test,the pressure is adjusted in the large cavitation channel to meet the cavitation number throughKT-identity method,which ensures that the model propeller loads are equal to full scale.In cavity simulation process,the steady flow field simulated by MRF method is used as an initial input to calculate the unsteady flow with sliding mesh method to simulate the rotation of the propeller,and then the propeller cavitation performance is predicted by activating the cavitation model.The number and density coefficient of nuclei chosen in Schnerr-Sauer cavitation model aren0=2×108anddNuc=1×10-4respectively.

The main PSV’s energy saving mechanism is to reduce the loss of swirl energy in ship wake generated by a propeller.Fig.4 shows the definition of the circumferential angle distribution.Figs.5-7 are the tangential velocity(Ut,the subscript t refers to tangential)distributions in front of the propeller.TheUinletis the reference velocity,which is used by inlet velocity.As shown in figures,when PSV is fixed,the tangential velocity distributions in front of the propeller change little.Figs.8-10 show the flowfield behind the propeller.The tangential velocity lines with PSV move down from 0.7Rto 0.9R,and the velocity peaks also decrease.The PSV induces an opposite rotational flow,which could reduce the loss of rotational energy of the propeller.

Fig.4 Sketch of circumferential position definition

Fig.5 Tangential velocity in front of propeller at 0.5R

Fig.6 Tangential velocity in front of propeller at 0.7R

Fig.7 Tangential velocity in front of propeller at 0.9R

Fig.8 Tangential velocity behind propeller at 0.5R

Fig.9 Tangential velocity behind propeller at 0.7R

Fig.10 Tangential velocity behind propellerat 0.9R

2.4 Propeller cavitation performance and induced hull pressure fluctuation

The predicted cavitation patterns on the propeller blades with and without PSV are compared in Fig.11 and Fig.12,respectively.

Fig.11 Simulation sketches at ballast draft condition without PSV(model scale)

Fig.12 Simulation sketches at ballast draft condition with PSV(model scale)

The cavity shape is identified by vapor iso-surface of 0.1.The change process of cavitation is basically the same whether with or without PSV.The main feature,the variation of the attached cavity with the rotational angels of propeller and the cavity collapse at the tail of the main cavity shows almost the same.The cavity first appeared at almost the same location atφ=-20° and grows up with blade rotating,then achieves the maximum area at aboutφ=20°.At each position,the area of cavity without PSV is a little larger than that with PSV.

By arranging the monitoring points on the stern surface of the ship,the hull pressure fluctuation induced by propeller cavity is investigated.The monitor positions are shown in Fig.13.

Fig.13 Arrangement of monitor points

The FFT signal processing program is used to calculate the pressure fluctuation spectrum,and the pressure fluctuation at full scale is predicted based on model value.The first blade frequency(1BF)amplitudes and the second blade frequency(2BF)amplitudes of the hull pressure fluctuation with and without PSV are shown in Fig.14 and Fig.15,respectively.When the PSV energy-saving device is installed,the 1BF and 2BF pressure fluctuation decreases about 33%and 20%respectively.In most situations,the cavitation patterns and the hull pressure fluctuations should be checked when using PSV to make sure there is no cavitation erosion and vibration risk.In this case,the pressure fluctuation and cavitation shape have been improved with the PSV installed.

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Fig.14 The 1BF amplitude of hull pressure fluctuation predicted with and without PSV

Fig.15 The 2BF amplitude of hull pressure fluctuation predicted with and without PSV

3 Conclusions

In this paper,the propeller cavitation patterns and the amplitudes of the first blade frequency(1BF)and the second blade frequency(2BF)with and without PSV are simulated,respectively.Some conclusions are reached as following:

(1)The uncertainty evaluation of the simulation method is carried out.The verification and validation of numerical simulation are achieved.The simulation uncertainty is about 1.72%.

(2)The self-propulsion performance of this single screw ship with or without PSV is calculated by using 1978 ITTC performance prediction method.The maximum energy-saving effect of the full scale ship is about 2.2%.

(3)The cavitation character of the target propeller with ship model is simulated.The hull pressure fluctuation decreases when the PSV is installed,and the cavitation extent with PSV is also a little smaller than that without PSV at each circumferential position.

Therefore,the simulation method in this paper has a good prediction accuracy to predict the ship self-propulsion performance.After the installation of this designed PSV,not only the energysaving effect can be obtained,but also the risk of cavitation erosion and vibration can be reduced.