基于黏性修正SST k-ω模型的水翼空化流数值模拟计算
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摘要
该研究利用开源平台Open FOAM中的interPhaseChangeFOAM求解器,应用SchnerrSauer空化模型,并结合黏性修正后的SSTk-ω模型,对二维水翼NACA0015及三维扭翼TWIST-11N进行了空化流数值模拟,从升力系数和空化脱落频率等方面对计算结果进行比较,验证了修正SST k-ω模型的可靠性,并对空化脱落机理进行了分析。首先对二维水翼NACA0015,应用了基于LES方法的Smagorinsky模型、基于RANS方法的标准SST k-ω模型和黏性修正SST k-ω模型三种不同的湍流模型,结果表明修正SSTk-ω模型能准确预报二维非定常空化的脱落频率,并且发现水翼尾部的回射流是空化脱落的主要原因。之后将修正SST k-ω模型应用于三维水翼TWIST-11N,发现应用该模型依旧能准确模拟出三维水翼的非定常空化,结果和Ji等人的结果十分接近。通过进一步对三维空化流的流场进行分析,发现三维空化流会出现主脱落及次脱落共两次空化脱落,分别由尾部回射流和侧向流导致。
In this paper, the cavitation flow around 2D hydrofoil NACA0015 and 3D hydrofoil TWIST-11 N are simulated with three different kinds of turbulence models – SST k-ω model,Smagorinsky model and modified SST k-ω model. All the numerical simulations are carried out by interPhaseChangeFoam solver in OpenFOAM with SchnerrSauer cavitation model. The lift coefficient and shedding frequency are compared with other papers to prove the reliability of modified SST k-ω model. The reasons for cavitation shedding are also analyzed. When it comes to 2D hydrofoil NACA0015, the case with modified SST k-ωturbulence model predicts the shedding frequency exactly. According to the simulation results, the shedding of the cavitation is caused by the re-entrant jet. Then the modified SST k-ω model is used in the simulations of cavitation around 3D hydrofoil TWIST-11 N. The results are compared with other papers, such as Ji. It shows that this model still performs satisfactorily.Analyzing the fields of cavitation flows, it can be found that there are two types of shedding in the 3D cavitation flows. These two types of shedding are known as primary shedding and secondary shedding. They are caused by the re-entrant jet and the side-entrant jet respectively.
In this paper, the cavitation flow around 2D hydrofoil NACA0015 and 3D hydrofoil TWIST-11 N are simulated with three different kinds of turbulence models – SST k-ω model,Smagorinsky model and modified SST k-ω model. All the numerical simulations are carried out by interPhaseChangeFoam solver in OpenFOAM with SchnerrSauer cavitation model. The lift coefficient and shedding frequency are compared with other papers to prove the reliability of modified SST k-ω model. The reasons for cavitation shedding are also analyzed. When it comes to 2D hydrofoil NACA0015, the case with modified SST k-ωturbulence model predicts the shedding frequency exactly. According to the simulation results, the shedding of the cavitation is caused by the re-entrant jet. Then the modified SST k-ω model is used in the simulations of cavitation around 3D hydrofoil TWIST-11 N. The results are compared with other papers, such as Ji. It shows that this model still performs satisfactorily.Analyzing the fields of cavitation flows, it can be found that there are two types of shedding in the 3D cavitation flows. These two types of shedding are known as primary shedding and secondary shedding. They are caused by the re-entrant jet and the side-entrant jet respectively.
引文
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[15]BENSOW R.Simulation of the unsteady cavitation on the Delft Twist11 foil using RANS,DES and LES[C].International Symposium on Marine Propulsors Workshop Proceedings,Hamburg,Germany,2011.
[16]FOETH E J,DOORNE C W H V,TERWISGA T V,et al.Time resolved PIV and flow visualization of 3D sheet cavitation[J].Experiments in Fluids,2006,40(4):503-513.
[17]FOETH E J,TERWISGA T V,DOORNE C W H V.On the collapse structure of an attached cavity on a three-dimensional hydrofoil[J].Journal of Fluids Engineering,2008,130(7):071303.
[18]FOETH E J.The structure of three-dimensional sheet cavitation[D].Doctoral Thesis,Wageningen,The Netherlands,Delft University of Technology,2008.
[2]KJELDSEN M.Spectral characteristics of sheet and cloud cavitation[J].Journal of Fluids Engineering,2000,122(3):481-487.
[3]JI B,LUO X W,WU Y L.Numerical analysis of unsteady cavitating turbulent flow and shedding horseshoe vortex structure around a twisted hydrofoil[J].International Journal of Multiphase Flow,2013,51(5):33-43.
[4]JI B,LUO X W,PENG X X,et al.Three-dimensional large eddy simulation and vorticity analysis of unsteady cavitating flow around a twisted hydrofoil[J].Journal of Hydrodynamics,Ser.B,2013,25(4):510-519.
[5]LU N X,BENSOW R E,BARK G.LES of unsteady cavitation on the delft twisted foil[J].Journal of Hydrodynamics,Ser.B,2010,22(5-supp-S1):784-791.
[6]WU X C,WANG Y W,HUANG C G.Effect of mesh resolution on large eddy simulation of cloud cavitating flow around a three-dimensional twisted hydrofoil[J].European Journal of Mechanics-B/Fluids,2016,55(1):229-240.
[7]SINGHAL A K,MAHESH M A,LU H Y,et al.Mathematical basis and validation of the full cavitation model[J].Journal of Fluids Engineering,2002,124(3):617-624.
[8]SCHNERR G H,SAUER J.Physical and numerical modeling of unsteady cavitation dynamics[C].Proceedings of the 4th International Conference on Multiphase Flow,New Orleans,USA,2001.
[9]KUNZ R F,BOGER D A,CHYCZEWSKI T S,et al.Apreconditioned Navier-Stokes method for two phase flows with application to cavitation prediction[J].Computers and Fluids,29(8):849-875.
[10]STUTZ B,REBOUD J L.Two-phase flow structure of sheet cavitation[J].Physics of Fluids,1997,9(12):3678-3686.
[11]LI D Q,GREKULA M,LINDELL P.A modified SSTk-ωturbulence model to predict the steady and unsteady sheet cavitation on 2D and 3D hydrofoils[C].Proceedings of the 7th International Symposium on Cavitation.Ann Arbor,Michigan,USA,2009.
[12]LI D Q,GREKULA M,LINDELL P.Towards numerical prediction of unsteady sheet cavitation on hydrofoils[J].Journal of Hydrodynamics,ser.B,2010,22(5):741-746.
[13]HOEKSTRA M,VAZ G.The partial cavity on a 2D foil revisited[C].Proc.7th Int.Sym.Cavitation,CAV2009,Ann Arbor,2009.
[14]OPREA I A,BUITEN B.Cavitation modeling using RANS approach[C].WIMRC 3rd International.Cavitation Forum,UK,2011.
[15]BENSOW R.Simulation of the unsteady cavitation on the Delft Twist11 foil using RANS,DES and LES[C].International Symposium on Marine Propulsors Workshop Proceedings,Hamburg,Germany,2011.
[16]FOETH E J,DOORNE C W H V,TERWISGA T V,et al.Time resolved PIV and flow visualization of 3D sheet cavitation[J].Experiments in Fluids,2006,40(4):503-513.
[17]FOETH E J,TERWISGA T V,DOORNE C W H V.On the collapse structure of an attached cavity on a three-dimensional hydrofoil[J].Journal of Fluids Engineering,2008,130(7):071303.
[18]FOETH E J.The structure of three-dimensional sheet cavitation[D].Doctoral Thesis,Wageningen,The Netherlands,Delft University of Technology,2008.