3-D Lagrangian-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis
|
摘要
In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model(FBDCM), a turbulence model and the Zwart-Gerber-Belamri(ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures(LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet,the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage Ⅲ, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.
In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model(FBDCM), a turbulence model and the Zwart-Gerber-Belamri(ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures(LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet,the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage Ⅲ, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.
In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model(FBDCM), a turbulence model and the Zwart-Gerber-Belamri(ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures(LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet,the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage Ⅲ, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.
引文
[1]Wang Y.,Wu X.,Huang C.et al.Unsteady characteristics of cloud cavitating flow near the free surface around an axisymmetric projectile[J].International Journal of Multiphase Flow,2016,85:48-56.
[2]Arndt R.E.A.Cavitation in vortical flows[J].Annual Review of Fluid Mechanics,2002,34:143-175.
[3]Arndt R.E.A.,Arakeri V.H.,Higuchi H.Some observations of tip-vortex cavitation[J].Journal of Fluid Mechanics,1991,229:269-289.
[4]Wang Y.,Xu C.,Wu X.et al.Ventilated cloud cavitating flow around a blunt body close to the free surface[J].Physical Review Fluids,2017,2(8):084303.
[5]Arndt R.E.A.Cavitation in fluid machinery and hydraulic structures[J].Annual Review of Fluid Mechanics,1981,13:273-328.
[6]Stutz B.,Reboud J.L.Experiments on unsteady cavitation[J].Experiments in Fluids,1997,22(3):191-198.
[7]Coutier-Delgosha O.,Devillers J.F.,Pichon T.et al.Internal structure and dynamics of sheet cavitation[J].Physics of Fluids,2006,18(1):017103.
[8]Makiharju S.A.,Gabillet C.,Paik B.G.et al.Timeresolved two-dimensional X-ray densitometry of a twophase flow downstream of a ventilated cavity[J].Experiments in Fluids,2013,54(7):1561.
[9]Iyer C.O.,Ceccio S.L.The influence of developed cavitation on the flow of a turbulent shear layer[J].Physics of Fluids,2002,14(10):3414-3431.
[10]Gopalan S.,Katz J.Flow structure and modeling issues in the closure region of attached cavitation[J].Physics of Fluids,2000,12(4):895-911.
[11]Aeschlimann V.,Barre S.,Djeridi H.Velocity field analysis in an experimental cavitating mixing layer[J].Physics of Fluids,2011,23(5):055105.
[12]Ji B.,Luo X.,Amdt R.E.A.et al.Numerical simulation of three dimensional cavitation shedding dynamics with special emphasis on cavitation-vortex interaction[J].Ocean Engineering,2014,87:64-77.
[13]Long X.,Cheng H.,Ji B.et al.Numerical investigation of attached cavitation shedding dynamics around the Clark-Y hydrofoil with the FBDCM and an integral method[J].Ocean Engineering,2017,137:247-261.
[14]Dittakavi N.,Chunekar A.,Frankel S.Large eddy simulation of turbulent-cavitation interactions in a venturi nozzle[J].Journal of Fluids Engineering,2010,132(12):121301.
[15]Callenaere M.,Franc J.P.,Michel J.M.et al.The cavitation instability induced by the development of a re-entrant jet[J].Journal of Fluid Mechanics,2001,444:223-256.
[16]Peng X.X.,Ji B.,Cao Y.T.et al.Combined experimental observation and numerical simulation of the cloud cavitation with U-type flow structures on hydrofoils[J].International Journal of Multiphase Flow,2016,79:10-22.
[17]Akhatov I.,Lindau O.,Topolnikov A.et al.Collapse and rebound of a laser-induced cavitation bubble[J].Physics of Fluids,2001,13(10):2805-2819.
[18]Kolar V.Vortex identification:New requirements and limitations[J].International Journal of Heat and Fluid Flow,2007,28(4):638-652.
[19]Huang B.,Zhao Y.,Wang G.Large eddy simulation of turbulent vortex-cavitation interactions in transient sheet/cloud cavitating flows[J].Computers and Fluids,2014,92:113-124.
[20]Ji B.,Luo X.,Wu Y.et al.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.
[21]Kubota A.,Kato H.,Yamaguchi H.A new modeling of cavitating flows-a numerical study of unsteady cavitation on a hydrofoil section[J].Journal of Fluid Mechanics,1992,240:59-96.
[22]Haller G.Lagrangian coherent structures[J].Annual Review of Fluid Mechanics,2015,47:137-162.
[23]Green M.A.,Rowley C.W.,Haller G.Detection of Lagrangian coherent structures in three-dimensional turbulence[J].Journal of Fluid Mechanics,2007,572:111-120.
[24]Hu C.,Wang G.,Chen G.et al.Three-dimensional unsteady cavitating flows around an axisymmetric body with a blunt headform[J].Journal of Mechanical Science and Technology,2015,29(3):1093-1101.
[25]Tseng C.C.,Liu P.B.Dynamic behaviors of the turbulent cavitating flows based on the Eulerian and Lagtangian viewpoints[J].International Journal of Heat and Mass Transfer,2016,102:479-500.
[26]Cheng H.Y.,Long X.P.,Ji B.et al.Numerical investigation of unsteady cavitating turbulent flows around twisted hydrofoil from the Lagrangian viewpoint[J].Journal of Hydrodynamics,2016,28(4):709-712.
[27]Tang W.,Chan P.W.,Haller G.Lagrangian coherent structure analysis of terminal winds detected by lidar.Part I:Turbulence structures[J].Journal of Applied Meteorology and Climatology,2011,50(2):325-338.
[28]Dular M.,Bachert R.,Schaad C.Investigation of a reentrant jet reflection at an inclined cavity closure line[J].European Journal of Mechanics B-Fluids,2007,26(5):688-705.
[29]Zhao Y.,Wang G.,Huang B.et al.Lagrangian investigations of vortex dynamics in time-dependent cloud cavitating flows[J].International Journal of Heat and Mass Transfer,2016,93:167-174.
[30]Haller G.Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence[J].Physics of Fluids,2001,13(11):3365-3385.
[31]Huang B.,Wang G.Y.,Zhao Y.Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model[J].Journal of Hydrodynamics,2014,26(1):26-36.
[32]Zwart P.J.,Gerber A.G.,Belamri T.A two phase flow model for predicting cavitation dynamics[C].ICMF 2004International Conference on Multiphase Flow,Yokohama,Japan,2004.
[33]Long Y.,Long X.P.,Ji B.et al.Verification and validation of URANS simulations of the turbulent cavitating flow around the hydrofoil[J].Journal of Hydrodynamics,2017,29(4):610-620.
[2]Arndt R.E.A.Cavitation in vortical flows[J].Annual Review of Fluid Mechanics,2002,34:143-175.
[3]Arndt R.E.A.,Arakeri V.H.,Higuchi H.Some observations of tip-vortex cavitation[J].Journal of Fluid Mechanics,1991,229:269-289.
[4]Wang Y.,Xu C.,Wu X.et al.Ventilated cloud cavitating flow around a blunt body close to the free surface[J].Physical Review Fluids,2017,2(8):084303.
[5]Arndt R.E.A.Cavitation in fluid machinery and hydraulic structures[J].Annual Review of Fluid Mechanics,1981,13:273-328.
[6]Stutz B.,Reboud J.L.Experiments on unsteady cavitation[J].Experiments in Fluids,1997,22(3):191-198.
[7]Coutier-Delgosha O.,Devillers J.F.,Pichon T.et al.Internal structure and dynamics of sheet cavitation[J].Physics of Fluids,2006,18(1):017103.
[8]Makiharju S.A.,Gabillet C.,Paik B.G.et al.Timeresolved two-dimensional X-ray densitometry of a twophase flow downstream of a ventilated cavity[J].Experiments in Fluids,2013,54(7):1561.
[9]Iyer C.O.,Ceccio S.L.The influence of developed cavitation on the flow of a turbulent shear layer[J].Physics of Fluids,2002,14(10):3414-3431.
[10]Gopalan S.,Katz J.Flow structure and modeling issues in the closure region of attached cavitation[J].Physics of Fluids,2000,12(4):895-911.
[11]Aeschlimann V.,Barre S.,Djeridi H.Velocity field analysis in an experimental cavitating mixing layer[J].Physics of Fluids,2011,23(5):055105.
[12]Ji B.,Luo X.,Amdt R.E.A.et al.Numerical simulation of three dimensional cavitation shedding dynamics with special emphasis on cavitation-vortex interaction[J].Ocean Engineering,2014,87:64-77.
[13]Long X.,Cheng H.,Ji B.et al.Numerical investigation of attached cavitation shedding dynamics around the Clark-Y hydrofoil with the FBDCM and an integral method[J].Ocean Engineering,2017,137:247-261.
[14]Dittakavi N.,Chunekar A.,Frankel S.Large eddy simulation of turbulent-cavitation interactions in a venturi nozzle[J].Journal of Fluids Engineering,2010,132(12):121301.
[15]Callenaere M.,Franc J.P.,Michel J.M.et al.The cavitation instability induced by the development of a re-entrant jet[J].Journal of Fluid Mechanics,2001,444:223-256.
[16]Peng X.X.,Ji B.,Cao Y.T.et al.Combined experimental observation and numerical simulation of the cloud cavitation with U-type flow structures on hydrofoils[J].International Journal of Multiphase Flow,2016,79:10-22.
[17]Akhatov I.,Lindau O.,Topolnikov A.et al.Collapse and rebound of a laser-induced cavitation bubble[J].Physics of Fluids,2001,13(10):2805-2819.
[18]Kolar V.Vortex identification:New requirements and limitations[J].International Journal of Heat and Fluid Flow,2007,28(4):638-652.
[19]Huang B.,Zhao Y.,Wang G.Large eddy simulation of turbulent vortex-cavitation interactions in transient sheet/cloud cavitating flows[J].Computers and Fluids,2014,92:113-124.
[20]Ji B.,Luo X.,Wu Y.et al.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.
[21]Kubota A.,Kato H.,Yamaguchi H.A new modeling of cavitating flows-a numerical study of unsteady cavitation on a hydrofoil section[J].Journal of Fluid Mechanics,1992,240:59-96.
[22]Haller G.Lagrangian coherent structures[J].Annual Review of Fluid Mechanics,2015,47:137-162.
[23]Green M.A.,Rowley C.W.,Haller G.Detection of Lagrangian coherent structures in three-dimensional turbulence[J].Journal of Fluid Mechanics,2007,572:111-120.
[24]Hu C.,Wang G.,Chen G.et al.Three-dimensional unsteady cavitating flows around an axisymmetric body with a blunt headform[J].Journal of Mechanical Science and Technology,2015,29(3):1093-1101.
[25]Tseng C.C.,Liu P.B.Dynamic behaviors of the turbulent cavitating flows based on the Eulerian and Lagtangian viewpoints[J].International Journal of Heat and Mass Transfer,2016,102:479-500.
[26]Cheng H.Y.,Long X.P.,Ji B.et al.Numerical investigation of unsteady cavitating turbulent flows around twisted hydrofoil from the Lagrangian viewpoint[J].Journal of Hydrodynamics,2016,28(4):709-712.
[27]Tang W.,Chan P.W.,Haller G.Lagrangian coherent structure analysis of terminal winds detected by lidar.Part I:Turbulence structures[J].Journal of Applied Meteorology and Climatology,2011,50(2):325-338.
[28]Dular M.,Bachert R.,Schaad C.Investigation of a reentrant jet reflection at an inclined cavity closure line[J].European Journal of Mechanics B-Fluids,2007,26(5):688-705.
[29]Zhao Y.,Wang G.,Huang B.et al.Lagrangian investigations of vortex dynamics in time-dependent cloud cavitating flows[J].International Journal of Heat and Mass Transfer,2016,93:167-174.
[30]Haller G.Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence[J].Physics of Fluids,2001,13(11):3365-3385.
[31]Huang B.,Wang G.Y.,Zhao Y.Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model[J].Journal of Hydrodynamics,2014,26(1):26-36.
[32]Zwart P.J.,Gerber A.G.,Belamri T.A two phase flow model for predicting cavitation dynamics[C].ICMF 2004International Conference on Multiphase Flow,Yokohama,Japan,2004.
[33]Long Y.,Long X.P.,Ji B.et al.Verification and validation of URANS simulations of the turbulent cavitating flow around the hydrofoil[J].Journal of Hydrodynamics,2017,29(4):610-620.