Large-Eddy Simulation of the Three-Dimensional Experiment on Richtmyer-Meshkov Instability Induced Turbulence

Author(s)
Jingsong Bai,
Tao Wang,
Kun Liu,
Lei Li,
Min Zhong,
Yang Jiang,
Mi Tang,
Jidong Yu,
Xiaoyang Pei,
Ping Li

Affiliation(s)

Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, China.

National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, China.

Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, China.

National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, China.

ABSTRACT

A program MVFT3D of large-eddy simulation is developed and performed to solve the multi compressible Navier- Stokes equations. The SGS dissipation and molecular viscosity dissipation have been analyzed, and the former is much larger than the later. Our test shows that the SGS dissipation of Vreman model is smaller than the Smagorinsky model. We mainly simulate the experiment of fluid instability of shock-accelerated interface by Poggi in this paper. The decay of the turbulent kinetic energy before the first reflected shock wave–mixing zone interaction and its strong enhancement by re-shocks are presented in our numerical simulations. The computational mixing zone width under double re-shock agreement well with the experiment, and the decaying law of the turbulent kinetic energy is consistent with Mohamed and Larue’s investigation. Also, by using MVFT3D we give some simulation results of the inverse Chevron model from AWE. The numerical simulations presented in this paper allow us to characterize and better understand the Richtmyer-Meshkov instability induced turbulence, and the code MVFT3D is validated.

A program MVFT3D of large-eddy simulation is developed and performed to solve the multi compressible Navier- Stokes equations. The SGS dissipation and molecular viscosity dissipation have been analyzed, and the former is much larger than the later. Our test shows that the SGS dissipation of Vreman model is smaller than the Smagorinsky model. We mainly simulate the experiment of fluid instability of shock-accelerated interface by Poggi in this paper. The decay of the turbulent kinetic energy before the first reflected shock wave–mixing zone interaction and its strong enhancement by re-shocks are presented in our numerical simulations. The computational mixing zone width under double re-shock agreement well with the experiment, and the decaying law of the turbulent kinetic energy is consistent with Mohamed and Larue’s investigation. Also, by using MVFT3D we give some simulation results of the inverse Chevron model from AWE. The numerical simulations presented in this paper allow us to characterize and better understand the Richtmyer-Meshkov instability induced turbulence, and the code MVFT3D is validated.

Cite this paper

J. Bai, T. Wang, K. Liu, L. Li, M. Zhong, Y. Jiang, M. Tang, J. Yu, X. Pei and P. Li, "Large-Eddy Simulation of the Three-Dimensional Experiment on Richtmyer-Meshkov Instability Induced Turbulence,"*International Journal of Astronomy and Astrophysics*, Vol. 2 No. 1, 2012, pp. 28-36. doi: 10.4236/ijaa.2012.21005.

J. Bai, T. Wang, K. Liu, L. Li, M. Zhong, Y. Jiang, M. Tang, J. Yu, X. Pei and P. Li, "Large-Eddy Simulation of the Three-Dimensional Experiment on Richtmyer-Meshkov Instability Induced Turbulence,"

References

[1] P. B. Putanik, J. G. Oakley, M. H. Anderson and R. Bonazza, “Experimental Study of the Richtmyer-Mesh- kov Instability Induced by a Mach 3 Shock Wave,” Shock Waves, Vol. 13, No. 6, 2004, pp. 413-429.

[2] D. Arnett, “The Role of Mixing in Astrophysics,” Astrophysical Journal Supplement Series, Vol. 127, No. 2, 2000, pp. 213-217. doi:10.1086/313364

[3] M. Boulet and J. Griffond, “Three-Dimensional Numerical Simulation of Experiments on Richtmyer-Meshkov Induced Mixing with Reshock,” 10th International Work- shop on the Physics of Compressible Turbulent Mixing (IWPCTM), Paris, 17-21 July 2006.

[4] V. I. Kozlov, “Simulation of SW/Turbulence Interactions,” 10th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM), Paris, 17-21 July 2006.

[5] B. Thornber, D. Drikakis and D. Youngs, “High Resolution Method for Planar Richtmyer-Meshkov Instabilities,” 10th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM), Paris, 17-21 July 2006.

[6] F. Poggi, M. H. Thorembey and G. Rodriguez, “Velocity Measurements in Turbulent Gaseous Mixtures Induced by Richtmyer-Meshkov Instability,” Physics of Fluids, Vol. 10, No. 11, 1998, pp. 2698-2712. doi:10.1063/1.869794

[7] M. Claude and G. Serge, “Two-Dimensional Navier- Stokes Simulations of Gaseous Mixtures Induced by Richtmyer-Meshkov Instability,” Physics of Fluids, Vol. 12, No. 7, 2000, pp. 1783-1798.

[8] J. S. Bai, J. H. Liu, T. Wang, L. Y. Zou, P. Li and D. W. Tan, “Investigation of the Richtmyer-Meshkov Instability with Double Perturbation Interface in Nonuniform Flows,” Physical Review E, Vol. 81, No. 5, 2010, Article ID: 056302. doi:10.1103/PhysRevE.81.056302

[9] J. S. Bai, L. Y. Zou, T. Wang, K. Liu, W. B. Huang, J. H. Liu, P. Li, D. W. Tan and C. L. Liu, “Experimental and Numerical Study of the Shcok-Accelerated Elliptic Heavy Gas Cylinders,” Physical Review E, Vol. 82, No. 5, 2010, Article ID: 056318. doi:10.1103/PhysRevE.82.056318

[10] J. S. Bai, P. Li, T. Wang, B. Xie, M. Zhong and S. H. Chen, “Computation of Compressible Multi-Viscosity- Fluid Flows,” Explosion and Shock Waves, Vol. 27, No. 6, 2007, pp. 515-521 (in Chinese)

[11] W. Vreman, “An Eddy-Viscosity Subbgrid-Scale Model for Tubulent Shear Flow: Algebraic Theory and Applications,” Phys fluids, Vol. 16, No. 10, 2004, pp. 3670-3681. doi:10.1063/1.1785131

[12] J. Smagorinsky, “General Circulation Experiments with the Primitive Equations,” Monthly Weather Review, Vol. 91, No. 3, 1963, pp. 99-164. doi:10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

[13] K. R. Bates, N. Nikiforakis and H. D. Richtmyer-Mesh- kov, “Instability Induced by the Interaction of a Shock Wave with a Rectangular Block of SF6,” Phys Fluids, Vol. 19, No. 3, 2007, Article ID: 036101, pp. 1-16.

[14] D. A. Holder and C. J. Barton, “Shock Tube Richtmyer- Meshkov Experiments: Inverse Chevron and Half Height,” 9th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM), July 2004, p. 43.

[15] B. Vreman, B. Geurts and H. Kuerten, “Large-Eddy Simulation of the Turbulent Mixing Layer,” Journal of Fluid Mechanics, Vol. 339, 1997, pp. 357-362. doi:10.1017/S0022112097005429

[16] F. F. Grinstein and G. Karniadakis, “Alternative LES and Hybrid RANS/LES,” Journal of Fluids Engineering, Vol. 124, No. 4, 2002, pp. 821-827. doi:10.1115/1.1518700

[17] J. S. Bai, T. Wang, L. Y. Zou, et al., “Numerical Simulation of the Hydrodynamic Instability Experiments and Flow Mixing,” Science in China Series G, Vol. 52, No. 12, 2009, pp. 2027-2040. doi:10.1007/s11433-009-0277-9

[18] D. K. Lilly, “The Representation of Small-Scale Tubulence in Numerical Simulation Experiments,” In: H. H. Goldstine, Ed., Proceedings of IBM Scientific Computing Symposium on Environmental Sciences, Yorktown Heights, New York, 1967, pp. 195-210

[19] U. Piomelli, W. H. Cabot, P. Moin, et al., “Subgrid-Scale Backscatter in Turbulent and Transitional Flows,” Physical Fluids A, Vol. 3, No. 7, 1991, pp. 1766-1771. doi:10.1063/1.857956

[20] B. Wang, H. Q. Zhang and X. L. Wang, “On Sub-Grid Scale Turbulence Characteristics,” Engineering Mechanics, Vol. 23, No. 2, 2006, pp. 47-51 (in Chinese).

[21] T. Wang, J. S. Bai, P. Li and K. Liu, “Large-Eddy Simulations of the Richtmyer-Meshkov Instability of Rectangular Interfaces Accelerated by Shock Waves,” Science China Physics, Mechanics & Astronomy, Vol. 53, No. 5, 2009, pp. 905-914.

[22] M. S. Mohamed and J. C. Larue, “The Decay Power Law in Grid-Generated Turbulence,” Journal of Fluid Mechanics, Vol. 219, 1990, pp. 195-201. doi:10.1017/S0022112090002919

[1] P. B. Putanik, J. G. Oakley, M. H. Anderson and R. Bonazza, “Experimental Study of the Richtmyer-Mesh- kov Instability Induced by a Mach 3 Shock Wave,” Shock Waves, Vol. 13, No. 6, 2004, pp. 413-429.

[2] D. Arnett, “The Role of Mixing in Astrophysics,” Astrophysical Journal Supplement Series, Vol. 127, No. 2, 2000, pp. 213-217. doi:10.1086/313364

[3] M. Boulet and J. Griffond, “Three-Dimensional Numerical Simulation of Experiments on Richtmyer-Meshkov Induced Mixing with Reshock,” 10th International Work- shop on the Physics of Compressible Turbulent Mixing (IWPCTM), Paris, 17-21 July 2006.

[4] V. I. Kozlov, “Simulation of SW/Turbulence Interactions,” 10th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM), Paris, 17-21 July 2006.

[5] B. Thornber, D. Drikakis and D. Youngs, “High Resolution Method for Planar Richtmyer-Meshkov Instabilities,” 10th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM), Paris, 17-21 July 2006.

[6] F. Poggi, M. H. Thorembey and G. Rodriguez, “Velocity Measurements in Turbulent Gaseous Mixtures Induced by Richtmyer-Meshkov Instability,” Physics of Fluids, Vol. 10, No. 11, 1998, pp. 2698-2712. doi:10.1063/1.869794

[7] M. Claude and G. Serge, “Two-Dimensional Navier- Stokes Simulations of Gaseous Mixtures Induced by Richtmyer-Meshkov Instability,” Physics of Fluids, Vol. 12, No. 7, 2000, pp. 1783-1798.

[8] J. S. Bai, J. H. Liu, T. Wang, L. Y. Zou, P. Li and D. W. Tan, “Investigation of the Richtmyer-Meshkov Instability with Double Perturbation Interface in Nonuniform Flows,” Physical Review E, Vol. 81, No. 5, 2010, Article ID: 056302. doi:10.1103/PhysRevE.81.056302

[9] J. S. Bai, L. Y. Zou, T. Wang, K. Liu, W. B. Huang, J. H. Liu, P. Li, D. W. Tan and C. L. Liu, “Experimental and Numerical Study of the Shcok-Accelerated Elliptic Heavy Gas Cylinders,” Physical Review E, Vol. 82, No. 5, 2010, Article ID: 056318. doi:10.1103/PhysRevE.82.056318

[10] J. S. Bai, P. Li, T. Wang, B. Xie, M. Zhong and S. H. Chen, “Computation of Compressible Multi-Viscosity- Fluid Flows,” Explosion and Shock Waves, Vol. 27, No. 6, 2007, pp. 515-521 (in Chinese)

[11] W. Vreman, “An Eddy-Viscosity Subbgrid-Scale Model for Tubulent Shear Flow: Algebraic Theory and Applications,” Phys fluids, Vol. 16, No. 10, 2004, pp. 3670-3681. doi:10.1063/1.1785131

[12] J. Smagorinsky, “General Circulation Experiments with the Primitive Equations,” Monthly Weather Review, Vol. 91, No. 3, 1963, pp. 99-164. doi:10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

[13] K. R. Bates, N. Nikiforakis and H. D. Richtmyer-Mesh- kov, “Instability Induced by the Interaction of a Shock Wave with a Rectangular Block of SF6,” Phys Fluids, Vol. 19, No. 3, 2007, Article ID: 036101, pp. 1-16.

[14] D. A. Holder and C. J. Barton, “Shock Tube Richtmyer- Meshkov Experiments: Inverse Chevron and Half Height,” 9th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM), July 2004, p. 43.

[15] B. Vreman, B. Geurts and H. Kuerten, “Large-Eddy Simulation of the Turbulent Mixing Layer,” Journal of Fluid Mechanics, Vol. 339, 1997, pp. 357-362. doi:10.1017/S0022112097005429

[16] F. F. Grinstein and G. Karniadakis, “Alternative LES and Hybrid RANS/LES,” Journal of Fluids Engineering, Vol. 124, No. 4, 2002, pp. 821-827. doi:10.1115/1.1518700

[17] J. S. Bai, T. Wang, L. Y. Zou, et al., “Numerical Simulation of the Hydrodynamic Instability Experiments and Flow Mixing,” Science in China Series G, Vol. 52, No. 12, 2009, pp. 2027-2040. doi:10.1007/s11433-009-0277-9

[18] D. K. Lilly, “The Representation of Small-Scale Tubulence in Numerical Simulation Experiments,” In: H. H. Goldstine, Ed., Proceedings of IBM Scientific Computing Symposium on Environmental Sciences, Yorktown Heights, New York, 1967, pp. 195-210

[19] U. Piomelli, W. H. Cabot, P. Moin, et al., “Subgrid-Scale Backscatter in Turbulent and Transitional Flows,” Physical Fluids A, Vol. 3, No. 7, 1991, pp. 1766-1771. doi:10.1063/1.857956

[20] B. Wang, H. Q. Zhang and X. L. Wang, “On Sub-Grid Scale Turbulence Characteristics,” Engineering Mechanics, Vol. 23, No. 2, 2006, pp. 47-51 (in Chinese).

[21] T. Wang, J. S. Bai, P. Li and K. Liu, “Large-Eddy Simulations of the Richtmyer-Meshkov Instability of Rectangular Interfaces Accelerated by Shock Waves,” Science China Physics, Mechanics & Astronomy, Vol. 53, No. 5, 2009, pp. 905-914.

[22] M. S. Mohamed and J. C. Larue, “The Decay Power Law in Grid-Generated Turbulence,” Journal of Fluid Mechanics, Vol. 219, 1990, pp. 195-201. doi:10.1017/S0022112090002919