Experimental and Numerical Study of The Shock-Accelerated Elliptic Heavy Gas Cylinders
We studied the evolution of elliptic heavy SF6
gas cylinder surrounded by air when accelerated by a planar
Mach 1.25 shock. A multiple dynamics imaging technology has
been used to obtain one image of the experimental initial
conditions and five images of the time evolution of elliptic
cylinder. We compared the width and height of the circular and
two kinds of elliptic gas cylinders, and analyzed the vortex
strength of the elliptic ones. Simulations are in very good
agreement with the experiments, but due to the different initial
gas cylinder shapes, a certain difference of the initial density
peak and distribution exists between the circular and elliptic
gas cylinders, and the latter initial state is more sensitive and
more inenarrable.
[1] J. W. Grove, R. Holmes, D. H. Sharp, Y. Yang, and Q. Zhang,
"Quantitative theory of Richtmyer-Meshkov instability," Phys. Rev. Lett.,
vol. 71, pp. 3473-3476, Nov. 1993.
[2] K. O. Mikaelian, "Growth rate of the Richtmyer-Meshkov instability at
shocked interfaces," Phys. Rev. Lett., vol. 71, pp. 2903-2906, Nov. 1993.
[3] D. Hill, C. Pantano, and D. Pullin, "Large-eddy simulation and multiscale
modelling of a Richtmyer-Meshkov instability with reshock," J. Fluid
Mech., vol. 557, pp. 29-61, Jun. 2006.
[4] K. O. Mikaelian, "Analytic Approach to Nonlinear Rayleigh-Taylor and
Richtmyer-Meshkov Instabilities," Phys. Rev. Lett., vol. 80, pp. 508-511,
Jan. 1998.
[5] S. Gupta, S Zhang, and N. J. Zabusky, "Shock interaction with a heavy
gas cylinder: Emergence of vortex bilayers and vortex-accelerated
baroclinic circulation generation," Laser and Particle Beams, vol. 21, pp.
443-448, Apr. 2003.
[6] K. Prestridge, P. Vorobieff, P. Rightley, and R. F. Benjamin, "Validation
of an Instability Growth Model Using Particle Image Velocimetry
Measurements," Phys. Rev. Lett., vol. 84, pp. 4353-4356, May 2000.
[7] N. J. Zabusky, and S. Zhang, "Shock-planar curtain interactions in two
dimensions: Emergence of vortex double layers, vortex projectiles, and
decaying stratified turbulence," Phys. Fluids, vol. 14, pp. 419-422, 2002.
[8] C. Tomkins, K. Prestridge, P. Rightley, and M. Marry-Lyon, "A
quantitative study of the interaction of two Richtmyer-Meshkov-unstable
gas cylinders," Phys. Fluids, vol. 15, pp. 986-1004, Mar. 2003.
[9] S. Kumar, P. Vorobieff, G. Orlice, A. Palekar, C. Tomkins, C.
Goodenough, M. Marry-Lyon, K. Prestridge, and R. F. Benjamin,
"Complex flow morphologies in shock-accelerated gaseous flows,"
Physica D, vol. 235, pp. 21-28, Nov. 2007.
[10] G. Layes, C. Mariani, G. Jourdan, L. Houas, F. Renaud, and D. Souffland,
"Experimental observations of the reflected shock effect on an accelerated
gas bubble interface," in Proc. 10th Int. Workshop on the Physics of
Compressible Turbulent Mixing, Paris, 2006.
[11] P. B. Puranik, J. G. Oakley, M. H. Anderson, and R. Bonazza,
"Experimental study of the Richtmyer-Meshkov instability induced by a
Mach 3 shock wave," Shock Waves, vol. 13, pp. 413-429, Jun. 2004.
[12] E. Meshkov, "Instability of the interface of two gases accelerated by a
shock wave," Fluid Dyn., vol. 4, pp. 101-104, 1972.
[13] J. S. Bai, J. H. Liu, and T. Wang, L. Y. Zou, P. Li, and D. W. Tan,
"Investigation of the Richtmyer-Meshkov instability with double
perturbation interface in nonuniform flows," Phys. Rev. E, vol. 81, pp.
056302, May 2010.
[14] P. Colella and P. R. Woodward, "The piecewise parabolic method (PPM)
for gas-dynamical simulations," J. Comput. Phys., vol. 54, pp. 174-201,
1984.
[15] W. Vreman, "An eddy-viscosity subgrid-scale model for turbulent shear
flow: Algebraic theory and applications," Phys. Fluids, vol. 16, pp.
3670-3681, Sep. 2004.
[16] J. S. Bai, T. Wang, P. Li, L. Y. Zou, and D. W. Tan, "Numerical analyse of
the turbulence mixing of re-shocks with a perturbation interface," Sci.
China Ser. G, vol. 39, pp. 1646-1653, Nov. 2009.
[17] C. A. Zoldi, in Applied Mathematics and Statistics, State University of
New York at Stony Brook, Doctor Dissertation, 2002.
[1] J. W. Grove, R. Holmes, D. H. Sharp, Y. Yang, and Q. Zhang,
"Quantitative theory of Richtmyer-Meshkov instability," Phys. Rev. Lett.,
vol. 71, pp. 3473-3476, Nov. 1993.
[2] K. O. Mikaelian, "Growth rate of the Richtmyer-Meshkov instability at
shocked interfaces," Phys. Rev. Lett., vol. 71, pp. 2903-2906, Nov. 1993.
[3] D. Hill, C. Pantano, and D. Pullin, "Large-eddy simulation and multiscale
modelling of a Richtmyer-Meshkov instability with reshock," J. Fluid
Mech., vol. 557, pp. 29-61, Jun. 2006.
[4] K. O. Mikaelian, "Analytic Approach to Nonlinear Rayleigh-Taylor and
Richtmyer-Meshkov Instabilities," Phys. Rev. Lett., vol. 80, pp. 508-511,
Jan. 1998.
[5] S. Gupta, S Zhang, and N. J. Zabusky, "Shock interaction with a heavy
gas cylinder: Emergence of vortex bilayers and vortex-accelerated
baroclinic circulation generation," Laser and Particle Beams, vol. 21, pp.
443-448, Apr. 2003.
[6] K. Prestridge, P. Vorobieff, P. Rightley, and R. F. Benjamin, "Validation
of an Instability Growth Model Using Particle Image Velocimetry
Measurements," Phys. Rev. Lett., vol. 84, pp. 4353-4356, May 2000.
[7] N. J. Zabusky, and S. Zhang, "Shock-planar curtain interactions in two
dimensions: Emergence of vortex double layers, vortex projectiles, and
decaying stratified turbulence," Phys. Fluids, vol. 14, pp. 419-422, 2002.
[8] C. Tomkins, K. Prestridge, P. Rightley, and M. Marry-Lyon, "A
quantitative study of the interaction of two Richtmyer-Meshkov-unstable
gas cylinders," Phys. Fluids, vol. 15, pp. 986-1004, Mar. 2003.
[9] S. Kumar, P. Vorobieff, G. Orlice, A. Palekar, C. Tomkins, C.
Goodenough, M. Marry-Lyon, K. Prestridge, and R. F. Benjamin,
"Complex flow morphologies in shock-accelerated gaseous flows,"
Physica D, vol. 235, pp. 21-28, Nov. 2007.
[10] G. Layes, C. Mariani, G. Jourdan, L. Houas, F. Renaud, and D. Souffland,
"Experimental observations of the reflected shock effect on an accelerated
gas bubble interface," in Proc. 10th Int. Workshop on the Physics of
Compressible Turbulent Mixing, Paris, 2006.
[11] P. B. Puranik, J. G. Oakley, M. H. Anderson, and R. Bonazza,
"Experimental study of the Richtmyer-Meshkov instability induced by a
Mach 3 shock wave," Shock Waves, vol. 13, pp. 413-429, Jun. 2004.
[12] E. Meshkov, "Instability of the interface of two gases accelerated by a
shock wave," Fluid Dyn., vol. 4, pp. 101-104, 1972.
[13] J. S. Bai, J. H. Liu, and T. Wang, L. Y. Zou, P. Li, and D. W. Tan,
"Investigation of the Richtmyer-Meshkov instability with double
perturbation interface in nonuniform flows," Phys. Rev. E, vol. 81, pp.
056302, May 2010.
[14] P. Colella and P. R. Woodward, "The piecewise parabolic method (PPM)
for gas-dynamical simulations," J. Comput. Phys., vol. 54, pp. 174-201,
1984.
[15] W. Vreman, "An eddy-viscosity subgrid-scale model for turbulent shear
flow: Algebraic theory and applications," Phys. Fluids, vol. 16, pp.
3670-3681, Sep. 2004.
[16] J. S. Bai, T. Wang, P. Li, L. Y. Zou, and D. W. Tan, "Numerical analyse of
the turbulence mixing of re-shocks with a perturbation interface," Sci.
China Ser. G, vol. 39, pp. 1646-1653, Nov. 2009.
[17] C. A. Zoldi, in Applied Mathematics and Statistics, State University of
New York at Stony Brook, Doctor Dissertation, 2002.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56644", author = "Jing S. Bai and Li Y. Zou and Tao Wang and Kun Liu and Wen B. Huang and Jin H. Liu and Ping Li and Duo W. Tan and CangL. Liu", title = "Experimental and Numerical Study of The Shock-Accelerated Elliptic Heavy Gas Cylinders", abstract = "We studied the evolution of elliptic heavy SF6
gas cylinder surrounded by air when accelerated by a planar
Mach 1.25 shock. A multiple dynamics imaging technology has
been used to obtain one image of the experimental initial
conditions and five images of the time evolution of elliptic
cylinder. We compared the width and height of the circular and
two kinds of elliptic gas cylinders, and analyzed the vortex
strength of the elliptic ones. Simulations are in very good
agreement with the experiments, but due to the different initial
gas cylinder shapes, a certain difference of the initial density
peak and distribution exists between the circular and elliptic
gas cylinders, and the latter initial state is more sensitive and
more inenarrable.", keywords = "About four key words or phrases in alphabeticalorder, separated by commas.", volume = "5", number = "4", pages = "597-5", }
