DOI: 10.17586/2226-1494-2016-16-3-550-558


NUMERICAL SIMULATION OF SHOCK WAVE REFRACTION ON INCLINED CONTACT DISCONTINUITY

P. V. Bulat, K. N. Volkov


Read the full article 
Article in Russian

For citation: Bulat P.V., Volkov K.N. Numerical simulation of shock wave refraction on inclined contact discontinuity. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 3, pp. 550–558. doi: 10.17586/2226-1494-2016-16-3-550-558

Abstract

We consider numerical simulation of shock wave refraction on plane contact discontinuity, separating two gases with different density. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes, implemented on unstructured meshes. Integration over time is performed with the use of the third-order Runge–Kutta stepping procedure. The procedure of identification and classification of gas dynamic discontinuities based on conditions of dynamic consistency and image processing methods is applied to visualize and interpret the results of numerical calculations. The flow structure and its quantitative characteristics are defined. The results of numerical and experimental visualization (shadowgraphs, schlieren images, and interferograms) are compared.


Keywords: numerical simulation, refraction, shock wave, contact discontinuity, visualization, level function method

Acknowledgements. The study was sponsored by the Ministry of Education and Science of the Russian Federation (agreement No14.575.21.0057, a unique identifier applied research RFMEFI57514X0057)

References

1. Uskov V.N., Bulat P.V., Arkhipova L.P. Gas-dynamic discontinuity conception. Research Journal of Applied Sciences, Engineering and Technology, 2014, vol. 8, no. 22, pp. 2255–2259.
2. Bulat P.V., Uskov V.N. Shock and detonation wave in terms of view of the theory of interaction gasdynamic discontinuities. Life Science Journal, 2014, vol. 11, no. 8, pp. 307–310.
3. Uskov V.N., Bulat P.V., Arkhipova L.P. Classification of gas-dynamic discontinuities and their interference problems. Research Journal of Applied Sciences, Engineering and Technology, 2014, vol. 8, no. 22, pp. 2248–2254.
4. Jahn R.G. The refraction of shock waves at a gaseous interface. Journal of Fluid Mechanics, 1956, vol. 1, no. 5, pp. 457–489. doi: 10.1017/S0022112056000299
5. Znamenskaya I.A., Ivanov I.E., Koroteeva E.Yu., Orlov D.M. Gas-dynamic phenomena accompanying shock-wave interactions with the cooling plasma of a pulsed surface discharge. Doklady Physics, 2011, vol. 56, no. 8, pp. 423–426. (In Russian). doi: 10.1134/S1028335811080064
6. Abd-El-Fattah A.M., Henderson L.F. Shock waves at a fast-slow gas interface. Journal of Fluid Mechanics, 1978, vol. 86, no. 1, pp. 15–32. doi: 10.1017/S0022112078000981
7. Abd-El-Fattah A.M., Henderson L.F. Shock waves at a slow-fast gas interface. Journal of Fluid Mechanics, 1978, vol. 89, no. 1, pp. 79–95. doi: 10.1017/S0022112078002475
8. Henderson L.F. On the refraction of shock waves. Journal of Fluid Mechanics, 1989, vol. 198, pp. 365–386. doi: 10.1017/S0022112089000170
9. Henderson L.F., Colella P., Puckett E.G. On the refraction of shock waves at a slow-fast gas interface. Journal of Fluid Mechanics, 1991, vol. 224, pp. 1–27.
10. Nouragliev R.R., Sushchikh S.Y., Dinh T.N. Theofanous T.G. Shock wave refraction patterns at interfaces. International Journal of Multiphase Flow, 2005, vol. 31, no. 9, pp. 969–995. doi: 10.1016/j.ijmultiphaseflow.2005.04.001
11. Samtaney R., Zabusky N.J. On shock polar analysis and analytical expressions for vorticity deposition in shock-accelerated density stratified interfaces. Physics of Fluids, 1993, vol. 5, no. 6, pp. 1285–1287.
12. Samtaney R., Pullin D.I. On initial-value and self-similar solutions of the compressible Euler equations. Physics of Fluids, 1996, vol. 8, no. 10, pp. 2650–2655.
13. Samtaney R. Suppression of the Richtmyer–Meshkov instability in the presence of a magnetic field. Physics of Fluids, 2003, vol. 15, no. 8, pp. L53–L56. doi: 10.1063/1.1591188
14. Wheatley V., Pullin D.I., Samtaney R. Regular shock refraction at an oblique planar density interface in magnetohydrodynamics. Journal of Fluid Mechanics, 2005, vol. 522, pp. 179–214. doi: 10.1017/S0022112004001880
15. Zeng S., Takayama K. On the refraction of shock wave over a slow-fast gas interface. Acta Astronautica, 1996, vol. 38, no. 11, pp. 829–838. doi: 10.1016/S0094-5765(96)00096-3
16. Yang X., Chern I.-L., Zabusky N.J., Samtaney R., Hawley J.F. Vorticity generation and evolution in shock-accelerated density-stratified interfaces. Physics of Fluids, 1992, vol. 4, no. 7, pp. 1531–1540.
17. Delmont P., Keppens R., van der Holst B. An exact Riemann solver based solution for regular shock refraction. Journal of Fluid Mechanics, 2009, vol. 627, pp. 33–53. doi: 10.1017/S0022112009006028
18. Pember R.B., Anderson R.W. Comparison of direct Eulerian Godunov and Lagrange plus remap, artificial viscosity schemes. Proc. 15th AIAA Computational Fluid Dynamics Conference. Anaheim, USA, 2001, no. 2001-2644.
19. Samtaney R., Meiron D.I. Hypervelocity Richtmyer–Meshkov instability. Physics of Fluids, 1997, vol. 9, no. 6, pp. 1783–1803.
20. Samtaney R. Visualization, extraction and quantification of discontinuities in compressible flows. Technical Report NASA No. 99-002, 1999.
21. Banuti D.T., Grabe M., Hannemann K. Steady shock refraction in hypersonic ramp flow. Proc. 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. San Francisco, 2011, no. 2011-2215. doi: 10.2514/6.2011-2215
22. Brouillette M. The Richtmyer–Meshkov instability. Annual Review of Fluid Mechanics, 2002, vol. 34, pp. 445–468. doi: 10.1146/annurev.fluid.34.090101.162238
23.
Dutta S., Glimm J., Grove J.W., Sharp D.H., Zhang Y. Error comparison in tracked and untracked spherical simulations. Computers and Mathematics with Applications, 2004, vol. 48, no. 10–11, pp. 1733–1747. doi: 10.1016/j.camwa.2003.08.014
24. Liu T.C., Khoo B.C., Yeo K.S. The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas-gas and gas-water cases. Computers and Fluids, 2001, vol. 30, no. 3, pp. 291–314. doi: 10.1016/S0045-7930(00)00022-0
25. Liu T.C., Khoo B.C., Yeo K.S. The simulation of compressible multi-medium flow. II. Applications to 2D underwater shock refraction. Computers and Fluids, 2001, vol. 30, no. 3, pp. 315–337. doi: 10.1016/S0045-7930(00)00021-9
26. Osher S.J., Fedkiw R.P. Level Set Method and Dynamic Implicit Surfaces. New York: Springer, 2003, 273 p. doi: 10.1007/b98879
27. Burago N.G., Kukudzhanov V.N. Overview of contact algorithms. Mechanics of Solids, 2005, vol. 40, no. 1, 45–87. (In Russian)
28. Fang B., Wang Y.-G., Yuan H. Reflection and refraction of shocks on an interface with a reflected rarefaction wave. Journal of Mathematical Physics, 2011, vol. 52, no. 7, art. 073702. doi: 10.1063/1.3600714
29. Volkov K.N., Deryugin Yu.N., Emel'yanov V.N., Kozelkov A.S., Teterina I.V. Difference Schemes in Gas Dynamic Problems on Unstructured Grids. Moscow, Fizmatlit Publ., 2014, 416 p. (In Russian)
30. Bulat P.V., Volkov K.N. Simulation of supersonic flow in a channel with a step on nonstructured meshes with the use of the WENO scheme. Journal of Engineering Physics and Thermophysics, 2015, vol. 88, no. 4, pp. 945–950. doi: 10.1007/s10891-015-1263-x
31. Bulat P.V., Volkov K.N. Use of WENO schemes for simulation of the reflected shock wave-boundary layer interaction. Journal of Engineering Physics and Thermophysics, 2015, vol. 88, no. 5, pp. 1163–1170. doi: 10.1007/s10891-015-1301-8
32. Vorozhtsov E.V. Klassifikatsiya Razryvov Techeniya Gaza kak Zadacha Raspoznavaniya Obrazov: Preprint № 2386 [Classification of the Gas Flow Discontinuities as a Pattern Recognition Task: Preprint № 2386]. Novosibirsk, ITPM Publ., 1986, no. 23–86.
33. Schalkoff R.J. Digital Image Processing and Computer Vision. New York, John Wiley & Sons, 1988, 489 p.
 



Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2018 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.

Яндекс.Метрика