NUMERICAL SIMULATION OF SHOCK WAVE DIFFRACTION OVER RIGHT ANGLE ON UNSTRUCTURED MESHES
Read the full article ';
For citation: Bulat P.V., Volkov K.N. Numerical simulation of shock wave diffraction over right angle on unstructured meshes. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 2, pp. 354–362. doi:10.17586/2226-1494-2016-16-2-354-362
Subject of Research. Numerical simulation results and investigation of shock wave diffraction of differentintensity on the flat right angleare presented. Method. The numerical model is based on the solution of unsteadyEuler equations for inviscid compressible gas. The finite volume method and explicit WENO-type difference scheme of the third-order of accuracyare used. Convective fluxesare calculated independently for each direction with the approximate Riemann solver(HLLC method). Time integration is performed with the Runge-Kutta method of the third order. Main Results. Flow structure and flowquantitative characteristicshave beendetermined. To visualize and interpret the results of numerical calculations theprocedure of identification and classification of gas-dynamic discontinuities has beenappliedbased on the use of dynamic compatibility conditions and methods of digital image processing. The results of calculations have beenpresented in the form of numerical shadow pictures, schlieren images and interferograms, and compared with the optical observations. Significantly better agreement with the experimental data has beendemonstrated as compared toconventionalnumerical methods. Application of numerical methods of high order accuracy has yielded a numerical solution which is free from non-physicaloscillations on the shock waves with minimal smearingoverdifference cells. Practical Relevance. The study of shock-wave phenomena is of interest for the solution of problems related to the impact of shock waves on the design elements, the operation of pulsed gas-dynamic devices, the use of shock waves in technological processes. Supersonic flows around angle configurations lead to interference and diffraction phenomena complicated by flow separation. These effects make complexthe calculation of such phenomena using conventional numericalmethods. The problem ofthe results interpretation is not less complicated one,as well, in particular, identification of gas-dynamic discontinuities.
Acknowledgements. The study was sponsored by the Ministry of Education and Science of the Russian Federation (agreement No 14.575.21.0057, unique applied research identifier RFMEFI57514X0057)
1. Zasukhin O.N., Bulat P.V., Prodan N.V. Development of methods base pressure. Fundamental'nye Issledovaniya, 2012, no. 6–1, pp. 273–279.
2. Zasukhin O.N., Bulat P.V., Prodan N.V. History of experimental research base pressure. Fundamental'nye Issledovaniya, 2011, no. 12–3, pp. 670–674.
3. Zasukhin O.N., Bulat P.V., Prodan N.V. Base pressure oscilations. Fundamental'nye Issledovaniya, 2012, no. 3–1, pp. 204–207.
4. Takayama K., Inoue O. Shock wave diffraction over a 90 degree sharp corner. Shock Waves, 1991, vol. 1, no. 4, pp. 301–312. doi: 10.1007/BF01418886
5. Bazhenova T.V., Gvozdeva L.G., Nettleton M.A. Unsteady interactions of shock waves. Progress in Aerospace Sciences, 1984, vol. 21, no. C, pp. 249–331. doi: 10.1016/0376-0421(84)90007-1
6. Tugazakov R.Ya. Effect of unsteady effects on the separation of supersonic flow from the aft edge of the streamlined body. TsAGI Science Journal, 2004, vol. 35, no. 1–2, pp. 21–31. (In Russian)
7. Skews B.W. The perturbed region behind a diffracting shock wave. Journal of Fluid Mechanics, 1967, vol. 29, no. 4, pp. 705–719. doi: 10.1017/S0022112067001132
8. Skews B.W., Law C., Muritala A., Bode S. Shear layer behavior resulting from shock wave diffraction. Experiments in Fluids, 2012, vol. 52, no. 2, pp. 417–424. doi: 10.1007/s00348-011-1233-9
9. Gnani F., Lo K.H., Zare-Behtash H., Kontis K. Experimental investigation on shock wave diffraction over sharp and curved splitters. Acta Astronautica, 2014, vol. 99, no. 1, pp. 143–152. doi: 10.1016/j.actaastro.2014.02.018
10. Hillier R. Computation of shock wave diffraction at a ninety degrees convex edge. Shock Waves, 1991, vol. 1, no. 2, pp. 89–98. doi: 10.1007/BF01414904
11. Sun M., Takayama J. The formation of a secondary shock wave behind a shock wave diffracting at a convex corner. Shock Waves, 1997, vol. 7, no. 5, pp. 287–295.
12. Genin F., Fryxell B., Menon S. Simulation of detonation propagation in turbulent gas-solid reactive mixtures. Proc. 41st AIAA/ASME/ASEE Joint Propulsion Conference and Exhibit. Tucson, AZ, 2005, art. 2005-3967.
13. Ray M.P., Puranik B.P., Bhandarkar U.V. Development and assessment of several high-resolution schemes for compressible Euler equations. International Journal of Computational Methods, 2014, vol. 11, no. 1, art. 1350049. doi: 10.1142/S0219876213500497
14. Quirk J.J. A cartesian grid approach with hierarchical refinement for compressible flows. ICASE Technical Report No. 94-31017, 1994.
15. Keats W.A., Lien F.-S. Two-dimensional anisotropic Cartesian mesh adaptation for the compressible Euler equations. International Journal for Numerical Methods in Fluids, 2004, vol. 46, no. 11, pp. 1099–1125. doi: 10.1002/fld.780
16. Yang J.-Y., Muljadi B.P. Simulation of shock wave diffraction over 90º sharp corner in gases of arbitrary statistics. Journal of Statistical Physics, 2011, vol. 145, no. 6, pp. 1674–1688. doi: 10.1007/s10955-011-0355-z
17. Reeves J.O., Skews B.W. Unsteady three-dimensional compressible vortex flows generated during shock wave diffraction. Shock Waves, 2012, vol. 22, no. 2, pp. 161–172. doi: 10.1007/s00193-012-0353-3
18. Srivastava R.S. On the vorticity distribution over a normal diffracted shock for small and large bends. Shock Waves, 2013, vol. 23, no. 5, pp. 525–528. doi: 10.1007/s00193-013-0434-y
19. Kontzialis C.V. Positivity-preserving limiters for discontinuous Galerkin discretizations on unstructured meshes. Proc. 20th AIAA Computational Fluid Dynamics Conference. Honolulu, USA, 2011, art. 2011-3836.
20. Speares W., Berzins M. A 3D unstructured mesh adaptation algorithm for time-dependent shock-dominated problems. International Journal for Numerical Methods in Fluids, 1997, vol. 25, no. 1, pp. 81–104.
21. Ripley R.C., Lien F.-S., Yovanovich M.M. Numerical simulation of shock diffraction on unstructured meshes. Computers and Fluids, 2006, vol. 35, no. 10, pp. 1420–1431. doi: 10.1016/j.compfluid.2005.05.001
22. Skews B.W. Shock wave diffraction on multi-facetted and curved walls. Shock Waves, 2005, vol. 14, no. 3, pp. 137–146. doi: 10.1007/s00193-005-0266-5
23. Banks J.W., Henshaw W.D., Schwendeman D.W., Kapila A.K. A study of detonation propagation and diffraction with compliant confinement. Combustion Theory and Modeling, 2010, vol. 12, no. 4, pp. 769–808. doi: 10.1080/13647830802123564
24. Abate G., Shyy W. Dynamic structure of confined shocks undergoing sudden expansion. Progress in Aerospace Sciences, 2002, vol. 38, no. 1, pp. 23–42. doi: 10.1016/S0376-0421(01)00016-1
25. Shyy W., Krishnamurty V. Compressibility effect in modeling complex turbulent flows. Progress in Aerospace Sciences, 1997, vol. 33, no. 9–10, pp. 587–645.
26. Bazarov S.B. Image processing in CFD. Proc. 8th International Conference on Computer Graphics and Visualization, GRAPHICON 1998. Moscow, Russia, 1998, pp. 258–264.
27. Volkov K.N., Deryugin Yu.N., Emel'yanov V.N., Kozelkov A.S., Teterina I.V. Raznostnye Skhemy v Zadachakh Gazovoi Dinamiki na Nestrukturirovannykh Setkakh [Difference Schemes in Gas Dynamic Problems on Unstructured Grids]. Moscow, Fizmatlit Publ., 2014, 412 p.
28. 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. 6, p. 1582. doi: 10.1007/s10891-015-1346-8
29. 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. 1203–1209. doi: 10.1007/s10891-015-1301-8
30. 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.
31. Van-Dyke M. Album of Fluid Motion. Parabolic Press, 1982, 176 p.
32. Liang S.M., Chen H. Flow visualization of numerically simulated blast waves discharging from open-ended duct. AIAA Journal, 2003, vol. 41, no. 12, pp. 2420–2428.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License