Analysis of gas-dynamic processes and development of model of flows in hypersonic shock tube

Authors: Kuzenov V.V. , Kotov M.A. Published: 06.02.2014
Published in issue: #1(94)/2014  


Category: Simulation of Processes  
Keywords: shock tube, gas dynamics equations, nonlinear quasimonotonous compact difference scheme, Runge-Kutta multistep method

The paper considers the simplified one-dimensional mathematical models of the processes, which describe both formation and propagation of shock waves, rarefaction waves, and contact discontinuities in shock tubes. These models are based on the quasi-one-dimensional equations of radiation gas dynamics. Experimental and theoretical studies of both the formation and propagation of shock waves, rarefaction waves and contact discontinuities using shock tubes have always been of significant interest and they are currently being developed. It results from the fact that the shock tubes are the most convenient tool of laboratory research in such contemporary fields of modern science and technology as aerophysics and chemical kinetics, gas dynamics and molecular physics. The flows of a multicomponent gas proves to be important for many modern technological and power facilities as well as in hypersonic aircraft. The multicomponent gas undergoes chemical conversions, oscillatory, and electron excitation. A relatively simple instrument for creating non-equilibrium processes in the gases is a shock wave propagating in a tube of a circular or rectangular crosssection. This cross-section geometry allows simplifying the gas-dynamic flow pattern in the working section.


[1] Riddell F.R. Study of hypersonic flows. New York-London, Acad. press, 1962. 513 p. (Russ. ed.: Issledovanie giperzvukovykh techenii. Sb. statei pod red. F.R. Riddella. Moscow, Mir Publ., 1964. 544 p.).

[2] Kovenia V.M., Yanenko N.N. Metod raschepleniia v zadachakh gazovoi dinamiki [Splitting method in gas dynamics problems]. Moscow, Nauka Publ., 1981. 304 p.

[3] Volkov K.N., Emelianov V.N. Modelirovanie krupnykh vikhrei v raschetakh turbulentnykh techenii [Large eddy simulation (LES) for the turbulent flow calculations]. Moscow, Fizmatlit Publ., 2008. 364 p.

[4] Marchuk G.I., Shaidurov V.V. Povyshenie tochnosti resheniia raznostnykh skhem [The improvment of difference scheme solution accuracy]. Moscow, Nauka Publ., 1979. 320 p.

[5] Dovgilovich L.E., Sofronov I.L. O primenenii kompaktnykh skhem dlia resheniia volnovogo uravneniia [On application of compact schemes for solving wave equations]. Moscow, Preprint No. 84 of Keldysh Institute of Applied Mathematics, IPM im. M.V. Keldysha Publ., 2008. 27 p. URL: http://library.keldysh.ru/preprint.asp?id=2008-84 (accessed 30.08.2013).

[6] Barth T.J. On unstructured grids and solvers in Computational Fluid Dynamics. Belgium, The von Karman Institute for Fluid Dynamics, 1990, Lecture Notes Series 1990-04.

[7] Saveliev A.D. Sostavnyie kompaktnyie skhemy vysokogo poriadka dlia modelirovaniia techeniia viazkogo gaza [High-order composite compact schemes for simulation of viscous gas flows. Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki [J. of Computational Mathematics and Mathematical Physics], 2007, vol. 47, No. 8, pp. 1387-1401 (in Russ.).

[8] Kotov M.A., Kuzenov V.V. Obzornyi analiz eksperimental’nykh issledovanii, vypolnennykh s pomoshch’iu nekotorykh tipov udarnykh trub. [A review of experimental investigations performed using some types of shock tubes]. Moscow, Preprint no. 1044 of RAS Appl. Mech. Inst., IPMech RAN Publ., 2013. 75 p.

[9] Kotov M.A., Kryukov I.A., Ruleva L.B., Solodovnikov S.I., Surzhikov S.T. Experimental Investigation Of An Aerodynamic Flow Of Geometrical Models In Hypersonic Aerodynamic Shock Tube. Proc. AIAA Wind Tunnel and Flight Testing Aero II, San Diego, June 24-27, 2013, no. 2013-2931. URL: http://arc.aiaa.org/doi/abs/10.2514/6.2013-2931(accessed 30.08.2013).

[10] Ovsiannikov L.V. Lektsii po osnovam gazovoi dinamiki [Lectures on the fundamentals of gas dynamics]. Moscow, Nauka, Publ., 1981. 368 p.