pp. 1051-1062 | Article Number: iejme.2016.094
Published Online: July 29, 2016
Article Views: 280 | Article Download: 319
The article considers the interference of shock of the same direction or, as they are called, catching-up shock waves. Purpose is to give a classification to the shock-wave structures that arise in this type of shocks interaction, and to determine the area of their existence. As a result of same direction shocks’ intersection a shock-wave structure forms ate the intersection point, containing the main shock, tangential discontinuity and one more reflected gas-dynamic discontinuity, the type of which is not known beforehand. The problem of determining the type of reflected discontinuity is the main problem, which must be solved in the study of catching-up shocks’ interference. The paper presents qualitative picture of shock-wave structures arising from the interaction of catching shock. The areas in which there is a regular and irregular interaction catching shocks. There are also areas in which the stationary solution is not available. The latest factor has determined the revival of interest in the theoretical study of given problem, because the facts of shock-wave structure’s sudden destruction inside the air intake of supersonic aircrafts at high Mach numbers were discovered. Is also relevant to investigate the possibility of using catching-up oblique shock waves to create an over-compressed detonation in promising detonation air-jet and rocket engines.
Keywords: Shock one-direction shocks, catching- up shocks, shock-wave structures, shocks interference, gas-dynamic discontinuities
Adrianov, A. L., Starykh, A. L. & Uskov, V. N. (1995) Interference of Stationary Gasdynamic Discontinuities. Novosibirsk. Publishing house “Nauka”. 180p.
Bulat, M. P. & Bulat, P. V. (2013) The analysis centric isentropic compression waves. World Applied Sciences Journal, 27(8), 1023-1026.
Bulat, P. V. (2013) Shock and detonation wave in terms of view of the theory of interference gasdynamic discontinuities. Part I. The geometric meaning of the equations of gas dynamics of supersonic flows. Fundamental Research, 10(9), 1951-1954.
Bulat, P. V. & Bulat, M. P. (2014) Discontinuity of gas-dynamic variables in the center of the compression wave. Research Journal of Applied Sciences, 8(23), 2343-2349.
Bulat, P. V. & Uskov, V .N. (2012) On the problems of designing diffusers ideal compression supersonic flow. Fundamental Research, 6(1), 178-184.
Bulat, P. V., Uskov, V. N. & Arkhipova, L. P. (2014a) Classification of gas-dynamic discontinuities and their interference problems. Research Journal of Applied Sciences, 8(22), 2248-2254.
Bulat, P. V., Uskov, V. N. & Arkhipova, L. P. (2014b) Gas-dynamic discontinuity conception. Research Journal of Applied Sciences, 8(22), 2255-2259.
Cai, Z., Fan, Y., Li, R. (2015) A framework on moment model reduction for kinetic equation. SIAM Journal on Applied Mathematics, 75(5), 2001-2023.
Omelchenko, A. V., Uskov, V. N. (1999) Optimum overtaking compression shocks with restrictions imposed on the total flow-deflection angle. Journal of Applied Mechanics and Technical Physics, 40(4), 638-646.
Roslyakov, G. S. (1965) Interaction of plane one-directional shock waves. In Numerical methods in gas dynamics. Moscow: Moscow State University Press, 28-51.
Solovchuk, M. A. & Sheu, T. W. H. (2010) Prediction of shock structure using the bimodal distribution function. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 81, 57-64.
Taniguchi, S., Arima, T., Ruggeri, T. & Sugiyama, M. (2014) Shock Wave Structure in a Rarefied Polyatomic Gas Based on Extended Thermodynamics. Acta Applicandae Mathematicae, 132(1), 583-593.
Uribe, F. J. (2016) Shock waves: The Maxwell-Cattaneo case. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 93(3), 35-46.
Uskov, V. N. (2000a) Optimal one-dimensional shock waves running on gas flow. Proceedings of XV Session of the International School on Models of Continuum Mechanics, 63-78.
Uskov, V. N. (2000b) Running One-Dimensional Shock Waves. St. Petersburg: BSTU “Voenmech” press. 224p.
Uskov, V. N. & Chernyshov, M. V. (2006) Special and extreme triple shock-wave configurations. Journal of Applied Mechanics and Technical Physics, 47(4), 492-504.
Uskov, V. N., Roslyakov, G. S. & Starykh, A. L. (1987) Interference of stationary one direction shock waves. Journal of USSR Academy of Science. Fluid Dynamics, 4, 143-152.
Vasiliev, E., Elperin, T. & Ben-Dor, G. (2008) Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge. Direct access: http://scitation.aip.org/content/aip/journal/pof2/20/4/10.1063/1.2896286.
Vekken, V. K. (1950) Limit positions of bifurcated shock waves. Mechanics, 4, 131-143.