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Article information
2015 , Volume 20, ¹ 2, p.29-43
Blokhin A.M., Biberdorf E.A.
Numerical resolution of the problem for a stationary real gas flow over a cone
We consider the model of a van der Waals gas flow that properly describes liquid, gaseous and two-phase states of a real medium. The term “two-phase state” is understood in the thermodynamical sense, i. e., it is a state in which a liquid and its vapor (liquid and gaseous phases) coexist in thermodynamical equilibrium. It should be noted that a two-phase state is not the same as a two-phase flow. For two-phase flows the liquid and, for example, solid phases are described by different equations, whereas in our case (for two-phase states) the liquid and gaseous phases obey the same system of equations. The appearance of regions of two-phase states is modelled solely by the van der Waals equation of state. In Section 1, taking into account the van der Waals equation of state, we simplify the system of equations and reduce it to a dimensionless form. The resulting problem is a nonstandard boundary value problem. We describe regions of variation of the dimensionless parameters γ∞, γ*, α and β describing certain medium states. We also introduce parameters specifying properties of a shock wave. In Section 2, we propose an algorithm for solving the obtained system of equations. This algorithm is based on solving a series of Cauchy problems. In the end of the paper we present the result of numerical simulations for the most interesting cases.
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Keywords: circular cone, van der Waals gas, boundary value problem, numerical algorithm
Author(s):
Blokhin Alexander Mikhailovich
Dr. , Professor
Position: Head of Laboratory
Office: Institute of Mathematics SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Koptyug ave, 4
Phone Office: (383) 329 76 75
E-mail: blokhin@math.nsc.ru
Biberdorf Elina Arnoldovna
PhD.
Position: Senior Research Scientist
Office: Institute of Mathematics SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Koptyug ave, 4
Phone Office: (383) 329 76 75
E-mail: biberdorf@ngc.ru
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[9] Blokhin, A.M., Bychkov, A.S., Myakishev, V.O. O vypolnenii usloviya Lopatinskogo v zadache ob obtekanii klina normal'nym gazom i gazom Van-der-Vaal'sa [About the Lopatinsky condition in the problem of the normal gas and van der Waals gas flow around a wedge]. Novosibirsk. Preprint. Institute of Mathematics SB RAS; 2012: 280. (In Russ.)
[10] Blokhin, A.M., Bychkov, A.S., Myakishev, V.O. Numerical analysis of feasibility of the neutral stability conditions for shock waves in the problem of a van der waals gas flow past a wedge. Journal of Applied and Industrial Mathematics. 2013; 7(2):131–141.
[11] Blokhin, A.M., Tkachev, D.L. An analisys of realization of neutral stability conditions forshock waves at the nonideal gas flow around a wedge. Technical Physics. (In press).
Bibliography link:
Blokhin A.M., Biberdorf E.A. Numerical resolution of the problem for a stationary real gas flow over a cone // Computational technologies. 2015. V. 20. ¹ 2. P. 29-43
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