Abstract
A natural assumption on the form of the calorific equations of state (internal energy) for one-dimensional motion was used to obtain the so-called gradient relations that give a one-to-one correspondence between the first partial spatial derivatives of the pressure, density, mass velocity (gradients of parameters) at shock and detonation fronts and the time derivative (acceleration) of the front. The assumption is based on the fact that, taking into account the thermal equation of state, the total internal energy, including both the thermodynamic part and potential chemical energy, can be represented as a function of pressure and density. This holds for both inert media and reaction products in the state of chemical equilibrium.
Similar content being viewed by others
References
R. Courant and K. Friedrichs, Supersonic Flow and Shock Waves, Interscience, New York (1948).
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, Pergamon Press, Oxford-Elmsford, New York (1987).
Ya. B. Zel’dovich, Theory of Combustion and Detonation of Gases [in Russian], Izd. Akad. Nauk SSSR, Moscow-Leningrad (1944).
V. V. Mitrofanov, Detonation of Homogeneous and Heterogeneous Systems [in Russian], Lavrent’ev Institute of Hydrodynamics, Sib. Div., Russian Acad. of Sci., Novosibirsk, (2003).
G. Cassen and J. Stanton, “The decay of shock waves,” J. Appl. Phys., 19, No. 9, 803–807 (1948).
L. I. Sedov, “General theory of one-dimensional motion of gas,” Dokl. Akad. Nauk SSSR, 85, No. 4, 723–726 (1952).
L. I. Sedov, Similarity and Dimensional Analysis, Academic Press, New York (1959).
A. A. Vasil’ev and Yu. A. Nikolaev, “Model of a nucleus of multifront gas detonation, Combust., Expl., Shock Waves, 12, No. 5, 667–674 (1976).
V. V. Rusanov, “Derivatives of gas-dynamic functions behind a curved shock wave,” Preprint No. 18, Institute of Applied Mathematics, USSR Acad. of Sci. (1973).
V. A. Levin and G. A. Skopina, “Behavior of a vortex velocity vector in supersonic flows behind discontinuity surfaces,” Teplofiz. Aéromekh., 13, No. 3, 381–389 (2007).
Yu. B. Rumer and M. Sh. Ryvkin, Thermodynamics, Statistical Physics, and Kinetics [in Russian], Nauka, Moscow (1977).
Yu. A. Nikolaev and P. A. Fomin, “Analysis of equilibrium flows of chemically reacting gases,” Combust., Expl., Shock Waves, 18, No. 1, 53–58 (1982).
E. S. Prokhorov, “Approximate model for analysis of equilibrium flow of chemically reacting gases,” Combust., Expl., Shock Waves, 32, No. 3, 306–312 (1996).
L. V. Ovsyannikov, Lectures on Fundamentals of Gas Dynamics [in Russian], Nauka, Moscow (1981).
K. P. Stanyukovich, Unsteady Motion of Continuous Media, Pergamon Press, New York (1960).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 5, pp. 92–94, September–October, 2009.
Rights and permissions
About this article
Cite this article
Prokhorov, E.S. Gradient relations at the front of shock and detonation waves. Combust Explos Shock Waves 45, 588–590 (2009). https://doi.org/10.1007/s10573-009-0070-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10573-009-0070-0