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Nonlinear Waves in a Reacting Mixture

  • M. Torrisi
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

The reacting mixture produced by a shock wave, moving in a polytropic gas, is considered in this paper.As well known C1D C23, assuming that the reactant and product are polytropic gas with the same adiabatic constant y, “the governing equation for axisymmetric flows are:
$$\begin{array}{*{20}{c}} {{\rho _t} + u{\rho _x} + \rho {u_x} = - \alpha \rho u/x}&{{\rm{ }}{u_t} + u{u_x} + {p_x}/p = 0}\\ {{e_t} + u{e_x} + (p/\rho ){u_x} = - \alpha (p/\rho )u/x}&{{\lambda _L} + u\lambda = \tilde w/\tilde \tau } \end{array}\;\;\;\;\;\;(\alpha = 1,2)$$
(1.1)
with the constitutive relations:
$$e(p + \rho (\gamma - 1)) - \lambda {q^2}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\tilde w = \tilde w(\rho ,p,\lambda )$$
(1.2 )
where ρ,u,p,e are density, particle velocity, pressure, internal energy respectively while λ is the dimensionless progress variable of exothermic chemical reaction representing the mass fraction of product (0≤λ≤1), \(\tilde{w}\) is rate function and finally \(\tilde{\rho}\) and qz are the rate constant and heat of reaction.

Keywords

Shock Wave Internal Energy Particle Velocity Constitutive Relation Nonlinear Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • M. Torrisi
    • 1
  1. 1.Dipartimento di MatematicaCataniaItaly

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