Nonlinear Waves in Active Media pp 250-256 | Cite as

# Nonlinear Waves in a Reacting Mixture

Conference paper

## 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 with the constitutive relations: 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 q

*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)

$$e(p + \rho (\gamma - 1)) - \lambda {q^2}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\tilde w = \tilde w(\rho ,p,\lambda )$$

(1.2 )

^{z}are the rate constant and heat of reaction.### Keywords

Combustion Acoustics## Preview

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© Springer-Verlag Berlin Heidelberg 1989