Numerical Simulations of Gaseous Detonations

Detonations with One-Step Chemistry

A popular model is a reaction mechanism just of one exothermic reaction

$A\longrightarrow B$

with the energy release

$h_A^0-h_B^0=:\Delta h^0>0$

and the reaction rate

$k^f(T) = k \exp (-E_A/{\cal R}T)\;.$

The production rates for this model read

$\dot \omega_A = - k \rho_A \exp (-E_A/{\cal R}T) \quad {\rm and} \qquad \dot \omega_B = -\dot \omega_A\;.$

Further, the species A and B are assumed to be calorically perfect gases with

$\gamma=\gamma_A=\gamma_B \;.$

In this case, the hydrodynamic pressure can be evaluated directly from the conserved quantities by

$p = (\gamma-1)(\rho e - \rho (1-Z)h_A^0-\rho Z h_B^0)\;.$

Under the additional assumption

the energy release is usually denoted by

$q_0:=\Delta h^0=h_A^0$

and the equation of state

$p = (\gamma-1)(\rho e - \rho (1-Z)\, q_0)$

is derived.

Subsections

-- RalfDeiterding - 14 Dec 2004

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