Numerical Simulations of Gaseous Detonations

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Detonations with One-Step Chemistry

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

$\displaystyle A\longrightarrow B $

with the energy release

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

and the reaction rate

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

The production rates for this model read

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

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

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

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

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

Under the additional assumption

$\displaystyle h_B^0=0 $

the energy release is usually denoted by

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

and the equation of state

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

is derived.


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last update: 06/01/04