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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

 h_B^0=0

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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