Numerical Simulations of Gaseous Detonations

Detonations with One-Step Chemistry

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

%MATHMODE{ A\longrightarrow B }%

with the energy release

%MATHMODE{ h_A^0-h_B^0=:\Delta h^0>0 }%

and the reaction rate

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

The production rates for this model read

%MATHMODE{ \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

%MATHMODE{ \gamma=\gamma_A=\gamma_B \;. }%

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

%MATHMODE{ p = (\gamma-1)(\rho e - \rho (1-Z)h_A^0-\rho Z h_B^0)\;. }%

Under the additional assumption

%MATHMODE{ h_B^0=0 }%

the energy release is usually denoted by

%MATHMODE{ q_0:=\Delta h^0=h_A^0 }%

and the equation of state

%MATHMODE{ p = (\gamma-1)(\rho e - \rho (1-Z)\, q_0) }%

is derived.

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Subsections

• Normalization
• Initial Conditions
• One-dimensional Simulations
• Two-dimensional Simulations
  • Computation 1, f=3.0, E0=50, Q0=50
  • Computation 2, f=1.2, E0=10, Q0=50
  • Computation 3, f=1.1, E0=20, Q0=2

• Three-dimensional Simulation
  • Regular Structure Simulation, f=1.2, E0=10, Q0=50

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-- RalfDeiterding - 14 Dec 2004