Improvement and extension of the generalized hard-sphere reaction probability model.
The GHS (Generalized Hard Sphere)-based standard reaction probability model commonly used in probabilistic particle methods is evaluated. We show that the original model has no general validity with respect to the molecular reaction. Mathematical consistency exists only for reactions with vanishing activation energy. For small energies close to the activation threshold the individual reaction probability for the special case of associative ionization of atomic nitrogen diverges. This makes the model extremely expensive, and nonphysical. An improved model is derived, and its implementation is verified on basis of the aforementioned reaction. Both models converge to the same value at large energies. The relative error of the original model with respect to the new model is independent of the particle pairing and, hence, of the reaction type. The error is smaller than 1% for collision energies in excess of 200 times the activation energy. For typical simulation problems like atmospheric high-enthalpy entry flows (assuming heavy-particle temperatures on the order of 10000 K) the relative error is in the order of 10(5)%.
Institute of Aerospace Thermodynamics, Universität Stuttgart, Stuttgart, Germany. matthias.schuebler@gmx.de
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Schübler
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Petkow
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Herdrich