Parametric study of shock-wave formation in a spatially inhomogeneous self-igniting medium for arrhenius combustion kinetics

Abstract

An approach to describing the formation and propagation of small gas-dynamic perturbations in a spatially inhomogeneous self-igniting medium for arbitrary chemical reaction kinetics was developed in a previous paper. In the present paper, the proposed approach is illustrated by studying the problem for a simple reaction with an Arrhenius reaction rate. A comparison of calculation results with the solution of the complete system of gas dynamics equations shows that the approach provides good accuracy of quantitative estimates.

Theoretical description of shock-wave formation in a spatially inhomogeneous combustible medium for chain-branching combustion kinetics

“…The main dimensionless parameters of the problem are the temperature at the center of the hot spot θ m , the effective activation energy ε a in the induction step, the temperature gradient g, the heat-release time τ hr , and the order of the reaction in the heat-release step n. The effect of the first three parameters on shock-wave formation for Arrhenius combustion reaction kinetics was studied in detail in [13]. It can be assumed that the results obtained for θ m , ε a and g remain qualitatively the same.…”

“…For a fixed value of g, the initial point X 0cr moves away from the center of the hot spot with increasing time τ hr . Unlike in the case of a simple reaction with an Arrhenius rate dependence [13], the Table 1 shows that the closer the values of the ratio (τ hr /τ ind )(X 0cr ) to each other [for example, (τ hr /τ ind )(X 0cr ) ≈ 0.1 for g = 0.005 and τ hr = 0.4 or for g = 0.002 and τ hr = 0.8], the smaller the differences between their corresponding values W sp (X 0cr ) and Y (τ cr , X cr ). Thus, the determining parameter of the problem is the ratio of the heat-release time to the induction time at the initial point of the critical characteristic (τ hr /τ ind )(X 0cr ) and not the absolute quantity τ hr .…”

“…The approach developed in [12] and employed to study shock-wave formation for Arrhenius combustion kinetics [13] is used. Chain-branching reaction is modeled by the two-step Korobeinikov-Levin model [14,15].…”