Heat and momentum losses in \({\text {H}}_{2}\)–\({\text {O}}_{2}\)–\({\text {N}}_{2}/{\textrm{Ar}}\) detonations: on the existence of set-valued solutions with detailed thermochemistry

Abstract

The effect of heat and momentum losses on the steady solutions admitted by the reactive Euler equations with sink/source terms is examined for stoichiometric hydrogen–oxygen mixtures. Varying degrees of nitrogen and argon dilution are considered in order to access a wide range of effective activation energies, \(E_{\textrm{a,eff}}/R_{\textrm{u}}T_{0}\), when using detailed thermochemistry. The main results of the study are discussed via detonation velocity-friction coefficient (D–\(c_{\textrm{f}}\)) curves. The influence of the mixture composition is assessed, and classical scaling for the prediction of the velocity deficits, \(D(c_{\textrm{f,crit}})/D_{\textrm{CJ}}\), as a function of the effective activation energy, \({E}_{\textrm{a,eff}}/R_{\textrm{u}} T_{0}\), is revisited. Notably, a map outlining the regions where set-valued solutions exist in the \(E_{\textrm{a,eff}}/R_{\textrm{u}}T_{0}\text {--}{\alpha }\) space is provided, with \(\alpha \) denoting the momentum–heat loss similarity factor, a free parameter in the current study.