Heat and momentum losses in H2–O2–N2/Ar detonations: on the existence of set-valued solutions with detailed thermochemistry

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_a,eff/R_uT₀, when using detailed thermochemistry. The main results of the study are discussed via detonation velocity-friction coefficient (D–c_f) curves. The influence of the mixture composition is assessed, and classical scaling for the prediction of the velocity deficits, D(c_f,crit)/D_CJ, as a function of the effective activation energy, E_a,eff/R_uT₀, is revisited. Notably, a map outlining the regions where set-valued solutions exist in the E_a,eff/R_uT₀--α space is provided, with α denoting the momentum–heat loss similarity factor, a free parameter in the current study.