Thermodynamic trajectories in detonations with stratified reactant mixtures

Incomplete mixing of non-premixed reactants has been cited as a potential cause for non-ideal wave strengths and combustion efficiencies in detonation-based combustors. To isolate the effects of mixture inhomogeneities, this work considers two-dimensional simulations of detonations in channels with stratified reactants. Stratification is imposed using the equivalence ratio of H${}_2$-air, which is prescribed with varying integral length scales. Adaptive mesh refinement and detailed chemical kinetics are used to capture the shocks and reaction zones at high spatiotemporal resolution. Increasing stratification yields larger and more irregular detonation cells, but only 3% deficits in mean wave speed from the mean mixture CJ speed. To examine the disparate local fluidic and thermodynamic processes contributing to the macroscopic wave dynamics, Lagrangian tracer “particles” are propagated with the local fluid velocity at simulation runtime. Statistics for particle trajectories are conditioned on the initial reactant composition (rich vs. lean) and local wave strength (over- vs. under-driven), allowing the effects of reactant mixedness and wave instabilities to be directly examined. Increasing stratification primarily affects the mean trajectories for rich and lean particles, as stratification partitions heat release between the different mixture compositions. This leads to larger discrepancies in mean temperature, total heat release, and the locations of the CJ points in $p$–$v$ space. However, the CJ points for rich and lean particles are located at roughly the same distances from the wave fronts. In addition, over- and under-driven particles experience nearly the same total heat release and entropy generation, but over-driven undergo greater shock losses while under-driven undergo greater heating losses. These results illustrate how the interplay of unsteady localized thermodynamic processes contribute to the global wave dynamics and mean post-detonation state, which are found to be reasonably well-approximated by the ZND solution for the mean mixture composition.

Novelty and Significance Statement

The Lagrangian analyses in this work provide direct access to the unsteady and highly localized processes contributing to the non-ideal dynamics of detonations in inhomogeneous reactant mixtures. This distinguishes the present work from others on stratified detonations, which have primarily analyzed wave dynamics in the Eulerian reference frame. To the authors’ knowledge, this work is the first to incorporate Lagrangian analyses into simulations of detonations with stratified fuel-air mixtures. The conditioning of particle trajectories on the initial reactant composition and local wave strength is also a methodological innovation. The results contribute to the fundamental understanding of stratified detonations and have direct implications for the wave behaviors observed in practical detonation-based propulsion and power generation applications.