Dimensional analysis and simplified modeling for the cellular structure of premixed gas-phase detonation numerical simulations with single-step kinetics

The current study presents a new simplified model for predicting the detonation cell dimensions obtained by multidimensional gas-phase detonation numerical simulations. Firstly, we present a dimensional analysis of the problem under several simplifying assumptions. We reveal that the normalized detonation cell width and length are approximately governed by only three dimensionless groups. Guided by this result, we develop a simple and analytical blast wave model that is governed by the exact same dimensionless groups. Then, we explore the influence of these dimensionless groups on the regular cellular structure obtained by gas-phase detonation numerical solutions. More specifically, we solve the 2-D compressible reactive Navier–Stokes equations with single-step kinetics and a calorically perfect gas equation of state, and analyze in detail the resulting numerical soot foils. According to these simulation results, we calibrate our new blast wave model to capture the numerically-obtained normalized detonation cell width and length within a maximum relative error of less than 20%. We further validate the new blast wave model against results from the literature and discuss in detail the new model limitations. Also, we show that the blast wave model can be coupled with a new optimization procedure for calibrating flow and reaction parameters to capture realistic detonation properties. Finally, we demonstrate that gas-phase detonation numerical simulations, with parameters derived via the new optimization procedure, can replicate the experimentally measured cell width with a maximum relative error of less than 15%.