Hydrodynamic Instabilities in Gaseous Detonations: Comparison of Euler, Navier–Stokes, and Large-Eddy Simulation

Abstract

A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed.