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.

Adaptive simulations of viscous detonations initiated by a hot jet using a high-order hybrid WENO–CD scheme

“…Due to the high resolution and low dissipation of the hybrid scheme, diffusion effect in viscous detonations should be dominated by the physical viscosity, while numerical dissipation in inviscid detonations can be almost entirely avoided. It has been reported that the diffusion effect mainly occurs at shear layers and unburned mixture boundaries [22]. The comparison between viscous and inviscid detonations showed that the growth of secondary instabilities (KH instability type) is suppressed in NS simulations [31,32].…”

“…In Fig.6(c), four secondary triple points coexist simultaneously thus generating more shear layers behind the triple points that undergo KH instability. Previous numerical and experimental investigations showed that in unstable detonations RM instability is the main mechanism for the generation of turbulent structures behind the detonation front [21], which indicated that the role of KH instability seems to be less important than that of the RM instability [22].…”

Detonation Simulations in Supersonic Combustible Mixtures with Nonuniform Species

“…[63,64] showed that from the comparison of detonations solved both by Euler and Navier-Stokes equations, diffusion effect has no crucial role in the overall structure of regular detonations due to the negligible effect of hydrodynamic instabilities. Therefore, the results obtained in this paper using Euler equations for regular detonations are nevertheless expected to give at least qualitatively correct conclusions.…”

Numerical Investigation on Detonation Control Using a Pulse Hot Jet in Supersonic Combustible Mixture

“…Previously Oran et al (Oran et al, 1998) Mahmoudi et al, 2013;Mahmoudi et al, 2014) showed that from the comparison between Euler and NS equations, diffusion effect has no role in regular detonations, due to the absence of hydrodynamic Therefore, the conclusions obtained in this paper using the inviscid Euler equations for regular detonations are nevertheless expected to give at least qualitatively correct descriptions of detonation features.…”