Simulation of shock–turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence

Abstract

The one-dimensional turbulence (ODT) methodology is extended to include an efficient compressible implementation and a model for capturing shock-induced turbulence is presented. Lignell et al. recently introduced a Lagrangian ODT implementation using an adaptive mesh. As the code operates in the incompressible regime (apart from constant-pressure dilatation) it cannot handle compressibility effects and their interactions with turbulence and chemistry. The necessary algorithmic changes to include compressibility effects are highlighted and our model for capturing shock–turbulence interaction is presented. To validate our compressible solver, we compare results for the Sod shock tube problem against a finite volume Riemann solver. To validate our model for shock–turbulence interaction, we present comparisons for a non-reactive and a reactive case. First, results of a shock traveling from light (air) to heavy (SF6) with reshock have been simulated to match mixing width growth data of experiments and turbulent kinetic energy results from LES. Then, for one-step chemistry calibrated to represent an acetylene/air mixture we simulate the interaction of a shock wave with an expanding flame front, and compare results with 2D simulation (2D-sim) data for flame brush formation and ensuing deflagration-to-detonation transitions (DDT). Results for the Sod shock tube comparison show that the shock speed and profile are captured accurately. Results for the non-reactive shock–reshock problem show that interface growth at all simulated Mach numbers is captured accurately and that the turbulent kinetic energy agrees in order of magnitude with LES data. The reactive shock tube results show that the flame brush thickness compares well to 2D-sim data and that the approximate location and timing of the DDT can be captured. The known sensitivity of DDT characteristics to details of individual flow realizations, seen also in ODT, implies that model agreement can be quantified only by comparing flow ensembles, which are presently unavailable other than in an ODT run-to-run sensitivity study that is reported herein.