Three-Dimensional Numerical Simulations of Spherical Flame Evolutions in Shock and Reshock Accelerated Flows

Abstract

The three-dimensional spherical flame evolutions induced by incident and reflected shock waves in a rectangular shock tube are numerically simulated using the compressible reactive Navier–Stokes equations with a single-step Arrhenius chemical reaction. Four cases, including variable parameters of flame size and number, shock wave strength, and mixture reactivity, are considered in order to investigate the effects of these parameters on the flame evolutions and detonation onsets. The three-dimensional visualized results and the time-dependent integral and statistical results for the shock–flame interactions are obtained. The morphology of the flame evolutions for all cases studied shows the severe distortion, expansion, and corrugation of flame disturbed by shock waves, especially by a reflected shock wave. The unstable flame produces the three-dimensional reactive shock bifurcation (RSB) structure, as the flame number, the shock wave strength, or the mixture reactivity increase. Further, detonations can occur in a later stage of flame evolution at the different three-dimensional spatial locations for different cases through the shock–detonation–transition (SDT) mechanism. Unlike the three-dimensional spatial dissimilarities of flame patterns and detonation initiation locations among cases studied, the time-dependent integral and statistical properties of flame developments prior to detonation onset show the more similar behaviors for all cases. During the passage of shock and reshock waves, the spherical flames are compressed and distorted, resulting in the vorticity deposition within flame and the well-mixing between the burned and unburned gases. Physical process dominates the compression phases of the flame evolution. Following the passage of the shock and reshock waves, the well-mixing facilitates the chemical heat release and expands (accelerates) the distorted flame. The chemical process becomes more prominent, especially under the reshock condition. In the flame expansion phases, the baroclinic effect is weakened, and the vortex stretching effect is enhanced with the development of flame. In addition, the well-mixing by the passages of shock waves promotes the chemical reaction of the flame, which in turn burns out the mixing zone of flame and therefore inhibits the mixing.

Keywords:

• Detonation onset
• Flame
• Instability
• Mixing
• Reactive shock bifurcation
• Shock wave

ACKNOWLEDGMENTS

This work was supported by the Natural Science Fund of China (Contract No. 10972107) and the Open Fund of State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology (Contract No. KFJJ12-4Y).

Notes

Ma: incident shock wave Mach number; W _i : incident shock wave speed relative to fluid ahead of wave; W _r : reflected shock wave speed relative to fluid ahead of wave; Ea/RT ₀: activation energy; N _f: number of initial spherical flames; R ₀: initial radius of single flame; V ₀: initial volume of single flame.