Numerical Study Of RM Instability On A Perturbed Interface Of Premixed Flame Induced By Shock Waves

Richtmyer-Meshkov(RM)instability is a behavior of small perturbation growth on an interface separating two different densities,when voticities on the interface are deposited due to the misalignment between gradients of density and pressure on the interface after an impulsive acceleration(e.g.,shock wave)hits the interface.It is a basically significant flow instability process.If the interface is chemically reactive,e.g.for a premixed flame,the RM instability may promote the mixing of unburned/burned mixture,enhance the combustion and even induce the detonations.The instability,which involves in complicated physical and chemical processes,is a common phenomenon in the context of many settings,both in nature and man-made events,such as insdustrial explosion events and supersonic combustion propulsion.However,some fundamental issues of RM instability are still not fully understood up to now.Moreover,reports in literatures about interactions between the shock waves and an initially perturbed interface with the sinuous shape are relatively few,especially about the multiple interactions.Based on this background,the detailed numerical studies of the interactions between shock waves and initially perturbed interfaces(including reactive interface or unreactive interface)were carried out.The two-dimensional,reactive,Navier-Stokes equations are employed to simulate the interactions,and high-resolution numerical schemes,including a ninth-order weighted essentially non-oscillatory(WENO),were used to perform the computations,based on the a GPU(Graphic Processing Unit)algorithm.The main work and the corresponding results are as follows:Firstly,the interactions of an initially perturbed unreacted interface with the successive shock waves were studied numerically.The developments of RM instability under the single mode and multi-mode perturbed conditions were analyzed systemtically.For the single mode perturbation,the development of spike plays a major role and the growth rate of mixing zone length of interface is affected by the initial perturbation after the reflection of shock wave.In addition,the growth rate also depends on whether the structure of "spike-in-bubble" is appeared or not.For the random multi-mode perturbations,the statistical parameters,such as the width and the average vorticity of mixing zone,are similar for different random multi-mode interfaces when the initial maximum amplitude and wavenumber of perturbation are the same for the different interfaces.Another finding is that the ratio of amplitude to average wavelength is an important parameter to describe the development of RM instibality of interface.The larger the ratio,the faster the interface perturbation develops.Secondly,the interactions of an initially perturbed premixed flame interface with the successive shock waves were studied numerically.Similarly,the developments of RM instability under the single mode and random multi-mode perturbed conditions were analyzed systemtically.For single mode perturbation,the strength of the incident shock wave has important influence on development of flame interface.The stronger the shock wave,the faster the perturbation growth before re-shock and the higher the chemical heat release rate after re-shock.The incremental heat release rate is not only due to the shock compression but also owing to the enhancements of mixing and combustion.For the same incident shock wave case,the developments of RM instability of flame interface are similar with those of inert interface before the re-shock but are less independent on the initial interface shape after the re-shock.For random multi-mode perturbations,the development of perturbations is similar with that of single mode perturbation before the re-shock.However,randomness of vortex distribution on the interface destabilizes the spike structures with small scale that integrate spike into the structures with large scale.The large scale structures promote the growth of mixing zone length and suppress the chemical reaction.Finally,a time sacle effect based on the multiple shock-flame interface interactions was studied.In consideration of characteristics of reactive RM instability,two main time scales,the time scale for chemical reaction ?c and the time scale for RM instability ?RM,play the important roles in the multiple interactions.A time scale decoupling assumption was proposed by introducing the concept of chemically frozen flow.Based on this assumption,?c is considered to be decoupled from ?RM,so that both time scales can be defined and determined independently.In order to obtain the ?RM a chemically frozen flow that removes the effect of chemical reactions is frist proposed in this paper.The two-dimensional visualizations of the perturbation development on the interface in reactive flows with those in chemically frozen flows were compared to find out the effects of chemical reaction in progress of shock-flame interactions.The consumption of reactant further reduces the density gradient on flame interface,and thus decreasing the baroclinic torque and subsequently weakening the vorticity in the flame region.The quantitative correlations between the ratio of ?c to ?RM and chemical heat release rate in all three cases are calculated.The good correlations indicate the advantage of the approaches to determine ?c and ?RM proposed in present study.The observation that the ratio of ?c to ?RM is independent of the initial strength of incident shock wave and initial perturbation suggest that the ratio reflects the nature of reactive RM instability,hence provides a new dimensionless parameter for understanding such flows.