High Resolution Numerical Simulation Of Bifurcation Characteristics In The Moving Reflected Shock/Boundary Layer Interaction

When an incident shock wave propagates in a shock tube closed at one end,a reflected shock wave is formed after collision through the closed wall,and the reflected shock wave interacts with the boundary layer to cause a shock bifurcation phenomenon.A series of high-precision numerical simulation works about such bifurcation problems in the moving reflected shock wave and boundary layer interaction have been done in this paper.Because the Computational Fluid Dynamics(CFD)is chosen as a mainly study tool,it can summarize the content of this paper from two aspects:numerical method and physical problem.In terms of numerical methods,an improved ghost cell immersed boundary method(IBM)firstly proposed is applied to simulate the supersonic compressive flows around the complex obstacles.The main improvement of this algorithm is the treatment of the solid boundary that both ghost points inside the solid domain and forcing points inside the fluid domain due to the extension of the boundary are chosen to reconstruct the flow information considering the effect of solid wall on fluid.This brings refined boundary with discrete points and strengthens the wall conditions,which plays the role of local mesh refinement.The fluid points are limited in a certain source space as the interpolating points of the inverse distance algorithm,which effectively avoids the fact that the interpolating points are too few to possibly lead to coincide with the forcing points.Secondly,a high-order large eddy simulation solver for the reactive flow is developed based on the Smagorinsky sub-grid model and a thickened flame model.The key to this solver is the adoption of an artificial hyper-viscous model and a Taylor-Galerkin compact(TTGC)scheme.The artificial super-viscosity model can accurately capture the shock wave and effectively suppress the spurious oscillation by introducing the shear-viscosity term and the volume-viscosity term related to the computational mesh.The two-step Taylor-expanded TTGC scheme features high accuracy and low numerical dissipation.In terms of physical problems,at first,the flow bifurcation of the reflected shock/laminar boundary layer interaction in the shock tube with a straight reflection wall is studied by a high-precision finite difference method.By extracting and analyzing the three-dimensional transient flow field information,the intrinsic instability of the shock bifurcation is confirmed systematically,and the entire recirculation vortex structure resembles a curved "earthworm",and its turbulent properties exhibit distinct anisotropic characteristics.Also,by mining information of the flow spatio-temporal evolution,it is observed that the upper and lower shock bifurcations exhibit asymmetry in the shock propagation forward,the mechanism of which is closely related to the intrinsic instability of shock bifurcation and the high-frequency shedding vortex in the recirculation zone.When the initial incident shock Mach number is 1.9,the vortex high-frequency shedding phenomenon occurs at the tail of the recirculation zone,which is similar to the Karman vortex street formed by the flow around the cylinder,and its dimensionless shedding frequency St is between 0.01 and 0.02.Secondly,the improved ghost-cell immersed boundary method is used to study the unstable propagation characteristics of the reflected shock wave and its triple points in the shock/wavy-wall interaction.By the analysis of the streamline topology,it is found that the transverse motion of the triple points and their collision lead to a staggered transverse wave system similar to the cellular structure in the shock gas.The triple point is used as an unstable disturbance source of the leading shock wave,and its internal disturbance intensity gradually decreases with time,resulting in a power function decrement of the transverse wave Mach number,and its decay at the highest incident shock Mach number is the fastest.As the amplitude of the fluctuating wall increases,the cellular structure is no longer a single regular pattern but presents a multimodal feature,which is the result of multiple collisions between the transverse wave and the wavy-wall.Thirdly,the bifurcation phenomenon of the reflected shock/laminar boundary layer interaction in the shock tube with a wavy reflection wall is solved by the same ghost cell IBM.Compared with two cases mentioned above,it is found that when the incident shock Mach number is 1.5,the motion shock front and transverse wave system are basically the same as the results in the case of periodic boundary condition,indicating that the boundary layer effect is not obvious.But when the incident shock Mach number is increased to 1.9,the whole process can be divided into three stages:initial stage,transitional stage and development stage.In the initial stage,the entire flow field is basically the same as the case of periodic boundary condition.In the transitional stage,the high-speed shear band after the leading shock gradually evolves into an "earthworm-like" vortex structure,which is basically the same as the structure of the recirculation zone in the case of the straight reflection wall.The shape of the shock front near the wall gradually transitions from a smooth curve to a segmented fold line.However,the transverse wave system in the shock gas is still clearly visible,which is basically the same as the case of periodic boundary condition.In the development stage,the trajectory of the triple point is basically consistent with the case of periodic boundary condition,indicating that the role of the boundary layer does not affect the transverse motion of the triple point.A shock bifurcation occurs near the wall and there is a continuous vortex shedding at the end of the earthworm,which is approximately the same as the shock bifurcation observed in the case of the straight reflection wall.However,the difference lies in the fact that the shedding vortex interacts with the transverse waves in the shock gas,and a scattering-like wave structure is formed,which is mixed with the transverse wave system,resulting in a highly uneven post-shock flow field.Finally,in order to explore the effect of shock bifurcation on flame propagation,the reactive flow solver developed by LES is used to study the interaction between reflected shock,flame and boundary layer,focusing on the mechanism of shock bifurcation leading to flame acceleration.When the burning is transmitted into the shock bifurcation,the non-uniform recirculation zone will act as a flame holder.On the one hand,the combustion gas in the bifurcation can provide continuous heat for the acceleration of the shock motion.On the other hand,the local supersonic zone provides power to the rapid propagation of the flame,enabling it to closely follow the shock front.