In ideal magnetohydrodynamics MHD, the Richtmyer-Meshkov instability can be suppressed by the presence of a magnetic field. The interface still undergoes some growth, but this is bounded for a finite magnetic field. A model for this flow has been developed by considering the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This was accomplished by analytically solving the linearized initial value problem in the framework of ideal incompressible MHD. To assess the performance of the model, its predictions are compared to results obtained from numerical simulation of impulse driven linearized, shock driven linearized, and nonlinear compressible MHD for a variety of cases. It is shown that the analytical linear model collapses the data from the simulations well. The predicted interface behavior well approximates that seen in compressible linearized simulations when the shock strength, magnetic field strength, and perturbation amplitude are small. For such cases, the agreement with interface behavior that occurs in nonlinear simulations is also reasonable. The effects of increasing shock strength, magnetic field strength, and perturbation amplitude on both the flow and the performance of the model are investigated. This results in a detailed exposition of the features and behavior of the MHD Richtmyer-Meshkov flow. For strong shocks, large initial perturbation amplitudes, and strong magnetic fields, the linear model may give a rough estimate of the interface behavior, but it is not quantitatively accurate. In all cases examined the accuracy of the model is quantified and the flow physics underlying any discrepancies is examined.

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This paper investigates the combustion regimes that are present in inlet-fueled, low compression scramjets. Injection of fuel in the inlet allows mixing to take place prior to ignition, and permits the fuel plumes to interact with strong shocks and rarefactions at the combustor entrance, which accelerates the mixing process. Consequently, the combustion is partially premixed. Wall-modeled large-eddy simulations (WMLES) are used to accurately resolve or model the turbulent flow structures occurring during the supersonic combustion process. Based on the WMLES data, spatial distributions of turbulent and chemical time scales can be extracted and used to determine the representative turbulent Damköhler and Reynolds numbers. The collective WMLES data is visualized using the Williams diagram, which shows that a wide range of combustion regimes are present throughout the supersonic combustion process. NomenclatureDa t Turbulent Damköhler number H Altitude, m J Momentum flux ratio Ka Karlovitz number k Turbulence kinetic energy, J/kg l 0 Integral length scale, m l c Chemical length scale, m l δ Reaction zone length scale, m M Mach numbeṙ m Mass flow rate, kg/s p Pressure, Pa q Dynamic pressure, Pa R N Leading edge radius, m Re t Turbulent Reynolds number Re u Unit Reynolds number s L Flame speed, m/s T Temperature, K u Velocity, m/s Turbulent dissipation, J/(kg s) η Kolmogorov length scale, m ν Laminar kinematic viscosity, m 2 /s τ c Chemical time scale, s τ δ Reaction zone time scale, s * PhD Student, School of Mechanical and Mining Enginieering, University of Queensland, Student Member AIAA.

Flow features for transverse sonic injection into supersonic crossflow. . 2.4Williams diagram for premixed and non-premixed turbulent combustion regimes adapted from [44,166,230] with additional experimental/numerical data.

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