A model of Mach reflection in axisymmetric steady overexpanded jets: Development and applications

This paper modifies the semi-analytical model (the MOCMR model) of Mach reflection in axisymmetric wedge-generated supersonic flow by Shoesmith and Timofeev (Shock Waves 31, 945–957 (2021)) to predict Mach reflection configurations at the axis of symmetry in an overexpanded jet just downstream from the exit of a nozzle. The jet flow is considered to be a steady, inviscid flow of an ideal gas with constant specific heats. Similar to the original MOCMR model, the MOCMR model for jet flow is based on a number of flowfields solved using the method of characteristics, a Mach stream flowfield solved by quasi-one-dimensional relations, and the three-shock theory at the triple point. The modifications include the incorporation of the jet boundary instead of a wedge surface, the addition of the Prandtl-Meyer expansion fan resulting from the interaction of the reflected shock with the jet boundary, and the method to efficiently and accurately resolve very small Mach disks. The results for flowfield structure and Mach disk radius and location are extensively compared with the experimental and numerical ones available in the literature as well as with the inviscid numerical simulations using an in-house adaptive unstructured finite-volume flow solver. The influence of various model assumptions on accuracy is examined. The proposed model is demonstrated to produce results of similar accuracy using considerably less computational resources as compared to time-marching CFD simulations, at the same time directly providing quantities which are difficult to extract from CFD flowfields. The application of the developed model lends additional support to the conjecture that seemingly regular reflections observed at the axis of symmetry in some physical experiments are due to insufficient optical resolution to discern a very small Mach disk. Furthermore, parametric studies are conducted for a range of exit Mach numbers and nozzle pressure ratios and the influence of these parameters on Mach disk radius and the slip line is examined.