Prediction of Mach stem height in compressible open jets. Part 1. Overexpanded jets

Abstract

The flow from a supersonic nozzle when operated at off-design conditions exhibits a wide variety of complex flow structures. The prominent ones are the shock reflections inside the jet. The two main types of shock interactions are the regular reflection (RR) and Mach reflection (MR). The prominent characteristic change in the shock pattern when an RR transforms into an MR is the appearance of the Mach stem with a subsonic region downstream of it. The estimation of the Mach stem height gives the size of the subsonic domain and is a direct method to predict the transition from RR to MR or vice versa. The present study is carried out to estimate the size of the Mach stem in an inviscid jet in the overexpanded regime. The analytical methods employed here are the extension of the techniques developed to estimate the Mach stem size in the wedge flows by Li & Ben-Dor (J. Fluid Mech., vol. 341, 1997a, pp. 101–125), Mouton & Hornung (AIAA J., vol. 45, issue 8, 2007, pp. 1977–1987) and Bai & Wu (J. Fluid Mech., vol. 818, 2017, pp. 116–140). The results from the analytical formulation have been compared with the high resolution computational and experimental results. The analytical method reveals that the open jet has a unique, stable MR configuration and forms an upper limit for achievable Mach stem height for the wedge flows. Apart from the estimation of Mach stem height, the growth rates of Mach stem where the RR–MR transition takes place are also calculated and compared with the ones corresponding to wedge flows.