Numerical investigation of the effects of base size on supersonic flow through a sudden duct enlargement

Abstract

An abrupt increase in duct cross-section is often found in pressure-reducing devices, valves of internal-combustion engines, flow control devices in pipe systems of power plants, launch tubes of the ballistic ranges, thrust augmentation systems for cruise missiles, zero secondary flow ejectors, etc. The objective of this study is to revisit the classical base flow fields in a wall-bounded supersonic flow past a sudden expansion, to study and exploit their dependence on the size of the enlarged part – termed as the base size. Two-dimensional numerical simulations are performed for a nozzle flow, which is suddenly expanded in a larger rectangular channel. Five different turbulence models have been utilized in this study. Flow determination near the base is influenced by the proper selection of the turbulence model. The numerical solutions are compared with available experimental data and good agreement is achieved with renormalization group k–ε turbulence model. This investigation is concerned with the determination of the base size, for which the jet characteristics and the base pressure become independent of the size of the enlarged part. For a given duct, base pressure tends to a minimum for a particular pressure ratio. In this study, the authors have been able to link the jet characteristics to the base size by both analytical and numerical methods. This has led to the conclusion that for a constant driving pressure, the base pressure asymptotically decreases when the base size is increased up to a critical value, and it becomes independent of the base size thereafter. It is believed that the results of this study can provide a better understanding of the wall-bounded supersonic flow past a sudden expansion. The relevance of the present observations in some of the engineering applications is also discussed.