Similarity laws for single-nozzle retropropulsion flow structures in reusable launch vehicles

Retropropulsion is a deceleration technique that directs thrust along the flight path and serves as the driving technology for vertical rocket recovery and reusability. The flow structure and scales of the retropropulsion flow field are governed by the complex interaction between the jet and the incoming freestream. To investigate this interaction in detail, high-fidelity numerical simulations of a single-nozzle retropropulsion configuration were employed in this work. The effects of thrust coefficients, freestream Mach numbers, and specific jet heat ratios on the flow field structure were systematically examined. Through quantitative analysis of the flow structure, the influence of these parameters was revealed on key flow features, such as the shape and location of shocks and the penetration depth of the jet. The results show that the thrust coefficient is the dominant parameter governing the flow structure. The axial position and characteristic scale of typical flow structures in the interaction region scale linearly with the square root of the thrust coefficient. Further analysis indicates that under hypersonic conditions, the flow structure is insensitive to the freestream Mach number. In contrast, the specific heat ratio of the jet gas affects the penetration and expansion behavior of the jet. Subsequently, the physical model based on the momentum conservation principle and the empirical relation are used to explain the mechanisms by which these parameters affect the flow field structure, thereby enhancing the understanding of retropropulsion flow fields.