Numerical Investigation of Recirculation Bubble Dynamics in Extremely Under-Expanded Jet Impingement with Non-Uniform Inflow Conditions

During lunar landing and takeoff, an extremely under-expanded jet from retrorocket engines generates a complex impingement flow, including multiple shocks and a near-field recirculation bubble, posing critical risks to lunar missions. To clarify the formation and evolution of the recirculation bubble, numerical simulations under non-uniform inflow conditions over a range of nozzle heights are performed using a compressible Navier–Stokes solver. The shock structures depend on the distance available for inflow development. Non-uniform total pressure ahead of the surface shock is the primary driver of the adverse pressure gradient that initiates the bubble. This non-uniformity originates from shock interactions at high nozzle heights and directly from the inflow conditions at low heights. Furthermore, the flow stabilizes rapidly at high nozzle heights, while strong unsteadiness persists at low heights. A dimensionless coefficient, C_RB, defined as the ratio of pressure difference to dynamic pressure along the recirculation bubble boundary, is proposed to characterize the interaction between the recirculation bubble and surface shock. Its steady-state variation with nozzle height reveals a distinct threshold below which both bubble size and intensity increase sharply, indicating a flow pattern transition.