Adaptive Control Volume Model for Predicting Pseudoshock Properties

An adaptive control volume (ACV) is developed to model pseudoshock properties as a function of the backpressure for supersonic internal flows. The formulation accounts for outlet Mach number nonuniformity using two primary independent variables and can be formulated under either attached or separated flow assumptions. The model is applied to a Mach 2 pseudoshock in a rectangular duct with area change and is validated against computational fluid dynamics solutions. Results demonstrate accurate prediction of the area-averaged Mach number and mass-averaged total pressure over a wide range of backpressures. Sensitivity analyses show that the solution is weakly dependent on the nonuniformity parameter once sufficiently large, while the turbulent momentum transport parameter strongly influences total pressure losses. Beyond validation, the ACV model provides insight into pseudoshock physics, permits reliable prediction of outlet quantities using only wall static pressure measurements, and offers potential for low-cost system monitoring and control in high-speed vehicle applications.