Bistability and Hysteresis in a Nonlinear Dynamic Model of Shock Motion

The study is motivated by a review of experimental and numerical evidences for the occurrence of bistability and hysteresis in supersonic inlets. By retaining the essential strongly nonlinear behaviors and the dominant system dynamics, a low-order model of the time-dependent behaviors of shock motion is developed to describe the bistability and hysteresis behaviors of shock motion in a supersonic inlet. Assumptions of inviscid and quasi-one-dimensional flow are invoked to ensure an analytic description of the dynamic process. Comparisons between the low-order model and unsteady computational fluid dynamics simulation results show the low-order model has the capability of qualitatively describing the bistability and hysteresis behaviors of shock motion.