Topological Geometry Interpretation of Supersonic Inlet Start/Unstart Based on Catastrophe Theory

U NSTART phenomenon is one of the most important issues of hypersonic inlets. If an inlet is not started, the mass capture will be greatly reduced, and the spillage drag will be excessive. For hypersonic air-breathing engines, inlet unstart will cause a large drop of both engine thrust and specific impulse, and it may cause catastrophic damage during hypersonic flight. Over the past decades, many investigations have been conducted to examine the mechanisms of inlet start and unstart. Mayer and Paynter [1,2] simulated an axisymmetric inlet unstart due to the variation of freestream variables such as temperature, velocity, and pressure. Neaves and McRae [3] simulated the 3-D inlet unstart caused by a combustor perturbation. Zha et al. [4,5] investigated unstart transient mechanism of a typical axisymmetric inlet at angle of attack. Cox et al. [6] presented several mechanisms of hypersonic inlet unstart, including backpressure unstart, overcontraction unstart, and angle of attack unstart. Van Wie and Kwok [7], Yuan and Liang [8], and others have observed the nonlinear catastrophe and hysteresis phenomena of inlet start/unstart. These studies have made contributions from different aspects. As from these studies, the start/unstart process is influenced by many factors, and the physical law is complex with strong nonlinearities such as catastrophe, hysteresis, etc. Because inlet unstart may cause catastrophic damage to the aircraft, it must be avoided and controlled during hypersonic flight. With this consideration, it is important to study the physical law of inlet start/unstart, for example, to study the catastrophe boundaries of inlet start/unstart at different operation conditions (different flight Mach number, angle of attack, flight height, and back pressure). The physical law of inlet start/unstart will be important for further application (i.e., avoid or control inlet unstart). As known, the transition between inlet start and unstart is mainly characterized by catastrophe, and such systems can be studied by catastrophe theory. With this consideration, this paper will try to use the topological geometry method in catastrophe theory to study the physical law of inlet start/unstart. In general, catastrophe theory permits the establishment of qualitative and general solutions of the catastrophe behaviors, and it can deal with complex systems with catastrophe properties. In this paper,first, the catastrophemechanism of inlet start/unstart is analyzed. Second, the nonlinear catastrophe, hysteresis, and bifurcation features of inlet start/unstart are simulated based on the topological geometrymethod in catastrophe theory, and the catastrophe boundaries of inlet start/unstart are obtained. Third, the physical laws inlet start/unstart are interpreted along typical control routes around the catastrophe boundaries.