Geometry Rule of Combustor–Inlet Interaction in Ramjet Engines

Abstract

Combustor–inlet interactions in ramjet engines are associated with such critical operation processes as combustion mode (ramjet mode/scramjet mode) transition and the onset of inlet unstart. Previous studies showed these critical operational processes were characterized by a nonlinear hysteresis property that originated from flow instabilities. This paper describes in detail, discusses, and comes to the conclusion that the complex hysteresis phenomena that are exhibited during the combustor–inlet interaction in a ramjet engine are governed by a certain mathematical rule: the butterfly geometry in Thom’s classification theorem. This conclusion is proved analytically under the assumption of inviscid flow. It shows the bifurcation set of a ramjet engine is a butterfly-shaped geometry. The butterfly geometry is higher in dimension than the formerly found cusp geometry, and it rules the hysteresis behaviors that are exhibited during combustion mode transition and inlet start/unstart, respectively. The formerly found cusp geometry is a local geometry of butterfly geometry. This invariance geometry rule offers not only an explanation of the known hysteresis behaviors but also a way of predicting the unknown hysteresis behaviors that are exhibited during combustor–inlet interaction in a ramjet engine. The hysteresis property introduces complex route-dependent behaviors to ramjet engines, and it is therefore necessary to have a global picture of various hysteresis phenomena for further understanding of the control problems of ramjet engines.