Empirical Equation for Self-starting Limit of Supersonic Inlets

Abstract

F OR hypersonic inlets that operate over a large Mach number range and use a combination of external and internal compression, it must be ensured that inlets can self-start at takeoverMach number. An unstarted inlet captures less airflowwith lower efficiency and higher aerodynamic and thermal loads compared with a started inlet. The starting problemwas recently studied bymany researchers [1–3]. The term started is used to denote operation under conditions where flow phenomena in the internal portion of the inlet do not alter the capture characteristics of the inlet [4]. An inlet can be unstarted by three reasons [4,5]: 1) The internal contraction is so large that the inlet is overcontracted to the point where the flow chokes at the inlet throat. 2) The back pressure is raised beyond the level that can be sustained by the inlet. 3) The formation of a large separated flowmakes the flow choked. At high Mach numbers, the unstarted flowfield is usually characterized by a large separated region. Self-starting indicates that the inlet will start without a change in inlet geometry. It is a significant feature in a fixed-geometry inlet design because it indicates that variable geometry is not necessary to restart the inlet . Preliminary estimates of the internal contraction ratio that will self-start can be obtained from theKantrowitz limit [7]. This limit is determined by assuming a normal shock at the beginning of the internal contraction and calculating the one-dimensional isentropic internal area ratio that will produce sonicflow at the throat. For a perfect gas the internal contraction ratio of Kantrowitz limit can be calculated as follows: