Limiting Contractions for Starting Prandtl-Meyer-Type Scramjet Inlets with Overboard Spillage

The air inlet is a crucial component of hypersonic airbreathing engines, which should decelerate and compress airflow with minimum losses. For efficient engine operation the inlet must be started, i.e., all incoming supersonic flow must be captured and the flow inside the inlet must be predominantly supersonic. Kantrowitz and Donaldson [1, 2] established the classical theory of flow starting in converging ducts. According to the theory, the limiting duct area ratio for spontaneous starting (or self-starting) is based on the flow condition at which a normal shock is positioned exactly at the duct entry and the post-shock subsonic flow isentropically accelerates along the duct to become sonic at the duct exit (i.e., the choked throat is considered). It is assumed that the flow is quasi-one-dimensional and quasi-steady. For exit-toentry area ratios exceeding the limiting values, which depend on freestream Mach number, the duct (inlet) flow would start on its own, upon the increase of freestream velocity fromzero to the required value. As follows fromthe Kantrowitz theory, limiting contractions for starting lead to low contraction inlets, which do not provide sufficient compression for scramjet operation. Practical, high-contraction inlets do not satisfy the Kantrowitz self-starting condition and would not start spontaneously. This constitutes a well-known inlet starting problem.