Supersonic Bleed Rate Model for a Circular Orifice Based on Geometric Similarity

Abstract

On the basis of the geometric similarity between polygons and circles, a bleed rate model of a supersonic inviscid circular hole is first established through a gradual approximation by regular polygons. The bleed mass-flow rate depends on the parameters at the entrance. A supersonic inviscid bleed choking model is further established by using the inflow Mach number and the pressure ratio when the expansion wave is parallel to the entrance. For a depthless hole at Mach 2.0 and with a pressure ratio of 0.5, the difference of flow coefficient predicted by the present model to that of computational fluid dynamics is 1.4% under nonchoking conditions. Under choking conditions with a pressure ratio of 0.1, the difference is 3.1%. Furthermore, the influence of the boundary layer on the bleed mass-flow rate is transformed into the influence of the displacement thickness on the effective size of the bleed hole. Based on that, the viscous bleed rate model is established, which shows a maximum error of 7.7% for a depthless bleed hole over laminar flow at Mach 4.0 and Reynolds number 2.590 × 10 5 . Compared with the reported results of the full bleed hole, the difference of the bleed mass-flow rate predicted by the present model is 3.8%.