Modeling the Effect of Stability Bleed on Back-Pressure in Mixed-Compression Supersonic Inlets

To stabilize the terminal normal shock on high-static pressure at outlet, called back-pressure p_out, stability bleed slots are used in the throat of mixed-compression supersonic inlets. In this paper, a model for the functional relation between the bleed flow rate m_bl and back-pressure p_out is established based on a bleed flow rate model (BFRM) in order to study the effect of stability bleed on the back-pressure in mixed-compression supersonic inlets. Given the inlet flow parameters M_in, p_in∗, and T_in∗, the plenum pressure p_pl at slots' outlet, the terminal normal shock position x_s in this model, the bleed flow rate m_bl, Mach number M_out, and back-pressure p_out were derived one by one from the basic laws of conservation. To study the effect of plenum pressure p_pl on subsonic flow of the divergent section behind the terminal normal shock, a correction coefficient κ is introduced to modify the Mach number M_out. Furthermore, numerical simulations based on Reynolds-Averaged Navier-Stokes equations were performed to analyze the functional relation between the bleed flow rate m_bl and back-pressure p_out. Computational fluid dynamics (CFD) results show that the present model agrees with the data.