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 $pout$⁠, 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 $mbl$ and back-pressure $pout$ 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 $Min$⁠, $pin*$⁠, and $Tin*$⁠, the plenum pressure $ppl$ at slots' outlet, the terminal normal shock position $xs$ in this model, the bleed flow rate $mbl$⁠, Mach number $M¯out$⁠, and back-pressure $pout$ were derived one by one from the basic laws of conservation. To study the effect of plenum pressure $ppl$ 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 $mbl$ and back-pressure $pout$⁠. Computational fluid dynamics (CFD) results show that the present model agrees with the data.