Numerical analysis of pseudo-shock flow diffusion phenomenon in variable cross-section ducts

Abstract

The pseudo-shock wave (PSW) region of flow diffusion, which appears when a supersonic flow in a duct decelerates to a subsonic flow, is a complicated process involving a multi-faceted interaction between the duct's peripheral boundary layer and the central shock-wave field. It is made up of an upstream shock train region, comprised of lambda and oblique shock waves, and a downstream mixing region, both of which significantly influence the effective performance of the desired flow diffusion process. In this article, the PSW in two variable-cross-sectional ducts, edge- and corner-varied in transforming from a rectangular to a circular duct moving downstream, was researched through computational fluid dynamics (CFD) numerical simulation. The PSW flowfields in circular and rectangular ducts were also computed to be counterparts. The identical inflow parameters ( Ma = 2.0, T0 = 298 K and P0 = 100 kPa) in combination with different pressure ratios ( Pb/ Pi = 2.8—3.8) were considered. The characteristics of the PSW phenomenon, such as the leading edge of the PSW, length of the shock train, mass-weighted average parameters at the exit, and so on, were analysed. For these cases, with the same pressure ratio Pb/ Pi = 3.8, the shock train length in the corner-varied duct is the shortest, and its capability of supporting backpressure is the weakest of the four ducts. For these cases, with the same leading edge of the PSW at X = 0.167 L, a shorter and wider corner flow separation region appears in the variable-cross-sectional edge-varied duct in comparison with the rectangular duct. With regard to the length of shock train, level of internal drag, and capability to support backpressure, the edge-varied duct is the superior design choice. An advantage of the edge-varied duct is the improved internal drag: an additive thrust is produced to partly offset the drag due to the duct's axial divergence-angle setting. Based on an analysis of the PSW flow pattern in these ducts, it has been established that the wall-pressure distributions of the shock train can be well predicted by the modified Waltrup formula after the introduction of an equivalent diameter and an exponent α for Reθ.