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 = 0.167L, 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.

[1]  Pseudo-shock in supersonic injection feeder , 1999 .

[2]  A. L. Addy,et al.  On the Starting Characteristics of Supersonic Ejector Systems , 1964 .

[3]  Kazuhide Mizobata,et al.  Numerical and experimental investigations on the mach 2 pseudo-shock wave in a square duct , 2003, J. Vis..

[4]  William H. Heiser,et al.  Hypersonic Airbreathing Propulsion , 1994 .

[5]  P. Merkli.  Pressure Recovery in Rectangular Constant Area Supersonic Diffusers , 1976 .

[6]  J. Dutton,et al.  Characteristics of multiple shock wave/turbulent boundary-layer interactions in rectangular ducts , 1990 .

[7]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[8]  E. P. Neumann,et al.  High-Efficiency Supersonic Diffusers , 1951 .

[9]  Walter C. Engelund,et al.  Integrated Aeropropulsive Computational Fluid Dynamics Methodology for the Hyper-X Flight Experiment , 2001 .

[10]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986 .

[11]  Hui-Jun Tan,et al.  Preliminary Study of Shock Train in a Curved Variable-Section Diffuser , 2008 .

[12]  Katherine Grendell,et al.  A Comparison Study of Rectangular and Chamfered Isolator Cross-Sectional Shape with Varied Divergence , 2004 .

[13]  S. Cox-Stouffer,et al.  The effect of aspect ratio on isolator performance , 2001 .

[14]  L. Crocco,et al.  B. One-Dimensional Treatment of Steady Gas Dynamics , 1958 .

[15]  Daniel B. Le,et al.  Shock Train Leading Edge Detection in a Dual-Mode Scramjet , 2006 .

[16]  F. Billig,et al.  Prediction of Precombustion Wall Pressure Distributions in Scramjet Engines , 1973 .

[17]  Pei Lin.  Geometric effects on precombustion shock train in constant area isolators , 1993 .

[18]  F. Billig,et al.  Structure of Shock Waves in Cylindrical Ducts , 1973 .

[19]  H. D. Kim,et al.  Mass-averaging pseudo-shock model in a straight flow passage , 1999 .

[20]  G. Mclafferty,et al.  Experimental results of shock trains in rectangular ducts , 1992 .

[21]  J. Dutton,et al.  Computations and experiments for a multiple normal shock/boundary-layer interaction , 1993 .

[22]  Yoshiaki Miyazato,et al.  Shock train and pseudo-shock phenomena in internal gas flows , 1999 .