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Mechanisms in the hypersonic laminar near wake of a blunt body

Published online by Cambridge University Press:  25 January 2018

W. Schuyler Hinman Open the ORCID record for W. Schuyler Hinman [Opens in a new window]  and
Craig T. Johansen
W. Schuyler Hinman
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N1N4, Canada
Craig T. Johansen*
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N1N4, Canada
*
†Email address for correspondence: [email protected]
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Abstract

A new theoretical framework, based on the analysis of Navier–Stokes solutions for the hypersonic laminar near wake of two-dimensional and axisymmetric blunt bodies, is presented. A semi-empirical relationship is derived between the free-stream Mach and Reynolds numbers and a characteristic wake Reynolds number. A control volume analysis was performed to assess the validity of some common assumptions used in the literature. Analysis of the momentum and vorticity equations is used to assess the dominant mechanisms of momentum transfer along and across the dividing streamline and centreline which enclose the near wake. An observed stagnation pressure gain along the dividing streamline is explained using the entropy transport equation, demonstrating an unbalance between entropy generation due to viscous dissipation and entropy diffusion. The rear-stagnation point flow is analysed using an analogy to a reversed flow jet which allows for the centreline Mach number to be solved. A new viscous–inviscid interaction theory is presented for the reattachment shock formation process for both planar and axisymmetric wakes. Finally, all of the sub-mechanisms are combined into an overall wake mechanism. The resulting equations constitute the first overall theoretical framework of the laminar near-wake mechanism including separation, reattachment, rear-stagnation point flow and dividing streamline stagnation pressure gain for both planar and axisymmetric near wakes. Scaling arguments are presented throughout the work for each of the key sub-mechanisms. Recommendations are made for how experimental and numerical results for the near wake should be presented. The equations and recommendations presented here are then used to perform a detailed disambiguation of laminar capsule studies in the literature.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves Wakes/Jets: Wakes/Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 33 - 75
Copyright
© 2018 Cambridge University Press 

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