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Blunt-body paradox and transient growth on a hypersonic spherical forebody

Pedro Paredes*, Meelan M. Choudhari, and Fei Li

  • Computational AeroSciences Branch, NASA Langley Research Center, Hampton, Virginia 23681, USA

  • *pedro.paredes@nasa.gov
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Phys. Rev. Fluids 2, 053903 – Published 24 May, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.053903

Abstract

Roughness-induced transient growth has emerged as a possible cause for transition in linearly stable boundary layer flows over spherical forebodies. This paper investigates the optimal growth of perturbations in the axisymmetric, laminar boundary layer over a hemisphere placed in a Mach 7.32 free stream, with the goals of contributing further insights and revisiting highly successful, transient-growth based prediction criteria for subcritical transition over blunt body configurations. Earlier predictions based on local-similarity approximation to the basic state are extended to a basic state that is obtained from the compressible Navier-Stokes equations and, hence, accounts for the presence of the bow shock, the nonsimilar development of the boundary layer, and the convex curvature of the body surface. The predicted transient growth characteristics are profoundly different from the previous body of results for boundary layer flows over flat plates and circular cones. More importantly, the selections of energy norm and objective function used to compute optimal growth exert a crucial influence on the optimal growth characteristics of a blunt body. With the conventional energy norm based on both kinetic and thermodynamic fluctuations, the highest energy gain from the input station to the output station occurs over relatively short optimization intervals in the vicinity of the stagnation point; however, the associated kinetic energy gain, which is more closely linked to transition via streak instabilities, is rather small in magnitude. On the other hand, the mean kinetic energy gain is maximized when the disturbance inflow location nearly coincides with the location corresponding to peak wall shear associated with the basic state. Assuming that the roughness-induced disturbance velocities are proportional to the roughness height, the maximum disturbance kinetic energy would be reached in the vicinity of the sonic point, which could explain the measured onset of transition within this region during prior wind-tunnel and flight experiments.

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Phys. Rev. Fluids 2, 053903– Published 24 May, 2017
  • Received 29 August 2016
Article part of CHORUS

Published by the American Physical Society

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