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Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation

Published online by Cambridge University Press:  24 June 2010

SERGIO PIROZZOLI ,
MATTEO BERNARDINI  and
FRANCESCO GRASSO
SERGIO PIROZZOLI*
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
MATTEO BERNARDINI
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
FRANCESCO GRASSO
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The interaction of a normal shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number M∞ = 1.3 and Reynolds number Reθ ≈ 1200 (based on the momentum thickness of the upstream boundary layer) is analysed by means of direct numerical simulation of the compressible Navier–Stokes equations. The computational methodology is based on a hybrid linear/weighted essentially non-oscillatory conservative finite-difference approach, whereby the switch is controlled by the local regularity of the solution, so as to minimize numerical dissipation. As found in experiments, the mean flow pattern consists of an upstream fan of compression waves associated with the thickening of the boundary layer, and the supersonic region is terminated by a nearly normal shock, with substantial bending of the interacting shock. At the selected conditions the flow does not exhibit separation in the mean. However, the interaction region is characterized by ‘intermittent transitory detachment’ with scattered spots of instantaneous flow reversal throughout the interaction zone, and by the formation of a turbulent mixing layer, with associated unsteady release of vortical structures. As found in supersonic impinging shock interactions, we observe a different amplification of the longitudinal Reynolds stress component with respect to the others. Indeed, the effect of the adverse pressure gradient is to reduce the mean shear, with subsequent suppression of the near-wall streaks, and isotropization of turbulence. The recovery of the boundary layer past the interaction zone follows a quasi-equilibrium process, characterized by a self-similar distribution of the mean flow properties.

JFM classification

Compressible Flows: Compressible boundary layers Compressible Flows: Shock waves Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010 , pp. 361 - 393
Copyright
Copyright © Cambridge University Press 2010

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Pirozzoli et al. supplementary movie

Transonic shock wave/boundary layer interaction. Animation of the pressure field in streamwise, wall-normal plane in the proximity of the interaction zone. Pressure is normalized by its free-stream value, and 32 contour levels are shown, from 0.77 to 1.53.

Download Pirozzoli et al. supplementary movie(Video)
Video 10.5 MB