Journal of Fluid Mechanics

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

SERGIO PIROZZOLIa1 c1, MATTEO BERNARDINIa1 and FRANCESCO GRASSOa1

a1 Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy

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.

(Received October 01 2009)

(Revised April 02 2010)

(Accepted April 06 2010)

(Online publication June 24 2010)

Key words:

  • compressible boundary layers;
  • shock waves;
  • turbulence simulation

Correspondence:

c1 Email address for correspondence: sergio.pirozzoli@uniroma1.it

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