Showing papers by "Sergio Pirozzoli published in 2010"

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

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.

On the dynamical relevance of coherent vortical structures in turbulent boundary layers

Abstract: The dynamical relevance of vortex tubes and vortex sheets in a wall-bounded supersonic turbulent flow at Mach number M = 2 and Reynolds number Re θ ≈ 1350 is quantitatively analysed. The flow in the viscous sublayer and in the buffer region is characterized by intense, elongated vorticity tongues forming a shallow angle with respect to the wall, whose characteristic length is O(200) wall units and whose size in the cross-stream direction is O(50) wall units. The formation of vortex tubes takes place starting from y + ≈ 10, and it is mainly associated with the roll-up and the interaction of vortex sheets. The analysis of the non-local dynamical effect of tubes and sheets suggests that the latter have a more important collective effect, being closely associated with low-speed streaks, and being responsible for a substantial contribution to the mean momentum balance and to the production of turbulence kinetic energy and enstrophy.

Analysis of unsteady effects in shock/boundary layer interactions

Abstract: The dynamics of interactions between impinging shock waves and turbulent boundary layers in supersonic flow is analyzed by mining a LES database developed for several strengths of the incoming shock. The primary effect of increasing the strength of the interaction is an increase in the size of the interaction zone and the formation of a sizeable recirculation bubble. A side consequence of the topological flow changes is the onset of very-low-frequency motions near the foot of the reflected shock, with characteristic frequencies that may be as small as three orders of magnitude less than those of the incoming boundary layer. The flow dynamics is analyzed by means of standard Fourier analysis, as well as non-standard dynamic mode decomposition. Both approaches highlight the occurrence of two distinct flow modes, the high-frequency one being associated with the turbulence dynamics, and the low-frequency one associated with pulsation of the separation bubble, accompanied by fore-and-aft motion of the reflected shock. Linear global stability analysis performed on the mean flow fields extracted from LES highlights the occurrence of a single, non-oscillatory exponentially growing mode, as well as the presence of slightly damped, low-frequency oscillatory modes, whose stability margin decreases with the strength of the interaction, and which feature a ‘breathing’ motion of the separation bubble.

Vorticity dynamics in turbulence growth

Abstract: The mechanisms of vorticity amplification in the formation of turbulence are investigated by means of direct numerical simulations of the Navier–Stokes equations with different initial conditions and Reynolds numbers. The simulations show good universality of the enstrophy evolution, that occurs in two stages. The first stage is dominated by the effect of vortex stretching, and it finishes with a k −3 power-law energy spectrum. The second stage is dominated by the action of viscosity on the small scales, and it finishes with a Kolmogorov k −5/3 energy spectrum.

IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction Wall pressure fluctuations in transonic shock/boundary layer interaction

Abstract: The structure of wall pressure fluctuations beneath a turbulent boundary layer interacting with a normal shock wave is investigated through direct numerical simulation (DNS). In the zeropressure-gradient (ZPG) region upstream of the interaction pressure statistics well compare with canonical boundary layers in terms of fluctuation intensities and frequency spectra. Across the interaction zone, the r.m.s. wall pressure fluctuations attain large values (in excess of ≈ 162dB), with an increase of about 7 dB from the upstream level. The main effect of the interaction on the frequency spectra is to enhance of the low-frequency Fourier modes, while inhibiting the high-frequency ones. Excellent collapse of frequency spectra is observed past the interaction zone when data are scaled with the local boundary layer units. In this region an extended ω −7/3 power-law behavior is observed, which is associated with the suppression of mean shear caused by the imposed adverse pressure gradient.