Turbulence in supersonic boundary layers at moderate Reynolds number

Abstract

We study the organization of turbulence in supersonic boundary layers through large-scale direct numerical simulations (DNS) at M-infinity = 2, and momentum-thickness Reynolds number up to Re-delta 2 approximate to 3900 (corresponding to Re-tau approximate to 1120) which significantly extend the current envelope of DNS in the supersonic regime. The numerical strategy relies on high-order, non-dissipative discretization of the convective terms in the Navier Stokes equations, and it implements a recycling/rescaling strategy to stimulate the inflow turbulence. Comparison of the velocity statistics up to fourth order shows nearly exact agreement with reference incompressible data, provided the momentum-thickness Reynolds number is matched, and provided the mean velocity and the velocity fluctuations are scaled to incorporate the effects of mean density variation, as postulated by Morkovin's hypothesis. As also found in the incompressible regime, we observe quite a different behaviour of the second-order flow statistics at sufficiently large Reynolds number, most of which show the onset of a range with logarithmic variation, typical of 'attached' variables, whereas the wall-normal velocity exhibits a plateau away from the wall, which is typical of 'detached' variables. The modifications of the structure of the flow field that underlie this change of behaviour are highlighted through visualizations of the velocity and temperature fields, which substantiate the formation of large jet-like and wake-like motions in the outer part of the boundary layer. It is found that the typical size of the attached eddies roughly scales with the local mean velocity gradient, rather than being proportional to the wall distance, as happens for the wall-detached variables. The interactions of the large eddies in the outer layer with the near-wall region are quantified through a two-point amplitude modulation covariance, which characterizes the modulating action of energetic outer-layer eddies

Probing high-Reynolds-number effects in numerical boundary layers

“…The larger absolute value of the peak found in the present compressible DNS, is likely to be a shortcoming of density scaling to fully account for compressibility effects in the near-wall layer. 17 Closer agreement is found with the correlation proposed by Metzger and Klewicki, 28 R + 11pk = 1.86 + 0.28 log 10 Re θ i (data are not shown).…”

“…16 In this paper we present novel data from turbulent boundary layer DNS, which extends the range of Reynolds number to Re τ ≈ 4000, thus meeting the constraints for the flow to be considered genuinely high-Reynolds. As in previous studies 17 at lower Reynolds number (Re τ 1100), the simulations are carried out in the low supersonic regime. Given the weakness of genuine compressibility effects in zero-pressure-gradient boundary layers in the low supersonic regime, the flow statistics provided by our DNS also carry over, with very little uncertainty, to the incompressible regime.…”

“…A detailed description of the numerical strategy is presented in Pirozzoli, 19 and a discussion of the flow physics for flow cases TBL1-3 is reported in Pirozzoli and Bernardini. 17 The TBL4 simulation has been performed in a domain extending for…”

Direct Numerical Simulation on Mach Number and Wall Temperature Effects in the Turbulent Flows of Flat-Plate Boundary Layer

“…The results show that the essential dynamics of the CTBL greatly resemble the incompressible case. Pirozzli et al [22] further to proposed the meticulous structure of a spatially evolving supersonic boundary layer by DNS with Ma ∞ = 2 up to Re τ ≈ 1120. Such a result provides possibilities to start probing the effects of high Reynolds numbers.…”

DNS of a spatially evolving hypersonic turbulent boundary layer at Mach 8

“…The results show that the essential dynamics of the turbulent boundary layer closely resemble the incompressible case. Pirozzli and Bernardini [6] proposed the meticulous structure of a spatially evolving supersonic boundary layer by DNS with Ma ∞ =2 up to Re  = 1120. Such a result allows us to start probing the effects of high Reynolds numbers.…”