Effect of geometry and Reynolds number on the turbulent separated flow behind a bulge in a channel

Abstract

Turbulent flow separation induced by a protuberance on one of the walls of an otherwise planar channel is investigated using direct numerical simulations. Different bulge geometries and Reynolds numbers -with the highest friction Reynolds number simulation reaching a peak of Re τ = 900 -are addressed to understand the effect of the wall curvature and of the Reynolds number on the dynamics of the recirculating bubble behind the bump. Global quantities reveal that most of the drag is due to the form contribution, whilst the friction contribution does not change appreciably with respect to an equivalent planar channel flow. The size and position of the separation bubble strongly depends on the bump shape and the Reynolds number. The most bluff geometry has a larger recirculation region, whilst the Reynolds number increase results in a smaller recirculation bubble and a shear layer more attached to the bump. The position of the reattachment point only depends on the Reynolds number, in agreement with experimental data available in the literature. Both the mean and the turbulent kinetic energy equations are addressed in such non-homogeneous conditions revealing a non-trivial behaviour of the energy fluxes. The energy introduced by the pressure drop follows two routes: part of it is transferred towards the walls to be dissipated and part feeds the turbulent production hence the velocity fluctuations in the separating shear layer. Spatial energy fluxes transfer the kinetic energy into the recirculation bubble and downstream near the wall where it is ultimately dissipated. Consistently, anisotropy concentrates at small scales near the walls irrespective of the value of the Reynolds number. In the bulk flow and in the recirculation bubble, isotropy is restored at small scales and the isotropy recovery rate is controlled by the Reynolds number. Anisotropy invariant maps are presented, showing the difficulty in developing suitable turbulence models to predict separated turbulent flow dynamics. Results shed light on the processes of production, transfer and dissipation of energy in this relatively complex turbulent flow where non-homogeneous effects overwhelm the classical picture of wall-bounded turbulent flows which typically exploits streamwise homogeneity.

On the structure of the self-sustaining cycle in separating and reattaching flows

“…This behaviour of q inverts while moving through the wake where turbulent kinetic energy increases again forming a local maximum in a region just behind the wake vortex centered at (x, y) ≈ (6.2, 0.15). For further details, see Mollicone et al (2017) where the energetics of separating and reattaching flows are assessed by analysing the mean and turbulent kinetic energy budgets.…”

Analyzing the spectral energy cascade in turbulent channel flow

“…Figure 18 shows the pressure diffusion spectral density [Eq. (20)]. For y + ≤ 10 in the lower Reynolds number flow, the pressure diffusion acts as an energy source, whereas, as the mid-channel is approached, the term acts as a sink across the affected scales.…”

“…In this way, a necessary task to completely describe the real dynamics, in the presence of the spatial fluxes induced by inhomogeneity, is the study of the spatial and the spectral behaviors of a turbulent plane channel flow and the impact of the Reynolds number. The simultaneous spectral/spatial analysis of the influence of the Reynolds number in the transport equation for the TKE in turbulent flow separation induced by a protuberance on one of the walls, performed by Mollicone et al, 20 shows great importance, especially when the influence of the energy flux of different scales is assessed for subgrid-scale closure models. 30 In this context, the present paper analyzes the energy flux in the complete physical space and spectral domain, allowing the direct correlation between different wall-parallel planes, and helps to unveil new important details of the energy transfer processes.…”

Large-eddy simulation of turbulent flow over a parametric set of bumps

“…Aspects of data that are representative for the class of flows can be distinguished from specific data for a single geometry. Mollicone et al (2017) also studied a family of bumps but all their bumps had separated flow.…”