High-resolution large-eddy simulation is used to investigate the mean and turbulence properties of a separated flow in a channel constricted by periodically distributed hill-shaped protrusions on one wall that obstruct the channel by 33% of its height and are arranged 9 hill heights apart. The geometry is a modification of an experimental configuration, the adaptation providing an extended region of post-reattachment recovery and allowing high-quality simulations to be performed at acceptable computing costs. The Reynolds number, based on the hill height and the bulk velocity above the crest is 10595. The simulated domain is streamwise as well as spanwise periodic, extending from one hill crest to the next in the streamwise direction and over 4.5 hill heights in the spanwise direction. This arrangement minimizes uncertainties associated with boundary conditions and makes the flow an especially attractive generic test case for validating turbulence closures for statistically two-dimensional separation. The emphasis of the study is on elucidating the turbulence mechanisms associated with separation, recirculation reattachment, acceleration and wall proximity. Hence, careful attention has been paid to resolution, and a body-fitted, low-aspect-ratio, nearly orthogonal numerical grid of close to 5 million nodes has been used. Unusually, the results of two entirely independent simulations with different codes for identical flow and numerical conditions are compared and shown to agree closely. Results are included for mean velocity, Reynolds stresses, anisotropy measures, spectra and budgets for the Reynolds stresses. Moreover, an analysis of structural characteristics is undertaken on the basis of instantaneous realizations, and links to features observed in the statistical results are identified and interpreted. Among a number of interesting features, a distinct ‘splatting’ of eddies on the windward hill side following reattachment is observed, which generates strong spanwise fluctuations that are reflected, statistically, by the spanwise normal stress near the wall exceeding that of the streamwise stress by a substantial margin, despite the absence of spanwise strain.

Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions

Direct numerical simulation databases of turbulent channel and pipe flow have been used in order to assess the energy transfer between resolved and unresolved motions in large‐eddy simulations. To this end, the velocity fields are split into three parts: a statistically stationary mean flow, the resolved, and the unresolved turbulent fluctuations. The distinction between the resolved and unresolved motions is based on the application of a cutoff filter in spectral space. Within the buffer layer a backward transfer of averaged kinetic energy from subgrid to grid‐scale turbulent motions has been found to exist, which is primarily caused by subgrid‐scale stresses aligned with the mean rates of strain. Such reverse transfer generally cannot be described by the simple eddy‐viscosity‐type subgrid models usually applied in large‐eddy simulations. The use of a conditional averaging technique revealed that the reverse transfer of energy within the near‐wall flow is strongly enhanced by coherent motions, such as the well‐known bursting events.

Subgrid‐scale energy transfer in the near‐wall region of turbulent flows

We analyse the wind and boundary layer properties of turbulent Rayleigh–Benard convection in a cylindrical container with aspect ratio one for Prandtl number Pr = 0.786 and Rayleigh numbers (Ra) up to 10^9 by means of highly resolved direct numerical simulations. We identify time periods in which the orientation of the large scale circulation (LSC) is nearly constant to be able to perform a statistical analysis of the LSC. The analysis is then reduced to two dimensions by considering only the plane
of the LSC. Within this plane the large scale circulation is treated as a wind with thermal and viscous boundary layers developing close to the horizontal plates. Special focus is set on the spatial development of the wind magnitude and the boundary layer thicknesses along the bottom plate. A method for the local analysis of the instantaneous boundary layer thicknesses is introduced which shows a dramatically changing wind magnitude along the wind path. Furthermore a linear increase of the viscous and thermal boundary layer thickness along the wind is observed for all considered Ra while their ratio is spatially constant but depends weakly on Ra. A possible explanation is a strong spatial variation of the wind magnitude and fluctuations in the boundary layer
region.

Boundary layers and wind in cylindrical Rayleigh–Bénard cells

DNS of a turbulent boundary layer with separation

Large-Eddy Simulation: A Critical Survey of Models and Applications

Statistically steady and two-dimensional high Reynolds number turbulent flat plate channel and boundary layer flow is simulated by numerical integration of the three-dimensional, time-dependent transport equations for grid scale (GS) quantities. Detailed comparisons of the numerical results are made witth measurements of statistical mean values. The structure of the fluctuating and instantaneous fields is displayed. Especially the influence of the treatment of the mean convection terms on the results is discussed.

R. Friedrich

Papers

Large-Eddy Simulation of Turbulent Boundary Layer and Channel Flow at High Reynolds Number