The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities

Strategies for turbulence modelling and simulations

The numerical simulation of high Reynolds number flows is hampered by model accuracy if the Reynolds-averaged Navier–Stokes (RANS) equations are used, and by computational cost if direct or large-eddy simulations (LES) that resolve the near-wall layer are employed. The cost of a calculation scales like the Reynolds number to the power 3 for direct numerical simulations, or 2.4 for LES, making the resolution of the wall layer at high Reynolds number infeasible even with the most advanced computers. In LES, an attractive alternative to compute high-Re flows is the use of wall-layer models, in which only the outer layer is resolved, while the near-wall region is modeled. Three broad classes of approaches are presently used: bypassing this region altogether using wall functions, solving a separate set of equations in the near-wall region, weakly coupled to the outer flow, or simulating the near-wall region in a global, Reynolds-averaged, sense. These approaches are discussed and their ranges of applicability are highlighted. Various unresolved issues in wall-layer modeling are presented.

Wall-layer models for large-eddy simulations

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

How should the resolution of an LES be estimated? There exist guidelines for boundary layers for how to create a grid in terms of the grid size expressed in viscous units. However, in other flow regions there are few – if any – guidelines for how to generate a grid that ensures accurate results. Worse, it is not even clear how to estimate the resolution after having carried out an LES. The present study evaluates the following quantities: energy spectra, dissipation energy spectra, two-point correlations, the ratio of SGS shear stress to resolved shear stress, the ratio of the SGS viscosity to the molecular and the ratio of the SGS dissipation due to the resolved fluctuating velocity gradients to that due to the mean velocity gradients. Two flows are analyzed, namely the flow in a plane asymmetric diffuser and decaying grid turbulence. The main conclusions are that two-point correlations are the best way to estimate the resolution and that energy spectra are not suitable. It is usually assumed that the SGS dissipation takes place at wavenumbers close to cut-off. The present work shows that this idealized picture is not true, but that the SGS dissipation takes place at rather low wavenumbers.

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How to estimate the resolution of an LES of recirculating flow

Assessment of realizability constraints in v2–f turbulence models

The paper evaluates a new method for prescribing synthesized turbulent inlet boundary conditions. When making LES, DES or hybrid LES-RANS, a precursor channel DNS is often used. The disadvantage of this method is that it is difficult to re-scale the DNS fluctuations to higher Reynolds numbers. In the present work, synthesized isotropic turbulent fluctuations are generated at the inlet plane with a prescribed turbulent length scale and energy spectrum. A large number of independent realizations are generated. A correlation in time between these realizations is introduced via an asymmetric, non-truncated time filter. In this way the turbulent time scale of the synthesized isotropic turbulent fluctuations is prescribed.

Hybrid LES-RANS: Inlet Boundary Conditions for Flows with Recirculation

This chapter discusses computation of the flow around a three-dimensional hill. The main bottle neck for using large eddy simulations at high Reynolds number is the requirement of very fine meshes near walls. Hybrid large eddy simulation-Reynolds averaged Navier-Stokes (LES-RANS) is invented to get rid of this limitation. The object of hybrid LES-RANS is to get rid of the requirement of high near-wall resolution in wall-parallel planes. In the near-wall region (the URANS region), a low-Re number RANS turbulence model (usually an eddy-viscosity model) is used. In the outer region (the LES region), the usual LES is used. In this method, unsteady RANS (URANS) is used near walls and at a certain distance from the wall, where the LES resolution is sufficiently good, a switch to LES is made. A one-equation RANS turbulence model is used in the URANS region and a one-equation SGS model is employed in the LES region. The matching between URANS and LES takes place in the inner log-region. An improved LES-RANS method is evaluated for computing the flow over a three-dimensional axi-symmetric hill. The improvement consists of adding instantaneous turbulent fluctuations (forcing conditions) at the matching plane between the LES and URANS regions in order to provide the equations in the LES region with relevant turbulent structures. © 2005 Elsevier B.V. All rights reserved.

Hybrid Les-Rans: Computation of the Flow Around a Three-Dimensional Hill

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Lars Davidson

Papers

How to estimate the resolution of an LES of recirculating flow

Assessment of realizability constraints in v2–f turbulence models

Hybrid LES-RANS: Inlet Boundary Conditions for Flows with Recirculation

Hybrid Les-Rans: Computation of the Flow Around a Three-Dimensional Hill

Modeling of Synthetic Anisotropic Turbulence and its Sound Emission