Olivier Brugiere, Universite Joseph Fourier, Grenoble, France

## Contents

## 1 Motivation

The flow over bodies with massive separation constitutes an important area of applications for LES. In many geometrie we can find this kind of flow like the 2D backward-facing step, the asymmetric diffuser or the periodic hill. We know experimental's data which was made by Almeida et al. [1] but in Mellen and al. [2] et Temmerman et al. [3] we can find that they have an influence of the side wall so the 1995 ERCOFTAC/IAHR workshop have cast a doubt on the true periodicity of the experimental configuration. But we have some data from LES with a good mesh like [[1]]. Flow over 2D periodic is in fact an experimental configuration with 9 hills. For the computational, we represent this configuration by a channel periodic with two half's hills like on the figure 1.

The probleme of this flow is the separtion bubble which is due to a adverse pressure gradient that's why this is a test case for many subgrid scale models (SGS) and for near-wall low.

## 2 Testcase description

### 2.1 Flow configuration

#### 2.1.1 Geometrical Parameters

- Hill's heigh :
- Streamwise distance :
- Normal wall heigh :
- Spanwise distance :

#### 2.1.2 Boundary condition

- Streamwise condition : periodicity
- Spanwise condition : periodicity
- Normal to streamwise : two walls

### 2.2 Simulation details

We have make the geometry on Gambit Fig 2 and the mesh is composed by .

The aim of my study is testing a posteriori near-wall low. To compare we are running three cases :

- With near-wall low
- With the Spalding Low [4]
- With the Mahart et al. low [5]

## 3 Numerical results

Results of the simulations are available in the paper written by Duprat et al. [6]

## 4 References

[1] Almeida, Durao and Heitor, 1993, Experimental thermal and fluid science, Vol. 7, pp. 87-101.

[2] Mellen, Frohlich and Rodi, 2000, Large Eddy Simulation of the flow over periodic hills, 16th IMACS World Congress , Lausanne. [2]

[3] Temmerman and Leschziner, 2001, Large Eddy Simulation of separated flow in a streamwise periodic channel construction, Int. Symp. on Turbulence and Shear Flow Phenomena, Stockholm, June 27-29. [3]

[4] Spalding, 1961, A single formula for the law of the wall, Jl. Appl. Mech., vol 28, pp. 455-457

[5] Manhart, Peller and Brun, 2008, Near-wall scaling for turbulent boundary layers with adverse pressure gradient, Theor. Comput. Fluid Dyn., vol 22 , pp. 243-260.

[6] Duprat, Balarac, Métais, Congedo, and Brugière, O., 2011, A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient. Physics of Fluids, 23, 015101.[4]

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