# Sig Turbulence / Channel Flow

Olivier Brugiere, Universite Joseph Fourier, Grenoble, France

## 1 Motivation

• Test avaiable subgrid scale (SGS) model
• Test wall model on easy configuration:
• cheap calculation
• easy to mesh
• ...
• Many DNS data base can be found (ex: the Kawmura laboratory [[1]]) to compare mean velocity and rms profiles

## 2 Testcase description

### 2.1 Flow configuration

#### 2.1.1 Boundary condition

Figure 1 : Flow configuration
• Streamwise condition : periodicity
• Spanwise condition : periodicity
• Normal to streamwise : two walls

#### 2.1.2 Geometrical Parameters

The Reynodls number of the flow is the same as Abe et al. [3] ($Re_{\tau} = 1020$). Thus the geometry is :

• Streamwise distance : $L_{x} = 12,8 h$
• Normal wall heigh  : $L_{y} = 2 h$
• Spanwise distance  : $L_{y} = 6,4 h$

### 2.2 Mesh generation

Figure 2 : Mesh for y+ = 200

We have done the mesh with an automatic tool (*.m4) which is composed by $Nx * Ny * Nz = 50 * 40 * 38$. The mesh is composed by 4 blocks:

• 2 blocks for the first cell close to the wall. (Hense, y+ can be imposed)
• 2 blocks in the center

### 2.3 Simulation details

The aim of my study is testing a posteriori near-wall law. We are running three cases :

• Without wall model
• With the Spalding law [1]
• With the Manhart et al. law [2]

## 3 Numerical results

Results of the simulations are available in the paper written by Duprat et al. [4]

## 4 References

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

[2] 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.

[3] Abe, Kawamura and Matsuo, Surface heat-flux fluctuations in a turbulent channel flow up to $Re_{\tau} = 1020$ with Pr = 0,025 and 0,71, 2004, Int. J. Heat and Fluid Flow, vol 25, pp. 404-419.

[4] Duprat, Balarac, Métais, Congedo, and Brugière, 2011, A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient. Physics of Fluids, 23, 015101.[2]

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