Sig Turbulence / Flow over Periodic Hills

Olivier Brugiere, Universite Joseph Fourier, Grenoble, France

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.

• 2D backward-facing step : it's a quick test case because of it's a 2D model but the separation bubble is determined by the spet geometry.
• Asymmetric diffuser : we know experimental's data which was made by Buice and Eaton [[1]]. Unfortunatly, the Reynolds number of the fow was necessarily slow ($Re_{\tau} = 180$).

Figure 1 : periodic hill

• Periodic Hills : 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 [[2]]. 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 : $h = 28 mm$
• Streamwise distance : $L_{x} = 9,0 h$
• Normal wall heigh  : $L_{y} = 3,035 h$
• Spanwise distance  : $L_{y} = 4,5 h$

2.1.2 Boundary condition

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

2.2 Simulation details

Figure 2 : Hill mesh

We have make the geometry on Gambit Fig 2 and the mesh is composed by $Nx \times Ny \times Nz = 118 \times 33 \times96$.

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

• • With near-wall low
  • With the Spalding Low [5]
  • Wiht the Mahart et al. low [6]

4 References

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

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

[3] Temmerman, 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.

[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.

Back to Sig Turbulence