======Flow over Periodic Hills====== =====LES by Temmerman and Leschziner===== ---- ====Flow Configuration==== Flow over 2D periodic hills, consisting of polynomial-shaped obstacles mounted on a flat plate with a recirculation region in their wake, as shown in . {{ figs:case081:cas81-geom.png |Flow geometry}} The test case is relevant for studying near-wall or/and subgrid-scale modelling in LES in the presence of separation and reattachment. The geometry retains the shape of the hill defined by Almeida et al (1992) (see [[case018|Case 18]] of this database). As the true periodicity of the Almeida et al experiment (case 18-B) was in question during the 1995 ERCOFTAC/IAHR workshop when it was considered as one of the test cases, the present LES was set up to provide a fully periodic case. The reference presented herein consists in a wall-resolving computation using the dynamic subgrid-scale model for a large-eddy simulation. ===Geometrical Parameters=== * Hill height: \(h = 28\) mm * Hill crests are separated by: \(L_x = 9h\) * Hill geometry is given as a series of spline functions, detailed in {{cdata:case081:geom.dat|geom.dat}} * Channel height: \(L_y = 3.035h\) ===Flow Parameters=== * Reynolds number: \(U_bh/\nu = 10 595\), based on the bulk velocity, \(U_b\), taken at the crest of the hill, and the hill height \(h\). * The flow is periodic in the streamwise direction. * The spanwise width of the LES computation is \(4.5h\). ====Simulation details==== The simulation was performed on a grid of approximately 5M nodes, covering a spanwise direction of 4.5 hill heights. The mesh was close to orthogonal, of low aspect ratio and mesh-expansion ratio below 1.05. The \(y^+\) value at the nodes closest to the wall was around 0.5, allowing the no-slip condition to be used directly. Statistical data was assembled over a period of 55 flow-through times, at a cost of approximately 50 000 processor hours on the Manchester CSAR Cray T3E computer. ====Available LES Data==== Separation is predicted at \(x=0.22h\) and reattachment at \(x=4.72h\). Typical mean streamlines are shown in . {{ figs:case081:hillstreamlines.jpg |Streamlines}} Profiles of the (\(U\)) and (\(V\)) mean velocities, Reynolds stresses \(\overline{u^2}\), \(\overline{v^2}\) and \(\overline{uv}\), and turbulent kinetic energy \(k\) are available at a number of \(x/h\) locations. All quantities are dimensionless (normalized using the bulk velocity, \(U_b\), and hill height, \(h\)). [[case081-plots|Sample plots]] of selected quantities are available. Compressed archive of the files can be downloaded from the link below, or files can be retrieved individually from the table. * {{cdata:case081:perh-allfiles.zip|perh-allfiles.zip}} * {{cdata:case081:perh-allfiles.tar.gz|perh-allfiles.tar.gz}} ^ \(x/h\) Location ^ File ^ | 0.05 | {{cdata:case081:data-001.dat|data-001.dat}} | | 0.5 | {{cdata:case081:data-002.dat|data-002.dat}} | | 1.0 | {{cdata:case081:data-003.dat|data-003.dat}} | | 2.0 | {{cdata:case081:data-004.dat|data-004.dat}} | | 3.0 | {{cdata:case081:data-005.dat|data-005.dat}} | | 4.0 | {{cdata:case081:data-006.dat|data-006.dat}} | | 5.0 | {{cdata:case081:data-007.dat|data-007.dat}} | | 6.0 | {{cdata:case081:data-008.dat|data-008.dat}} | | 7.0 | {{cdata:case081:data-009.dat|data-009.dat}} | | 8.0 | {{cdata:case081:data-010.dat|data-010.dat}} | ====Previous Numerical Solutions==== Mellen et al. (2000) reported the first LES of this case. They, and later Temmerman et al. (2001), have performed a series of subgrid scale models and wall-treatment sensitivity tests, taking the LES results on a fine grid where no wall functions applied (data given herein) as a reference. The exact value of reattachment point was found to vary with SGS model and grid. Some a priori tests can also be found in Jang et al. (2001). ====Related Publications==== - Almeida, G.P., Durao, D.F.G., Heitor, M.V. (1992). [[https://doi.org/10.1016/0894-1777(93)90083-U|Wake flows behind two dimensional model hills]]. //Exp. Thermal and Fluid Science//, Vol. 7, p. 87. - Jang, Y-J., Temmerman, L., Leschziner, M.A. (2001). Investigation of anisotropy-resolving turbulence models by reference to highly resolved LES data for separated flow, //Proc. ECCOMAS Computational Fluid Dynamics Conference//, Swansea. - Mellen, C.P., Fröhlich, J., Rodi, W. (2000). {{figs:case081:ifh_paper.pdf|Large Eddy Simulation of the flow over periodic hills}}, //Proc. 16th IMACS World Congress//, Lausanne. - Temmerman, L., Leschziner, M.A. (2001). {{figs:case081:tsfp2_09032001.pdf|Large Eddy Simulation of separated flow in a streamwise periodic channel constriction}}, //Proc. Int. Symp. on Turbulence and Shear Flow Phenomena//, Stockholm. ---- Indexed data: case : 081 title : Flow over Periodic Hills author* : Temmerman, Leschziner year : 2001 type : LES flow_tag* : 2d, separated, varying_cross_section