Large–Eddy Simulations for Complex Flow Geometries

The investigation of flows in technical applications (automobile, CPU cooling, ...) becomes increasingly affordable through numerical simulation and larger computers, but the numerical simulation of turbulent flows with methods describing the full features of the flow are even way beyond today’s supercomputers as theoretically, statistical disturbances would have to be treated down to a molecular–sized level. As turbulence is critical for technical applications (i.e. mixing or heat transfer), the investigation of these highly statistical flows is very important in today’s development of increasingly complex technical applications.

For the numerical calculation of turbulent flows, Large–Eddy Simulations (LES) are entering the stage of industrial usability. The principle of the numerical scheme is the direct simulation of large eddies, which are the energy–containing structures. These resolved eddies are generating smaller and smaller structures as the flow dissipated energy from large to small scales which are below the size of the numerical resolution. The energy content of these small scales has to be modeled in the equations, as they cannot be resolved. This is done with a so–called turbulence model, which takes into account the dissipation rate of isotropic turbulence but neglects the structure of the eddies as they are believed to be generic in nature. In our project at the HLRB at the LRZ München, we try to model the dissipation of the small eddies through tailored dissipation of the numerical model which then behaves as a turbulence model. The technical application of LES usually comes with complex geometries (for example a motor–cycle driver on his/her bike), where the generation of a suitable body–aligned mesh takes up considerable time and the validity of the result is dependent on the quality of the mesh. So we are working on methods where complex obstacles are immersed in very simple meshes, that is, the surfaces defining the geometry cut through the mesh. In following such an approach, meshing is fast, can be fully automated, and is much less a source of uncertainty towards the quality of the result.

Figure 1: Speedup – reference value with 32 cores

As an example, we have chosen a simplified geometry that exhibit the same complex flow features as the problem cited above: A three–dimensional circular cylinder subjected to a uniform flow at a velocity perpendicular to the cylinder axis. A parameter, which describes the character of the flow regime, is the Reynolds number. The Reynolds number describes the relation of inertial forces to viscous forces. At the considered Reynolds number of Re = 3,900, the flow separates from the cylinder at an angle of about 88° taken from the line of symmetry of the geometry. The large vortices that detach from the cylinder periodically alternating from the top and bottom side of the cylinder very rapidly break down in smaller scales and turbulence develops. The calculations were done on an adaptive, locally refined grid with a total of 7 million cells. Qualitatively good agreement is reached with the results of other calculations: the typical pressure tubes for the p–isosurfaces corresponds with the results reported by Fröhlich [1]. Instabilities in spanwise direction give rise to the elongated structures for the x–vorticity reported by Kravchenko [2] (Fig. 2). The unsteady computation delivers a statistical development of the turbulent wake of the cylinder and was carried out on 512 processors in about 300,000 CPUh with our parallelized code INCA (Solver for the (In)compressible Navier–Stokes equations on Cartesian Adaptive grids [3–6]). INCA was also tested for its parallel performance (Fig. 1). The speedup (reference case: 32 cores) scales almost linearly with the number of processors.

With the implicit LES code INCA, almost arbitrary shapes of boundaries are realizable. In case the time evolution of a complex flow is of interest (e.g. vortex shedding from the back of a vehicle and its noise generation) or the statistical turbulent data are needed for more accurate design purposes, the presented method can deliver dependable results. With the increase in computing power, these type of computations come into reach for the design of high technology products.

Figure 2: Instantaneous pressure iso–contours in the turbulent cylinder wake

Collaborators

References

[1] Fröhlich, J., Rodi, W., Kessler, Ph., Parpais, S., Bertoglio, J. P., Laurence, D. “Large Eddy Simulation of Flow around Circular Cylinders on Structured and Unstructured Grids”, CNRS DFG Collaborative Research Programme, Vieweg, Braunschweig 66, pp. 319–338, 1998

[2] Kravchenko, A., Moin, P. “Numerical Studies of Flow over a Circular Cylinder at ReD = 3900”, Physics of Fluids 12, p. 403, 2000

[3] Hickel, S., Adams, N. A. “Implicit LES Applied to Zero–Pressure–Gradient and Adverse–Pressure–Gradient Boundary–Layer Turbulence”, International Journal of Heat and Fluid Flow 29, pp. 626–63, 2008

[4] Hickel, S., Adams, N. A., Domaradzki, J. A. “An Adaptive Local Deconvolution Method for Implicit LES”, Journal of Computational Physics 213, pp. 413–436, 2006

[5] Hickel, S., Adams, N. A. “On Implicit Subgrid–Scale Modeling in Wall–Bounded Flows”, Physics of Fluids 19, pp. 105–106, 2007

[6] Hu, X. Y, Khoom B. C., Adams, N. A. Huang, F. L. “A Conservative Interface Method for Compressible Flows”, Journal of Computational Physics 219, pp. 553–578, 2006

• Christian Stemmer

Department for Aerodynamics, TU München

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