By Fabrice Mathey, Turbulence Modeling Expert, Fluent France, and Davor Cokljat, Senior Principal Developer, Fluent Europe

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The automotive industry has a high demand for reliable simulation methods capable of tackling the complex turbulent air flow around vehicles. CFD is a valuable tool that can provide detailed information on performance (lift and drag), acoustics, and more. The prediction of external aerodynamics has greatly challenged CFD, however, because of the highly turbulent, massively separated flow that can occur behind automobiles of modern design.

The unstructured mesh for the RANS simulation

Large eddy simulation (LES) can have greater success than RANS methods in predicting separation at the rear of a vehicle. The main obstacle to this success, however, is the near wall resolution required to capture the structure of the flow in the boundary layer. This resolution can be far too expensive at a high Reynolds number, because a finer grid is needed for this regime. To overcome this hurdle, a study was undertaken in which a multi-domain RANS-LES approach is applied to the simulation of the Ahmed body. The simulation uses an interface condition between the RANS and LES sub-domains that is based on the vortex method of Sergent (1), and adapted for general flow conditions in FLUENT 6.2 (2).

The block structured mesh used for the LES calculation that followed the RANS calculation

The Ahmed body model (3) is a generic automotive bluff body with a slant back of variable angle. In spite of the relatively simple geometry, the flow around it reproduces the basic aerodynamic features of the flow around real cars. For slant angles smaller than a critical value, α=30°, the dominant structures are two strong longitudinal counter-rotating vortices that form at the edges of the slant. These vortices are responsible for a significant part of the lift and drag. Thus any CFD methodology capable of accurately predicting this flow pattern has enormous potential for guiding improvements to automobile stability and fuel consumption.

Mean streamwise velocities (top) and velocity fluctuations (middle) above the slant, and pressure coefficient on span-wise profiles that show a pressure drop near the edge (bottom)

A full configuration of a 25° reference angle Ahmed car model was first solved with a steady RANS approach in FLUENT, using the V2F turbulence model. The V2F model is similar to the standard k-ε model, but incorporates anisotropy in the near-wall turbulence, and does not need to rely on wall functions. The Reynolds number of the flow, based on the incoming velocity and car height, H, is Re=7.68x10⁵. Owing to the plane of symmetry, only one-half of the car body and its surroundings was included in the computational domain. The mesh was refined inside the boundary layer and inside the anticipated wake region. The boundary layer was resolved using 24 layers of prisms, while the rest of the grid consisted of tetrahedral cells. The body was placed in an open channel with a cross section of 10H x 7H. The channel inlet is located 6.3H from the front face of the body, and the channel outlet is located 10H from rear face of the body.

Mean velocity pathlines from the LES solution (left) are in good agreement with the experiment (right, (3))

After the completion of the V2F calculation, the solution domain was divided into two sub-domains, and an LES solution was performed in one of them. The LES sub-domain was restricted to the region above the rear slant and in the wake of the body, and a block structured grid containing 1.6 million cells was created. The boundary layers were fully resolved with a resolution above the slant of y+ < 2. The LES domain obtained its inflow velocity profiles from the separate RANS calculation and the vortex method boundary condition. After a statistical steady state was reached, the LES simulation was run for an additional 15,000 time steps, corresponding to 25 flow passes through the domain.

Pathlines computed by CFD (left) show the pair of longitudinal counter-rotating vortices that were observed in the experiments (right, (3))

LES predictions of the mean and RMS stream-wise velocities above the slant were found to be in very good agreement with experimental values (4). It is particularly noteworthy that the flow reattachment is well predicted by the simulation. The computed and measured mean stream-wise velocity profiles inside the wake region are also in good agreement. Predictions of the surface pressure coefficient along the slant at the symmetry plane also agree closely with measured data. Span-wise profiles of the pressure coefficient show a pressure drop close to the edge. These low pressure regions are the footprints of the stream-wise longitudinal vortices, and their locations are well predicted by the simulation.

Vortical structures, visualized by the second invariant of the deformation tensor, colored by streamwise velocity

References:

1. E. Sergent; PhD Thesis, L'Ecole Centrale de Lyon, 2002.
2. F. Mathey, D. Cokljat, J.P. Bertoglio, E. Sergent; In Turbulence, Heat and Mass Transfer 4, Proceedings of the International Symposium on Turbulence, Heat and Mass Transfer, Antalya, Turkey, 2003; K. Hanjalic, Y. Nagano, M. Tummers, Eds.; New York: Begell House, 2003.
3. S.R. Ahmed, G. Ramm, G. Faltin; SAE Paper 1984, no. 840300.
4. H. Lienhart, S. Becker; SAE Paper 2003, no. 2003-01-0656.

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