Finite Element Method - Application using Fastflo
3D turbulent flow over a car
The Fastflo solution to this benchmark problem was
presented at the May 1996 meeting of the World User Association in Applied
Computational Fluid Dynamics [1]. The geometry data of the car were
provided by Daimler-Benz and describe the 205 cross sections and wheels of
the model car. In the experiment conducted by Daimler-Benz, both the car
and the ground were stationary, and the incoming air speed was 180 km/h. A
Reynolds number of Re=2.64x106 was considered, based on the air
speed, the length of the model car (810 mm) and the kinematic viscosity of
air at 294 K.
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Finite element mesh on car surface, symmetry
plane and ground
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Particle pathlines around car and pressure
shading on car surface
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Velocity in symmetry plane and kinetic energy
shading on car surface
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Velocity arrows on symmetry plane, including
the wake
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Kinetic energy distribution near floor, and
velocity around car surface
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Pressure distribution on floor, and velocity
around car surface
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Experimental measurements of pressure distribution on the car body were
also provided by Daimler-Benz, after the Fastflo solution was
obtained. The mesh, partially shown in the figures, was generated with an
in-house mesh generator. It contains a total of 85,542 nodes. The
computing domain is as recommended by the WUA-CFD Secretariat in the case
description document. There are about two car lengths from car front to
the upstream boundary, five car lengths to the downstream boundary and six
car heights away in the surrounding boundary.
The inlet conditions of uniform velocity and turbulence intensity (of
5%) on upstream boundary and a slip condition on part of upstream
horizontal plane were as described in the case description document. The
downstream boundary condition was taken to be free normal stress. A
no-slip condition was applied on surfaces of the car body, wheels and the
ground. On the surrounding far field boundaries, the stress free condition
was used.
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Flow details around the front wheel
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Particle pathlines around car body
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Particle pathlines around car surface
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Contours of turbulent viscosity in the
symmetry plane
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Contours of pressure distribution on the car
surface
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Contours of dissipation rate of kinetic energy
on car surface
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An operator splitting algorithm [2] with variable timestep was used.
The standard k-epsilon model was employed for modelling the
turbulence. CG and GMRES iterative solvers were used for the symmetric and
asymmetric linear systems respectively.
The computations were done on a DEC Alpha 300 workstation with a single
175 MHz processor. About 30 time steps were needed to reach a steady state
solution, which typically took about 66 CPU hours for this particular
mesh.
The figures show the mesh, particle pathlines, velocity vectors, shaded
surfaces and contour plots for the pressure, kinetic energy and turbulent
visosity. The pressure coefficient distribution along the symmetry plane
on the upper car surface was compared against experimental measurements
and showed excellent agreement.
References
[1] X.-L. Luo, A.N. Stokes and N.G. Barton, Turbulent flow around a
car body - Report of Fastflo solutions, WUA-CFD Freiburg (1996).
[2] R. Glowinski and O. Pironneau, Finite element method for Navier-Stokes
equations, Annual Review of Fluid Mechanics, 24,167-204
(1992).
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