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SPECIAL SECTION ON RANS/LES/DES/DNS: THE FUTURE PROSPECTS OF TURBULENCE MODELING

Flow Around a Simplified Car, Part 2: Understanding the Flow

[+] Author and Article Information
Siniša Krajnović

Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, SE-41296 Gothenburg, Swedensinisa@chalmers.se

Lars Davidson

Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden

J. Fluids Eng 127(5), 919-928 (May 16, 2005) (10 pages) doi:10.1115/1.1989372 History: Received July 26, 2004; Revised May 16, 2005

Results of a large eddy simulation (LES) are used to explore the flow around a generic car model. A new, refined picture of this flow is established. Many parts and aspects of this flow are studied and explained. The development of the instantaneous flow and its resulting time-averaged flow are depicted. Large differences are found between the instantaneous and the time-averaged flows. Special attention is given to the flow above the rear slanted surface. The origin, the development, and the interactions of the instantaneous vortices in this part of the flow are presented for the first time. This instantaneous flow is shown to be very unsteady and to contain a large number of different vortices that range in size from those of the size of the body over the intermediate hairpin-like vortices to very small coherent structures. Besides the variety in the length scales, the flow covers a wide spectrum of the time scales from the relatively steady motion of the cone-like trailing vortices on the slanted edges to highly frequent collisions of the hairpin-like vortices in the region of the attachment on the rear slanted surface.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of an unstable node (UN), stable focus (SF), and saddle point (SP). NBL and PBL are negative and positive bifurcation lines, respectively.

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Figure 2

Geometry of the Ahmed body. View from the side of the body. Note that z=0 is the ground plane and x=0 and y=0 are at the position of the rear vertical surface and the symmetry plane of the body, respectively.

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Figure 3

Time-averaged trace lines on the surface of the body showing the roof and the lateral vortices. View of the front of the body from above and the lateral side.

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Figure 4

Time-averaged trace lines on the surface of the body. Zoom of region C in Fig. 3 showing two foci, Fful and Ffsl.

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Figure 5

Time-averaged trace lines on the surface of the body showing the vortices on the lateral side and underneath the body. View of the front of the body from below and the lateral side.

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Figure 6

Time-averaged trace lines on the surface of the body. Zoom of region E in Fig. 5 showing one stable Nfsd and one unstable node Nfsu, saddle point Sfsd and focus Ffdl.

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Figure 7

The isosurface of the instantaneous second invariant of the velocity gradient, Q=4000, around the lower lateral edge. Ti are the instantaneous structures that average to become the time-averaged vortex in Fig. 9. M indicates the approximate position of merging of λ vortices on the lateral side with the Ti structures. View of the body from below and the lateral side.

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Figure 8

Time-averaged trace lines on the surface of the body. Zoom of region D in Fig. 3 showing saddle point Sfsl.

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Figure 9

Time-averaged streamline projected onto planes: (a) x=−2.08H, (b) x=−1.39H, (c) x=−0.69H, (d) x=0 (the plane of the rear vertical surface), (e) x=0.21H, and (f) x=0.38H. View from the front of the lower left edge of the body. Note that z and y axes in the figure do not indicate the origin of the coordinate system. The real y=0 is at the position of the symmetry plane of the body. Flow is from the observer into the plane.

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Figure 10

The isosurface of the instantaneous second invariant of the velocity gradient, Q=6500. The time difference between two pictures is tU∞∕H=0.055. Flow is from left to right and the view is from the lateral side and above the body. The sharp edge between the roof and the slanted surface is denoted by Ss and the slanted lateral edge is denoted by Sl. Vortices are colored by the streamwise velocity. The white vortices are traveling downstream and the black vortices are traveling upstream.

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Figure 11

(a) The isosurface of the instantaneous second invariant of the velocity gradient, Q=6500. View is from behind and the lateral side of the right slanted edge. Note that only core parts of the cone vortices are shown. The cone vortices are colored by the vorticity component in the streamwise direction ωx. Vortices colored with black and white have clockwise and counter-clockwise directions of rotation, respectively. (b) Schematic representation of the mantles of vortices Tr1, Tr2, and Tr3 seen from behind the body. The positions of NBLbl and PBLbl near the opposite lateral side are also shown in Fig. 1.

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Figure 12

Time-averaged streamlines and velocity vectors projected onto plane x=−0.8H. View from the front of the upper left lateral edge. Flow is from the observer into the plane. Note that z=0 is the ground plane and that the z and y axes in the figure do not indicate the origin of the coordinate system. The real x=0 and y=0 are at the position of the rear vertical surface and the symmetry plane of the body, respectively.

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Figure 13

Time-averaged trace lines on the rear slanted surface of the body. View of the lateral, slanted, and rear vertical faces of the body.

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Figure 14

Time-averaged trace lines on the surface of the body. (a) Zoom of the patterns in Fig. 1 showing NBLbu and NBLbm. (b) Zoom of the patterns in Fig. 1 showing saddle point Sbco. (c) Zoom of the unsteady reattachment in Fig. 1. Coordinates (x∕H,y∕H) are given for lower left and upper right corners in all three figures. The lateral sides are located at y=±0.675H.

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Figure 15

(a) Time-averaged streamlines and velocity vectors projected onto symmetry plane y=0 showing the flow above the slanted surface. The velocity vectors are extrapolated and plotted on coarser grid than that used in the simulation to make the direction of the flow visible. (b) Zoom A from (a). (c) Zoom B from (a). The direction of rotation of vortices is indicated by the vorticity component in the y direction (i.e., ωy+ and ωy− are positive and negative vorticity components, respectively).

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Figure 16

Time-averaged trace lines on the surface of the body. (a) Zoom of the patterns in Fig. 1 showing the stable focus, Pb. (b) Zoom of the patterns in Fig. 1 showing the negative and positive bifurcation lines, NBLbl and PBLbl, respectively. Coordinates (x∕H,y∕H) are given for lower left and upper right corners in both figures. NBLbl and PBLbl are also shown in Fig. 1.

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Figure 17

(a) Vortex cores of the time-averaged vortices wrapped in the streamlines that are generated using vortex cores as a source. Time-averaged trace lines are shown on the surface. View from behind the body. (b) Zoom of (a). (Note that streamlines STRl are removed in this zoom for clarity.)

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Figure 18

Time-averaged trace lines on the surface of the body. Zoom of the flow structures from Fig. 1 showing (a) the lower left corner of the slanted surface and (b) the lower right corner of the slanted surface. Coordinates (x∕H,y∕H) are given for lower left and upper right corners in both figures.

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Figure 19

Time-averaged near-wake flow. (a) Time-averaged streamlines projected onto planes (from left to right in the figure): x=1.389H(−0.675H⩽y⩽0,0.174H⩽z⩽0.833H), x=0.868H(−0.675H⩽y⩽−0.278H,0.174H⩽z⩽0.833H), x=0.347H(−0.675H⩽y⩽−0.382H,0.174H⩽y⩽1.042H), y=0(−0.59H⩽x⩽0,0.174H⩽z⩽0.833H) and y=0.521H(−0.59H⩽x⩽0,0.174H⩽z⩽0.833H). (b) Isosurfaces of the static pressure, p=−0.16 and p=−0.19. Lhl and Lhr are cores of the legs of vortex Uh. (b) Schematic representation of the time-averaged wake flow. Note that only half of the horseshoe vortices Ul and Uh for y⩽0 and y⩾0, respectively, are shown.

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