Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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Tracking Vortices Over Large Distances Using Vorticity Confinement
Tracking Vortices Over Large Distances Using Vorticity Confinement
Pages 950-962
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From page 950... ...
In order to obtain a rough estimate for the grid sizes required to capture accurately typical trailing edges vortices, consider a helicopter blade with radius r = 5m and a vortex of size ~ = 10cm. The element size required to describe such a vortex will be smaller than h = lcm (10 elements across the vortex zone)
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From page 951... ...
This is not the case in well resolved boundary layers close to solid surfaces. In fact, it was found that switching on vorticity confinement in these highly resolved regions could lead to numerical instabilities.
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From page 952... ...
The primary vortex generated by the delta wing rapidly enters regions of low mesh density. Figure 2b shows the vorticity and pressure contours for planes located at 30%, 50% and 70% root chord length for the case with vorticity confinement terms switched on and the vorticity confinement coefficient cat,.
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From page 953... ...
A.. / Figure lb Finite NACA0012 Wing: Surface Pressure, Vorticity in 4 Cut Planes and Vortex Core (4 Cut Planes: x = 1.05,2,5,9; cat.
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From page 954... ...
Figure to Finite NACA0012 Wing: Comparison of Vorticity in 4 Cut Planes 4 Cut Planes: x = 1.05, 2, 5, 9 (left: cv = 0; right: cv = 0.1) ~1 Figure ld Finite NACA0012 Wing: Comparison of Helicity in 4 Cut Planes (4CutPlanes: x = 1.05,2,5,9)
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From page 955... ...
in Planes x = 0.3, 0.5, 0.7 Figure 2c Delta Wing: Comparison of Vorticity for Plane x = 0.5
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From page 956... ...
x Cv=0.05 0 Cv=0.1 ~ 6< - 11 ~ ,.~.- _. _ ~ .,_.~ ~-'e' 0 0.2 0.4 0.6 0.8 1 X Figure 2d Delta Wing: Comparison of Cp for Plane x = 0.7 0.6 0.4 c' 0.2 o -0.2 -0.4 -0.e Present Results, Cv=O.O Walhorn's Results -- ~ 135 140 1 4t5 150 160 Figure 3b 2-D Cylinder: Comparison of C~, for Re = 110 Figure 3a 2-D Cylinder: Surface Mesh 0.8 0.6 0.4 0.2 o -0.2 -0.4 -0.6 -0.8 -1 150 155 160 90 .
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From page 957... ...
Re= 110 ,t= 146 Re=llO,t=146 Re= 110 ,t= 148 Re = 110 , t = 148 Re= 110 ,t= 150 Re = 110, t = 150 Re=llO,t=152 Re = 110, t = 152 Re = 110 , t = 154 Figure 3d 2-D Cylinder: Pressure Contours without Vorticity Confinement (cv = 0) Re = 110 , t = 154 Figure Be 2-D Cylinder: Pressure Contours with Vorticity Confinement (cv = 0.25)
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From page 958... ...
Re = 190, t = 108 Re = 190, t = 108 Re= 190 ,t= 110 Re=l90,t=110 Re= 190 ,t= 112 Re=l90,t=112 Re = 190 , t = 114 Re = 190, t = 114 Re= 190 ,t= 116 Figure 3f 2-D Cylinder: Pressure Contours without Vorticity Confinement act, = 0) Re=l90,t=116 Figure 3g 2-D Cylinder: Pressure Contours with Vorticity Confinement act, = 0.2)
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From page 959... ...
Figure 4c Submarine: Surface Pressure Contours and Absolute Velocity Contours at Two Cut Planes CONCLUSIONS AND OUTLOOK A general vorticity confinement term for unstructured grids has been derived, implemented and found to be successful for some cases. The vorticity confinement terms are of the form: f = g(Re`~,h~c~,ph2V~ x
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From page 960... ...
S., "Vortex Breakdown Effects on the Low-Speed Aerodynamic Characteristics of Slender Delta Wings in Symmetrical Flow," Royal Aeronautical Society Journal, vol.
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From page 961... ...
To accommodate this grid refinement with Vorticity Confinement, the parameter specifying the strength of the Vorticity Confinement term ~ ~ ~ was made to be proportional to grid size so that it automatically vanished in the fine-grid boundary layer region, but was able to confine the convecting vortex in the external, coarse-grid region. When using unstructured grids, which have rapidly changing cell sizes, care must be taken not only that £ varies properly with cell size, but also that the confinement correction does not extend beyond the vortex core due to numerical artifacts of the implementation.
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From page 962... ...
The authors have chosen to implement a vorticity confinement method, which is shown to improve the resolution of vortices propagating in the far field. In the paper, the authors correctly note that the vorticity confinement term acts as a body force.
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