Symmetry Breaking and Unsteady Transition
Investigators
V. C. Patel & Tim A. Johnson
Research Objective
This research is concerned with the kinematic and dynamic processes in bluff body
wakes. In particular, the wake of an isolated sphere in uniform flow is considered and
serves as a simplified representation of general three-dimensional hydro- and aerodynamic
bodies.
Approach
Both experimental and computational methods have been used. Experimental flow
visualization techniques, including standard dye injection as well as laser-induced
fluorescence (LIF), have been used to reveal the behavior of the wake for both steady and
unsteady flow regimes. IIHR's small
glass-walled towing tank provided an accurate and stable flow field for the
experiments. |
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Fig 1. Dye visualization of the unsteady near wake at a
Reynolds number of 300.
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Fig 2. Laser-induced fluorescence of the unsteady near
wake at a Reynolds number of 300.
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| Numerical solutions of the flow past a sphere were obtained
using an unsteady Navier-Stokes solver. The method uses second-order finite-difference
approximations in space and time with a pressure Poisson equation to satisfy the
continuity equation. A dual time stepping approach is adopted for accurate temporal
resolution. |
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Accomplishments
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Fig 3. Calculated streamlines colored by velocity at Re =
100. Flow is steady and axisymmetric and exhibits a large (~D) toroidal vortex in the near
wake.
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Fig 4. Vorticity contours at Re = 100. The contours show
the extension of the sphere's boundary layer vorticity into the wake but fail to reveal
the spiraling toroidal vortex obvious in Figure 3.
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Fig 5. To reveal the vortical structure of the wake, the
lambda-2 method of Jeong and Hussain (Jeong, J and Hussain, F., 1995, "On the
Identification of a Vortex," JFM, Vol. 285, pp. 69-94.) is applied to the flow. The
blue contour defines the vortical region, capturing the toroidal vortex and the convex
boundary layer flow over the shoulder of the sphere.
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Fig 6. By Re = 211 the axial symmetry of the flow past
the sphere breaks down although the flow remains temporally steady. This figure shows
select streamlines at Re = 250. The top figure shows that the x-y plane remains a symmetry
plane. In the bottom figure the result of the symmetry-breaking mechanism is clear: An
instability of the toroidal vortex core produces a "tornado effect" whereby
fluid is pulled through the core by a centrifugally generated azimuthal pressure gradient.
Entrainment of fluid into the wake balances the movement of core fluid.
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Fig 7. A comparison of computational particle traces
to experimental dye visualization results shows remarkable agreement. The top and bottom
views correspond to those of Figure 6 and clearly illustrate the presence of a symmetry
plane and the downstream release of wake fluid.
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Fig 8. The vortical structure of the wake at Re = 250
is revealed by the lambda-2 method. One quadrant of the structure has been cut away to
show the location of the sphere and the internal structure of the contour. The tilting of
the wake vortex is obvious, as are the legs of the streamwise vortices leaving the near
wake.
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Fig 9. By Re = 270, the flow field becomes unsteady
but periodic. Streamlines colored by pressure are shown here for every quarter period at
Re = 300. The unsteadiness results from the rapid growth of a portion of the wake vortex.
The section of the vortex formed in the separating shear layer at t = T/2 quickly outgrows
its equilibrium strength fueled by "tornado" core-flow stretching. As it
increases in strength, it eventually cuts itself from the wake and sheds.
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Fig 10. Numerical streaklines show the shedding of
so-called hairpin vortices from the sphere. This picture compares well to numerous dye
visualizations, the experimental equivalent of streaklines.
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Fig 11.This animation shows the shedding vortical
structures at Re = 300 computed using Jeong and Hussain's lambda-2 method. Along with the
hairpin vortices revealed by the numerical streaklines, oppositely-oriented induced
hairpins can be observed shedding from the sphere.
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