2 results
Wake structure of a transversely rotating sphere at moderate Reynolds numbers
- M. GIACOBELLO, A. OOI, S. BALACHANDAR
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- Journal:
- Journal of Fluid Mechanics / Volume 621 / 25 February 2009
- Published online by Cambridge University Press:
- 12 February 2009, pp. 103-130
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The uniform flow past a sphere undergoing steady rotation about an axis transverse to the free stream flow was investigated numerically. The objective was to reveal the effect of sphere rotation on the characteristics of the vortical wake structure and on the forces exerted on the sphere. This was achieved by solving the time-dependent, incompressible Navier–Stokes equations, using an accurate Fourier–Chebyshev spectral collocation method. Reynolds numbers Re of 100, 250 and 300 were considered, which for a stationary sphere cover the axisymmetric steady, non-axisymmetric steady and vortex shedding regimes. The study identified wake transitions that occur over the range of non-dimensional rotational speeds Ω* = 0 to 1.00, where Ω* is the maximum velocity on the sphere surface normalized by the free stream velocity. At Re = 100, sphere rotation triggers a transition to a steady double-threaded structure. At Re = 250, the wake undergoes a transition to vortex shedding for Ω* ≥ 0.08. With an increasing rotation rate, the recirculating region is progressively reduced until a further transition to a steady double-threaded wake structure for Ω* ≥ 0.30. At Re = 300, wake shedding is suppressed for Ω* ≥ 0.50 via the same mechanism found at Re = 250. For Ω* ≥ 0.80, the wake undergoes a further transition to vortex shedding, through what appears to be a shear layer instability of the Kelvin–Helmholtz type.
Superfluid spherical Couette flow
- C. PERALTA, A. MELATOS, M. GIACOBELLO, A. OOI
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- Journal:
- Journal of Fluid Mechanics / Volume 609 / 25 August 2008
- Published online by Cambridge University Press:
- 31 July 2008, pp. 221-274
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We solve numerically for the first time the two-fluid Hall–Vinen–Bekarevich–Khalatnikov (HVBK) equations for an He-II-like superfluid contained in a differentially rotating spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor–Couette flow. The simulations are conducted for Reynolds numbers in the range 1 × 102≤Re≤3 × 104, rotational shear 0.1≤ΔΩ/Ω≤0.3, and dimensionless gap widths 0.2≤δ≤0.5. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by δ and ΔΩ/Ω. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as Re increases, and their shapes become more complex, especially in the superfluid component, with multiple secondary cells arising for Re > 103. The torque exerted by the normal component is approximately three times greater in a superfluid with anisotropic Hall–Vinen (HV) mutual friction than in a classical viscous fluid or a superfluid with isotropic Gorter–Mellink (GM) mutual friction. HV mutual friction also tends to ‘pinch’ meridional circulation cells more than GM mutual friction. The boundary condition on the superfluid component, whether no slip or perfect slip, does not affect the large-scale structure of the flow appreciably, but it does alter the cores of the circulation cells, especially at lower Re. As Re increases, and after initial transients die away, the mutual friction force dominates the vortex tension, and the streamlines of the superfluid and normal fluid components increasingly resemble each other. In non-axisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. For misaligned spheres, the flow is focal throughout most of its volume, except for thread-like zones where it is strain-dominated near the equator (inviscid component) and poles (viscous component). A wedge-shaped isosurface of vorticity rotates around the equator at roughly the rotation period. For a freely precessing outer sphere, the flow is equally strain- and vorticity-dominated throughout its volume. Unstable focus/contracting points are slightly more common than stable node/saddle/saddle points in the viscous component, but not in the inviscid component. Isosurfaces of positive and negative vorticity form interlocking poloidal ribbons (viscous component) or toroidal tongues (inviscid component) which attach and detach at roughly the rotation period.