Unsteady separated fluid flows around a sphere in the wide range of the Reynolds and Froude numbers

Unsteady separated fluid flows around a sphere in the wide range of the Reynolds and Froude numbers

Gushchin, V.A.
Matyushin, P.V.

2006-09-06

The homogeneous (1 < Re < 5000000) and stratified (0.004 < Fr < 1, 10 < Re < 1000) viscous incompressible fluid flows around a sphere have been investigated by means of the direct numerical simulation (DNS) and the visualization of the vortex structures in the wake. In case of the homogeneous fluid at 200 < Re < 1000 the detailed formation mechanisms of vortices (FMV) in the sphere wake have been described for the different unsteady periodical flow regimes (270 < Re < 290, 290 < Re < 320, 320 < Re < 400, 400 < Re < 700 and Re > 700) and the six basic FMV have been selected; at 290 < Re < 320 a new flow regime has been discovered; at 50000 < Re < 5000000 the preliminary results are presented. The following six basic FMV work during the period in the different parts of the flow: 1) in the recirculation zone a new vortex ring (or semi-ring) is generated near the sphere surface due to the Kelvin-Helmholtz instability (1k), the two vortex filaments connected with a new vortex ring are formed (1f), the main vortex ring is displaced closer to the sphere surface (1d); 2) the side parts of the vortex envelope (surrounding the recirculation zone) are stretched downstream (2s), the top or bottom edge of the vortex envelope is rolling up cylindrically and detached (2t/b); 3) in the outer flow the head of the vortex loop (facing upwards (t) or downwards (b)) is generated (3t/b). In case of the stratified fluid the four different flow regimes have been simulated (0.004 < Fr < 1, 10 < Re < 1000); for the first time the complex 3D vortex structures of these flows have been shown; the high gradient sheets of density have been observed near the poles of the resting sphere and the moving sphere (Fr < 0.02). For DNS the explicit numerical method SMIF-MERANGE (second-order accuracy in space, minimum scheme viscosity and dispersion, monotonous) has been used. For the visualization of the vortex structures in the sphere wake the isosurfaces of the imaginary part of the complex-conjugate eigen-values of the velocity gradient tensor have been used.

stratification
formation mechanisms of vortices
incompressible fluid
numerical simulation
sphere wake
visualization

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Conference proceedings

conference paper

(c) 2006 Gushchin, V.A.; Matyushin, P.V.