Vortex formation mechanisms in the wake behind a sphere for 200 < Re < 380

Abstract

Direct numerical simulation and visualization of three-dimensional separated flows of a homogeneous incompressible viscous fluid are used to comprehensively describe different mechanisms of vortex formation behind a sphere at moderate Reynolds numbers (200 ≤ Re ≤ 380). For 200 < Re ≤ 270 a steady-state rectilinear double-filament wake is formed, while for Re > 270 it is a chain of vortex loops. The three unsteady periodic flow patterns corresponding to the 270 < Re ≤ 290, 290 < Re ≤ 320, and 320 < Re ≤ 380 ranges are characterized by different vortex formation mechanisms. Direct numerical simulation is based on the Meranzh (SMIF) method of splitting in physical factors with an explicit hybrid finite-difference scheme which possesses the following properties: secondorder approximation in the spatial variables, minimal scheme viscosity and dispersion, and monotonicity. Two different vortex identification techniques are used for visualizing the vortex structures within the wake.

Nonlinear evolution of instabilities behind spheres and disks

“…The results of recent numerical and theoretical investigations (Bouchet et al, 2006;Fabre et al, 2008;Gushchin and Matyushin, 2006;Meliga et al, 2009;Pier, 2008;Shenoy and Kleinstreuer, 2008) display a similar sequence of transitions. Our experimental observations overlap with, and extend, the Reynolds number range of these investigations.…”

Mathematical modling of the 3D separated viscous fluid flows

“…The good efficiency of this β-visualization technique has been demonstrated in [7]. The clear relationship between the isolines of the perturbation of the salinity in the vertical plane (the traditional way of the representation of the internal waves, Figure 4a) and the horizontal arc-shaped vortex structures (the new 3D way of the representation of the internal waves using β-visualization technique, Figures 3b, 4b) is shown at Figure 4.…”

“…is the generation of the forward part of the upward-and downward-oriented VLs [7]. Thus a new subregime has been discovered at 290 < Re 320 [7] due to SMIF and β -visualization technique.…”

“…The efficiency of the method SMIF and the greater power of supercomputers make it possible adequately to model the 3D separated incompressible viscous flows past a sphere (Figure 1b-d) and a circular cylinder ( Figure 2) at moderate Reynolds numbers [5][6][7][8][9][10][11][12][13] and the air, heat and mass transfer in the clean rooms [14].…”

“…Thus a new subregime has been discovered at 290 < Re 320 [7] due to SMIF and β -visualization technique. At 5·10 4 ≤ Re ≤ 4·10 5 the monotonous reduction of the time-averaged total drag coefficient has been observed (from value 0.455 to 0.155) due to LTT in BL.…”