Direct numerical simulation of the transitional separated fluid flows around a sphere and a circular cylinder

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

“…Such pattern is still unchanged at Re = 200 as depicted in Fig. 4 and reported in Gushchin et al (2002) in which the first instabilities occur within 275 < Re < 295. It is important to mention that the streamlines deviate correctly from the sphere, as a result of the l 2 norm below 10 -2 for all Reynolds numbers simulated.…”

3D Visualization of the separated fluid flows

“…The steady flows for 200 Re d 270 are characterised by the existence of non-zero lift/side and torque moment coefficients (see (Magarvey and Bishop, 1961), (Johnson and Patel, 1999), (Gushchin et al, 1998(Gushchin et al, , 2001(Gushchin et al, , 2002). (Sakamoto and Haniu, 1990) give a Strouhal number range of 0.150-0.165 and the numerical result (Johnson and Patel, 1999) gives the value of 0.137 for Strouhal number.…”

“…For this investigation the cylindrical coordinate system (O-type grid) is used: x = R cosT, y = R sinT, z = z , where x, y, z are streamwise, lift and spanwize directions, accordingly. From the methodical calculations for 2D circular cylinder (see (Gushchin et al, 2002)) the following conclusions were made: for moderate Reynolds numbers (100 d Re d 400) the grid in radial and circumferential directions should be at least 180 x 180 or 240 x 240, the number of the points in the boundary layer can be taken not less than 5, the location of the outer boundary 23.78d with usual ( =(1,0,0)) or non-reflecting boundary conditions is sufficient to see the effects in the near wake region (0.5d < x < 10d) (d is the diameter of the cylinder). The set of the 3D calculations for the optimal flow parameters (grid size (r, T, z) -240x240x72, 10 points in the boundary layer, location of the outer boundary -23.78d, the length of the cylinder -L=7.5d) was executed for Re=220,240,260,280,300,320,340,360,400.…”

“…Detailed investigations of the structure of the sphere wake in the homogeneous fluid have been initiated in (Magarvey and Bishop, 1961) and prolongated in Haniu, 1990, 1995), (Gushchin and Matyushin, 1997), (Johnson and Patel, 1999), (Gushchin et al, 1998(Gushchin et al, , 2001(Gushchin et al, , 2002 and other papers. In spite of these papers, the detailed formation mechanism of vortices in the sphere wake is still unclear.…”

Mathematical modling of the 3D separated viscous fluid flows

“…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].…”