Three-dimensional numerical simulations of the transition of flow past a cube

Abstract

The wake of a cube placed in a uniform flow is numerically studied. The present study concentrates on the first two transitions, one spatial and the other a temporal one. Computations are carried out for a Reynolds number range of 20-300. Starting from a steady symmetric flow, the transition to asymmetric steady flow occurs at a Reynolds number between 216 and 218. The loss of symmetry increases with increasing Reynolds number. The asymmetric steady flow experiences a Hopf bifurcation at a Reynolds number between 265 and 270 and becomes unsteady but maintains the planar symmetry. The transitions of the present study are compared to the transitions of flow past a square cylinder and a sphere. The transition sequence and flow structures match closely to that of a sphere. The drag and side force coefficients are calculated and it is observed that they are in accordance with the spatial structures of the wake. The drag coefficient is found to decrease with Reynolds number in the steady flow regime. Similarly, one component of the side force coefficients increases while the other component remains zero with increasing Reynolds number for the asymmetric flow.

Experimental investigation of flow behind a cube for moderate Reynolds numbers

“…As it is difficult to identify this place directly, we have interpolated the positive and negative values in the vicinity of zero, which gave us the required length L of the recirculation zone (normalised using a cube edge length d). Figure 6 presents the results obtained, which agree in trend with the numerical values reported by Saha (2004) (see results in his table IV). Three additional values were inferred by the present authors from the streamlines pictures of Saha (2004) (see his figures 10b, 14a and 14b) at the highest Re values.…”

“…The hairpins appear on one side only, as a result of the deformation and tilting of the vortex ring formed immediately behind the obstacle. This process is analogous to those presented in Saha (2004) for the cube and in Johnson & Patel (1999) for the sphere.…”

“…The planar symmetry and its orientation are preserved from the previous regime. Based on streamlines, Saha (2004) presents the temporal behaviour of shed hairpin vortices over a single period. The results are strikingly similar to those observed for the sphere in Johnson & Patel (1999).…”

Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles

“…Saha [76] observed numerically that the flow regimes and the corresponding transition Reynolds numbers of the flow past a cube are very similar to that past a sphere, i.e. it also undergoes a steady symmetric, a steady planar symmetric and an unsteady planar symmetric regime.…”

Generation of vortices by a streamwise oscillating cylinder

“…where ψ can be an arbitrary transport quantity, but it particularly refers to the velocities here, and m u represents the average u-velocity at the exit boundary (Orlanski, 1976;Saha, 2004).…”