Abstract
The transition of viscous fluid flow around the square cylinder placed in a computational domain with a sudden expansion at low Reynolds numbers (Re) is investigated numerically by using the lattice Boltzmann method. The flow analysis is based on various Reynolds numbers and expansion ratios of the channel for different gap spacing ratios (g*), and both the Re and gap spacing ratios are studied for g* = 1, 5, and 10 and Re = 75, 100, 125, and 150, respectively. Here, g* = g/D, where g is the expansion ratio of the flow and D is the diameter of the cylinder. From the flow phenomena, we observed that the flow remains symmetric to a certain level depending on low Reynolds numbers. Hydrodynamic forces of the cylinder are strongly based on the expansion ratios. The effect of various Reynolds numbers and gap spacing ratios on the lift forces and drag coefficient is also analyzed. The bifurcation phenomena of asymmetric to nonasymmetric states occur with the increase in Reynolds numbers and expansion and spacing ratios.
Highlights
The sudden expansion (SE) of an incompressible fluid flow is one of the important flow phenomena in the case of transition of fluid flow from one flow regime to another
The bifurcation of sudden expansion flow phenomena has been computed experimentally at low Reynolds numbers by both Durst et al.13 and Chedron et al.;14 they examined that the behavior of flow is symmetric at low Reynolds numbers, and for higher Reynolds numbers, which is more than 185, the behavior of flow is asymmetric near sudden expansion, which is based on the maximum velocity and height of the upstream computational domain for the flow
Shapira et al.16 estimated a higher value of critical Reynolds number as compared to Chedron et al.14 for an expansion ratio of 1:2 and estimated that the behavior of sudden expansion flow is symmetric for a critical Reynolds number that is in between 150 and 180 for a ratio of 1:2 in which the critical Re is based on the upstream computational height of the channel
Summary
The sudden expansion (SE) of an incompressible fluid flow is one of the important flow phenomena in the case of transition of fluid flow from one flow regime to another. Milos and Acrivos numerically investigated the sudden expansion flow (SEF) for uniform inlet profile and observed that the steady solution of flow exists for different expansion ratios. Milos et al. carried out the complete computations of Navier-Stokes equations for sudden expansion flows up to Re = 1000 based on various expansion ratios (ER). For critical Re = 40.45 and 80.45 based on computational upstream, the semiheight and height of the channel, respectively, were discussed by Fearn et al. for an expansion ratio of 1:3, and it was analyzed that the flow is symmetric for these critical Reynolds numbers. Abbot and Kline analyzed the sudden expansion flow and investigated the turbulent flow depending on the Re and expansion ratios of the flow They observed that the flow downstream to the computational domain is asymmetric.
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