Low-Re flow past an isolated cylinder with rounded corners

Abstract

Highlights• DNS on the separation and transition of flow past a partially rounded cylinder.• The effect of the corner radius of the cylinder is studied.• Investigation on time-averaged flow, unsteady flow, turbulent statistics and 3D flow pattern.• There are drastic variations of the flow pattern between the square cylinder and the partially rounded cylinder, and between the latter and the circular cylinder.• Non-time-periodicity is significant in the shear layer and at the reattachment point. AbstractDirect numerical simulation is performed for flow past an isolated cylinder at Re = 1, 000. The corners of the cylinder are rounded at different radii, with the non-dimensional radius of curvature varying from R + = R/D = 0.000 (square cylinder with sharp corners) to 0.500 (circular cylinder), in which R is the corner radius and D is the cylinder diameter. Our objective is to investigate the effect of the rounded corners on the development of the separated and transitional flow past the cylinder in terms of timeaveraged statistics, time-dependent behavior, turbulent statistics and three-dimensional flow patterns. Numerical results reveal that the rounding of the corners significantly reduces the time-averaged drag and the force fluctuations. The wake flow downstream of the square cylinder recovers the slowest and has the largest wake width. However, the statistical quantities do not monotonically vary with the corner radius, but exhibit drastic variations between the cases of square cylinder and partially rounded cylinders, and between the latter and the circular cylinder. The free shear layer separated from the R + = 0.125 cylinder is the most stable in which the first roll up of the wake vortex occurs furthest from the cylinder and results in the largest recirculation bubble, whose size reduces as R + further increases. The coherent and incoherent Reynolds stresses are most pronounced in the near-wake close to the reattachment point, while also being noticable in the shear layer for the square and R + = 0.125 cylinders. The wake vortices translate in the streamwise direction with a convection velocity that is almost constant at approximately 80% of the incoming flow velocity. These vortices exhibit nearly the same trajectory for the rounded cylinders and are furthest away from the wake centerline for the square one. The flow past the square cylinder is strongly three-dimensional as indicated by the significant primary and secondary enstrophy, while it is dominated by the primary enstrophy (ω 2 z ) for the rounded cylinders.

Quantification of wake unsteadiness for low-Re flow across two staggered cylinders

“…The codes for the direct simulation and stability-sensitivity analysis have been successfully employed in our earlier works 28–41 for low- Re flow across one single or two tandem cylinders of various geometries, and the results are in good agreement with the benchmark results in the literature through careful comparisons (see, e.g., Table 1 in Zhang et al. 35 and Table 3 in Zhang et al.…”

“…The discretized equations are solved using our in-house second-order code based on fractional step method 27 which has been well verified in our earlier works. 28–41 The time step size is around 0.005 d / U 0 . The simulations are initialized with ( u, v, p ) = (1.0, 0.0, 0.0) and no artificial perturbation is added; the flow is first steady but then loses its stability as integrating in physical time and becomes perfectly time-periodic after a certain duration as reflected by the shedding vortices.…”

Effect of Corner Radius in Stabilizing the Low-Re Flow Past a Cylinder

“…For the super-critical two-and three-dimensional flows at Re∼O(10 2 −10 3 ), Sohankar et al [16] found that the aerodynamic quantities, such as the mean and fluctuating lift and drag coefficients, are substantially affected by the cylinder geometry. Recent numerical and experimental studies [17][18][19] confirmed that the flow pattern is determined by the corner radius of a partially rounded cylinder. By rounding the corners of a square cylinder with a small radius of curvature, the formation of the shedding vortices are initialized further downstream away from the cylinder compared with both the circular and square geometries, and results in the streamwise expansion of the recirculation bubbles.…”

“…The two-dimensional direct simulation is performed by our in-house code used in previous studies [19,[24][25][26]. The governing equations (1) are discretized on the grid using a second-order central difference scheme.…”

Effect of surface curvature on destabilization and unsteadiness of low-Re flow across two tandem elliptic cylinders

“…The governing equations were solved using our in-house finite difference code which has been well validated for flow across bluff bodies. 27–35 The time marching in one physical step consists of three sub-steps including the predictor step for velocity, the solution of pressure and the corrector step for velocity. The differential equations for the sub-steps are formulated as:…”