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Steady flow around an inclined torus at low Reynolds numbers: lift and drag coefficients. (English) Zbl 1410.76312

Summary: The steady flow around an inclined torus has received little attention in the hydrodynamics literature, despite being relevant to many engineering and biological processes, such as the sedimentation of fluidized particles and the motion of natural micro-swimmers. In this study, we perform three-dimensional direct numerical simulations of the flow around an inclined torus over a range of aspect ratios \((2\leqslant A\kern -4 pt R\leqslant 3)\), inclination angles \((0 \leqslant \theta \leqslant 90^\circ)\) and Reynolds numbers \((10 \leqslant \text{Re}\leqslant 50)\), with a focus on the steady flow regime preceding the onset of vortex shedding. For a fixed Re, we find that as the torus inclines from a flow-normal orientation (\(\theta = 0^\circ\)) to a flow-parallel orientation (\(\theta = 90^\circ\)), the drag coefficient (\(C_{D}\)) decreases monotonically, while the lift coefficient (\(C_{L}\)) first increases from zero, reaches a maximum at \(40^\circ \leqslant \theta \leqslant 50^\circ\) and then returns to zero owing to top-down symmetry at full inclination. The decrease in \(C_{D}\) with \(\theta\) is caused by a decrease in the pressure drag, with almost no change in the viscous drag. The variation in \(C_{L}\) with \(\theta\) is caused by the pressure lift dominating the viscous lift. With increasing Re, the overall trends in \(C_{D}\) and \(C_{L}\) remain qualitatively unchanged but their quantitative values decrease. Compared with the effects of \(\theta\) and R, those of are relatively weak for the specific flow conditions examined here. We conclude by performing a nonlinear regression analysis to generate curve fits for \(C_{D}\) and \(C_{L}\) in terms of \(A\kern -4 pt R\kern +4 pt\), \(\theta\) and Re.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76D25 Wakes and jets
76F65 Direct numerical and large eddy simulation of turbulence
Full Text: DOI

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