Characteristics of laminar flow past a sphere in uniform shear

Abstract

Numerical simulations are performed to investigate the characteristics of laminar flow past a sphere in uniform shear. The Reynolds numbers considered are Re=300, 425, and 480 based on the inlet center velocity uc and sphere diameter d. The nondimensional shear rate K of inlet uniform shear is varied from 0 to 0.15, where K=∣∇u∣d∕uc (∣∇u∣) and ∣∇u∣ is the shear rate at inlet. For all Reynolds numbers investigated, the head of the hairpin vortex loop is always located on the high-velocity side in uniform shear. The flow maintains planar symmetry at Re=300. At Re=425 and 480, the temporal variation in the azimuthal angle of the hairpin vortex formation appearing in the uniform inlet flow is greatly reduced in uniform shear, but the flows still keep asymmetry for most inlet shear rates. However, in the cases of K=0.075 and 0.1, at Re=425, the flows become planar symmetric and their characteristics of formation and evolution of the hairpin vortex loops are different from those of asymmetric flows. In most cases, except the instances showing planar symmetry at Re=425, the Strouhal number and time-averaged drag and lift coefficients increase with increasing inlet shear rate. On the other hand, for K=0.075 and 0.1, showing planar symmetry at Re=425, three different vortices are shed in the wake, resulting in three distinct peak frequencies. Finally, a hysteresis phenomenon switching from planar symmetry to asymmetry (or vice versa) depending on the initial condition is observed at Re=425 and 450, implying that small variations in the flow or initial conditions change the flow field at these Reynolds numbers.