A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers.

*(English)*Zbl 1012.76052Numerical simulations of uniform flow past a sphere are presented for Reynolds numbers from 100 to 500. The Navier-Stokes equations are discretized in three-dimensional space using a Galerkin-type finite element method. A velocity-pressure segregated algorithm using an explicit scheme is implemented for unsteady problems. Extensive computations at \(Re=100\) are first carried out in order to determine optimal parameters for the simulations, as well as to examine the computational convergence. Unsteady flow fields are successfully calculated by introducing an artificial perturbation into the simulation. The development of asymmetric stationary wakes at \(\operatorname {Re}>250\) is obtained numerically, which is consistent with experimental observations by others. The occurence of periodic vortex shedding behind the sphere at \(\operatorname {Re}>375\) and shed vortices detaching from a fixed location on the sphere at these Reynolds numbers are also in agreement with experimental observations. Additionally, the author presents consistent with experiment statistical characteristics of unsteady flow field such as drag, separation angle and Strouhal number. With a further increase of Re to 500, irregularly shaped vortices begin to appear in addition to well-organized vortices, as observed in experiments. Spectral analysis reveals a periodic fluctuation of vortex detachment location, the period of which is about four times longer than that of individual vortex shedding.

Reviewer: Titus Petrila (Cluj-Napoca)

##### Keywords:

Navier-Stokes equations; unsteady wake; sphere; Galerkin finite element method; velocity-pressure segregated algorithm; explicit scheme; artificial perturbation; asymmetric stationary wakes; periodic vortex shedding; drag; separation; Strouhal number; vortex detachment location
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