Large eddy simulation of the wake behind a sphere with and without density stratification at Re = 3 700

Abstract

To enhance understanding of the flow characteristics around a sphere in both stratified and unstratified (UNS) fluids, large eddy simulations (LES) were conducted using a temperature-dependent density model at Re = 3 700. The simulations were performed for flow around a sphere under UNS and stratified conditions (Fr = 3). Horizontal and vertical vorticity, velocity, and streamline distributions were compared, and the evolution of vortex structures in the wake was analyzed. Furthermore, we quantified the velocity deficit, the root mean square (rms) of velocity components in all directions, and the turbulent kinetic energy (TKE) distribution. Additionally, the horizontal and vertical wake lengths were examined. The results demonstrate that the employed numerical simulation method accurately captures the behavior of stratified fluids, with outcomes in close agreement with experimental and numerical findings from previous studies. In the case of homogeneous fluid, a lower density value results in a faster decay of the velocity deficit. In stratified fluids, the vortex structures in the wake evolve through three distinct stages: 3-D, non-equilibrium (NEQ), quasi-two-dimensional (Q2D). For x / D > 2, the rms velocity in the vertical direction exceeds that in the other two directions. In UNS fluid, the TKE distribution forms a vertically elongated spindle shape, while in stratified fluid, it assumes an elliptical shape, being vertically compressed and horizontally expanded. The vertical extent of the density and density gradient distributions surpasses that of the wake.