Stratified flow past a sphere at moderate Reynolds numbers

TL;DR

This study uses numerical simulations to explore how stratification affects flow patterns around spheres at moderate Reynolds numbers, revealing different wake structures and flow regimes as stratification varies.

Contribution

It provides new insights into stratified flow dynamics past bluff bodies, especially regarding the influence of stratification and viscosity on wake features and flow separation.

Findings

Flow patterns become similar at low Froude numbers for different Reynolds numbers.

Identification of lee-wave instability and vortex shedding regimes at specific Froude numbers.

Numerical results agree with experimental data, validating the simulation approach.

Abstract

A numerical study of stably stratified flows past spheres at Reynolds numbers $Re=200$ and $Re=300$ is reported. In these flow regimes, a neutrally stratified laminar flow induces distinctly different near-wake features. However, the flow behaviour changes significantly as the stratification increases and suppresses the scale of vertical displacements of fluid parcels. Computations for a range of Froude numbers $Fr\in [0.1,\infty]$ show that as Froude number decreases, the flow patterns for both Reynolds numbers become similar. The representative simulations of the lee-wave instability at $Fr=0.625$ and the two-dimensional vortex shedding at $Fr=0.25$ regimes are illustrated for flows past single and tandem spheres, thereby providing further insight into the dynamics of stratified flows past bluff bodies. In particular, the reported study examines the relative influence of viscosity and stratification on the dividing streamline elevation, wake structure and flow separation. The solutions of the Navier-Stokes equations in the incompressible Boussinesq limit are obtained on unstructured meshes suitable for simulations involving multiple bodies. Computations are accomplished using the finite volume, non-oscillatory forward-in-time (NFT) Multidimensional Positive Definite Transport Algorithm (MPDATA) based solver. The impact and validity of the numerical approximations, especially for the cases exhibiting strong stratification, are also discussed. Qualitative and quantitative comparisons with available laboratory experiments and prior numerical studies confirm the validity of the numerical approach.