Loughborough University
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Stratified flow past a sphere at moderate Reynolds numbers

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posted on 2021-05-18, 07:47 authored by Francesco Cocetta, Mike Gillard, Joanna SzmelterJoanna Szmelter, Piotr K Smolarkiewicz
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∈[0.1,∞] 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.


This work was supported in part by the funding received from the EPSRC studentship grant 1965773, Horizon 2020 Research and Innovation Programme (ESIWACE Grant agreement no. 675191, ESCAPE Grant agreement no. 671627 and ESCAPE2 Grant agreement no. 800897).



  • Mechanical, Electrical and Manufacturing Engineering

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Computers & Fluids






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This is an Open Access Article. It is published by Elsevier under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

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Dr Mike Gillard. Deposit date: 17 May 2021

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