A centrifugal buoyancy formulation for Boussinesq-type natural convection flows applied to the annulus cavity problem

Peyman Mayeli, Gregory J. Sheard

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Traditionally, the Boussinesq approximation is adopted for numerical simulation of natural convection phenomena where density variations are supposed negligible except through the gravity term of the momentum equation. In this study, a recently developed formulation based on a Boussinesq approximation is presented in which the density variations are also considered in the advection terms. Extending density-variations to the advection terms captures centrifugal effects arising from both bulk enclosure rotation and within individual vortices, and thus more accurate results are expected. In this respect, the results of the proposed formulation are compared against the conventional Boussinesq simulations and weakly compressible approximation in the concentric horizontal annulus cavity. A new relation is established which maps the magnitude of the non-Boussinesq parameter of incompressible flow to the corresponding relative temperature difference of a compressible flow simulation which is in agreement with the maximum allowed Gay-Lussac number to avoid unphysical density values. For comparison purposes, variations of different thermo-fluid parameters including average and local Nusselt number, entropy generation, and skin friction up to Ra = 105 are computed. Results obtained under the proposed approximation agree with the classical Boussinesq approximation up to Ra = 103 for large non-Boussinesq parameter corresponding to the large relative temperature difference, but at Ra = 105, computed thermo-fluid parameters via the two approaches are not identical which justifies the inclusion of large Gay-Lussac number for convection dominated regime in natural convection problems.

Original languageEnglish
Pages (from-to)683-702
Number of pages20
JournalInternational Journal for Numerical Methods in Fluids
Issue number3
Publication statusPublished - Mar 2021


  • annulus cavity
  • Boussinesq approximation
  • control volume finite-element method
  • Gay-Lussac
  • non-Boussinesq approximation
  • weakly compressible

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