A centrifugal buoyancy formulation for Boussinesq‐type natural convection flows applied to the annulus cavity problem. (1st September 2020)

• Record Type: Journal Article
• Authors: Mayeli, Peyman; Sheard, Gregory J.
• Is Part Of: International journal for numerical methods in fluids. Volume 93:Number 3(2021)
• Page Start: 683
• Page End: 702
• Publication Date: 2020-09-01
• Subjects: annulus cavity -- Boussinesq approximation -- control volume finite‐element method -- Gay‐Lussac -- non‐Boussinesq approximation -- weakly compressible; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4904
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: 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 = 10 5 are computed. Results obtained under the proposed approximation agree with the classical Boussinesq approximation up to Ra = 10 3 for large non‐Boussinesq parameter corresponding to the large relative temperature difference, but at Ra = 10 5, 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. Abstract : A rather new formulation for Boussinesq‐type natural convection flows is presented in which the density variations are considered in advection terms as well as buoyancy term. Such a treatment causes the Froude number inclusion in the momentum equations which its action is to modify the effective direction of the gravity locally throughout the flow.