Natural convection and entropy generation in square and skew cavities due to large temperature differences: A Gay–Lussac‐type vorticity stream‐function approach. (7th April 2021) - Mayeli, Peyman; Sheard, Gregory J.
Abstract: In this study, a benchmark natural convection problem is studied under a Gay–Lussac‐type approximation incorporating centrifugal effects in the context of a new vorticity‐stream‐function approach. This approximation differs from the classic Boussinesq approximation in that density variations are considered in the advection term as well as the gravity term in the momentum equations. Such a treatment invokes Froude number as a non‐Boussinesq parameter deviating results from the classic Boussinesq approximation. It is also shown how the Gay–Lussac parameter may be expressed by its equivalent relative temperature difference. Numerical simulation of natural convection in square and skewed cavities are performed up to Ra = 10 6 and ϵ = 0.3 at Pr = 0.71. Results obtained with new approximation are compared against the weakly compressible approach and the conventional Boussinesq approximation in terms of the average and local Nusselt number, coefficient of friction and entropy generation. Comparing the local Nusselt number indicates a negligible difference between Gay–Lussac type and the Boussinesq approximations even at a high relative temperature difference, with both deviating from the weakly compressible approach. Comparing coefficient friction results obtained by the Gay–Lussac‐type approximation against the weakly compressible approach confirms superior numerical data in some regions of the physical domain with less deviation for rotating flows in comparison with the Boussinesq approximation. Finally, comparing the computational cost of the numerical simulation shows at least 8% less computational cost when governing equations are solved via secondary variables using a central scheme rather than primitive variables. Abstract : A Gay–Lussac‐type vorticity stream‐function approach is presented for non‐Boussinesq treatment of natural convection phenomena in which, the density variations are extended to the advection terms as well as gravity term. Such a treatment leads to the Gay–Lussac parameter inclusion in the momentum equation, which its action is to modify the effective direction of the gravity locally throughout the flow. Obtained results under the Gay‐Lussac type approach are compared against the classical Boussinesq approximation as well as weakly compressible approach at high relative temperature differences in steady and transient states.