A low-Mach methodology for efficient direct numerical simulations of variable property thermally driven flows. (April 2019)

• Record Type: Journal Article
• Authors: Demou, A.D.; Frantzis, C.; Grigoriadis, D.G.E.
• Is Part Of: International journal of heat and mass transfer. Volume 132(2019)
• Page Start: 539
• Page End: 549
• Publication Date: 2019-04
• Subjects: Low-Mach approximation -- Variable properties -- Natural convection -- Direct numerical simulation -- Differentially heated cavity; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2018.12.018
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: An efficient methodology for thermally-driven low-Mach flows is proposed. The Poisson equation is transformed into a constant coefficient equation. Validation considers a wide range of temperature differences and Rayleigh numbers. The potential of the methodology is demonstrated with a series of 3D simulations. Significant effects of the temperature difference are revealed and discussed. Abstract: Thermally driven flows can be approximated as constant property flows only when temperature differences are relatively small. In that case, the Oberbeck-Boussinesq approximation holds and the set of governing equations is simplified. For larger temperature differences, the variation of the fluid properties with temperature cannot be ignored and in the case of gasses the governing equations take the low-Mach form. This significantly complicates the numerical solution of variable property against constant property flows because of the emergence of a variable coefficient Poisson equation for the pressure. In the present study, a numerical methodology for the direct numerical simulation of thermally driven low-Mach flows is presented. In this framework, a pressure-splitting scheme is utilised to transform the variable coefficient Poisson equation for the pressure into a constant coefficient Poisson equation, improving the efficiency of the numerical solution. The consistent boundary conditions for the pressure are derived and presented. Furthermore, the proposed methodology is validated for the natural convection of air inside a differentially heated cavity, for a wide range of temperature differences, both within and outside the limits of applicability of the Oberbeck-Boussinesq approximation. Finally, to demonstrate the potential of this methodology, the three-dimensional natural convection of air inside a differentially heated cavity is simulated for a Rayleigh number Ra = 2.0 × 10 9 and for temperature differences Δ T = 50 K, 100 K, and 200 K. It is found that, with increasing temperature difference, the symmetry around the centre of the cavity that characterises the Oberbeck-Boussinesq solution is lost. In addition, the laminar-turbulent transition point on the heated and cooled walls changes position, moving to a more upstream position on the heated wall and a more downstream position on the cooled wall.