Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4

Abstract

A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

Variable Property Effects in Momentum and Heat Transfer

“…5. Whereas DNS results from (Trias et al, 2010a;Trias et al, 2010b;Trias et al, 2007) and our own LES results are close to each other, RANS results show larger deviations. Some numerical details are given in table 3.…”

Simulation of Solid Particles Behavior in a Heated Cavity at High Rayleigh Numbers

“…Most of the earlier works can be classified in three main groups, namely, cavities where the flow is due to internal heat generation, cavities heated from below (Rayleigh-Benard configuration), and those heated from the sides (differentially heated cavity) (Thatcher et al 1996;Trias et al 2007Trias et al , 2010aPuragliesi et al 2011). These earlier works have shown, despite the simplicity of cavity geometry, the resulting convective flows and the temperature fields could become quite complex.…”

“…Computer simulations of laminar and turbulent natural convections in the differentially heated cavity were reported in (de Vahl Davis and Jones 1983;de Vahl Davis 1983;Hortmann et al 1990;Le Quéré 1991;Dixit and Babu 2006;Trias et al 2007Trias et al , 2009Trias et al , 2010Puragliesi et al 2011).…”

“…They found that the particles can be trapped in convective recirculation region of the flow while the other parts of the flow are particlefree. Trias et al (2007), however, performed a series of twoand three-dimensional simulations of a differentially heated airfilled cavity with an aspect ratio of 4 with adiabatic horizontal walls. Their results showed that the differences between twoand three-dimensional simulations become significant only for Rayleigh numbers higher than 6.4 × 10 8 for which the flow is fully turbulent.…”

Parameter-Free Symmetry-Preserving Regularization Modelling of Turbulent Natural Convection Flows

“…Since now the performance of the C 4 approximation has been successfully tested for a turbulent channel flow [3] and an air-filled (Pr = 0.71) differentially heated cavity (DHC) of height aspect ratio A = 4 at Ra-numbers (based on the cavity height) 10 10 [5, 6] and 10 11 [7] by means of direct comparison with the DNS results [8,9,10]. In the latter cases, the filter width ε was treated as a parameter.…”