Abstract

Natural convection in superimposed layers of fluids heated from below is commonly observed in many industrial and natural situations, such as crystal growth, coextrusion processes and atmospheric flow. The stability analysis of this system reveals a complex dynamic behavior, including potential multiplicity of stationary states and occurrence of periodic regimes. In the present study, a linear stability analysis (LSA) is performed to determine the convection onset as a function of imposed boundary conditions, geometrical configuration and specific perturbations with different wavenumbers. To investigate the effects of the non-linear terms neglected by the linear stability analysis, a direct numerical simulation of the full nonlinear problem is performed with the use of CFD techniques. The numerical simulations results show an excellent agreement with the LSA results near the convection onset and an increase in the deviation as the Rayleigh number increases beyond the critical value.

Highlights

  • Single layer Rayleigh-Bénard (RB) convection is one of the most widely studied systems in the transport phenomena field, mainly because the large number of applications and the relative simplicity of the governing equations

  • Direct numerical simulation (DNS) of the full non-linear set of governing equations using modern computational fluid dynamic (CFD) based techniques will be performed and compared to the results obtained through linear stability analysis (LSA)

  • For Raρ = 103 the critical Rayleigh number is approximately 1163, the results shown in Figure 4–a are very close to the critical value

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Summary

INTRODUCTION

Single layer Rayleigh-Bénard (RB) convection is one of the most widely studied systems in the transport phenomena field, mainly because the large number of applications and the relative simplicity of the governing equations. The presence of a second fluid layer significantly increases the system complexity and can affect the stability in many ways, as for example through competition of convective modes in each layer, control of one layer over the other one, interface deformation and unstable convective modes controlled by interfacial tension gradients Due to this complex dynamical behavior and the large number of governing parameters, the stability of double layer Rayleigh-Bénard convection is still poorly understood. Direct numerical simulation (DNS) of the full non-linear set of governing equations using modern computational fluid dynamic (CFD) based techniques will be performed and compared to the results obtained through linear stability analysis (LSA)

MATHEMATICAL MODEL
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