LINEAR STABILITY ANALYSIS AND DIRECT NUMERICAL SIMUALATION OF DOUBLE-LAYER RAYLEIGH-BÉNARD CONVECTION

LINEAR STABILITY ANALYSIS AND DIRECT NUMERICAL SIMUALATION OF DOUBLE-LAYER RAYLEIGH-BÉNARD CONVECTION

FONTANA, É.; MANCUSI, E.; SOUZA, A. A. U. DE; SOUZA, S. M. A. G. U.

Artigo:

Natural convection in superimposed layers of fluids heated from below is commonly observed in many industrial and natural situations, such as crystal growth, co-extrusion 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.

Natural convection in superimposed layers of fluids heated from below is commonly observed in many industrial and natural situations, such as crystal growth, co-extrusion 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.

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DOI: 10.5151/chemeng-cobeq2014-0798-23753-137645

Referências bibliográficas

• [1] ANDEREK, C. D.; COLOVAS, P. W.; DEGEN, M. M.; RENARDY, Y. Y. Instabilities in two layer Rayleigh-Bénard convection: Overview and outlook. Int. J. of Engineering Science, v. 36, p. 1451 – 1470, 1998.
• [2] CARDIN, P.; NATAF, H. C.; DEWOST, P. Thermal coupling in layered convection: evidence for an interface viscosity control for mechanical experiments and marginal stability analysis. J. of Physics II, v. 1, p. 599 – 622, 1991.
• [3] CHANDRASEKHAR, S. Hydrodynamic and Hydromagnetic Stability. [S.l.]: Clarendon Press, 1961.
• [4] FONTANA, É; MANCUSI, E.; SOUZA, A. A. U.; SOUZA, S. M. A. G. U. Flow regimes for liquid water transport in a tapered flow channel of proton exchange membrane fuel cells (PEMFCs), J. Power Sources, v. 234, p. 260 – 271, 2013.
• [5] FUDYM, O.; PRADERE, C.; BATSALE, J. C. An analytical two-temperature model for convection–diffusion in multilayered systems: Application to the thermal characterization of microchannel reactors. Chem. Eng. Science, v. 62, p. 4054 – 4064, 2007.
• [6] LI, Y. R.; WANG, S. C.; WU, S. Y.; PENG, L. Asymptotic solution of thermocapillary convection in thin annular two-layer system with upper free surface. Int. J. of Heat and Mass Transfer, v. 52, p. 4769 – 4777, 2009.
• [7] MANCUSI, E.; FONTANA, É; SOUZA, A. A. U.; SOUZA, S. M. A. G. U. Numerical study of two-phase flow patterns in the gas channel of PEM fuel cells with tapered flow field design. Int. J. Hydrogen Energy, v. 39, n. 5, 2261 – 2273, 2014.
• [8] PELLEW, A.; SOUTHWELL, R. V. On maintained convective motion in a fluid heated from below. Proc. of the Royal Society, v. 176, n. 966, p. 312 – 342, 1940.
• [9] PRAKASH, A.; YASUDA, K.; OTSUBO, F.; KUWAHARA, K.; DOI, T. Flow coupling mechanisms in two-layer Rayleigh–Bénard convection. Exp. in Fluids, v. 23, p. 252 – 261, 1997.
• [10] RASENAT, S.; BUSSE, F. H.; REHBERG, I. A theoretical and experimental study of double-layer convection. J. of Fluid Mechanics, v. 199, p. 519 – 540, 1989.

Como citar:

FONTANA, É.; MANCUSI, E.; SOUZA, A. A. U. DE; SOUZA, S. M. A. G. U.; "LINEAR STABILITY ANALYSIS AND DIRECT NUMERICAL SIMUALATION OF DOUBLE-LAYER RAYLEIGH-BÉNARD CONVECTION", p-5625-5632. In: Anais do XX Congresso Brasileiro de Engenharia Química - COBEQ 2014 [= Blucher Chemical Engineering Proceedings, v.1, n.2]. São Paulo: Blucher, 2015.
ISSN 23591757, DOI 10.5151/chemeng-cobeq2014-0798-23753-137645