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Communication Dans Un Congrès Année : 2014

High-Order Numerical Implementation of Surface Radiation for the Coupling with Natural Convection in an Air-Filled Square Cavity

Résumé

Natural convection in a cavities without radiation has been the subject of many investigations with many practical applications and it became a benchmark problem for testing CFD codes. Although surface radiation is far from negligible in natural convection in air-filled cavities, studies including the interaction between the two phenomena remain still sparse. The main purpose of this work is the development of accurate numerical methods for the study of the coupling of natural convection with surface radiation in air-filled cavities, in view also of providing a benchmark problem and reference solutions. Since the standard radiosity method using view factors can yield only second-order spatial accuracy, a new formulation using pointwise radiosity and integration by parts is proposed. The numerical implementation of the new formulation is based on appropriate quadratures for numerical integration and differentiation and is tested in a spectral Chebyshev collocation method and a fourth-order finite-difference method. Results obtained at RaH = 10^4 and 10^5 show respectively spectral and fourth-order convergence for the convective and radiative Nusselt numbers. The spectral implementation also confirms that a much coarser mesh can be employed for surface radiation compared to the one used for the solution of the Navier-Stokes equations, without decreasing the accuracy of the numerical results. This is an important observation for future 3D simulations in which the large number of surface elements becomes a major stumbling block.
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Dates et versions

hal-01282637 , version 1 (04-03-2016)

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Ronnie Knikker, Shihe Xin, Ren Dai. High-Order Numerical Implementation of Surface Radiation for the Coupling with Natural Convection in an Air-Filled Square Cavity. International Heat Transfer Conference, 2014, Kyoto, France. ⟨10.1615/IHTC15.cnv.009092⟩. ⟨hal-01282637⟩
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