Numerical simulation of multicellular natural convection in air-filled vertical cavities

Abstract

Abstract. The paper deals with 2D laminar natural convection in vertical air-filled cavities of aspect ratio 20, 30 and 40 with differentially heated sidewalls. The airflow and heat transfer were simulated numerically with an in-house Navier-Stokes code SINF. The focus is on the appearance of stationary vortex structures, "cat's eyes", and their transition to unsteady regime in the Rayleigh number range from 4.8×10 3 to 1.3×10 4 . The dependence of the predicted flow features and the local and integral heat transfer on the aspect ratio value is analysed.

Comparative analysis of nondimensionalization approaches for solving the 2‐D differentially heated cavity problem

“…The values of the magnitudes of the streamfunction for Approaches II (Figure 7) and III decrease as the Rayleigh number increases, which facilitates convergence and obtains the numerical solution for high Ra values. Note that the orders of magnitude of the maximum values of the streamfunction for Ra = 10 7 obtained with Approach I are almost 3 × 10 3 times greater than those obtained with Approach II, 3,35–39 and 1 × 10 6 greater than those obtained with Approach III, which clearly influences the stability and numerical solution 40–43 . This can be seen in Table 5, where the computation times in minutes are reported for different Ra values and different mesh sizes.…”

“…) , respectively. Three different nondimensionalization approaches were employed and designated as Approach I, 2,14,16,31,34 Approach II, 3,[35][36][37][38][39] and Approach III. [40][41][42][43] 2.1.…”

“…The system of elliptical PDEs formed by Equations ( 6)-(18d) was solved by orthogonal collocation method [33][34][35][36][37][38][39][40][41][42][43][44][45] (using Legendre polynomials and the computational code NEWCOL2L, as described in Jiménez-Islas. 46 The discretized equations were solved using the modified Newton's method (Equation 20) with LU factorization, and finite differences were employed to approximate the partial derivatives of the Jacobian matrix.…”

“…The governing equations for both cases can be rewritten using the streamfunction‐vorticity forms ( ψ ‐ ω ) ψ $$$ \left({U}_x=-\frac{\partial \psi }{\partial y},{U}_y=\frac{\partial \psi }{\partial x}\right) $$$ and ω $$$ \left(\omega =\frac{\partial {U}_y}{\partial x}-\frac{\partial {U}_x}{\partial y}\right) $$$, respectively. Three different nondimensionalization approaches were employed and designated as Approach I , 2,14,16,31,34 Approach II , 3,35–39 and Approach III 40–43 …”