Three-dimensional natural convective states in a narrow-gap horizontal annulus. (Q2767770)

Using numerical methods, this paper studies the buoyancy-driven flow in a narrow-gap annulus formed by two concentric horizontal cylinders. The flow consists of a fluid layer which is bounded by two concentric horizontal cylinders of length \(l\) with inner and outer radii \(r_i\) and \(r_0\) respectively, and by two vertical endwalls. The temperature of the inner cylinder is greater than that of the outer cylinder \((T_i> T_0),\) and the endwalls are impermeable and adiabatic. The non-dimensional radius ratio \(R= r_0/r_i\) and gap aspect ratio \(A=l/(r_0- r_i)\) characterize the narrow gap annulus geometry. The dimensionless axial length is defined as \(L= l/r_i\). A cylindrical coordinate system \((r,\Phi,z)\) is employed where the angular coordinate \(\Phi\) is measured with reference to the upward vertical. The computational domain has been chosen to encompass the full radial \((1\leq r\leq R)\), angular \((-\pi\leq\Phi\leq\pi)\), and axial \((0\leq z\leq L)\) extent of the annulus for all numerical simulations.NEWLINENEWLINE This problem has been considered for the first time in the literature. The governing equations are formulated in terms of vorticity and vector potential. These parabolic equations subjected to specific boundary conditions are solved numerically by a three-dimensional three-level time-splitting ADI method, and the elliptic equations are solved by the extrapolated Jacobi scheme. Three-dimensional numerical solutions for a wide range of annulus radius ratios and Rayleigh numbers as well as for different Prandtl numbers are shown to be in agreement with similar results from previous experimental and numerical studies. The thermal instability as the formation of three-dimensional secondary flows, and the effects of Rayleigh number and annulus geometry on the flow and temperature fields are elucidated.NEWLINENEWLINE There are many very interesting results reported by the authors in this paper, but we will mention only the following ones: the onset of thermal instabilities leads to the development of three-dimensional flow in the upper portion of the annulus consisting of multiple counter-rotating rolls; at low Rayleigh numbers, the flow in a narrow-gap annulus is similar to that in annuli with larger \(R\), with two-dimensional crescent-shaped patterns present in the core region and a three-dimensional rotational structure located in the upper portion of the annulus at each endwall; the temperature field and the inner and outer cylinder Nusselt number distributions at the top of the annulus are significantly affected by the longitudinal rolls.