Numerical study of natural convection in a horizontal annular channel with a rotating inner cylinder - Narygin, Eduard Igorevich; Zubkov, Pavel Tikhonovich (Computational Continuum Mechanics, 2025)
This paper presents a numerical study of the natural convection of a viscous incompressible fluid that completely fills a horizontal annular channel. The temperature difference at the outer boundary produces convection, which can cause the rotation of the inner cylinder around its axis. The cylinder is assumed to rotate without friction. The Boussinesq approximation is used as a mathematical model. The problem is solved numerically by the algorithm SIMPLER. The equation of motion of the inner cylinder is derived from the law of conservation of angular momentum. The choice of a numerical integration method for the equation of motion of the inner cylinder does not affect the result. The influence of the dimensionless parameters on the flow structure and the angular velocity of the inner cylinder was studied. Dimensionless parameters vary within the ranges: Grashof number 103...2·105, Prandtl number 0.5...15, the dimensionless thermal conductivity of the cylinder 0...∞, and the cylinder inner radius 0.05...0.9. Numerical simulations have shown that the flow structure affects the angular velocity of the inner cylinder, which reaches its maximum in the case of a single-cell flow and at a minimum internal radius. As the Grashof number increases, the maximum possible angular velocity of the inner cylinder increases monotonically and is realized at large inner radius values. The Prandtl number has an opposite effect on the cylinder rotation velocity. If it decreases, then the angular velocity becomes extremely high at smaller inner radius values. An increase in the dimensionless thermal conductivity leads to the growth of the angular velocity, but it reaches a maximum at a smaller inner radius. The influence of the considered parameters on the angular velocity is determined by the change in the structure of the flow in the annular channel. The research results may be useful in the development of technical devices with an annular channel and a rotating inner cylinder.