Contribution à l’étude théorique des transferts thermiques combines aux écoulements de fluide dans un conduit annulaire fixe et en rotation soumis à un gradient de température.

Abstract

This research work is a numerical simulation of forced and mixed convectionthreedimensional of a fluid characterized by thermo-dependencethree-dimensional of a fluid characterized by thermo-dependenceof physical properties(viscosity and thermal conductivity),confined between two rotating horizontal cylinders of the Rotor-Stator type.Subjected to a differential temperature gradient imposed on the side surfaces of the two cylinders, this duct is closed at both ends by two fixed and adiabatic walls. The finite volume method is used for the discretization of the conservation equations which govern this flow as well as the initial and boundary conditions. Second order discretization schemes are used such as the Adams-Bashforth scheme, and the fully implicit centered difference scheme. The velocity-pressure coupling is treated with the SIMPLER algorithmand the systems of algebraic equations obtained are solved iteratively by the ADI method based on Thomas's algorithm. The non-dimensional numbers controlling the solution of the problem,the Taylor number (Ta)which reflects the rotating dynamic forces applied to the fluid within the air gap,the Prandtl number (Pr) which is a characteristic of the fluidand finally the Richardson number (Ri) which reflects the effect of the thermal forces applied on the fluid. The forced and mixed convection results represent an in-depth study of the effects of dynamic and thermal forces for different Richardson numbers and different values of the rotational velocity of the inner cylinder as well as the instability mechanisms of the different regimes that appear.Graphic representations are used to provide explanations in several forms (current lines, angular velocity iso-values, pressure iso-values, etc.) as well as the heat transfer represented by the Nusselt number for each case. The effects of the different control parameters (aspect ratio, form factor) on the flow and the instability mechanisms of the different regimes as well as heat transfer are also studied.