Harmonic mechanical excitations of steady convective instabilities: A means to get more uniform heat transfers in mixed convection flows?

摘要

In laminar mixed convection flows, steady thermoconvective patterns generate non uniform heat and/or mass transfers at walls that can be detrimental in some industrial processes. For instance the longitudinal thermoconvective patterns of Poiseuille-Rayleigh-Benard (PRB) flows generate non uniform thin films or coatings when they are present in cold wall horizontal Chemical Vapor Deposition (CVD) reactors. The aim of this paper is to show that, when the basic steady flow is convectively unstable against an unsteady flow regime, introducing small harmonic mechanical excitations in the basic flow may enable to obtain more uniform time averaged heat transfers. More specifically, three-dimensional direct numerical simulations are used to characterize the temperature field and wall heat transfer associated with unsteady wavy convective instabilities of PRB flows that result from harmonic excitations of the longitudinal thermoconvective rolls at channel inlet. A design of experiments is used to build cubic response surfaces of the different quantities analyzed (growth length of the wavy rolls, magnitude of their spanwise oscillations, wall Nusselt number ...) on a wide range of the flow parameters. Air PRB flows (Pr = 0.71) in channels of aspect ratios equal to Width/Height = 10 and 150 ≤ Length/Height ≤ 300, for Reynolds numbers 100 ≤ Re ≤ 300 and Rayleigh numbers 5000 ≤ Ra ≤ 16,000 are considered. Comparisons with experiments are presented and a good agreement is obtained. The optimal conditions to have uniform heat transfers on the horizontal walls of PRB flows correspond to the minimal growth length of the wavy rolls until saturation and the maximum magnitude of their spanwise oscillations. They are approximately obtained for moderate Reynolds number (Re ≈ 150), high Rayleigh numbers (Ra ≈ 15,000), low excitation frequency and rather high excitation magnitude. A discussion of these results for the applications to CVD in horizontal rectangular reactors at atmospheric pressure is finally proposed.