Computational model for the dynamic stabilization of the Rayleigh-Bénard instability in rectangular enclosures

Abstract

When fluid within a container is heated from the bottom, onset of convection occurs when Rayleigh number, gβΔTℓ3νχ, exceeds some critical value. If an acoustic field is imposed on the fluid in the container, the critical Rayleigh number is a strong function of the frequency and amplitude of that acoustic field as noted by Swift and Backhaus [J. Acoust. Soc. Am. 126(5), 2009]. Results will be reported for a linear model constructed to predict the modified critical Rayleigh number, based on a full field solution of the hydrodynamic equations using the approach of Gelfgat [J. Comp. Phys. 156, 1999]. The spatial portion of the differential equations was solved using the Galerkin method, and the dynamic stability was determined using Floquet analysis. One of the benefits of the approach compared to the averaging methods used by Gershuni and Lyubimov, [Thermal Vibration Convection (Wiley, New York, 1998)] is that the parametric stability boundary can also be recovered. This study includes a variety of container aspect ratios, boundary conditions, and Rayleigh numbers ranging from 103 to 108. [Work supported by the Office of Naval Research and ARL Exploratory and Foundational Research Program.]