Dynamic stabilization of the Rayleigh-Bénard instability in a cubic cavity

Abstract

The dynamic stability of the Rayleigh-Bénard instability with vertical vibration in a cubic container is computationally modeled. Two periodic parametric drives are considered (sinusoidal and rectangular), as well as two thermal boundary conditions on the sidewalls (insulating and conducting). The linearized equations are solved using a spectral Galerkin method and Floquet analysis. Floquet analysis recovers both the synchronous and the subharmonic regions of instability. The conditions necessary for dynamic stability are reported for Rayleigh numbers from critical to 107 and for Prandtl numbers in the range of 0.1-7.0, and the approach produces maps over a wide range of Rayleigh number and vibration parameters for stability. The linear model is compared to data set available in the literature [G. W. Swift and S. Backhaus J. Acoust. Soc. Am. 126, 2273 (2009)] where the performance of system simulating an inverted pulse tube cryocooler is measured. The relevant instability for this case is the synchronous instability. Over this limited data set, the model appears to bound the empirically observed conditions for stability, but in some cases the model would seem to predict significantly higher required periodic acceleration amplitudes that appear to have been observed by Swift. Comparison with another data set is on-going. [Research supported by the Office of Naval Research and ARL Exploratory and Foundational Research Program.]