A computational model for the dynamic stabilization of Rayleigh-Bénard convection in a cubic cavity

摘要

The dynamic stability of Rayleigh-Bénard convection with vertical vibration in a cubic container is computationally modeled. Two 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. Both the synchronous and the subharmonic regions of instability are recovered. The conditions necessary for dynamic stability are reported for a range of Rayleigh numbers from critical to 10~7 and for Prandtl numbers in the range of 0.1-7. The linear model is compared to the data set available in the literature where the performance of an inverted pulse tube cryocooler is measured.