Rayleigh Bénard convective instability of a fluid under high-frequency vibration

Abstract

The generation of two-dimensional thermal convection induced simultaneously by gravity and high-frequency vibration in a bounded rectangular enclosure or in a layer is investigated theoretically and numerically. The horizontal walls of the container are maintained at constant temperatures while the vertical boundaries are thermally insulated, impermeable and adiabatic. General equations for the description of the time-averaged convective flow and, within this framework, the generalized Boussinesq approximation are formulated. These equations are solved using a spectral collocation method to study the influence of vibrations (angle and intensity). Hence, a theoretical study shows that mechanical quasi-equilibrium (i.e., state in which the averaged velocity is zero but the oscillatory component is in general non-zero) is impossible when the direction of vibration is not parallel to the temperature gradient. In the other case, it is proved that the mechanical equilibrium is linearly stable up to a critical value of the unique stability parameter, which depends on the vibrational field. In this paper, it is shown that high-frequency vertical oscillations can delay convective instabilities and, in this way, reduce the convective flow. The isotherms are oriented perpendicular to the axis of vibration. In the case where the direction of vibration is perpendicular to the temperature gradient, small values of the Grashof number, the stability parameter, induce the generation of an average convective flow. When the aspect ratio is large enough, the character of the bifurcation is practically the same as in the limiting case of an infinitely long layer.

Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement

“…On the other hand, under normal gravity conditions, Gershuni et al (24) theoretically analyzed the linear stability of double diffusive convection in the presence of high-frequency vibration and determined the conditions of quasi-equilibrium. It was further found that vibration can generate or delay convective instabilities depending on the mutual orientation of the vibration axis and gravity (25,26). Specifically, vertical vibration that is parallel to the gravity has been used to stabilize the unstable thermal gradients (27), even in the turbulent regime (28,29).…”

Experimental Evidence of Thermal Vibrational Convection in a Nonuniformly Heated Fluid in a Reduced Gravity Environment

“…The fundamental treatise [1] comprises a systematic study of convective flows induced by high and finite frequency vibrations in closed and infinite cavities. Thermovibrational convection in square, rectangular, and cubic cavities was widely investigated providing a variety of mean flow structures and bifurcation scenarios [5][6][7][8]. Influence of vibration on double diffusive convection with the Soret effect was analyzed in [9].…”

A review of fluid instabilities and control strategies with applications in microgravity

“…Secondary forcing can also be used delay or manipulate the Rayleigh-Bénard instability. As with the Rayleigh-Taylor instability, high frequency vertical vibrations (in this case, parallel to the temperature gradient) can suppress convection [30,61,160] as can modulation of the applied temperatures [31] or the addition of an oscillatory shear flow [76]. Closed-loop (feedback) control strategies have been investigated, with many based on the application of inhomogeneous perturbations to the heat flux at the lower boundary [67,116].…”