ABSTRACT
This paper presents the results of an experimental investigation of the parametric stabilization of Rayleigh-Bénard convection through the imposition of sinusoidal vibration. The ability to dynamically stabilize Rayleigh-Bénard convection using acceleration modulation is of interest to groups who design and study thermoacoustic machines as the introduction of parasitic convection can have deleterious effects on the desired operation and thermodynamic efficiency of the device. These performance issues caused by suspected convective instability have been seen both in traveling wave thermoacoustic refrigerators and cryogenic pulse tube chillers. This paper reports the results of an experiment intended to determine the vibratory, fluidic, and geometric conditions under which a small, rectangular container of statically unstable fluid may be stabilized by vertical vibration with comparison to the computational methods of R. M. Carbo [J. Acoust. Soc. Am. 135, 654-668 (2014)]. Measurements are obtained using a large-displacement kinematic shaker of an original design with the convecting gas characterized using both thermal transport measurements and flow visualization employing tracer particles illuminated by a diode laser light sheet phase-locked to the shaker. These experiments are believed to be the first demonstrating the suppression of convection through vibration in rectangular containers.
ABSTRACT
This note describes a shaker system capable of high peak-velocity, large amplitude, low frequency, near-sinusoidal excitation that has been constructed and employed in experiments on the inhibition of Rayleigh-Bénard convection using acceleration modulation. The production of high peak-velocity vibration is of interest in parametric excitation problems of this type and reaches beyond the capabilities of standard electromagnetic shakers. The shaker system described employs a kinematic linkage to two counter-rotating flywheels, driven by a variable-speed electrical motor, producing peak-to-peak displacements of 15.24 cm to a platform mounted on two guide rails. In operation, this shaker has been demonstrated to produce peak speeds of up to 3.7 m/s without failure.
ABSTRACT
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.
ABSTRACT
The parametrically driven, damped, inverted pendulum can be dynamically stabilized in particular regions of the parameter space. The impact of damping on dynamic stabilization can be stabilizing or destabilizing depending on the location in parameter space (i.e., drive frequency and amplitude). Floquet analysis and numerical simulations were used to determine the stable regions. An experiment was conducted that verifies the model. Physical explanations and simple bounding approximations are provided to summarize findings. The utility of the highly damped pendulum results are illustrated by drawing the analogy to dynamic stabilization of the Rayleigh-Taylor instability: it permits ready demonstration that dynamic stabilization is impossible in that system absent surface tension.
