Viscoelastic Thermovibrational Flow Driven by Sinusoidal and Pulse (Square) Waves

The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered: a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e., that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional, and nonlinear form for a representative set of parameters (generalized Prandtl number Prg=8, normalized frequency Ω=25, solvent-to-total viscosity ratio ξ=0.5, elasticity number ϑ=0.1, and vibrational Rayleigh number Raω=4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh–Bénard (RB) convection in a Newtonian fluid (i.e., producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves.

Vibroconvective Patterns in a Layer under Translational Vibrations of Circular Polarization

This article experimentally investigates thermal vibrational convection in horizontal layers, subject to circular translational oscillations in the horizontal plane. The definite direction of translational vibrations lacks investigation, and the case of a layer heated from above is considered. At large negative values of the gravitational Rayleigh number, the thermovibrational convection appears in a threshold manner with an increase in the vibration intensity. Our results show that in the case of strong gravitational stabilization, thermovibrational convection develops in the form of patterns with strong anisotropy of spatial periods in orthogonal directions. The vibroconvective patterns have the form of parallel rolls divided along their length into relatively short segments. The layer thickness determines the distance between the rolls, and the longitudinal wavelength, depends on the Rayleigh number. Convective cells are studied using the noninvasive thermohromic methodic. It is found that when using the tracers for flow visualization, the concentration and type of the visualizer particles have a serious impact on the shape of the observed vibroconvective structures. In particular, the presence of even a small number of tracers (used in the study of velocity fields by the PIV method) generates flows and intensifies the heat transfer below the threshold of thermovibrational convection excitation.

Thermal vibrational convection of a pseudoplastic fluid in a rectangular cavity

Thermal vibrational convection of a pseudoplastic fluid in a closed rectangular cavity, which is in zero gravity and performing longitudinal high-frequency linearly polarized vibrations, is studied. The temperature gradient is perpendicular to the direction of vibration. The system of equations of thermovibrational convection of a Williamson pseudoplastic fluid is given. The problem was solved by the finite difference method. The effect of vibrations on the structure and intensity of flows is investigated. The magnitude of the vibrational effect on the liquid was determined by the vibrational Grashof number. The dependences of the maximum of the stream function and the Nusselt number, which determines the heat flux through the boundary of the cavity, on the vibrational Grashof number are obtained. The threshold values of the vibrational Grashof number and the Nusselt number corresponding to a change in the flow regime are determined. At small values of the Grashof vibration number in the cavity, a slow four-vortex symmetric flow is observed. With an increase in the vibrational impact, an intense three-vortex motion arises in the cavity, which transforms into five vortex-like motion. For the five vortex flows, there exists the region of Grashof vibration numbers, where this flow is oscillatory in nature. With increasing degree of non-Newtonian fluid, initially periodic oscillations become chaotic.