Convective modes of pseudoplastic fluid in a square cavity caused by high-frequency vibrations under reduced gravity
DOI:
https://doi.org/10.7242/1999-6691/2024.17.2.19Keywords:
pseudoplastic fluid, nonlinear viscous fluid, convection, vibrations, thermovibrational convection, numerical methods, reduced gravityAbstract
In this paper, we investigate convective modes of pseudoplastic fluid in a square cavity with solid perfectly heat-conducting boundaries under reduced gravity. The cavity performs vertical linearly polarized high-frequency vibrations. Between the vertical walls of the cavity a temperature drop is prescribed in the direction perpendicular to vibrations and the field of gravity. The fluid rheology is described using the Williamson model. The problem is solved based on the averaged thermovibration convection equations for nonlinear viscous fluids. The vibration intensity is determined by the vibration parameter V, which is proportional to the ratio of the amplitude of the vibration acceleration to the free-fall acceleration and does not depend on the temperature difference. The problem is found to have two types of solutions, which we call Newtonian and non-Newtonian modes. These solutions correspond to different convective structures, for which the dependences of the maximum of the stream function and the Nusselt number on the Grashof number are derived. We use these dependences for determining at different values of rheological parameters the threshold values of the Grasgof numbers, corresponding to the change in the modes of stationary averaged convection and the critical Grasgof numbers, corresponding to the loss of stability of stationary averaged flow and the occurrence of oscillatory modes of averaged convection. The structures of different modes of averaged stationary and oscillatory convection are studied. The results obtained for the Newtonian mode have shown that at small values of the Grasgoff number, a slow one-vortex stationary convective flow is realized in the cavity. With increasing the Grasgoff number it transforms into a three-vortex flow. A further increase in the Grasgoff number results in the appearance of a four-vortex convective flow, which eventually transforms again into a three-vortex motion. At even greater Gr, the stationary averaged motion becomes unstable and the oscillatory modes appear in the cavity. For the non-Newtonian mode, a stationary convective flow is the basic flow pattern detected in the cavity; the oscillatory modes are not observed in the whole investigated range of the Grasgoff numbers.
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