Abstract
Direct numerical simulations and linear stability analysis are performed to study the three-dimensional electro-thermo-convective (ETC) flow between two parallel plates under a simultaneously applied temperature difference and voltage. Entropy generation analysis and hexagonal pattern analysis are used to illustrate the transient evolution and stationary dissipative structures of an ETC flow. Numerical simulations with a large computational domain are first performed to reproduce the experimentally observed motion pattern under strong unipolar charge injection. The results show that an infinitesimal random perturbation first grows into a rolls pattern, then partially breaks up into polygons, and finally evolves into hexagons after a long period of transition. Linear stability analysis is conducted to obtain the stability criteria (electric Rayleigh number and Rayleigh number ) and the critical wave number of the ETC flow, and these critical values are found to be consistent with the numerically obtained ones. In addition, it is found that the basic features of the numerically obtained ETC hexagonal flow pattern agree with those of the analytically derived cell pattern. By entropy generation analysis of ETC in a periodic region, it is found that the formation of the rolls pattern has a larger total entropy generation and a larger mean-square temperature gradient than the hexagon pattern, which means that the rolls pattern is more stable than the hexagon under this specific simulation condition.
3 More- Received 11 January 2022
- Accepted 28 March 2022
DOI:https://doi.org/10.1103/PhysRevFluids.7.043701
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