Hydrothermal waves in two-dimensional liquid layers with sudden changes in the available cross-section

Lappa, Marcello (2017) Hydrothermal waves in two-dimensional liquid layers with sudden changes in the available cross-section. International Journal of Numerical Methods for Heat and Fluid Flow, 27 (11). pp. 2629-2649. ISSN 0961-5539

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    Abstract

    Purpose – Hydrothermal waves represent the preferred mode of instability of the so-called Marangoni flow for a wide range of liquids and conditions. The related features in classical rectangular containers have attracted much attention over recent years owing to the relevance of these oscillatory modes to several techniques used for the production of single crystals of seminconductor or oxide materials. Control or a proper knowledge of convective instabilities in these systems is an essential topic from a material/product properties saving standpoint. The purpose of this study is to improve our understanding of these phenomena in less ordinary circumstances. Design/methodology/approach – This short paper reports on a numerical model developed to inquire specifically about the role played by sudden changes in the available cross-section of the shallow cavity hosting the liquid. Although accounting for the spanwise dimension would be necessary to derive quantitative results, our approach is based on the assumption of two-dimensional flow, which, for high-Pr fluids, is believed to retain the essence of the involved physical processes. Findings – Results are presented for the case of a fluid with Pr=15 filling an open container with a single backward-facing or forward-facing step on the bottom wall or with an obstruction located in the center. It is shown that the presence of steps in the considered geometry can lead to a variety of situations with significant changes in the local spectral content of the flow and even flow stabilization in certain circumstances. The role of thermal boundary conditions is assessed by considering separately adiabatic and conducting conditions for the bottom wall. Originality/value – Although a plethora of studies have been appearing over recent years motivated, completely or in part, by a quest to identify new means to mitigate these instabilities and produce accordingly single crystals of higher quality for the industry, unfortunately, most of these research works were focusing on very simple geometries. In the present paper, the causality and interdependence among all the kinematic and thermal effects mentioned above is discussed. Keywords – Marangoni flow, hydrothermal waves, Finite difference method, variable section geometries.