Stability of Thermocapillary Flow in High-Prandtl-Number Liquid Bridges Exposed to a Coaxial Gas Stream
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ORIGINAL ARTICLE
Stability of Thermocapillary Flow in High-Prandtl-Number Liquid Bridges Exposed to a Coaxial Gas Stream Mario Stojanovic1
· Hendrik C. Kuhlmann1
Received: 8 April 2020 / Accepted: 23 July 2020 © The Author(s) 2020
Abstract The stability of thermocapillary flow in a liquid bridge made from 5 cSt silicone oil (Pr = 68) is computed numerically. To improve the numerical model as compared to the standard approach, we consider the flow in the liquid bridge fully coupled to the flow in the ambient gas, temperature-dependent material parameters, and a dynamically deforming liquid–gas interface. We address the full two-phase-flow problem of interest for the space experiment JEREMI and investigate the effect of a steady axisymmetric coaxial gas flow which is imposed at the inlet of the annular gap between the liquid bridge and the outer confining cylinder. Under zero-gravity the flow is primarily driven by the imposed temperature gradient with viscous stresses from the gas phase being small. However, the heat transfer between liquid and the gas, and thus the temperature fields are strongly affected by the forced flow in the gas phase. As a result the stability of the steady axisymmetric flow depends sensitively on the flow direction and the temperature of the gas. If the temperature of the gas is identical to that of the support rod of the liquid bridge a gas stream opposing the thermocapillary stresses strongly destabilizes the basic flow. In a co-flow configuration the basic state is stabilized. Curves of neutral Reynolds numbers as functions of the strength of the annular gas flow are discussed for two aspect ratios of the liquid bridge. Keywords Thermocapillary flow · Liquid bridge · Stability analysis · Two-phase flow · Heat transfer
Introduction The thermocapillary flow in liquid bridges and its stability have been widely studied as a fundamental model for crystal growth from the melt, see e.g. Cr¨oll et al. (1991), Wanschura et al. (1997), and Leypoldt et al. (2000). Despite of all investigations, the heat transfer between the liquid bridge and the ambient gas is poorly understood and most difficult to control. In the past, most numerical studies addressed the problem considering only the liquid phase, neglecting viscous stresses from the gas phase and modeling This article belongs to the Topical Collection: The Effect of Gravity on Physical and Biological Phenomena Guest Editor: Valentina & Shevtsova Mario Stojanovic
[email protected] Hendrik C. Kuhlmann [email protected] 1
Institute of Fluid Mechanics and Heat Transfer, TU Wien, 1060, Vienna, Austria
the heat transfer between liquid and gas by Newton’s law (Nienh¨user and Kuhlmann 2002; Wanschura et al. 1995). These assumption can lead to a poor numerical prediction of the real flow and its stability. Recent experiments revealed that the heat transfer across the interface strongly affects the stability boundaries of the axisymmetric steady flow (Yano et al. 2017). This observation has also been confirmed by numerica
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