Horizontal convection driven by nonuniform radiative heating in liquids with different surface behavior
Graphical abstract
Introduction
When nonuniform heating or cooling is applied along one of the horizontal boundaries of the liquid layer, natural convection circulation develops, which is called horizontal convection [1]. It received some attention, mainly in the context of geophysical flows. Meridional overturning circulation in oceans, which advects warm water from subtropical regions to high latitudes, can be partly explained by horizontal convection, driven by solar radiation heat flux difference near the equator and near the poles. At smaller scale, horizontal convection, associated with nonuniform radiation and evaporation, can provide mixing of water in lakes. Also, it is important for industrial processes, which involve potentially nonuniform heating of liquid from above, in particular for glass production. High-temperature glass melt is processed in glass furnace with several burners heating the melt surface from above in order to provide melting of the floating raw material and to avoid inhomogeneous crystallization. Horizontal convection promotes mixing of the glass melt and thus improves the homogeneity of the produced glass sheets.
In most papers devoted to horizontal convection nonuniform heating was applied along the base of liquid tank. In these studies [2], [3], [4] numerical simulations of the flow were performed for various ranges of Rayleigh number and tank aspect ratio and scaling of Nusselt number, boundary layer thickness and circulation intensity was obtained. Boundary layer stability was also analyzed [5]. Experimental investigations, including temperature profiles measurements using thermistors, qualitative schlieren visualizations, dye visualizations of the flow and measurements of heat flux distribution at the tank bottom, were conducted by Mullarney et al. [2] and Sanmiguel Vila et al. [6]. Horizontal convection in liquid nonuniformly heated from above was mostly studied numerically for large Prandtl numbers typical for glass production problems [7], [8], [9]. Note that in all these studies nonuniform temperature profile was prescribed at the top boundary and no-slip conditions were imposed at all the boundaries of liquid volume. Simulations for no-slip and stress-free conditions at the top boundary were performed by Chiu-Webster et al. [10], and it was shown that in the limit of infinite Prandtl number different boundary conditions yield the same scaling, though Nusselt number obtained in stress-free case is about 60% larger. Both configurations with heating applied along the top and bottom rigid boundaries were considered in experimental study by Wang and Huang [11]. Velocity fields for horizontal convection steady state were obtained using PIV.
Studies of horizontal convection in liquids with free surface heated by radiation are less numerous, though this problem formulation is more relevant both to ocean circulation and to glass production. Steady-state flow patterns and temperature fields were visualized by Kurosaki et al. [12] using holographic interferometry and tracer particles. Silicon oil was used as working liquid, and surface flow associated with Marangoni convection was observed. In contrast, PIV measurements for horizontal convection in water, carried out by Wȧhlin et al. [13], showed that surface velocity is close to zero. The authors of [13] explained this by the influence of surface film, as experiments were performed in large water tanks for several days and it was not possible to avoid presence of surfactants in water. Though they did not perform measurements in other liquids, they predicted that ’the flow may be very sensitive to the boundary conditions for the horizontal velocity at the free surface’. Horizontal convection driven by radiative heating of the free surface was also investigated by Shmyrov et al. [14] for bidistilled water with addition of insoluble surfactant. Surfactant transport by the surface flow resulted in formation of two flow regions, separated by the surface stagnation point. Marangoni convection was observed in region with clean surface, whereas in region, covered with surfactant, surface layer was stagnant and convective vortex was located below. Note that water surface was cleaned by aspiration prior to addition of surfactant, which was required for Marangoni convection to be observed.
In the present study we investigate the effect of different boundary conditions for horizontal velocity at the free surface upon the flow structure and heat transfer during the development of horizontal convection in liquid heated by infrared radiation from above. Instant velocity and temperature fields are measured using PIV and BOS for convection in distilled water and ethanol, which exhibit different surface behavior. Earlier study of convective plume generated by a horizontal heated wire and impacting the free surface [15] in these two liquids showed that velocity of heat wave propagation along the surface is several times larger in ethanol due to presence of Marangoni flow, absent in distilled water. Using Marangoni flow, produced by local heating of the liquid surface with laser radiation, for surface cleaning and microparticles manipulation was proposed in [16], [17], [18], which implies that presence or absence of Marangoni flow can significantly alter horizontal convection flow, at least in shallow tanks. As in [15], we directly compare experimental data to results of numerical simulations, performed with different boundary conditions for horizontal velocity, representing surface behavior of water and ethanol. The paper is organized as follows. Section 2 describes the employed experimental techniques and equipment. In Section 3 mathematical problem is formulated and numerical method is outlined. The results of experimental measurements and numerical simulations are presented and discussed in Section 4. Conclusions are drawn in Section 5.
Section snippets
Experimental techniques and equipment
Experiments are performed in rectangular tank with internal dimensions mm, made of 3-mm window glass (Fig. 1). Radiation from a ceramic heater mm passes through rectangular aperture with dimensions mm, cut in a special screen, and heats the liquid surface. In order to minimize heat transfer through the screen, the screen is made from a 40-mm-high cardboard box with all the walls covered with aluminium foil, reflecting radiation. Thus, nearly uniform irradiation of
Numerical modeling
Liquid flow in vertical plane XY is simulated by solving unsteady 2D Navier-Stokes equations in low-Mach approximationwith empirical correlations for temperature dependencies of liquid density, viscosity, thermal conductivity and specific heat given in Appendix A.
Bottom and side walls of the tank are assumed adiabatic. Third-kind boundary condition is imposed
Results and discussion
Heating the liquid surface results in pressure imbalance and free surface deformation. A convex crest is formed in irradiated region, which corresponds to positive pressure perturbation. Warm liquid below the surface is forced to flow towards the side walls and two counter-rotating vortices are formed below the edges of irradiated region (Fig. 5). This is buoyancy-driven horizontal convection, which is observed both in distilled water and ethanol. However, in liquids, which exhibit Marangoni
Conclusions
In this study, liquid temperature and velocity fields during the development of horizontal convection driven by nonuniform heating of free surface have been measured using BOS and PIV. Experiments have been performed in distilled water and ethanol, which are known to exhibit different surface behavior. In both liquids ’partial penetration’ is observed – the circulation flow is mostly restricted to a shallow surface layer. However, comparison of the results, obtained in different liquids, shows
Conflict of interest
The authors declare that there is no conflict of interest.
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