Effects of Gravity, Shear and Surface Tension in Internal Condensing Flows: Results From Direct Computational Simulations

Abstract

The paper presents accurate numerical solutions of the full two-dimensional governing equations for steady and unsteady laminar/laminar internal condensing flows. The results relate to issues of better design and integration of condenser-sections in thermal management systems (looped heat pipes, etc.). The flow geometry, in normal or zero gravity, is chosen to be the inside of a channel with film condensation on one of the walls. In normal gravity, film condensation is on the bottom wall of a tilted (from vertical to horizontal) channel. It is found that it is important to know whether the exit conditions are constrained or unconstrained because nearly incompressible vapor flows occur only for exit conditions that are unconstrained. For the incompressible vapor flow situations, a method for computationally obtaining the requisite exit condition and associated stable steady/quasi-steady solutions is given here and the resulting solutions are shown to be in good agreement with some relevant experimental data for horizontal channels. These solutions are shown to be sensitive to the frequency and amplitude of the various Fourier components that represent the ever-present and minuscule transverse vibrations (standing waves) of the condensing surface. Compared to a vertical channel in normal gravity, shear driven zero gravity cases have much larger pressure drops, much slower wave speeds, much larger noise sensitive wave amplitudes that are controlled by surface tension, and narrower flow regime boundaries within which vapor flow can be considered incompressible. It is shown that significant enhancement in wave-energy and/or heat-transfer rates, if desired, are possible by designing the condensing surface noise to be in resonance with the intrinsic waves.

Effects of exit-condition, gravity, and surface-tension on stability and noise-sensitivity issues for steady condensing flows inside tubes and channels

“…The numerical scheme used here exploits the rigorous analytical and numerical knowledge that exists (see [19]) for solving a reduced hyperbolic form of the interface tracking equation-this ensures convergence and accuracy of both the amplitude and the phase of the predicted interfacial waves. Due to an algorithm improvement, the convergence, grid independence, and satisfaction of all interface/boundary conditions for the results reported here are better than what were reported in [1,2].…”

“…The in-tube geometry (see Fig. 1a) is considered here while some new and improved results for the horizontal and zero gravity channel flow cases-formulated elsewhere [1,2]-are also presented. The results are important for a qualitative understanding of experiments (see, e.g., [3]) dealing with the behavior of a condenser-section (typically of hydraulic diameters in millimeter or sub-millimeter range).…”

“…The simulation tool used here is more completely described in [1,2]. The interface tracking equation used here and in [1,2] is the same one that is used for locating the interface in the interface capturing approaches for flow with phase-change (level-set method of Son and Dhir [12], etc.)…”

“…The interface tracking equation used here and in [1,2] is the same one that is used for locating the interface in the interface capturing approaches for flow with phase-change (level-set method of Son and Dhir [12], etc.) or without phase-change (level-set method of Sussman et al [13], VOF method of Hirt and Nichols [14], etc.…”

Analysis of laminar film condensation over vertical permeable hollow short fins

“…They concluded that the elliptical section tube has a clear improvement of the vapor condensation over horizontal cylinder. Recently, the stability of the condensing flows has been discussed numerically and experimentally in several works [23][24][25][26][27]. The effect of the free-stream vapor-striking angle on the condensation over a vertical plate was analyzed by Khaled et al [28].…”