Three-Dimensional Mathematical Model of the Liquid Film Downflow on a Vertical Surface

Abstract

Film downflow from captured liquid without wave formation and its destruction is one of the most important aspects in the development of separation equipment. Consequently, it is necessary to create well-organized liquid draining in areas of captured liquid. Thus, the proposed 3D mathematical model of film downflow allows for the determination of the hydrodynamic parameters of the liquid film flow and the interfacial surface. As a result, it was discovered that the interfacial surface depends on the proposed dimensionless criterion, which includes internal friction stress, channel length, and fluid density. Additionally, equations for determining the averaged film thickness, the averaged velocity vectors over the film thickness, the longitudinal and vertical velocity components, and the initial angle of streamline deviation from the vertical axis were analytically obtained.Energies 2020, 13, 1938 2 of 15 the fluid film movement, heat and mass transfer in column equipment, the separation of gas-liquid mixtures, and fluid flow in heat exchangers. Scientists for the above purpose have investigated the heat and mass transfer processes occurring in microchannels [3][4][5][6] and free and induced liquid film flow over different surfaces [7][8][9][10][11][12][13][14][15][16][17][18] and inside of different channels [19][20][21][22][23][24][25]. This flow occurs due to the influence of various forces, which determine the film formation or destruction, and the inclination angle of the surface. At the same time, the developed mathematical models and correlation coefficients proposed for them should consider each of the above process features, and the possibility of changing the physical state of the flow components forms a liquid film (condensation, evaporation).The liquid film motion inside of microchannels was considered in [3][4][5][6] by the application of numerical and experimental methods as well as developing mathematical models. The research [3] describes the development of the criterion model for the prediction of the critical heat flux premature caused by periodic liquid film movement in microchannels. The research implements the simplifications and assumptions for the Navier-Stokes equations, such as neglecting the gravity and inertia forces, considering the film movement only along the channel, and introducing the lubrication approximation. The authors of [4] studied the falling water film movement inside of microchannel with the "water-carbon dioxide" mixing section. The obtained results consider the mass exchange between two phases by numerical simulation for the case of laminar flow and multiphase VOF (volume of fluid) model with the indirect comparison between the numerical simulation and experimental results. The Lattice Boltzmann method (LBM) is commonly used for liquid flow motion in microchannels [5,6], especially in cases of studying hydrodynamic phenomena during the heat-mass transfer processes [6], which involve formation and breakup process of the liquid film in this channel type.Studies on falli...

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