Falling Liquid Film Research Articles

Heating of non-Newtonian falling liquid film on a horizontal tube

The problem of heat transfer to non-Newtonian laminar falling liquid films on horizontal tubes is investigated theoretically for constant heat flux and isothermal conditions imposed at the inner periphery of the tube. The local and average heat transfer coefficients are obtained as function of the system parameters by conjugating the convective transport of heat to the liquid film to the thermal conduction in the material of the tube in the peripheral direction. The results indicate that the average heat transfer coefficient can be described successfully by three dimensionless groups characterizing the dynamic flow characteristics of the film, modified Prandtl number and the index of the power law variation of the rate of angular shear deformation of the fluid with respect to the shear stress.

Heat Transfer Analysis of Local Evaporative Turbulent Falling Liquid Films

A theoretical study has been conducted for evaporative heating of turbulent free-falling liquid films inside long vertical tubes. The methodology of the present work is based on splitting the energy equation into homogeneous and nonhomogeneous problems. Solving these simple problems yields a rapidly converging solution, which is convenient for computational purposes. The eigenvalues associated with the homogeneous problem can be computed efficiently, without missing any one of them, by the sign-count algorithm. A new correlation for the local evaporative heat transfer coefficient along the tube length is developed over wide ranges of Reynolds and Prandtl numbers. Furthermore, the average heat transfer coefficient is correlated as a function of Reynolds and Prandtl numbers as well as the interfacial shear stress. A correlation for the heat transfer coefficient in the fully developed region is also presented in terms of Reynolds and Prandtl numbers. Typical numerical results showed excellent agreement of the present approach with the available data in the literature. Moreover, a parametric study is made to illustrate the general effects of various variables on the velocity and temperature profiles.

Thermocapillary breakdown of subcooled falling liquid films

Combined with a force-balance model for a stable dry patch, an analysis is developed to predict film breakdown. Experiments were conducted with water, 2-propanol, and ethylene glycol, over a film Reynolds number range and various degrees of subcooling

The Effect of Heating Surface Configuration on the Heat Transport Characteristics of Closed Two-Phase Thermosyphons.

Experiments were conducted to investigate the effect of heating surface configuration on the heat transport characteristics of closed two-phase thermosyphons by using four kinds of heating surface : smoth, artificially roughened and two grooved surfaces. The working fluids tested were water, methanol and refrigerant R113. The results show that making the heating surface rough is effective in improving both the heat transport efficiency and the performance limit compared with the smooth heating surface. Cutting longitudinal grooves on the heating surface is also effective in improving the heat transport efficiency since the area of the heating surface is increased. However, the heat transfer rate is not always increased at the performance limit by cutting the grooves. The rewetting of the heating surface with a falling liquid film was also examined.

Chaotic Characteristics in Time-Varying Thickness of Falling Liquid Film.

Time-spatial measurements were carried out on the thickness of liquid film falling inside a vertical tube. It was examined how both locations of initiation in waviness and coalescence-separation of waves depend on liquid film Reynolds number. Fractal analysis of time-series signals of liquid film thickness reveals that wavy characteristics of falling film are a deterministic random phenomenon, i.e., a chaos. Comparison between fractal dimension, waviness in falling film and power spectral density of film thickness suggests that waves including higher-frequency components roughly correspond to larger values of the fractal dimension. Two different types of axial variations in fractal dimension and standard deviation of liquid holdup were found. The boundary of these on a map of axial distance vs. film Reynolds number is simply specified by a wave behavior transition film Reynolds number of 200∼350.

Variational formulation of three‐dimensional viscous free‐surface flows: Natural imposition of surface tension boundary conditions

AbstractWe present a new surface‐intrinsic linear form for the treatment of normal and tangential surface tension boundary conditions in C0‐geometry variational discretizations of viscous incompressible free‐surface flows in three space dimensions. The new approach is illustrated by a finite (spectral) element unsteady Navier‐Stokes analysis of the stability of a falling liquid film.

Direct contact condensation and momentum transfer in turbulent separated flows

Analysis of the turbulent velocity and shear stress distribution in a separated two-phase flow shows that both the wall and interface shear contribute to the dissipation of energy in the liquid film. A suitably averaged turbulent energy dissipation provides Kolmogorov velocity and length scales in the liquid film. These scales are used in a turbulent eddy based surface renewal theory for condensation and evaporation of saturated vapor onto or from its liquid. The theory accurately predicts experimental data for horizontal, concurrent condensation of steam on water. Theoretical results agree with the form of existing turbulent correlations for heat and mass transfer processes such as condensation onto a falling liquid film and mass, momentum and heat transfer at the interface in separated flows. Comparison of the theory to previous work is included and guidelines for empirical correlations of data are given.

Analysis of passive cooling in a vertical finite channel using a falling liquid film and buoyancy-induced gas-vapor flow

A fundamental study of the coupled effects of a falling, partially vaporizing liquid film and buoyancy-induced gas-vapor flow in a vertical one-sided heated channel is presented for different film Reynolds numbers, liquid film inlet temperatures, wall heat fluxes and channel spacings. The transient (elliptic) gas-phase transport equations are solved numerically in conjunction with the laminar (parabolic) liquid film equations. The validated computer simulation model is used to depict transient developments of streamlines, gas-phase parameters and interfacial quantities as well as steady-state velocity profiles, temperature profiles and averaged Nusselt number distributions. The present analysis may contribute to the solution of passive cooling problems associated with electronic equipment operations, manufacturing processes, modern nuclear power plant designs and numerous environmental phenomena.

Nonlinear waves on the surface of a falling liquid film. Part 1. Waves of the first family and their stability

The paper is devoted to a theoretical analysis of nonlinear two-dimensional waves on the surface of a liquid film freely falling down a vertical plate. Using a model system of equations, steady-state travelling periodical wave regimes have been found numerically. It is shown that some of them agree quantitatively with experimental results. The question of the stability of various wave regimes with respect to two-dimensional infinitesimal disturbances is examined. The most-amplified disturbances are evaluated.

A numerical study of the non-absorbable effects on the falling liquid film absorption

A numerical study for the simultaneous heat and mass transfer in a falling liquid film absorption process with the presence of non-absorbable gases is presented. Water vapor mixed with air as the non-absorbables being absorbed into a falling smooth aqueous lithium chloride film flow was chosen as the model problem for the study. The finite difference numerical calculation was proceeded by marching downward from the top end, owing to the parabolic type energy and concentration equations for both liquid and gas phases. The results indicate that the local non-absorbable gas concentration is much higher at the gas-liquid interface than that in the ambient, hence the local vapor pressure is lowered there such that the absorption driving potential of the vapor pressure difference is reduced. The resulting reduction of the absorption rate due to the presence of the non-absorbables suggests that its effect must be carefully considered in the application of absorption heat pump design. The present study can provide some useful information for this purpose.

A numerical solution of the wavy motion on a falling liquid film

AbstractWavy motion in falling liquid films enhances heat and mass transfer significantly; therefore, it is important to successfully model this motion for the purpose of heat and mass transfer calculations. In this study, a simple and promising numerical spectral method is developed to solve the periodic wavy film flow equations. With the wave number and the wave celerity specified to be those of the most unstable waves from existing linear stability analysis, the results are found to be good when compared with the existing experimental data for small (Re < 50) and moderate (50 < Re < 150) Reynolds numbers. It is worth noting that many important absorption problems fall in the low and moderate Reynolds number regimes. For higher Reynolds number flows (Re > 150), the solutions are still obtainable but may not be realistic owing to the invalidity of the linear stability analysis and the asymptotic wavy‐state assumption in the high Reynolds number flow.

Statistical investigation of the relationship between interfacial waviness and sensible heat transfer to a falling liquid film

Experiments are performed to provide an insight into the heat transfer aspects of a wavy liquid film. Local film thickness and liquid temperature are measured simultaneously using a thermal conductance thickness probe and fast response thermocouples as the wavy film falls over an electrically heated wall. Liquid temperature at a fixed distance from the wall generally increases in the thin substrate portion of the film and decreases within the large waves. Temperature shows complex excursions within the large waves due to turbulent eddies and to the relative liquid motion between the large wave and the surrounding substrate. The measurements are examined with the aid of statistical tools to investigate the relationship between film thickness and liquid temperature at various film Reynolds numbers and heat fluxes. The correlation between the two variables is stronger at higher heat fluxes compared to lower fluxes. A crossspectrum analysis shows a distinct band of dominant frequencies in the relationship between the two variables.

Evaporative cooling of liquid film through interfacial heat and mass transfer in a vertical channel—I. Experimental study

An experimental study is performed to study the evaporative cooling of the falling liquid film through interfacial heat and mass transfer in a vertical channel. The measured wall temperature, heat and mass transfer rates are specifically presented for the systems with water film evaporation and ethanol film evaporation over wide ranges of liquid mass flow rate, channel width and liquid inlet temperature. The results show that the influences of the evaporative latent heat transfer on the cooling of the liquid film depend largely on the inlet liquid film temperature and liquid mass rate. Effective evaporative cooling results for a higher inlet liquid film temperature and a smaller liquid mass flow rate.

Dryout stability and inception at low flow rates

A theoretical model for the heat flux required to maintain a stable hot patch on a heated surface cooled by a falling liquid film is developed. The theoretical model is based on an existing analytical solution of the two-dimensional heat equation with boundary conditions supplied by heat transfer coefficient correlations appropriate to the fluid conditions at the hot dry patch and at the wet region from the patch. Using physically reasonable correlation forms for the dry patch and wet region heat transfer coefficients, the heat flux is expressed as a function of the liquid film Reynolds number. Existing experimental data were compiled, collected, and used to obtain the correlating lines. The data cover the one-dimensional (low Biot number) region, and indicate that laminar and turbulent liquid film conditions occur. Corresponding correlating equations are obtained from the analytical results. For laminar flow, the dryout heat flux is q d = 0.27 Re 0.5, and for turbulent flow q d = 0.017 Re 0.9, with an uncertainty of the order of ± 50%.

Flow Patterns of Falling Liquid Film Observed near an Obstacle.

The purpose of this study is to investigate the mechanism of various flow patterns of falling liquid film flow observed near an obstacle on a flow channel. In this report, a bend on the channel was chosen as the obstacle and the behavior of a ring-shaped swelling of the liquid film, which appears near the obstacle at a low flow rate, is considered. The Weber number at which the swelling shifts from the upside to the downside of the bend is theoretically estimated. The experimental results for the swelling behavior agree well with those of the above theory. Moreover, in order to investigate the characteristics of the stationary wave observed in the upstream side of the swelling, the wavelength and the damping rate of the amplitude were measured by the needle contact method. The measured results agree with the theoretical ones which were considered by the authors in the preceding report.

Nonlinear mass transfer between a gas and a falling liquid film. 3. Multicomponent mass transport

A solution is obtained for the problem of multicomponent mass transfer between a gas and a falling liquid film. The case is considered in which the mass transfer of one of the components is limited by the nonlinear mass transport in the gas phase. The rates of multicomponent mass transport in the gas and liquid phases are determined.

Cooling of a falling liquid film through interfacial heat and mass transfer

A numerical analysis was carried out to study the detailed heat transfer characteristics for a falling liquid ethanol film by solving the respective governing equations for the liquid film and the induced gas flow together. Meanwhile an experimental system was set up to measure the overall cooling of the film. The measured data are in good agreement with the numerical predictions. It was observed that the cooling of the liquid film is mainly caused by the latent heat transfer connected with the vaporization of the liquid film. Significant liquid cooling results for the system with a high inlet liquid temperature or a low liquid flowrate.

Nonlinear mass transfer between a gas and a falling liquid film. 1. Numerical analysis

A numerical analysis is carried out of the kinetics of nonlinear mass transfer between a gas and a falling liquid film. The nonlinear effect which is considered is the result of intensive mass transfer. Under these conditions the large mass flux induces a secondary flow at the phase interface. The mass transport in both phases takes into account the influence of the intensive mass transfer on the hydrodynamic behavior. An equation is obtained for the rate of absorption is greater than the rate of desorption under conditions of intensive mass transfer.

Numerical approaches for computation of fronts

AbstractMoving fronts and pulses appear in many engineering applications like flame propagation and a falling liquid film. Standard computation methods are inappropriate since the problem is defined over an infinite domain and a steady‐state solution exists only for a certain front velocity. This work presents a transformation that converts the original problem into a boundary‐value problem within a finite domain, in a way that preserves the behavior at the boundaries. Good low‐order approximations can be obtained as demonstrated by two examples. In another approach, a central element of adjustable length is incorporated into a three‐element structure where the edge‐elements obey known asymptotic solutions. That yields multiplicity of travelling fronts in an infinite domain but it successfully approximates standing wave solutions in a finite domain. The approximate solutions are shown to obey the qualitative features known for the exact solutions, like asymptotic solutions or the bifurcation set–the boundary where a new solution emerges or disappears.

GAS ABSORPTION WITH INSTANTANEOUS CHEMICAL REACTION IN A FALLING FILM FOR PARALLEL AND COUNTERCURRENT FLOWS

A theoretical analysis is presented for the absorption of a gas accompanied by instantaneous chemical reaction with a dissolved reagent in a falling liquid film of liquid. The reaction occurs on a moving front inside the liquid film separating the zones containing either of the reactants. The governing equations are solved by using a coordinate transformation to immobilize the reaction front. The effects of the different system parameters on the reaction front profile, absorption rate and enhancement factor are presented for both cocurrent and countercurrent flow of the gas. In the former case the reaction front profile shows a maximum, but in the later case it is monotonic in the axial distance along the film. The enhancement factor plots exhibit maxima in both the cases.