Liquid Film Model Research Articles

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Aircraft icing

Evaporative heat transfer from thin liquid film on a heated cylinder

Simulating a porous surface that is partially saturated with a liquid, a two-dimensional meniscus attaching two adjacent cylinders with the same diameter is studied under heating and convective conditions. A thin liquid film model is presented to predict thin film thickness and evaporative heat transfer coefficient. Experiments are carried out to characterize the temperature and geometry of a liquid meniscus. The evaporating thin film length is determined from measured surface temperature and meniscus shape. The surface temperature data is correlated and used to derive the evaporative heat transfer coefficient with the aid of conjugate heat transfer using a finite element code. The results are compared reasonably with the thin film model. The effects of Bond number, spacing between cylinders and heating power on thin film geometry and heat transfer characteristics are discussed. Correlations to predict the evaporative heat transfer coefficient and ratio of evaporative heat transfer rate to total heat rate are presented.

Influence of the Wall Temperature on the Mixture Preparation in Di Gasoline Engines

Influence of the Wall temperature on the Mixture Preparation in DI Gasoline Engines — Spray- wall interaction and liquid film models are developed, validated and used to provide better understanding of fuel distribution in a DI gasoline engine with a wide concept. Numerical calculations including combustion were performed to study the influence of piston temperature on mixture preparation under stratified charge operating conditions. During cold operation or cold start, up to 25% of injected mass forms a liquid film on the piston bowl bottom. This largely affects the combustion efficiency. Increasing piston temperature decreases the gasoline unburned film amount. No significant liquid film remains on the piston when its temperature exceeds the mean of the boiling and Leidenfrost temperatures. This result agrees well with the available experimental obervations which confirm the absence of liquid film when piston temperature exceeds 460 K.

Thermodynamics of plane-parallel liquid films

Different approaches to the construction of the thermodynamics of plane-parallel thick and thin liquid (emulsion and foam) films are reviewed. The thin liquid film models (membrane of zero thickness, membrane of finite thickness, two interacting dividing surfaces in the film) are examined from the point of view of their experimental applications.

Spacer Effect on Liquid Film Flow and Critical Power in BWR Fuel Bundles

Liquid film thickness measurements and flow pattern observations near a spacer have been carried out using 4×4 and 9×9 mock-up fuel bundles with air-water co-current flow. The spacer had two different effects on the liquid film flow in the downstream region: (a) liquid droplet entrainment and deposition induced by turbulence enhancement in gas core flow; and (b) liquid droplet entrainment and deposition induced by a direct interaction of liquid film flow and spacer elements. The former effect was taken into account for development of a new spacer model to estimate dependence of critical power on spacer pitch. The liquid film model, including the spacer model, was confirmed to predict the critical power with high accuracy.

Spacer Effect on Liquid Film Flow and Critical Power in BWR Fuel Bundles.

Liquid film thickness measurements and flow pattern observations near a spacer have been carried out using 4×4 and 9×9 mock-up fuel bundles with air-water co-current flow. The spacer had two different effects on the liquid film flow in the downstream region: (a) liquid droplet entrainment and deposition induced by turbulence enhancement in gas core flow; and (b) liquid droplet entrainment and deposition induced by a direct interaction of liquid film flow and spacer elements. The former effect was taken into account for development of a new spacer model to estimate dependence of critical power on spacer pitch. The liquid film model, including the spacer model, was confirmed to predict the critical power with high accuracy.

Studies on Pool Boiling Heat Transfer. 4th Report. Thickness of Liquid Macrolayer Formed Beneath Vapour Masses.

Macrolayer thickness was determined on the basis of the relationship qCHF=δ1ρ1Hfgf, which was derived from the dry-out model of liquid film formed repeatedly on heated surfaces. Critical heat flux qCHF is measured on a horizontal heated disk of 20mm in diameter in the range of pressures from 0.02 MPa to 0.4 MPa for water and ethanol. Departure frequency of large coalesced bubbles, which entirely cover the heated disk, was calculated from the relationship f=0.215{g(ρ1-ρv)/ρ1}5/9/(ν1·D3)1/9. Theoretical relationships correlating the obtained data of macrolayer thickness are derived by the dimensional analysis, under the assumptions that a macrolayer is formed by the coalescence of primary bubbles or coalesced bubbles. The macrolayer data are well correlated with the derived correlations.

Calculating hydrodynamics problems for a liquid film flowing radially on a flat horizontal surface

AbstractA mathematical hydrodynamic model of a thin liquid film flowing radially on a flat horizontal surface has been elaborated. The model consisted of continuity and momentum equations which were resolved by means of the integral method. In fact, several versions of the model were examined; they differed mainly in film velocity distribution. The predictions of the different versions were then compared with liquid film thicknesses obtained from experimental investigation. The best version was applied in further calculations.

The mechanism for the long-wave instability in thin liquid films

A physical mechanism for the long-wave instability of thin liquid films is presented. We show that the many diverse systems that exhibit this instability can be classified into two large groups. Each group is studied using the model of a thin liquid film with a deformable top surface flowing down a rigid inclined plane. In the first group, the top surface has an imposed stress, while in the other, an imposed velocity. The proposed mechanism shows how the details of the energy transfer from the basic state to the disturbance are handled differently in each of these cases, and how a common growth mechanism produces the unstable motion of the disturbance.

Coherency Strain Energy in any Crystal System: Applications to in Situ Observations of Cigm in Calcite

AbstractIn situ observations of CIGM in CaCO3 bicrystals with a SrCO3 solute source were made. The change in boundary orientation and migration rate were compared with solute concentration. The liquid film model for coherency strain Induced migration was generalized to any non-cubic system and applied to CaCO3-SrCO3. The coherent layer was modeled as a thin film on an infinite half-space. The strain energy was found from solution of the Hooke's law expressions transformed to the appropriate coordinate system. For triclinic or monoclinic films the strain tensor was found by an eigenvector decomposition of the transformation matrix that defined the lattice parameter change with composition. High anisotropy of Vegard's law constants for CaCO3-SrCO3 caused (111) to have the lowest coherency strain per unit solute. Surfaces perpendicular to (111) in coherent equilibria were predicted to have half the solute concentration and three times the migration driving force of those perpendicular to (111). However, no correlation between solute concentration and boundary orientation was observed. Ambiguous and contradictory evidence for a relationship between solute concentration, boundary orientation, and migration rate was found. The self-stress state of a grain boundary in a solute diffusion field may be better modelled as hydrostatic rather than plane stress. Hydrostatic compression may interact with the boundary excess volume and cause a PV driving force for migration. Predictions based on coherent equilibrium at a surface have not been tested for that geometry in calcite; they should be tested before they are applied to grain boundaries.

Gas-liquid autoxidation reactors

A procedure for the simulation of autoxidation gas-liquid reactors has been developed based both on mathematical models and laboratory experiments. It has been shown that the complex radical chain mechanism of the autoxidation process can be simulated through two global parallel reactions, whose rates are obtained by assuming pseudo-steady-state concentration values for all the radical species involved. Using ethylbenzene autoxidation as a model reaction, an experimental analysis has been performed in order to estimate all the kinetic parameters of the model. The effect of the interaction between gas-liquid mass-transfer phenomena and the complex kinetic mechanism on the overall performance of an autoxidation reactor has been examined in detail within the framework of the liquid film model.

Boiling Heat Transfer With Freon 11 (R11) in Brazed Aluminum, Plate-Fin Heat Exchangers

The results of laboratory experiments with Freon 11 (R11) flowing in an electrically heated, serrated-fin test section to measure local boiling coefficients over a wide range of vapor quality, with mass fluxes up to 150 kg/m2 s, heat fluxes to 4 kW/m2, and pressure from 3–7 bar, are reported. These low mass and heat fluxes reflect the industrial process application of these heat exchangers where exceedingly small temperature differences may exist between streams. Results are compared with the very similar boiling characteristics previously reported elsewhere for the same test section, with liquid nitrogen as a test fluid under comparable flow conditions. A simple method using the Reynolds number of the total flow regarded as a liquid has been used to correlate boiling heat transfer coefficients with quality for both fluids. The use of a liquid-film flow model to produce a nondimensional correlation connecting the Nusselt, Reynolds, and Prandtl numbers of the film is discussed.

Hydrodynamic and heat transfer analysis of two-phase annular flow with a new liquid film model of turbulence

A new method is presented for the analysis of hydrodynamics and heat transfer of two-phase annular flows with turbulent liquid films. Based on the experimental observation, the liquid film in two-phase annular flow is divided into a continuous layer adjacent to the channel surface and into a wavy layer close to the liquid-gas interface. In the continuous liquid layer region of the film, it is argued that the turbulence structure is similar to the structure of single phase turbulent pipe flow, and in the wavy layer region of the film, it is assumed that the eddy diffusion length is proportional to the thickness of this region. Experimental data in upflow and downflow confirmed the validity of the basic assumption of the turbulent structure in the film, and revealed the value for the wavy layer momentum diffusivity. This diffusivity is found to have a lower value than in the single phase pipe flow at the equivalent distances from the channel wall. The two-layer liquid film structure is integrated into an analysis for the prediction of hydrodynamics and heat transfer in annular two-phase flows. Analytic results are compared to the results of other analytical models and to the experimental data in upflow, downflow and horizontal flow. In all cases considered, very good comparison is achieved in both hydrodynamics and heat transfer.

Gas—liquid partition chromatographic separations in columns packed with porous particles — a model for uniform thickness liquid film

A linear mathematical model for gas—liquid chromatography is presented for application to either analytical or larger-scale equipment. The model includes the effects of axial dispersion, interparticle mass transfer, intraparticle gas diffusion, and diffusion in a thin, uniform thickness liquid film. The governing differential equations are solved in the Laplace transform domain for a general input pulse. Temporal moments of the output pulses are expressed in terms of geometrical, equilibrium and transport parameters. The moment theory is related to HETP and to resolution of separation. The optimization of the process and scale-up to industrial size are discussed.

Smectic model for liquid films on solid surfaces. Part 1.—Application to monolayer boundary lubrication

A qualitative theory of films of hydrocarbon solutions of fatty acids described in a previous publication correlates many experimental data. According to this theory the fatty acid molecules and solvent molecules are arranged in layered structures similar to those in smectic mesophases. A simplified method for calculating the attractive energy between two such layers is described. The fatty acid molecules are assumed to behave as hard rods of constant electric polarizability and diamagnetic susceptibility. A potential describing the interaction between two rods is derived and used in a lattice sum calculation to compute the total energy of interaction of two layers as a function of average separation of molecules within a layer, relative position of the two layers and the distance between layers. Calculation of frictional force and coefficient of friction by means of this model show good agreement with a similar calculation of Cameron if the proper assumption about the relative magnitude of energy as a function of relative position is made.