Correlations for the mass transfer rate of droplets in vertical upward annular flow

New correlations for the deposition rate and entrainment rate of droplets in vertical upward annular flow were developed from simple models and available experimental data. In the correlation for the deposition rate, the superficial gas velocity was used as the parameter of primary importance at low droplet concentration while the droplet concentration itself at high droplet concentration. In correlating the rate of droplet entrainment, the ratio of interfacial shear force to the surface tension force acting on the surface of liquid film was the appropriate scaling parameter to correlate the experimental data measured in varied conditions. The experimental data for air–water annular flow were used in the development of the present correlations since extensive databases were available. It was however confirmed that the present model provides satisfactory agreements with the experimental data for high-pressure steam–water annular flow.     

Heat and mass transfer in the liquid film on a vertical wall in roll-wave regime

The investigation of thin liquid film flowing down a vertical wall in the roll-wave regime in presence of heat and mass transfer through the free surface is presented. The roll-wave equation taking into account heat and mass transfer through the liquid–vapor interface has been derived. The self-similar solutions of the progressive-wave type for film thickness have been obtained. The families of discontinuous solutions have been constructed, where the progressive waves are conjugated with each other or with “residual” film thickness through the strong discontinuity. As an example, the calculations of the condensate water film flowing down a vertical surface are presented.     

Experimental study on convective boiling heat transfer in vertical narrow-gap annular tube

IntroductionConvechve boiling or highly subcooled single-Phaseforced convention in micro-channels is an effeCtivecooling meChedsm with a wide ~ge of aPPlications.Among these are the COOling of such diverse system as. accelerator abets, high power resistive magnets,compact fission ~ cores, fusion ~ blankets,advanced space thermal management systems,manufachang and materials Processing OPerations, andhigh-density multi~chip modules in supe~ andOther modular eleCtronics. These devices involv…     

Heat- mass transfer and flow characteristics of two-phase countercurrent annular flow in a vertical pipe

Experimental and theoretical results on flow, heat and mass transfer characteristics for the countercurrent flow of air and water in a vertical circular pipe are compared. An experimental setup was designed and constructed. Hot water is introduced through a porous section at the upper end of a test section and flows downward as a thin liquid film on the pipe wall while the air flows countercurrently. The air and water flow rates used in this study are those before the flooding is reached. A developed mathematical model is separated into three parts: A high Reynolds number turbulence model, in which the local state of turbulence characteristics consists of the turbulent kinetic energy (k) and its dissipation rate (ϵ).The transport equations for both k and s are solved simultaneously with the momentum equation to determine the kinetic turbulence viscosity, the pressure drop, interfacial shear stress and then the friction factor at the film/core interface; Heat and mass transfer models are proposed in order to estimate the distribution of the temperature and the mass fraction of water vapor in gas core. The results from the model are compared with the present experimental ones. It can be shown from the present study that the influence of the interfacial wave phenomena is significant to the pressure loss, and the heat and mass transfer rate in the gas phase.     

Effect of packing geometry on the rate of mass and heat transfer at a vertical tube imbedded in fixed bed under single and two phase flow

Rates of liquid–solid mass transfer and heat transfer (by analogy) were studied in an annular reactor with a packed annulus. Two types of inert fixed bed packing were used namely, cylinders and Raschig rings. The electrochemical technique which involves measuring the limiting current of the cathodic reduction of ferricyanide ion in a large excess of sodium hydroxide was used in the present study. Variables studied are packing geometry, packing size, gas and liquid superficial velocities and physical properties of the solution. The presence of inert fixed bed in the annulus enhanced the rate of mass transfer and the rate of heat transfer at the outer wall of the inner cylinder by a factor ranging from 1.1 to 6.1 depending on the packing geometry, particle size and both the liquid and gas superficial velocities. The present data were compared with the previous data on the packed annulus with inert spherical packing. For single phase liquid flow the mass transfer enhancement ratio increases in the order: Raschig rings > cylinders > spheres, while in the case of two phase flow, spheres gave the highest enhancement ratio. For the present range of conditions it was found that, as the particle size decreases the enhancement ratio increases. All data were correlated in the form of dimensionless equations.Possible practical applications of the present study such as design of fixed bed reactor internal cooler, prediction of the rate of diffusion controlled corrosion of vertical tube cooler imbedded in a fixed bed reactor and design of annular double tube catalytic and electrochemical reactors with a fixed bed turbulence promoter were highlighted.     

Numerical analysis for flow,heat and mass transfer in film flow along a vertical fluted tube

We conducted a three-dimensional numerical investigation of the flow, heat and mass transfer characteristics of the fluted evaporating tube with films flowing down on both the inside and outside tube walls. Condensation occurs along the outside wall while evaporation takes place on the free surface of the inside film. The three-dimensional transport equations for momentum and energy were solved by using the finite volume method (FVM). The free-surface shape is tracked by using the moving-grid technique that satisfies the space conservation law (SCL). Because of the secondary motion of the fluid, the film becomes thin at the crest whereas it thickens at the valley. The velocity and temperature fields were successfully predicted for various flute shapes.     

Pool boiling heat transfer in vertical annular crevices

Effects of vertical annuli on nucleate pool boiling heat transfer of water at atmospheric pressure have been obtained experimentally. Experiments were performed for annuli with a height of 570 mm and gap sizes of 3.9 and 15 mm. Through the tests, tube bottom confinement (open or closed) has been investigated, too, and the whole results are compared with a single unconfined tube. According to the results, the annular condition gives much increase in heat transfer coefficients at moderate heat fluxes. Its effect is observed much greater for the bottom-closed tube condition.     

MHD effect on flow structures and heat transfer characteristics of liquid metal-gas annular flow in a vertical pipe

The magnetohydrodynamic (MHD) effect on the flow structures and heat transfer characteristics was studied numerically for a liquid metal-gas annular flow under a transverse magnetic field. The side layers, in which the velocity was increased, appeared near the eastern and western sidewalls in an annular MHD flow as in a single-phase liquid metal MHD flow. Temperature distribution in the liquid film, and the Nusselt number distribution in the angular direction were influenced by the flow structures with the side layers. Consequently heat transfer rate was higher at the eastern/western sidewalls than that at the southern/northern walls. The pressure drop in the MHD annular flow is of the same order of magnitude as in the single-phase MHD pipe flow under similar liquid metal flow condition.     

Heat and mass transfer for liquid film evaporation along a vertical plate covered with a thin porous layer

The purpose of this work is to evaluate the heat and mass enhancement of liquid film evaporation by covering a porous layer on the plate. Liquid and gas streams are approached by two coupled laminar boundary layers incorporated with non-Darcian modes. The numerical solution is obtained by utilizing a fully implicit finite difference method and examined in detail for the effects of porosity ε, porous layer thickness δ, ambient relative humidity ϕ and Lewis number Le on the average heat and mass transfer performance. It is shown that the heat and mass transfer performance may be enhanced by the presence of a porous layer. Both the average Nusselt and Sherwood numbers are increased with the decrease of ε, δ and ϕ. In addition, the influence of ε on the heat and mass transfer is significantly increased as δ is increased.     

Boiling heat transfer characteristics of R-113 in a vertical small diameter tube under natural circulation condition

Boiling heat transfer characteristics of freon R-113 are experimentally investigated in a vertical small diameter tube, D=1.45 mm and L=100 mm at a wide pressure range of 19-269 kPa under natural circulation condition. Except the entrance region of the test section, the flow regime is annular in view of the measured vapor flux. The pool boiling correlations of Stephan and Abdelsalam and McNelly equally well predict the experimental data within an error of ±20%. No enhancement of heat transfer coefficient is obtained although D/B is less than 1.5, which differs from the finding of Klimenko.     

Numerical investigation of the heat and mass transfer in a vertical tube evaporator with the three-zone analysis

A numerical study for the flow, heat and mass transfer characteristics near the inflow region of the vertical evaporating tube with the films flowing down on both the inside and outside tube walls has been carried out. Condensation occurs along the outside wall and evaporation at the free surface of the inside film. The transport equations for momentum and energy are parabolized by the boundary-layer approximation and solved by using the marching technique. In this kind of numerical approach, the accurately predicting the early stage is really important because a small error at the previous step can produce the amplified big error at the next step. To accurately predict the flow at the inflow region of the vertical evaporating tube, the calculation domain of two film flow regions and tube wall is solved simultaneously. The interesting heat transfer characteristics revealed through this three-zone simulation, such as the evaporation delay and the temperature inflection at the very near inflow region are found and discussed along the discrepancy between the inner film inlet temperature and the saturation temperature. The case that the inner film comes in with the saturation temperature shows a good performance. The velocity and temperature fields as well as the amounts of the condensed and evaporated mass in both inner and outer films are predicted for the various conditions.     

CFD modeling of mass transfer in annular reactors

A computational fluid dynamics (CFD) investigation of single-phase flow mass transfer prediction in annular reactors was conducted. Different hydrodynamic models including laminar, standard k–ε, realizable k–ε, Reynolds stress (RSM), and the Abe-Kondoh-Nagano (AKN) (a low Reynolds number turbulence model) were evaluated against experimental data in terms of their mass transfer predication capabilities. The laminar model predicted successfully the average mass transfer in the flows under laminar regime (Re < 1500). Among the four evaluated turbulence models, the AKN model provided a better prediction of the average mass transfer rates in the systems when operated both under transitional and turbulent conditions (3000 < Re < 11000). The RSM performed very similarly to the AKN model, except for the entrance region of the reactors where it predicted lower mass transfer rates. These results make the AKN and RSM models very attractive to be integrated in CFD-based simulations of turbulent annular reactors.     

Research on convective condensation heat transfer for a gas mixture in a vertical tube

This paper discusses the convective condensation of a gas mixture in a vertical tube. A mathematical model was derived by combining a modified film model and Nusselt's condensation theory. The effect of wall temperature on film thickness and interfacial temperature was predicted and film thickness was calculated. When compared with the gas phase resistance method, the film model is better. The phenomenon of SO₂ absorption into condensate is illustrated and discussed. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(4): 219–228, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20011     

Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations

This work examines the effects of the modified Darcy number, the buoyancy ratio and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid.     

Comparison of frictional pressure drop models during annular flow condensation of R600a in a horizontal tube at low mass flux and of R134a in a vertical tube at high mass flux

This study compares well-known two-phase pressure drop models with the experimental results of a condensation pressure drop of (i) R600a in a 1 m long horizontal smooth copper tube with an inner diameter of 4 mm, outer diameter of 6 mm and (ii) R134a in a 0.5 m vertical smooth copper tube with an inner diameter of 8.1 mm and outer diameter of 9.52 mm. Different vapour qualities (0.45–0.9 for R600a and 0.7–0.95 for R134a), various mass fluxes (75–115 kg m^?2 s^?1 for R600a and 300–400 for R134a kg m^?2 s^?1) and different condensing temperatures (30–43 °C for R600a and 40–50 °C for R134a) were tested under annular flow conditions. The quality of the refrigerant in the test section was calculated considering the temperature and pressure obtained from the experiment. The pressure drop across the test section was directly measured with a differential pressure transducer. The most agreeable correlations of various available options were then identified according to the results of analysis during annular flow regime.     

Cocurrent turbulent mixed convection heat and mass transfer in falling film of water inside a vertical heated tube

A detailed numerical study has been conducted in order to analyse the combined buoyancy effects of thermal and mass diffusion on the turbulent mixed convection tube flows. Numerical results for air-water system are presented under different conditions. A low Reynolds number k-ε turbulent model is used with combined heat and mass transfer analysis in a vertical heated tube. The local heat fluxes, Nusselt and Sherwood numbers are reported to obtain an understanding of the physical phenomena. Predicted results show that a better heat transfer results for a higher gas flow Reynolds number Re, a higher heat flux q_w or a lower inlet water flow Γ₀. Additionally, the results indicate that the convection of heat by the flowing water film becomes the main mechanism for heat removal from the wall.     

Prediction of evaporation heat transfer coefficient based on gas–liquid two-phase annular flow regime in horizontal microfin tubes

A physical model of gas–liquid two-phase annular flow regime is presented for predicting the enhanced evaporation heat transfer characteristics in horizontal microfin tubes. The model is based on the equivalence of a periodical distortion of the disturbance wave in the substrate layer. Corresponding to the stratified flow model proposed previously by authors, the dimensionless quantity Fr₀ = G/[gd_eρ_v(ρ_l ? ρ_v)]^0.5 may be used as a measure for determining the applicability of the present theoretical model, which was used to restrict the transition boundary between the stratified-wavy flow and the annular/intermittent flows. Comparison of the prediction of the circumferential average heat transfer coefficient with available experimental data for four tubes and three refrigerants reveals that a good agreement is obtained or the trend is better than that of the previously developed stratified flow model for Fr₀ > 4.0 as long as the partial dry out of tube does not occur. Obviously, the developed annular model is applicable and reliable for evaporation in horizontal microfin tubes under the case of high heat flux and high mass flux.     

Artificial neural network techniques for the determination of condensation heat transfer characteristics during downward annular flow of R134a inside a vertical smooth tube

In this study, the best artificial intelligence method is investigated to estimate the measured convective heat transfer coefficient and pressure drop of R134a flowing downward inside a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm during annular flow numerically. R134a and water are used as working fluids in the tube side and annular side of a double tube heat exchanger, respectively. The ANN training sets have the experimental data of in-tube condensation tests including six different mass fluxes of R134a such as 260, 300, 340, 400, 456 and 515 kg m^− 2 s^− 1, two different saturation temperatures of R134a such as 40 and 50 °C and heat fluxes ranging from 10.16 to 66.61 kW m^− 2. The quality of the refrigerant in the test section is calculated considering the temperature and pressure obtained from the experiment. The pressure drop across the test section is directly measured by a differential pressure transducer. Input of the ANNs are the measured values of test section such as mass flux, heat flux, the temperature difference between the tube wall and saturation temperature, average vapor quality, while the outputs of the ANNs are the experimental condensation heat transfer coefficient and measured pressure drop in the analysis. Condensation heat transfer characteristics of R134a are modeled to decide the best approach using several artificial neural network (ANN) methods such as multilayer perceptron (MLP), radial basis networks (RBFN), generalized regression neural network (GRNN) and adaptive neuro-fuzzy inference system (ANFIS). Elimination process of the ANN methods is performed by means of 183 data points, divided into two sets randomly, obtained in the experiments. Sets of test and training/validation include 33 and 120/30 data points respectively for the elimination process. Validation process, in terms of various experimental conditions, is done by means of 368 experimental data points having 68 data points for test set and 300 data points for training set. In training phase, 5-fold cross validation is used to determine the best value of ANNs control parameters. The ANNs performances were measured by means of relative error criteria with the usage of unknown test sets. The performance of the method of multi layer perceptron (MLP) with 5-13-1 architecture and radial basis function networks (RBFN) were found to be in good agreement, predicting the experimental condensation heat transfer coefficient and pressure drop with their deviations being within the range of ± 5% for all tested conditions. Dependency of outputs of the ANNs from input values is also investigated in the paper.     

Hydrodynamics and mass transfer in decaying annular swirl flow

This paper reports an electrochemical study of local mass transfer behaviour in decaying annular swirl flow. Initially, flow visualisation experiments were conducted to observe the general behaviour of the flow. It was found that the swirl angle decays exponentially along the tube. Measurements of pressure drop across the vaned swirl generators were correlated in terms of the inverse of the square of the tangent of the vane angle and approximately the square of the mean fluid velocity for vane angles of 30° and over. Measurements of the axial distribution of local mass transfer coefficient for the inner rod were carried out using the electrochemical limiting diffusion current technique and results were correlated for each swirl generator, in the Reynolds number range 3300–50000. It was found that the relative enhancement of mass transfer in swirl flow increases as the vane angle increases and Reynolds number decreases.     

A theoretical study of evaporative heat transfer in high‐velocity two‐phase flow of air–water in a small vertical tube

A theoretical study was performed to investigate the evaporative heat transfer of high‐velocity two‐phase flow of air–water in a small vertical tube under both heating conditions of constant wall temperature and constant heat flux. A simplified two‐phase flow boundary layer model was used to evaluate the evaporative heat transfer characteristics of the annular two‐phase flow. The analytical results show that the gravitational force, the gas–liquid surface tension force, and the inertial force are much smaller than the frictional force and hence can be neglected for a small tube. The evaporative heat transfer characteristics of the small tube with constant wall temperature are quite close to those of the small tube with constant heat flux. The mechanism of the heat transfer enhancement is the forced convective evaporation on the surface of the thin liquid film. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(5): 430–444, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10110