Numerical study of cavitating flow characteristics of liquid helium in a pipe

The fundamental characteristics of the two-dimensional cavitating flow of liquid helium in a vertical pipe near the lambda point are numerically investigated to realize the further development and high performance of new cryogenic superfluid cooling systems. It is found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow based on the thermomechanical effect is conspicuous in the large gas phase volume fraction region where the liquid to gas phase change with cavitation actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase.     

A simplified model of gas–liquid two‐phase flow pattern transition

An experiment of upward gas–liquid two‐phase flow was conducted in an air–water isothermal system under atmospheric pressure. The differential pressure was measured at the fully developed section by using a variable reluctance type transducer to classify the flow patterns and their transitions. The flow behavior was observed with a high‐speed video camera. The probability density function (PDF) of the differential pressure signal was employed to identify the flow pattern. A simplified one‐dimensional flow model was proposed to clarify dominant factors affecting the formation and transitions of flow patterns. The model dealt with the gas‐component advection based on the spatiotemporal void fraction behaviors by considering the gas compressibility, the wake, and the liquid phase redistribution mechanism. The simulation results of the model indicated four kinds of the void wave patterns (ripple‐like, rectangular, distorted rectangular, and uniform wave patterns) depending on gas and liquid volumetric fluxes. These void wave patterns corresponded well to the experimentally observed flow patterns. The transitions among void wave patterns agree well with the Mishima–Ishii flow pattern map. The friction loss estimated by the present model coincides fairly well with Chisholm's empirical formula. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 445–461, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20029     

A study on un‐fully developed slug flow in a vertical tube

Gas‐liquid co‐current vertical slug flow was studied in a vertical Plexiglas tube. Taylor bubbles and liquid slug lengths and their rising velocities were measured by means of a pair of conductivity probes under un‐fully developed flow conditions. The influences of the superficial velocity of gas and liquid on slug flow parameters were examined. Using statistical analysis on the length of Taylor bubbles, the probability distribution of the length of the Taylor bubbles was obtained, which obeyed a normal distribution under a significance level of α = 0.05. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 235–242, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20063     

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     

Three‐dimensional simulation of water droplet movement in PEM fuel cell flow channels with hydrophilic surfaces

Water management is one of the critical issues in proton exchange membrane fuel cells, and proper water management requires effective removal of liquid water generated in the cathode catalyst layer, typically in the form of droplets through cathode gas stream in the cathode flow channel. It has been reported that a hydrophilic channel sidewall with a hydrophobic membrane electrode assembly (MEA) surface would have less chance for water accumulation on the MEA surface. Therefore, a comprehensive study on the effect of surface wettability properties on water droplet movement in flow channels has been conducted numerically. In this study, the water droplet movements in a straight flow channel with a wide range of hydrophilic surface properties and effects of inlet air velocities are analyzed by using three‐dimensional computational fluid dynamics method coupled with the volume‐of‐fluid (VOF) method for liquid–gas interface tracking. The results show that the water droplet movement is greatly affected by the channel surface wettability and air flow conditions. With low contact angle, droplet motion is slow due to more liquid–wall contact area. With high air flow velocities, increasing the contact angle of the channel surface results in faster liquid water removal due to lesser liquid–wall contact area. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of thermal–hydraulic characteristics in a proton exchange membrane fuel cell

The thermal–hydraulic characteristics of a proton exchange membrane fuel cell (PEMFC) are numerically simulated by a simplified two‐phase, multi‐component flow model. This model consists of continuity, momentum, energy and concentration equations, and appropriate equations to consider the varying flow properties of the gas–liquid two‐phase region in a PEMFC. This gas–liquid two‐phase characteristic is not considered in most of the previous simulation works. The calculated thermal–hydraulic phenomena of a PEMFC are reasonably presented in this paper, which include the distributions of flow vector, temperature, oxygen concentration, liquid water saturation, and current density, etc. Coupled with the electrochemical reaction equations, current flow model can predict the cell voltage vs current density curves (i.e. performance curves), which are validated by the single‐cell tests. The predicted performance curves for a PEMFC agree well with the experimental data. In addition, the positive effect of temperature on the cell performance is also precisely captured by this model. The model presented herein is essentially developed from the thermal–hydraulic point of view and can be considered as a stepping‐stone towards a full complete PEMFC simulation model that can help the optima design for the PEMFC and the enhancement of cell efficiency. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of liquid viscosity on inception of disturbance waves and droplets in gas–liquid annular two‐phase flow

The structure of gas–liquid two‐phase flow is investigated in order to establish a reliable criterion for the development of disturbance waves and droplets considering the effects of liquid viscosity. The structure of the gas–liquid interface and the flow rate of droplets entrained in gas are measured simultaneously at five kinematic viscosities (1.0, 3.2, 9.9, 30, 70 mm²/s). The time‐series traces of liquid film thickness measured by five holdup probes reveal that the inception of disturbance waves occurs at a liquid Reynolds number of 200 or a non‐dimensional liquid film thickness of 6.5. It is also shown that droplets are generated before the inception of disturbance waves with increasing liquid kinematic viscosity at a liquid velocity of 0.02 to 0.03 m/s. As previously published criteria for the inception of droplets are found to be unsatisfactory, a new critical condition for droplet generation balancing the interfacial shear stress $τi$ with the wave height h and surface tension σ is proposed: $τih/σ=0.025$. This relation describes the action of shear force and surface tension on wave crests, and is notably independent of liquid viscosity. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 529–541, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20176     

Two‐phase flow convective condensation of refrigerant mixtures under gas/liquid injection

The influence of gas/liquid injection on two‐phase flow condensation heat transfer characteristics of some refrigerant mixtures in horizontal enhanced surface tubing is presented. Correlations were proposed to predict the impact of the gas/liquid injection on the heat transfer characteristics such as average heat transfer coefficient of R‐507, R‐404A, R‐410A, and R‐407C in two‐phase flow condensation inside enhanced surface tubing. The data also revealed that gas, liquid and gas/liquid injection is beneficial at certain gas/liquid injection ratios to the heat transfer coefficient depending upon the Reynolds number and the condensation point of the refrigerant mixtures in question. It was also evident that the proposed condensation correlations and the experimental data were applicable to the entire heat and mass flux, investigated in the present study under gas/liquid injection conditions. The deviation between the experimental and predicted under gas/liquid injection were less than ± 10, for the majority of data. Copyright © 2005 John Wiley & Sons, Ltd.     

Along‐channel flooding prediction of polymer electrolyte membrane fuel cells

Non‐uniform current distribution in polymer electrolyte membrane (PEM) fuel cells results in local over‐heating, accelerated ageing, and lower power output than expected. This issue is quite critical when a fuel cell experiences water flooding. In this study, the performance of a PEM fuel cell is investigated under cathode flooding conditions. A two‐dimensional approach is proposed for a single PEM fuel cell based on conservation laws and electrochemical equations to provide useful insight into water transport mechanisms and their effect on the cell performance. The model results show that inlet stoichiometry and humidification, and cell operating pressure are important factors affecting cell performance and two‐phase transport characteristics. Numerical simulations have revealed that the liquid saturation in the cathode gas distribution layer (GDL) could be as high as 20%. The presence of liquid water in the GDL decreases oxygen transport and surface coverage of active catalyst, which in turn degrades the cell performance. The thermodynamic quality in the cathode flow channel is found to be greater than 99.7%, indicating that liquid water in the cathode gas channel exists in very small amounts and does not interfere with the gas phase transport. A detailed analysis of the operating conditions shows that cell performance should be optimized based on the maximum average current density achieved and the magnitude of its dispersion from its mean value. Copyright © 2010 John Wiley & Sons, Ltd.     

Prediction method of critical power by film flow rate measurement and subchannel analysis

This paper presents a method that can estimate the critical power of boiling water reactors, BWRs, with regard to spacer geometry. The current experimental method for estimating the critical power for BWR design requires many trained experts and expensive facilities to conduct the experiments. In the present method, the liquid film flow rate of adiabatic gas‐liquid two‐phase flow and a subchannel analysis of the actual BWR flow condition are measured experimentally and analyzed. In the experiment, deposition enhancement coefficients of three spacer geometries—a ferrule, an egg‐crate, and a ferrule spacer with twisted tape (CYCLONE spacer)—were estimated by measuring the liquid film flow rate of air‐water two‐phase flow flowing up in a vertical square (4 × 4) rod bundle that simulated the rod bundle of a BWR. Using these coefficients, the critical powers for bundles using each type of spacer geometry were calculated in the subchannel analysis. This method was validated using previous critical power data in the actual BWR flow condition. The critical powers predicted by this method agreed well with those of the experimental data. The result confirmed the effectiveness of this experiment‐simulation combined method, as well as the advantage over current experimental methods in terms of human and facility costs. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(5): 309–323, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20069     

Non‐isothermal multi‐phase modeling of PEM fuel cell cathode

In this study, numerical simulation has been carried out for the heat transfer and temperature distribution in the cathode of polymer electrolyte membrane fuel cells along with the multi‐phase and multi‐species transport under the steady‐state condition. The commercial software, COMSOL Multiphysics, is used to solve the conservation equations for momentum, mass, species, charge and energy numerically. The conservation equations are applied to the solid, liquid and vapor phases in the bipolar plate and gas diffusion (GDL) and catalyst layers of a two‐dimensional cross section of the cathode. The catalyst layer is assumed to be a finite domain and the water production in the catalyst layer is considered to be in the liquid form. The temperature distribution in the cathode is simulated and then the effects of the relative humidity of the air stream, the permeability of the cathode and the flow channel shoulder to channel width ratio are investigated. It is shown that the highest temperature change, both in the in‐plane and across‐the‐plane directions, occurs in the GDL, while the highest temperature is reached in the catalyst layer. The distribution of temperature in the bipolar plate is shown to be relatively uniform due to the high thermal conductivity of the plate. A decrease in the inlet relative humidity of the air stream results in the decrease of the maximum temperature due to the absorption of heat during the evaporation of liquid water in the GDL and catalyst layer. The non‐uniformity of the temperature distribution, especially in the catalyst layer, is observed with the increase of the permeability of the cathode. Similarly, the decrease of the channel shoulder to channel width ratio leads to a non‐uniform distribution of temperature especially under the channel areas. Copyright © 2009 John Wiley & Sons, Ltd.     

Structure and void fraction in a liquid slug for gas–liquid two‐phase slug flow

The distribution of gas and liquid in a gas–liquid two‐phase slug flow was measured using semi‐supermultiple point‐electrode probes. Based on the measurements, the wake zone behind a gas slug and the low void‐fraction zone in a liquid slug were defined, and the void fractions of the two zones were determined. The data revealed that the void fraction of the wake zone increased with superficial gas velocity, yet was virtually independent of superficial liquid velocity. Nondimensional head was proposed as an informative characteristic of this system, accounting for the momentum change of the liquid in the wake zone. It was clarified that the nondimensional head was closely related to the void fraction of the wake zone. A good practical relationship was found between the nondimensional head and the lengths of a swelling liquid‐front zone and the wake zone. Furthermore, empirical correlations were proposed for the void fraction in the wake zone, the mean void fraction in the liquid slug, and the lengths of the swelling liquid‐front zone and the wake zone. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(4): 257–271, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10029     

The flow characteristics of an upward gas‐liquid two‐phase flow in a vertical tube with a wire coil: Part 2. Effect on void fraction and liquid film thickness

An experimental study has been carried out to clarify the characteristics of the void fraction and the liquid film thickness of the air‐water two‐phase flow in vertical tubes of 25‐mm inside diameter with wire coils of varying wire diameter and pitch. The flow pattern in the experiment on the average void fraction and the local void fraction distribution in cross section was a bubble flow, and the liquid film thickness was in the region of semiannular and annular flows. It is clarified from these experiments that the average void fraction in tubes with wire coils is lower than that in a smooth tube and decreases with the wire diameter owing to the centrifugal force of the swirl flow which concentrates bubbles at the center of the tube, that the local liquid film thickness becomes more uniform with a decrease in the pitch of the wire coil, and that the liquid film becomes thicker after the passage through the wire coil with an increase in the wire diameter. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(8): 652–664, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10067     

Investigation of mass transport and cell performance on μDMFC with different anode flow fields

The study systematically analyzes the performance of micro direct methanol fuel cell (μDMFC) with different flow fields. A two‐phase three‐dimensional model is developed to evaluate the mass transport accurately. The transport of methanol and air, the pressure distribution, the anode saturation, and the methanol crossover are numerically observed, the under‐rib convection is also investigated numerically. The flow fields with an active area of 0.64 cm² are fabricated on silicon wafers by micro electromechanical system technology. Performance of μDMFCs with different flow fields is sorted as: double‐serpentine flow field (DSFF) > single‐serpentine flow field (SSFF) > triple‐serpentine flow field (TSFF), and the dynamic test results indicate the cell with DSFF takes the shortest time to reach a stable power output when compared with other cells. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical investigation of unsteady aerodynamics of a Horizontal‐axis wind turbine under yawed flow conditions

In the present study, unsteady flow features and the blade aerodynamic loading of the National Renewable Energy Laboratory phase VI wind turbine rotor, under yawed flow conditions, were numerically investigated by using a three‐dimensional incompressible flow solver based on unstructured overset meshes. The effect of turbulence, including laminar‐turbulent transition, was accounted for by using a correlation‐based transition turbulence model. The calculations were made for an upwind configuration at wind speeds of 7, 10 and 15 m/sec when the turbine rotor was at 30° and 60° yaw angles. The results were compared with measurements in terms of the blade surface pressure and the normal and tangential forces at selected blade radial locations. It was found that under the yawed flow conditions, the blade aerodynamic loading is significantly reduced. Also, because of the wind velocity component aligned tangent to the rotor disk plane, the periodic fluctuation of blade loading is obtained with lower magnitudes at the advancing blade side and higher magnitudes at the retreating side. This tendency is further magnified as the yaw angle becomes larger. At 7 m/sec wind speed, the sectional angle of attack is relatively small, and the flow remains mostly attached to the blade surface. At 10 m/sec wind speed, leading‐edge flow separation and strong radial flow are observed at the inboard portion of the retreating blade. As the wind speed is further increased, the flow separation and the radial flow become more pronounced. It was demonstrated that these highly unsteady three‐dimensional aerodynamic features are well‐captured by the present method. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical Investigation of Nanofluid Mixed‐Convection Flow in the Entrance Region of a Vertical Channel Partially Filled with Porous Medium

In this article, transient two‐dimensional mixed convection of nanofluids in the entrance region of a vertical channel has been studied carefully. The geometry under consideration consisted of a parallel‐plate channel partly filled with a porous medium with a constant wall temperature. In the free flow region, the two‐dimensional flow field has been governed by the Navier–Stokes equations. The general formulation of the momentum equations accounting for the inertial and the viscous effects in the presence of a porous medium has been used. Viscous dissipation effects have also been incorporated in the thermal energy equation. Effects of Brownian diffusion and thermophoresis have also been included for nanoparticles in the nanofluid. The governing equations have been given in terms of the stream function‐vorticity formulation and have been non‐dimensionalized and then solved numerically subject to appropriate boundary conditions. The characteristics of the flow and temperature fields have been presented in the terms of mixed‐convection parameter (GR), Brinkman number (Br), Darcy number (Da), Lewis number (Le), and other important parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 607–627, 2014; Published online 21 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21099     

Slug flow heat transfer in a semi‐infinite microtube with temperature jump wall condition

This paper presents an analytical solution of steady‐state heat transfer for laminar, two‐dimensional, and rarefied gas flow in a semi‐infinite microtube. To account for the slip‐flow characteristics of microscale heat transfer, temperature jump condition at the wall has been included in the model while the fluid velocity is assumed to be constant (slug flow). The solution yields closed form expressions for fully‐developed Nusselt numbers in terms of Knudsen number and Prandtl number under both isothermal and isoflux wall conditions. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20263     

Transport mechanisms and performance simulation of a PEM fuel cell

A three‐dimensional, gas–liquid two‐phase flow and transport model has been developed and utilized to simulate the multi‐dimensional, multi‐phase flow and transport phenomena in both the anode and cathode sides in a proton exchange membrane (PEM) fuel cell and the cell performance with different influencing operational and geometric parameters. The simulations are presented with an emphasis on the physical insight and fundamental understanding afforded by the detailed distributions of velocity vector, oxygen concentration, water vapor concentration, liquid water concentration, water content in the PEM, net water flux per proton flux, local current density, and overpotential. Cell performances with different influencing factors are also presented and discussed. The comparison of the model prediction and experimental data shows a good agreement. Copyright © 2007 John Wiley & Sons, Ltd.     

Thermal radiation effects of a high‐temperature developing laminar flow in a tube

The thermal radiation effects of a high‐temperature developing laminar flow in a tube are investigated numerically. The two‐dimensional steady flow and heat transfer are considered for an absorbing‐emitting gray medium, whose density is dependent on the temperature. The governing equations of the coupled process are simultaneously solved by the discrete ordinate method combined with the control volume method. For a moderate optical thickness, the velocity distribution, the temperature distribution, and the radial heat flux distribution in the medium as well as the heat flux distribution on the tube wall are presented and discussed. The results show that the thermal radiation effects of a high‐temperature medium are significant under a moderate optical thickness. The flow and convective heat transfer are weakened, and the development of temperature distribution is accelerated noticeably. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(5): 299–306, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20018     

Numerical simulation of two‐phase cross flow in the gas diffusion layer microstructure of proton exchange membrane fuel cells

The cross flow in the under‐land gas diffusion layer (GDL) between 2 adjacent channels plays an important role on water transport in proton exchange membrane fuel cell. A 3‐dimensional (3D) two‐phase model that is based on volume of fluid is developed to study the liquid water‐air cross flow within the GDL between 2 adjacent channels. By considering the detailed GDL microstructures, various types of air‐water cross flows are investigated by 3D numerical simulation. Liquid water at 4 locations is studied, including droplets at the GDL surface and liquid at the GDL‐catalyst layer interface. It is found that the water droplet at the higher‐pressure channel corner is easier to be removed by cross flow compared with droplets at other locations. Large pressure difference Δp facilitates the faster water removal from the higher‐pressure channel. The contact angle of the GDL fiber is the key parameter that determines the cross flow of the droplet in the higher‐pressure channel. It is observed that the droplet in the higher‐pressure channel is difficult to flow through the hydrophobic GDL. Numerical simulations are also performed to investigate the water emerging process from different pores of the GDL bottom. It is found that the amount of liquid water removed by cross flow mainly depends on the pore's location, and the water under the land is removed entirely into the lower‐pressure channel by cross flow.