Numerical simulation and experimental validation of coiled adiabatic capillary tubes

The objective of this study is to extend and validate the model developed and presented in previous works [O. García-Valladares, C.D. Pérez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: mathematical formulation and numerical model, Applied Thermal Engineering 22 (2) (2002) 173–182; O. García-Valladares, C.D. Pérez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part II: experimental validation and parametric studies, Applied Thermal Engineering 22 (4) (2002) 379–391] to coiled adiabatic capillary tube expansion devices working with pure and mixed refrigerants. The discretized governing equations are coupled using an implicit step by step method. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpies, temperatures, pressures, vapor qualities, velocities, heat fluxes, etc.) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretized. The numerical model allows analysis of aspects such as geometry, type of fluid (pure substances and mixtures), critical or non-critical flow conditions, metastable regions, and transient aspects. Comparison of the numerical simulation with a wide range of experimental data presented in the technical literature will be shown in the present article in order to validate the model developed.     

Numerical simulation and validation of HFC-134a fluid flow through short-tube orifices considering metastable conditions

One-dimensional numerical modelling of the fluid-flow behaviour inside short-tube orifices (expansion devices) has been carried out. Governing equations (continuity, momentum, energy, and entropy) for describing the fluid flow have been solved by using a fully implicit step-by-step method. A numerical treatment has been codified for considering thermodynamic and flow transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). Sudden contraction and enlargement at inlet and outlet sections were also considered. Fluid-flow variables (e.g., enthalpies, temperatures, pressures, mass fractions, and heat fluxes) and thermophysical and transport properties of fluid were numerically evaluated at each grid point in a discretized domain. The physical model used for solving the fluid-flow problem enabled an analysis of geometry, fluid type, critical and non-critical flow conditions, metastable regions, and transient effects to be performed. A comparison and validation analyses of the simulation results were carried out by using a wide range of mass flow rate experimental data (N_o = 634), which have been reported in the literature for the refrigerant 134a. Using a comprehensive statistical analysis, based on weighted linear regressions with an outlier detection/rejection algorithm at 95% of confidence level, the prediction performance of the numerical model was evaluated. Linear relationships between mass flow rate (predicted) and experimental mass flow rate data were statistically demonstrated. A global statistical evaluation of deviation errors between mass flow rate experimental data and predicted simulation results was also calculated. Average deviation error of ±8.9% was consistently computed between numerical model and experimental data, which demonstrates the good capability of the model developed for predicting the fluid-flow processes.     

Numerical simulation of capillary-tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part II: experimental validation and parametric studies

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behaviour of capillary-tube expansion devices working with pure and mixed refrigerants has been developed and presented in part I of this article. The accuracy of the detailed simulation model is demonstrated in this paper by comparison with experimental data from the technical literature.Results presented include both metastable flow modelling and non-metastable flow modelling, homogeneous and separated flow model for metastable flow and the used of different empirical correlation needed in the numerical model. Comparisons of model prediction between various approaches are discussed.Numerical results and parametric studies for concentric capillary tube-suction line heat exchangers have also been presented.     

A simulation for predicting the refrigerant flow characteristics including metastable region in adiabatic capillary tubes

Assumptions that no metastable flow phenomenon and flow in two-phase region is homogeneous have been used exclusively to study the flow characteristics in capillary tubes used as an expansion and controlling device in refrigerating systems. However, some experimental results show that due to the delay of vapourization, the onset of vapourization may not take place at the end of the sub-cooled liquid region. The two-phase flow in small diameter tubes may be also not entirely homogeneous due to phase interaction. In this paper, a mathematical model based on conservations of mass, energy and momentum is presented to simulate the refrigerant flow in adiabatic capillary tubes. Different from most previous studies, the metastable flow region is accounted in the model and the annular flow is also assumed to take place in the two-phase region. The model is validated by comparing with the experimental data reported in literature. The agreement between experimental and simulation results indicates that the model with appropriate correlations of pressure at vapourization and slip ratio can be used to predict the two-phase flow behaviour of refrigerant in capillary tubes. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical simulation of gas-contaminated refrigerant two-phase flow through adiabatic capillary tubes

An unfavorable effect of gas impurities on the throttling process inside a small-diameter tube, i.e. a capillary tube, has been studied in detail. A special testing capillary tube equipped with precise temperature and pressure sensors has been used for an experimental investigation of the capillary flow of a saturated fluorocarbon refrigerant, R218, contaminated by dissolved nitrogen. The gas impurities significantly affected the throttling process, since the two-phase flow started notably earlier than in the case of pure refrigerant flow. Moreover, the gas contamination resulted in a decreased mass flow rate of refrigerant delivered through the capillary tube. A comprehensive numerical model has been developed to simulate the capillary flow of gas-contaminated refrigerant. The model takes into account two coincident thermodynamic events: the throttling process of the refrigerant (solvent) and the gradual release of the dissolved gas impurities (solute) from the refrigerant liquid phase. The gas release is in principle described by using the temperature correlation of the Henry’s law constant. The model considers adiabatic, thermodynamically equilibrated capillary flow with homogeneous two-phase flow. The numerical simulation is in good agreement with our experimental data measured for R218 contaminated by nitrogen.     

Numerical analysis of refrigerant flow along non-adiabatic capillary tubes using a two-fluid model

This work presents a numerical model to simulate steady state refrigerant flow along capillary tube-suction line heat exchangers, commonly used in small refrigeration systems. The flow along the straight and horizontal capillary tube is divided into two regions: a single-phase and a two-phase flow region. The flow is taken as one-dimensional and the metastable flow phenomenon is neglected. The two-fluid model is employed for the two-phase flow region, considering the hydrodynamic and the thermodynamic non-equilibrium between the liquid and vapor phases. Comparisons are made with experimental measurements of the mass flow rate and temperature distribution along capillary tube-suction line heat exchangers working with refrigerant R134a in different operating conditions. The results indicate that the present model provides a good estimation of the refrigerant mass flow rate. Moreover, comparisons with a homogeneous model are also made. Some computational results referring to the quality, void fraction and velocities of each phase are also presented and discussed.     

Numerical analysis of two-phase flow in condensers and evaporators with special emphasis on single-phase/two-phase transition zones

A numerical study of the thermal and fluid-dynamic behaviour of the two-phase flow in ducts under condensation or evaporation phenomena is presented. The numerical simulation has been developed by means of the finite volume technique based on a one-dimensional and transient integration of the conservative equations (continuity, momentum and energy). The discretized governing equations are solved using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) which allows back flow phenomena. Special emphasis is performed on the treatment of the transition zones between the single-phase and two-phase flow. The empirical inputs of single-phase and two-phase flow, including sub-cooled boiling and dry-out, have been adapted by means of adequate splines in the transition zones where the heat transfer correlations available in the literature are not suitable. Different numerical aspects have been evaluated with the aim of verifying the quality of the numerical solution. The mathematical model has been validated by comparison with experimental data obtained from literature considering condensation and evaporation processes. This comparison shown the improvements in the numerical solution not only in the transition zone but also in all condenser and evaporator ducts, when the special treatment for transitions is used. Illustrative results on double-pipe heat exchanger are also presented.     

Numerical investigation of transient responses of a PEM fuel cell using a two-phase non-isothermal mixed-domain model

In this paper, a transient two-phase non-isothermal PEM fuel cell model has been developed based on the previously established two-phase mixed-domain approach. This model is capable of solving two-phase flow and heat transfer processes simultaneously and has been applied herein for two-dimensional time-accurate simulations to fully examine the effects of liquid water transport and heat transfer phenomena on the transient responses of a PEM fuel cell undergoing a step change of cell voltage, with and without condensation/evaporation interfaces. The present numerical results show that under isothermal two-phase conditions, the presence of liquid water in the porous materials increases the current density over-shoot and under-shoot, while under the non-isothermal two-phase conditions, the heat transfer process significantly increases the transient response time. The present studies also indicate that proper consideration of the liquid droplet coverage at the GDL/GC interface results in the increased liquid saturation values inside the porous materials and consequently the drastically increased over-shoot and under-shoot of the current density. In fact, the transient characteristics of the interfacial liquid droplet coverage could exert influences on not only the magnitude but also the time of the transient response process.     

Numerical analysis of adiabatic flow of refrigerant through a spiral capillary tube

In the present work, a homogenous model including the metastable liquid region has been developed for the adiabatic flow of refrigerant through the spiral capillary tube. In order to develop the model, both liquid region and two phase region have been discretized into infinitesimal segments to take into account the effect of varying radius of curvature of spiral tube on the friction factor. The effect of the pitch of spiral on the mass flow rate of refrigerant and capillary tube length has been investigated. A comparison of flow characteristics of refrigerant R22 and its alternatives, i.e., R407C and R410A has been made at different operating conditions at the inlet of the capillary tube and it has been found that the flow characteristics of R22 and R407C are almost similar for a given condenser pressure and degree of subcooling at the inlet of capillary tube.     

Steady saturation distribution in hydrophobic gas-diffusion layers of polymer electrolyte membrane fuel cells: A pore-network study

A pore-network model is developed to simulate liquid water transport in a hydrophobic gas-diffusion layer (GDL) during the operation of polymer electrolyte membrane fuel cells (PEMFCs). The steady saturation distribution in GDLs is determined through a numerical procedure using a pore-network model combined with invasion-percolation path-finding and subsequent viscous two-phase flow calculation. The simulation results indicate that liquid water transport in hydrophobic GDLs is a strongly capillary-driven process that almost reaches the pure invasion-percolation limit with zero capillary number. A uniform flux condition is found to better reflect the actual phenomenon occurring at the inlet boundary for liquid water entering a GDL than a uniform pressure condition. The simulation further clarifies the effect of the invaded pore fraction at a uniform-flux inlet boundary in modifying water transport in GDLs. Finally, the effect of the GDL thickness on the steady saturation distribution is investigated.     

Numerical investigation of effective parameters of falling film evaporation in a vertical-tube evaporator

Wastewater treatment is one of the most effective solutions to manage the problem of water scarcity. Falling film evaporators are excellent technology in wastewater treatment plants. These wastewater evaporators provide high heat transfer, short residence time in the heating zone, and high-purity distilled water. In the present study, the mechanism of turbulent falling film evaporation in a vertical tube has been investigated. A model has been developed for symmetrical two-dimensional pure and saline water flow in a vertical tube under constant wall heat flux. The numerical simulation has been carried out by a commercial computational fluid dynamics code. The evaporation of saturated liquid film is simulated utilizing a two-phase volume of fluid method and Tanasawa phase-change model. The main objective of this study is to evaluate the effects of water salinity, liquid Reynolds number, wall heat flux, and liquid film thickness on the two-phase heat transfer coefficient and vapor volume fraction. The numerical heat transfer coefficients are compared with the obtained results by Chen's empirical correlation. With a MAPE ≤ 11%, this study proves that the numerical method is highly effective at predicting the heat transfer coefficient. Moreover, the empirical coefficient of the Tanasawa model and the minimum thickness of the falling film are determined.     

A semi-implicit numerical scheme for a transient two-fluid three-field model on an unstructured grid

A three-dimensional (3D) unstructured hydrodynamic solver for transient two-phase flows has been developed for a 3D component of a nuclear system code and a component-scale analysis tool. A two-fluid three-field model is used for the two-phase flows. The three fields represent a continuous liquid, an entrained liquid, and a vapor field. An unstructured grid is adopted for realistic simulations of the flows in a complicated geometry. The semi-implicit ICE (Implicit Continuous-fluid Eulerian) numerical scheme has been adapted for an unstructured non-staggered grid. This paper presents the numerical method and the preliminary results of the calculations. The results show that the modified ICE scheme is robust and predicts the phase changes and the flow transitions due to a boiling and a flashing very well.     

蒸汽直接加热冷水的汽液界面压力振荡特性仿真研究

为探究蒸汽直接加热冷水过程中汽液界面瞬态压力振荡及两相流动特性,选用基于热平衡原理的凝结模型、大涡模拟湍流模型和流体体积分数多相流模型,对管道内蒸汽直接加热冷水过程进行了数值模拟,并将数值模拟获取的压力振荡与实验值进行了对比分析。结果表明,数值模拟获取的压力振荡时域特征与实验测量值吻合较好,汽液界面呈现显著的瞬态压力梯度波动,界面压力波动导致附近冷水流场结构发生瞬态剧烈变化。     

An assessment of friction factor and viscosity correlations for model prediction of refrigerant flow in capillary tubes

In this paper, a homogeneous model including the metastable liquid and metastable two‐phase region is presented to assess the effects of various friction factor equations and two‐phase viscosity correlations on simulating the behaviour of capillary tubes. Both straight and coiled capillary tubes are considered and R‐22 is used for comparison. The predicted pressure distribution, tube lengths or mass flow rates are compared with experimental data reported in literature. It is confirmed that the predicting accuracy with homogeneous model can be improved by employing the suitable correlations of friction factor and two‐phase viscosity. For straight capillaries, the Churchill and Colebrook friction factor correlations give almost the same simulating results. However, the numerical results show that the optimum combination of correlations of friction factor and two‐phase viscosity may be different when compared with different experimental data. For coiled capillaries, the Mori and Nakayama friction factor correlation agrees well with Ito's formula for single liquid‐phase flow. Together with Giri's friction factor equation for two‐phase flow, Cicchitti viscosity model best predicts the measured mass flow rate with an average error of 4.88%. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of liquid water and gas flow in a channel and a simplified gas diffusion layer model of polymer electrolyte membrane fuel cells using the lattice Boltzmann method

Numerical simulations using the lattice Boltzmann method (LBM) are developed to elucidate the dynamic behavior of condensed water and gas flow in a polymer electrolyte membrane (PEM) fuel cell. Here, the calculation process of the LBM simulation is improved to extend the simulation to a porous medium like a gas diffusion layer (GDL), and a stable and reliable simulation of two-phase flow with large density differences in the porous medium is established. It is shown that dynamic capillary fingering can be simulated at low migration speeds of liquid water in a modified GDL, and the LBM simulation reported here, which considers the actual physical properties of the system, has significant advantages in evaluating phenomena affected by the interaction between liquid water and air flows. Two-phase flows with the interaction of the phases in the two-dimensional simulations are demonstrated. The simulation of water behavior in a gas flow channel with air flow and a simplified GDL shows that the wettability of the channel has a strong effect on the two-phase flow. The simulation of the porous separator also indicates the possibility of controlling two-phase distribution for better oxygen supply to the catalyst layer by gradient wettability design of the porous separator.     

Visualization and Numerical Simulations of Condensing Flow in Small Diameter Channels

ABSTRACT

The understanding of two-phase flow mechanisms during condensation inside small diameter channels is fundamental to design compact condensers. When dealing with small geometries, experimental investigation can be invasive and the measurement of heat transfer coefficients with low uncertainties becomes difficult. For these reasons, numerical simulations by means of the volume of fluid method are an interesting tool to study two-phase flows and they can also be used in support to experimental investigation. In the present work, first steady-state numerical simulations of R134a condensation inside horizontal channels are presented: the results are used to analyse the effect of the diameter (1 mm and 3.4 mm) on the two-phase flow and heat transfer. Since waves occur at the vapor–liquid interface and they cannot be modelled under the hypothesis of steady-state operating conditions, transient simulations (2-D axisymmetric) have also been performed to investigate the influence of waves on the condensation process. The two-phase flow has also been experimentally investigated and visualizations are compared to the numerical results.     

单面加热竖直窄通道内环状流沸腾传热特性

基于汽芯的动量方程和液膜的质量和动量方程,建立了单面均匀热流竖直窄通道内环状流沸腾传热模型,利用数值法对方程组进行求解,得出了环状流区域的液膜厚度,并进一步预测了环状流两相沸腾传热系数。研究表明:模型预测的两相沸腾传热系数比Mahmound关联式计算值偏小;将不同工况下的291组环状流两相沸腾传热系数实验值与模型预测值进行对比,平均绝对误差为12.7%。     

Shaker-based heat and mass transfer in liquid metal cooled engine valves

The highly transient process of the working combustion engine generates a “shaker-effect” inside the hollow valve stem where liquid sodium carries the heat from the hot valve head to the valve stem. Here it can pass through the valve guide, based on convective heat transfer and thermal conduction. The efficiency of these transport mechanisms is still not clearly understood, since the design of many liquid cooled valves is mostly based on empirical knowledge and can lead under certain conditions to a breakdown of the system. A simulation of the processes during the movement of the valve including detailed insight into the highly transient and complex two-phase flow phenomena as well as the heat transfer has been realized by means of direct numerical simulation (DNS) based on the volume-of-fluid (VOF) method. The influence of several relevant influencing factors such as the geometry, the acceleration and the liquid fill level were studied. It was found that the fill level is one of the most influencing factors regarding the efficiency of the heat transfer whereas the influence of geometrical dimensions and in particular the aspect ratio of the cavity were almost negligible in our setup. By averaging the fluid flow and the temperature field it has been shown that liquid cooled valves are more efficient compared to a solid valve but clustering of the liquid filling can appear which causes a temporal breakdown of the “shaker-effect”. In addition the influence of the spatial resolution is shown and 2D vs. 3D simulation setups are compared. To our knowledge, no similar heat transfer predictions of the presented type are published in the literature.     

Three-dimensional transient two-phase study of the cathode side of a PEM fuel cell

A three-dimensional transient two-phase isothermal model has been developed for the cathode side of a proton exchange membrane fuel cell (PEMFC). This has been done in order to fully investigate the effects and the time variation of liquid water formation as well as the gas phase transport under the start up condition. It is considered that the generated water in the cathode catalyst layer (CL) is liquid water and that the gas diffusion layer (GDL) is hydrophobic. A non-equilibrium water condensation-evaporation is also assumed. The time variations of liquid water distribution in along-channel and through-plane directions are investigated. This is to determine the liquid water accumulation at the start up time (above the channel under the CL), then the movement of the liquid water in the domain and the final accumulation at the steady state condition (above the rib and near the CL). It has also been found that it takes less time for a high average current density to attain the steady state condition which is due to the capillary pressure gradient inside the porous media. Validation of the numerical results has been implemented via a polarization curve comparison with the experimental data. Both sets show good agreement.     

Direct numerical simulation of mass transfer from Taylor bubble flow through a circular capillary

In this work mass transfer during a Taylor bubble flow regime has been investigated by a volume of fluid (VOF) based numerical method. The hydrodynamics of Taylor bubble flow through a circular capillary has been simulated in a single unit cell by a moving reference frame. The validity of Taylor bubble hydrodynamics simulation has been checked by comparing the liquid film thickness and the relative bubble velocity obtained from computational fluid dynamics (CFD) simulations with reported empirical correlations and experimental results. The conservation equation of tracer has been solved in whole of flow domain for simulating mass transfer from Taylor bubble to surrounding liquid. The tracer concentrations in the cells that are either completely or partially filled with the gas phase are assigned the equilibrium concentration by employing the concept of internal boundary condition. By this concept an artificial diffusion of tracer has been appeared in the simulations. In order to eliminate this artificial diffusion, the advection scheme in the tracer conservation equation has been modified by using the two film mass transfer model. The simulation of mass transfer from a single bubble has been validated by comparing the CFD results with reported experimental data. Afterwards, the effects of capillary number, unit cell length and capillary diameter variation on mass transfer from Taylor bubble has been investigated.