Two-phase flow model of refrigerants flowing through helically coiled capillary tubes

This paper presents a numerical study of the flow characteristics of refrigerants flowing through adiabatic helically coiled capillary tubes. The theoretical model is based on conservation of mass, energy and momentum of the fluids in the capillary tube. The two-phase flow model developed was based on the homogeneous flow assumption. The viscosity model was also based on recommendations from the literature. The developed model can be considered as an effective tool for designing and optimizing capillary tubes working with newer alternative refrigerants. The model is validated by comparison with the experimental data of Kim et al. (2002) for R-22, R-407C and R-410A, and Zhou and Zhang (2006) for R-22. The results obtained from the present model show reasonable agreement with the experimental data. The proposed model can be used to design helical capillary tubes working with various refrigerants.     

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.     

Non-adiabatic capillary tube flow: a homogeneous model and process description

This paper presents a homogeneous model of refrigerant flow through capillary tube–suction line heat exchangers, which are widely used in small vapour compression refrigeration systems. The homogeneous model is based on fundamental conservation equations of mass, momentum and energy. These equations are solved simultaneously through iterative process. Churchill’s correlation [3] is used to calculate single-phase friction factors and Lin et al. [6] correlation for two-phase friction factors. The single-phase heat transfer coefficient is calculated by Gnielinski’s equation [5] while two-phase flow heat transfer coefficient is assumed to be infinite. The model is validated with previous experimental and analytical results. The present model can be used in either design calculation (calculate the capillary tube length for given refrigerant mass flow rate) or simulation calculation (calculate the refrigerant mass flow rate for given capillary tube length). The simulation model is used to understand the refrigerant flow behaviour inside the non-adiabatic capillary tubes.     

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 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.     

Modelling of capillary tubes behaviour with HCFC 22 ternary alternative refrigerants

In this paper, a numerical model is presented for predicting capillary tube performance using new ternary mixtures proposed as alternatives to R 22. The model has been established after the fluid flow conservation equations written for a homogeneous refrigerant fluid flow under saturated, subcooled and two- pase conditions. Numerical results showed that the proposed model in question fairly simulated experimental on ternary refrigerant mixtures and fairly predicted the capillary tube behaviour under the investigated; subcooled, saturated, and two-phase flow conditions. © 1998 John Wiley & Sons, Ltd.     

Two-Phase Flow Modeling in Microchannels and Minichannels

In this article, three different methods for two-phase flow modeling in microchannels and minichannels are presented. They are effective property models for homogeneous two-phase flows, an asymptotic modeling approach for separated two-phase flow, and bounds on two-phase frictional pressure gradient. In the first method, new definitions for two-phase viscosity are proposed using a one-dimensional transport analogy between thermal conductivity of porous media and viscosity in two-phase flow. These new definitions can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach. In the second method, a simple semitheoretical method for calculating two-phase frictional pressure gradient using asymptotic analysis is presented. Two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the final method, simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient in minichannels and microchannels. In all cases, the proposed modeling approaches are validated using the published experimental data.     

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 modeling of two-phase refrigerant flow through adiabatic capillary tubes

Literature shows that the homogeneous flow assumption has been commonly used in most of the adiabatic capillary tube modeling studies due to its simplicity. The slip effect between the two phases was often not considered in this small diameter capillary tube. This paper attempts to exploit the possibility of applying the equilibrium two-phase drift flux model to simulate the flow of refrigerant in the capillary tube expansion devices. Attempts have been made to compare predictions with experimental results. The details flow characteristics of R134a in a capillary tube, such as distribution of pressure, void fraction, dryness fraction, phase’s velocities and their drift velocity relative to the center of the mass of the mixture are presented.     

An inspection of viscosity model for homogeneous two-phase flow pressure drop prediction in a horizontal circular micro-channel

This study analyzes several well-known two-phase viscosity models in order to address the appropriate correlations among them for application to micro-channel. Pressure drop data is obtained from adiabatic two-phase air–water flow experiments. A fused silica channel, 320 mm long, with an inside diameter of 0.53 mm is used as the test section. The measured data is compared with the homogeneous flow predictions calculated using the existing viscosity models and detailed comparisons are discussed.     

Flow boiling of liquid nitrogen in micro-tubes: Part I – The onset of nucleate boiling, two-phase flow instability and two-phase flow pressure drop

This paper is the first portion of a two-part study concerning the flow boiling of liquid nitrogen in the micro-tubes with the diameters of 0.531, 0.834, 1.042 and 1.931 mm. The contents mainly include the onset of nucleate boiling (ONB), two-phase flow instability and two-phase flow pressure drop. At ONB, mass flux drops suddenly while pressure drop increases, and apparent wall temperature hysteresis in the range of 1.0–5.0 K occurs. Modified Thom model can predict the wall superheat and heat flux at ONB. Moreover, stable long-period (50–60 s) and large-amplitude oscillations of mass flux, pressure drop and wall temperatures are observed at ONB for the 1.042 and 1.931 mm micro-tubes. Block phenomenon at ONB is also observed in the cases of high mass flux. The regions for the oscillations, block and stable flow boiling are classified. A physical model of vapor patch coalesced at the outlet is proposed to explain the ONB oscillations and block. Vapor generation caused by the flash evaporation is so large that it should be taken into account to precisely depict the variation of mass quality along the micro-tube. The adiabatic and diabatic two-phase flow pressure drop characteristics in micro-tubes are investigated and compared with four models including homogeneous model and three classical separated flow models. Contrary to the conventional channels, homogeneous model yields better prediction than three separated flow models. It can be explained by the fact that the density ratio of liquid to vapor for nitrogen is comparatively small, and the liquid and vapor phases may mix well in micro-tube at high mass flux due to small viscosity of liquid nitrogen, which leads to a more homogeneous flow. Part II of this study will focus on the heat transfer characteristics and critical heat flux (CHF) of flow boiling of liquid nitrogen in micro-tubes.     

Two-phase air-water flow in micro-channels: An investigation of the viscosity models for pressure drop prediction

Adiabatic two-phase air-water flow is experimentally studied in this work. Two channels, made of fused silica, with different diameters of 0.53 and 0.15 mm are used as test sections. The void fraction data for both tubes are obtained by image analysis. For the larger channel, the void fraction is found to be a linear relationship with the volumetric quality. In the case of the smaller one, however, the non-linear void fraction is obtained. The measured frictional pressure drop data are compared with the predictions regarding the homogeneous flow assumption. Several well-known two-phase viscosity models are subsequently evaluated for applicability to micro-channels.     

Effects of coil diameter and pitch on the flow characteristics of alternative refrigerants flowing through adiabatic helical capillary tubes

This paper presents the effects of various geometries of helical capillary tubes on the flow characteristics of alternative refrigerants flowing through adiabatic helical capillary tubes. The theoretical model is based on the conservation of mass, energy and momentum of fluids in the capillary tube. The two-phase flow model developed was based on a homogenous flow assumption. The model was validated by comparing it with the experimental data of published in literature for R-22, particularly various pairs of refrigerants. It was found conventional refrigerants had lower capillary lengths than alternative refrigerants. For all pairs, the numerical results showed that the traditional refrigerants consistently gave lower pressure drops for both single-phase and two-phase flows, which resulted in longer tube lengths. The results show that coil diameter variation (less than 300 mm) for helical capillary tube geometries affected the length of helical capillary tubes. However, pitch variation (more than 300 mm) had no significant effect on the length of helical capillary tubes. This adiabatic helical capillary tube model can be used to integrate system models working with alternative refrigerants for design and optimisation.     

Effect of system pressure on the steady state performance of a CO2 based natural circulation loop

In the present work the effect of system pressure on the steady state performance of a CO₂ based natural circulation loop with end heat exchangers is studied. For a given geometry, the loop pressure (or CO₂ inventory) is considered as an input and its influence on the system performance is obtained. The system operates as a single-phase loop or a two-phase loop depending upon the loop pressure, when other parameters such as external fluid temperatures and external fluid flow rates are kept fixed. Hence the model developed considers both single and two-phase flow regimes. For the two-phase flow, a homogeneous model is used and the influence of different two-phase viscosity models on system performance is observed. Results show that when other things are kept constant, the heat carrying capacity of the loop increases initially as the loop pressure is decreased, reaches a peak and then starts decreasing with further decrease in loop pressure. From the value of optimum pressure at which heat transfer rate becomes maximum, one can obtain the required optimum amount of CO₂ to be charged into a particular system as the property variation of CO₂ along the loop can be obtained by using the model presented. Thus it is expected that the present study will be useful in the design and optimization of natural circulation loops based on carbon dioxide.     

Correlations for sizing adiabatic capillary tubes

This paper presents new correlations for the practical sizing of adiabatic capillary tubes used as an expansion device in small refrigerating and air-conditioning systems. The governing equation based on conservation of mass, energy and momentum is modelled. The developed model is used as an effective tool for studying the effects of relevant parameters on capillary tube length and developing the correlation. In this model, Colebrook's equation is used to determine the friction factor. The two-phase viscosity models are varied depending on the type of refrigerant and are based on the recommendations from past research. By varying the model input parameters, it is possible to show that for all refrigerants, the length decreases as the mass flow rate increases, increases as subcooling increases, increases as tube diameter increases, decreases as tube roughness increases and increases as condensing temperature increases. After the developed model is validated by comparing with existing experimental data, correlations for sizing capillary tubes, which contains the relevant parameters, namely condensing temperature, degree of subcooling, refrigerant mass flow rate, capillary tube inner diameter and roughness, are presented. Different from previous studies, correlations are presented for an extensive number of refrigerants and a wide range of operations. The developed correlations are validated with previous studies and found to agree well with the experimental data. The correlations can be used to integrate with system models working with alternative refrigerants for practical design and optimization. Copyright © 2003 John Wiley & Sons, Ltd.     

Preliminary study of polymer melt rheological behavior flowing through micro-channels

Determination of melt rheological behavior within micro-structured geometry is very important for the accurate simulation modeling of micro-molding. Yet investigation of micro-melt rheology is difficult due to the lack of commercial equipment. In this study, melt viscosity measurement system for polymer melt flowing through micro-channel was established using a micro-channel mold operated at a mold temperature as high as the melt temperature. Form measured pressures and volumetric flow rate both capillary flow model and slit flow model were used for the calculation of viscosity utilizing Rabinowitsch and Walters corrections. It was found that the measured viscosity values in the test ranges are significantly lower (about 30% to 80% lower) than those obtained from traditional capillary rheometer no matter what capillary flow model or slit model are used for analysis. As micro-channel size decreases, the percentage reduction in viscosity also increases. This indicates microscopic scale melt rheological behavior is different from that of macroscopic scale and that current simulation packages are not suitable for micro-molding simulation without considering this difference.     

基于反问题理论的汽液两相上升流流型预测与实验研究

汽液两相流流型的测量在两相流研究中占有重要地位。应用均相流模型建立了圆管内汽液两相上升流压力分布,基于反问题理论反演了汽液两相的物性参数,将反演结果与流型图结合,精确地预测了管内流型,计算结果与实验结果进行了对比,误差小于5%。提出的反演流型的方法,可以推广到水平管、螺旋管,为工程上的汽液两相流设备安全性分析、稳定性分析等提供了一种简单可靠的技术方法。     

Analysis on the adiabatic flow of R407C in capillary tube

In this paper the adiabatic flow in the capillary tube is analyzed and modeled for R407C, which is a non-azeotropic mixed refrigerant and one of the alternatives to R22. The equations of energy, continuity and pressure drop through a capillary tube are presented. A mathematical model of the sub-cooled flow region and the two-phase flow region is developed. The results of the calculation show that this numerical model is capable of providing an effective means to analyze components’ performance in optimizing and controlling a R407C air-conditioning system.     

A comparison of flow characteristics of refrigerants flowing through adiabatic straight and helical capillary tubes

This paper presents a numerical investigation of the flow characteristics of helical capillary tubes compared with straight capillary tubes. The homogenous two-phase flow model developed is based on the conservation of mass, energy, and momentum of the fluids in the capillary tube. This model is validated by comparing it with the experimental data of both straight and helical capillary tubes. Comparisons of the predicted results between the straight and helical capillary tubes are presented, together with the experimental results for straight capillary tubes obtained by previous researchers. The results show that the refrigerant flowing through the straight capillary tube provides a slightly lower pressure drop than that in the helical capillary tube, which resulted in a total tube length that was longer by about 20%. In addition, for the same tube length, the mass flow rate in the helical capillary tube with a coil diameter of 40 mm is 9% less than that in the straight tube. Finally, the results obtained from the present model show reasonable agreement with the experimental data of helical capillary tubes and can also be applied to predict the flow characteristics of straight capillary tubes by changing to straight tube friction factors, for which Churchill's equation was used in the present study.     

Effect of Void Fraction and Two-Phase Dynamic Viscosity Models on Prediction of Hydrostatic and Frictional Pressure Drop in Vertical Upward Gas–Liquid Two-Phase Flow

In gas–liquid two-phase flow, the prediction of two-phase density and hence the hydrostatic pressure drop relies on the void fraction and is sensitive to the error in prediction of void fraction. The objectives of this study are to analyze dependence of two-phase density on void fraction and to examine slip ratio and drift flux model-based correlations for their performance in prediction of void fraction and two-phase densities for the two extremes of two-phase flow conditions, that is, bubbly and annular flow or, alternatively, the low and high region of the void fraction. It is shown that the drift flux model-based correlations perform better than the slip ratio model-based correlations in prediction of void fraction and hence the two-phase mixture density. Another objective of this study is to verify performance of different two-phase dynamic viscosity models in prediction of two-phase frictional pressure drop. Fourteen two-phase dynamic viscosity models are assessed for their performance against 616 data points consisting of 10 different pipe diameters in annular flow regime. It is found that none of these two-phase dynamic viscosity models are able to predict the frictional pressure drop in annular flow regime for a range of pipe diameters. The correlations that are successful for small pipe diameters fail for large pipe diameters and vice versa.