Numerical study on the formation of Taylor bubbles in capillary tubes

Numerical simulations have been carried out for the transient formation of Taylor bubbles in a nozzle/tube co-flow arrangement by solving the unsteady, incompressible Navier–Stokes equations. A level set method was used to track the two-phase interface. The calculated bubble size, shape, liquid film thickness, bubble length, drift velocity, pressure drop and flow fields of Taylor flow agree well with the literature data. For a given nozzle/tube configuration, the formation of Taylor bubbles is found to be mainly dependent on the relative magnitude of gas and liquid superficial velocity. However, even under the same liquid and gas superficial velocities, the change of nozzle geometry alone can drastically change the size of Taylor bubbles and the pressure drop behavior inside a given capillary. This indicates that the widely used flow pattern map presented in terms of liquid and gas superficial velocities is not unique.     

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.     

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.     

Flow characteristics of pure refrigerants and refrigerant mixtures in adiabatic capillary tubes

This paper provides the results of simulations using an adiabatic capillary tube model which is developed to study the flow characteristics in adiabatic capillary tubes used as a refrigerant control device in refrigerating systems. The developed model can be considered as an effective tool of capillary tubes' design and optimization for systems using newer alternative refrigerants. The model is validated by comparing with the experimental data of Li et al. and Mikol for R12 and Melo et al. for R134a. In particular, it has been possible to compare various pairs of refrigerants. It is found that the conventional refrigerants consistently give longer capillary lengths than the alternative refrigerants. For all pairs, the conventional refrigerant consistently give lower pressure drops for both single-phase and two-phase flow which resulted in longer tube lengths. In addition, an example of capillary tube selection chart developed from the present numerical simulation is shown. The chart can be practically used to select the capillary tube size from the flow rate and flow condition or to determine mass flow rate directly from a given capillary tube size and flow condition. The results of this study are of technological importance for the efficient design when systems are assigned to utilize various alternative refrigerants.     

Flow characteristics of refrigerants flowing through capillary tubes – A review

A comprehensive review of the literature on the flow of various refrigerants through the capillary tubes of different geometries viz. straight and coiled and flow configurations viz. adiabatic and diabatic, has been discussed in this paper. The paper presents in chronological order the experimental and numerical investigations systematically under different categories. Flow aspects like effect of coiling and effect of oil in the refrigerants on the mass flow rate through the capillary tube have been discussed. Furthermore, the phenomenon of metastability and the correlations to predict the underpressure of vaporization have also been discussed. The paper provides key information about the range of input parameters viz. tube diameter, tube length, surface roughness, coil pitch and coil diameter, inlet subcooling and condensing pressure or temperature. Other information includes type of refrigerants used, correlations proposed and methodology adopted in the analysis of flow through the capillary tubes of different geometries operating under adiabatic and diabatic flow conditions. It has been found from the review of the literature that there is a lot more to investigate for the flow of various refrigerants through different capillary tube geometries.     

Distribution parameter and drift velocity of drift-flux model in bubbly flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for bubbly flow regime. The constitutive equation that specifies the distribution parameter in the bubbly flow has been derived by taking into account the effect of the bubble size on the phase distribution, since the bubble size would govern the distribution of the void fraction. A comparison of the newly developed model with various fully developed bubbly flow data over a wide range of flow parameters shows a satisfactory agreement. The constitutive equation for the drift velocity developed by Ishii has been reevaluated by the drift velocity calculated by local flow parameters such as void fraction, gas velocity and liquid velocity measured under steady fully developed bubbly flow conditions. It has been confirmed that the newly developed model of the distribution parameter and the drift velocity correlation developed by Ishii can also be applicable to developing bubbly flows.     

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.     

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.     

Exergy assessment of an optimized capillary tube‐based transcritical CO2 heat pump system

A capillary tube‐based CO₂ heat pump is unique because of the transcritical nature of the system. The transcritical cycle has two independent parameters, pressure and temperature, unlike the subcritical cycle. A comparative study for various operating conditions, based on system COP and exergetic efficiency, of a capillary tube and a controllable expansion valve‐based transcritical carbon dioxide heat pump systems for simultaneous heating and cooling at 73 and 4°C, respectively, is presented here. Two optimized capillary tubes having diameter of 1.5 and 1.6 mm are compared with an equivalent controllable throttle valve. Heat transfer and fluid flow effects are included in the gas cooler and evaporator model and capillary tube employs the homogeneous flow model to simulate two‐phase flow. Subcritical and supercritical thermodynamic and transport properties of CO₂ are calculated employing a precision in‐house property code. Optimization of effective distribution of total heat exchanger area ratio between gas cooler and evaporator is investigated. The exergetic efficiency is better in case of the capillary tube than that of a controllable throttle valve‐based system. Capillary tube‐based system is shown to be quite flexible regarding changes in ambient temperature, almost behaving to offer an optimal pressure control just like the controllable expansion valve yielding both, maximum system COP and maximum exergetic efficiency. Relatively at a smaller diameter, the capillary tube exhibits better exergetic efficiency. Capillary tube length is the critical parameter that influences system optimum conditions. The exergy flow diagram exhibits that compressor, gas cooler and capillary tube contribute a larger share, in that order, to system irreversibility. It is fairly established in this study that a capillary tube can be a good engineering option for small capacity systems in lieu of an expansion valve, which has been thought of as the only possible solution to attain the pressure optimization, an important feature of all transcritical CO₂ systems. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

A parametric study of refrigerant flow in non-adiabatic capillary tubes

This paper presents a parametric analysis of refrigerant flow through capillary tube–suction line heat exchangers, used in domestic refrigeration systems. The analysis is based on a homogeneous model developed by the authors. The model is based on the numerical solution of fundamental equations of conservation of mass, momentum and energy of refrigerant flow. The refrigerant flow characteristics are investigated by varying thermodynamic (e.g. condensing temperature, evaporating temperature, inlet sub-cooling, suction line superheat) and geometric parameters (e.g. inlet adiabatic length, heat exchanger length and internal diameter of the capillary tube) of the capillary flow. The source of divergence in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the capillary heat exchanger.     

Algebraic solution of capillary tube flows: Part I: Adiabatic capillary tubes

Capillary tube flows have been solved through both numerical and analytical approaches. The former requires a reasonable understanding of the governing equations of heat and fluid flow, thermodynamic relations, numerical methods, and computer programming, and therefore are not the suitable approach for most refrigeration and air-conditioning practitioners. Some simpler procedures based on different strategies for analytically solving the capillary tube flow have been proposed in the literature, although iterative loops for calculating the mass flow rate are still required. The aim of this work is to advance a semi-empirical algebraic model to solve adiabatic capillary tube flows using a relatively simple set of thermodynamic relations and being explicit for the mass flow rate calculation. Comparisons with a comprehensive experimental data set, taken with the refrigerants HFC-134a and HC-600a, has shown that the model predicts more than 90% and nearly 100% of all data within ±10% and ±15% error bands, respectively.     

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.     

Refrigerant flow in capillary tube: An assessment of the two-phase viscosity correlations on model prediction

The homogeneous flow model has been widely used to analyse the two-phase flow of refrigerant in a capillary tube of a vapour compression refrigeration system. However, to effectively apply the model, it is necessary to use an appropriate two-phase friction factor with a suitable two-phase viscosity correlation. In this paper, the effects of the various two-phase viscosity correlations on the homogeneous flow model prediction are assessed by comparing with the predicted pressure drops along the capillary tube with measured data.     

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.     

Algebraic solution of capillary tube flows. Part II: Capillary tube suction line heat exchangers

Capillary tube suction line heat exchangers have been modeled using both numerical and analytical approaches. The former requires a reasonable understanding of the governing heat and fluid flow equations, thermodynamic relations, numerical methods, and computer programming, and therefore are not suitable for most refrigeration and air-conditioning practitioners. Alternatively, empirical algebraic formulations for diabatic capillary tube flows have been proposed in the literature, in spite of their lack of generality and accuracy. This paper introduces a physically consistent, unconditionally convergent, easy-to-implement semi-empirical algebraic model for capillary tube suction line heat exchangers, with the same level of accuracy as found with more sophisticated first-principles models. The methodology treats the refrigerant flow and the heat transfer as independent phenomena, thus allowing the derivation of explicit algebraic expressions for the refrigerant mass flow rate and the heat exchanger effectiveness. The thermal and hydraulic models are then conflated through the so-called Buckingham-π theorem using in-house experimental data collected for diabatic capillary tube flows of refrigerants HFC-134a and HC-600a. Comparisons between the model predictions and the experimental data revealed that more than 90% and nearly 100% of all data can be predicted within ±10% and ±15% error bands, respectively.     

Numerical modelling of alternative refrigerants to HCFC‐22 through capillary tubes

In this paper, a numerical model is presented for predicting capillary tube performance using new alternative refrigerants to HCFC‐22. The model has been established after the fluid flow conservation equations written for a homogeneous refrigerant fluid flow under saturated, sub‐cooled and two‐phase conditions. Numerical results showed that the proposed model in question fairly simulated our experimental data and fairly predicted the capillary tube behaviour under different conditions. The results also indicated that a system using R‐407C would experience smaller pressure drop compared to R‐410A and R‐410B. Copyright © 2000 John Wiley & Sons, Ltd.     

Prediction of capillary tubes with alternative refrigerants to CFC‐502

A numerical model is presented in this paper, for predicting capillary tube performance using new alternative refrigerants to CFC‐502. The model has been established after the fluid flow conservation equations written for a homogeneous azeotropic refrigerant fluid flow under saturated, sub‐cooled and two‐phase conditions. The study was limited to the following azeotropic mixtures; R‐507, R‐404A, and quaternary mixture (R32/R125/R134a/R143a). Numerical results showed that the proposed model in question fairly simulated our experimental data and fairly predicted the capillary tube behaviour under different conditions. The results also indicated that a system using R‐507 would experience smaller pressure drop across the capillary compared to the other alternatives under question. Copyright © 2001 John Wiley & Sons, Ltd.     

Determination of the void fraction and drift velocity in a two-phase flow with a boiling solar collector

This paper presents an approach to determine the void fraction and the drift velocity in a two-phase flow with a boiling solar collector using easily obtained experimental data. The solar collector operates in a thermal siphon circuit, where the working fluid absorbs solar radiation mostly while boiling. The vapor bubbles release their latent heat in a condenser, while heating up a flow of water–glycol. Two numerical procedures are developed to calculate the void fraction because its experimental values cannot be easily measured. The use of a flow meter causes an additional pressure drop in the thermal siphon circuit and, consequently, changes the circulated mass flow rate. The first numerical procedure is based on a force balance in the thermal siphon loop and is used to estimate the total mass flow rate and the void fraction in the circuit. The second uses a drift flux correlation to estimate the void fraction and the drift velocity. Both procedures use the experimental values for the vapor mass flow rate, which is determined by an energy balance in the condenser. The volumetric flow rate of the water–glycol mixture and its temperature difference across the condenser are experimentally measured. The pipe length of the two-phase flow in the solar collector is experimentally determined using 44 thermocouples attached to the back of flow channels in the absorber plate. The results show that the two numerical models compare well and that either one can be used to estimate the void fraction in the two-phase flow solar circuit.     

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.