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 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.     

Experimental analysis of capillary tubes behaviour with some HCFC‐22 alternative refrigerants

In this paper, an experimental study is presented to enhance our understanding of the capillary tube behaviour using some new alternative refrigerants to HCFC‐22. An experimental setup fully instrumented was used to gather the behaviour of three different capillary tube geometries with R‐410B, R‐407C, and R‐410A under various conditions; saturated, sub‐cooled and two‐phase. Experimental data showed that R‐410B has the highest pressure drop along the capillary tubes compared to the alternatives under question and also has the highest temperature drop along the capillary tube. The data also showed that R‐407C has similar capillary behaviour to that of R‐22. The results clearly demonstrated that the pressure drop is significantly influenced by the diameter of the capillary tube, the type of refrigerant and inlet conditions to the capillary tube. The data also showed that the capillary pressure drop decreases with the increase of the capillary diameter. There is clear evidence that the component concentration of the refrigerant mixture significantly affects the capillary tube behaviour and particularly the pressure drop along the capillary tube length. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

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.     

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.     

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 investigation of refrigerant flow through non-adiabatic capillary tubes

A mathematical model is developed to study flow characteristics in non-adiabatic capillary tubes. The theoretical model is based on conservation of mass, energy and momentum of fluids in the capillary tube and suction line. The mathematical model is categorized into three different cases, depending on the position of the heat exchange process. The first case is considered when the heat exchange process starts in the single-phase flow region, the second case is determined when the heat exchange process starts at the end of the single-phase flow region, and the last case is considered when the heat exchange process takes place in the two-phase flow region. A set of differential equations is solved by the explicit method of finite-difference scheme. The model is validated by comparing with the experimental data obtained from previous works. The results obtained from the present model show reasonable agreement with the experimental data. The present non-adiabatic capillary tube model can be used to integrate with system models working with alternative refrigerants for design and optimization.     

Heat transfer and pressure drop during flow boiling of pure refrigerants and refrigerant/oil mixtures in tube with porous coating

The experimental stand and procedure for flow boiling investigations are described. Experimental data for pure R22, R134a, R407C and their mixtures with polyester oil FUCHS Reniso/Triton SEZ 32 in a tube with porous coating and smooth, stainless steel reference tube are presented. Mass fraction of oil was equal to 1% or 5%. During the tests inlet vapour quality was set at 0 and outlet quality at 0.7. Mass velocity varied from about 250 to 500 kg/m²s. The experiments have been conducted for average saturation temperature 0 °C. In the case of flow boiling of pure refrigerants, the application of a porous coating on inner surface of a tube results in higher average heat transfer coefficient and simultaneously in lower pressure drop in comparison with the flow boiling in a smooth tube for the same mass velocity. Correlation equation for heat transfer coefficient calculation during the flow boiling of pure refrigerants inside a tube with porous coating has been proposed.     

Evaporation of R407C/oil mixtures inside corrugated and micro-fin tubes

The paper reviews the evaporation of R407C data currently available in the literature. The experimental rig and procedure are discussed. Experimental data about the evaporation for the pure R407C and R407C/oil mixtures in two smooth tubes and two enhanced tubes are also presented. The performance benefits of the micro-fin tube and corrugated tube are quantified and discussed. During tests inlet vapour quality was set 0 and outlet quality 0.7. Mass flux density varied from about 250 to 500 kg/m² s. The experiments have been conducted for average saturation temperature 0 °C.     

Numerical model for matching of coiled adiabatic capillary tubes in a split air conditioner using HCFC22 and HC290

The present work presents a simple model for matching coiled capillary tubes and the refrigerant charge in a split air conditioner when the other components are fixed. The system model is composed of sub-models for the key components, i.e., a lumped model for the compressor, zone models for the condenser and the evaporator, and a four flow region distributed model for the coiled adiabatic capillary tube in series with the liquid tube. The C-M-N method is employed to calculate the friction factors in the coiled capillary tube. HCFC22 and HC290 are used for the simulations. The comparison of the model prediction with experimental data shows the errors are less than ±5% except for the mass flow rate with a maximum deviation of 8.63%. The results confirm that both the cooling capacity and input power are slightly reduced when HCFC22 is replaced by HC290 with the coiled capillary tube and refrigerant charge matched to the HC290 refrigerant. The results also show that when coil diameter is reduced from 0.3 m to 0.04 m, the capillary tube length is reduced by about 10% for both HCFC22 and HC290. This model can be used to design components for small air conditioning systems using HCFC22 and HC290.     

Use of infrared thermography for the study of evaporation in a square capillary tube

In this paper we report experimental results on evaporation of a volatile wetting liquid in a capillary tube of square internal cross section, when conditions are such that liquid films develop along the tube internal corners under the effect of capillary forces, as the bulk meniscus recedes inside the tube. Combining an infrared thermography technique with visualizations by ombroscopy makes it possible to determine the time-space evolution of the temperature minimum on the capillary outer surface together with the bulk meniscus position within the tube. When the tube is held horizontal, the temperature minimum stays at the tube entrance and the evaporation rate reaches a stationary value. In contrast with the horizontal case, the position of the temperature minimum changes when the bulk meniscus has sufficiently receded inside the tube when the tube is vertical and opened at the top. The rate of evaporation then decreases significantly. This is explained by the thinning of the corner films in the vertical tube entrance region, under the conjugated effects of gravity and viscous forces up to the depinning of the films from the tube entrance. When the tube is held horizontal, the capillary effects are dominant and the film thickness remains essentially constant in the tube entrance region. This analysis is supported by a simple model of liquid flow within the corner films.     

Numerical analysis of an air condenser working with the refrigerant fluid R407C

As CFC (clorofluorocarbon) and HCFC (hydrochlorofluorocarbon) refrigerants which have been used as refrigerants in a vapour compression refrigeration system were know to provide a principal cause to ozone depletion and global warming, production and use of these refrigerants have been restricted. Therefore, new alternative refrigerants should be searched for, which fit to the requirements in an air conditioner or a heat pump, and refrigerant mixtures which are composed of HFC (hydrofluorocarbon) refrigerants having zero ODP (ozone depletion potential) are now being suggested as drop-in or mid-term replacement. However also these refrigerants, as the CFC and HCFC refrigerants, present a greenhouse effect.The zeotropic mixture designated as R407C (R32/R125/R134a 23/25/52% in mass) represents a substitute of the HCFC22 for high evaporation temperature applications as the air-conditioning.Aim of the paper is a numerical–experimental analysis for an air condenser working with the non azeotropic mixture R407C in steady-state conditions. A homogeneous model for the condensing refrigerant is considered to forecast the performances of the condenser; this model is capable of predicting the distributions of the refrigerant temperature, the velocity, the void fraction, the tube wall temperature and the air temperature along the test condenser. Obviously in the refrigerant de-superheating phase the numerical analysis becomes very simple. A comparison with the measurements on an air condenser mounted in an air channel linked to a vapour compression plant is discussed. The results show that the simplified model provides a reasonable estimation of the steady-state response and that this model is useful to design purposes.     

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.     

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.     

DISJOINING PRESSURE EFFECT ON THE WETTING CHARACTERISTICS IN A CAPILLARY TUBE

A mathematical model capable of predicting the wicking height formed by a wetting liquid in a vertical, heated capillary tube was developed. The model incorporates the disjoining pressure, the fluid flow and heat transfer in the thin film region, and the thermocapillary effects. Evaluation of the modeling predictions indicates the meniscus radius of curvature at the vapor - liquid interface increases significantly with increasing heat flux, resulting in an increase in the contact angle due to the surface tension variation, disjoining pressure, and fluid flow in the evaporating thin film. The increase in the contact angle is shown to be the principal reason that the static wicking height in capillary tubes is typically greater than the dynamic wicking height observed during dynamic flow conditions. In addition to the individual contributions of the dynamic flow effect and the contact angle variation, both of these parameters are presented and discussed as a function of the tube diameter. In order to verify the analytical model, comparisons with previously obtained experimental data are made. The verified analytical model presented and developed here provides a better understanding of the wetting phenomena occurring in a heated capillary tube and has applicability in a wide range of applications.