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.     

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.     

Mass flow rate correlation for two-phase flow of R218 through a capillary tube

This paper presents some experimental results of refrigerant two-phase flow through a capillary tube. The data was obtained for fluorinert refrigerant R218, which is used in some special vapor cooling circuits, e.g. in various particle detectors at the CERN international research centre. An analytical correlation for mass flow rate of R218 was prepared on the bases of dimensionless parameters derived from the Buckingham π-theorem. Two approaches were compared: (a) the conventional power law function and (b) correlation determined with the use of an artificial neural network. Measured data were also correlated with other mass flow rate correlations presented in literature.     

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 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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: mathematical formulation and numerical model

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. The discretised 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 (enthalpy, temperatures, pressures, vapour quality, velocities, heat fluxes, etc.) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretised. 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, adiabatic or non-adiabatic capillary tubes and transient aspects. Comparison of the numerical simulation with experimental data presented in the technical literature will be shown in part II of the present article.     

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.     

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.     

Numerical analysis of discrete phase induced effects on a gas flow in a turbulent two-phase free jet

The paper addresses numerical simulation of turbulent two-phase flow in a long vertical tube and turbulent two-phase free jet formed at the tube outlet, analyzing agreement between the numerical results and the results of corresponding experimental investigation carried out earlier.In the numerical analyses conducted, gas phase was modeled as an air flow (having a mass flow-rate in the range of 1.25–4.00 g/s), while the sand particles of two different sizes (0.25–0.30 and 0.8–1.0 mm) represented a discrete phase (particle to gas mass flow ratio of 0.72–4.08) in the two-phase flow considered. Gas-particle interaction was analyzed based on the gas velocities in the particle-laden two-phase flow and the particle-free gas flow, calculated and measured at various locations along the longitudinal axis and radius of the jet.Mathematical model of continuous phase flow was developed based on the single phase flow models, with certain corrections introduced to account for the effects of particles in the flow. In the simulation model developed, the flow analyzed was modeled as a two-phase mixture, with Eulerian simulation used to account for the gas phase behavior and the Lagrangian simulation modeling the particle movement in the two-phase flow considered. In order to appropriately close the system of time-averaged equations, k–ε turbulent model, deemed the most reliable, was used. Phase coupling i.e. fluid-particle interaction was modeled using the PSI-CELL concept. The results obtained via numerical simulation have shown a good agreement with the experimental data acquired.