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.     

Reverse heat transfer and re-condensation phenomena in non-adiabatic capillary tubes

A numerical simulation model for lateral capillary tube-suction line heat exchangers is presented here to analyze its performance characteristics in small vapour compression refrigeration systems (e.g. domestic refrigerators). Appropriate heat transfer correlations have been used to illustrate the reverse heat transfer and re-condensation phenomena inside the tubes. Some convergence problems were encountered during the execution of the model when lower vapour temperature inside the suction line caused the two-phase refrigerant inside the capillary tube to re-condense within the heat exchange region. Therefore, a relationship between the re-condensation phenomenon and the divergence problem has been analyzed in the paper. The modelling was performed with two refrigerants, namely HFC-134a and HC-600a. Further, a simple theoretical equation has been developed to express the re-condensation phenomenon in non-adiabatic capillary tubes.     

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

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

Non-adiabatic capillary tube flow with isobutane

This work reports the results of an experimental study on concentric capillary tube–suction line heat exchangers commonly used as expansion devices in household refrigerators and freezers. Heat exchanger performance (mass flow rate and suction line outlet temperature) with the hydrocarbon HC-600a was experimentally evaluated for a range of heat exchanger geometries and operating conditions. The tests were planned and performed following a statistically based methodology. Based on the resulting database empirical correlations were developed to predict the refrigerant mass flow rate and the suction line outlet temperature.     

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.     

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.     

Dimensional analysis on the evaporation and condensation of refrigerant R-134a in minichannel plate heat exchangers

Two-phase flow analysis for the evaporation and condensation of refrigerants within the minichannel plate heat exchangers is an area of ongoing research, as reported in the literatures reviewed in this article. The previous studies mostly correlated the two-phase heat transfer and pressure drop in these minichannel heat exchangers using theories and empirical correlations that had previously been established for two-phase flows in conventional macrochannels. However, the two-phase flow characteristics within micro/minichannels may be more sophisticated than conventional macrochannels, and the empirical correlations for one scale may not work for the other one. The objective of this study is to investigate the parameters that affect the two-phase heat transfer within the minichannel plate heat exchangers, and to utilize the dimensional analysis technique to develop appropriate correlations. For this purpose, thermo-hydrodynamic performance of three minichannel brazed-type plate heat exchangers was analyzed experimentally in this study. These heat exchangers were used as the evaporator and condenser of an automotive refrigeration system where the refrigerant R-134a flowed on one side and a 50% glycol–water mixture on the other side in a counter-flow configuration. The heat transfer coefficient for the single-phase flow of the glycol–water mixture was first obtained using a modified Wilson plot technique. The results from the single-phase flow analysis were then used in the two-phase flow analysis, and correlations for the refrigerant evaporation and condensation heat transfer were developed. Correlations for the single-phase and two-phase Fanning friction factors were also obtained based on a homogenous model. The results of this study showed that the two-phase theories and correlations that were established for conventional macrochannel heat exchangers may not hold for the minichannel heat exchangers used in this study.     

Study on Flow Behavior and Heat Exchange Characteristics of a Capillary Tube-Suction Line Heat Exchanger

The present research is to develop a homogenous mathematical model to simulate capillary tube-suction line heat exchanger (CT-SL HX) based on the fundamentals of conservations of mass, momentum and energy with comprehensive experimental result validations. The computer model is fully validated by 72 experimental data with error bands of ±15%, ±2°C and ±35% on the mass flow rate prediction, the suction pipe outlet temperature, and the heat exchange estimation respectively. The results suggest that the internal diameter of the capillary tube, and the heat-transfer length of the CT-SL HX have demonstrated an apparent impact on the capillary tube outlet conditions and heat transfer across the segment.     

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.     

Two-phase flow of refrigerants during evaporation under constant heat flux in a horizontal tube

This paper presents the results of simulations using a two-phase separated flow model to study the heat transfer and flow characteristics of refrigerants during evaporation in a horizontal tube. A one-dimensional annular flow model of the evaporation of refrigerants under constant heat flux is developed. The basic physical equations governing flow are established from the conservation of mass, energy and momentum. The model is validated by comparing it with the experimental data reported in literature. The present model can be used to predict the variation of the temperature, heat transfer coefficient and pressure drop of various pure refrigerants flowing along a horizontal tube. It is found that the refrigerant temperature decreases along the tube corresponding to the decreasing of its saturation pressure. The liquid heat transfer coefficient increases with the axial length due to the reducing thickness of the liquid film. The evaporation rate of liquid refrigerant tends to decrease with increasing axial length, due to the decreasing latent heat transfer through the liquid–vapor interface. The developed model can be considered as an effective tool for evaporator design and can be used to choose appropriate refrigerants under designed conditions.     

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.     

Theoretical analysis of ammonia-water absorption cycles for refrigeration and space conditioning systems

This paper presents an investigation of an ammonia-water absorption cycle for solar refrigeration, airconditioning and heat pump operations at higher heat supply temperatures. The system consists of a solar driven generator, rectifier, condenser, evaporator, absorber and heat exchangers for preheating and subcooling within the system. A steady state thermodynamic cycle analysis based on mass and heat balances along with the state equations for the thermodynamic properties of the ammonia-water mixture has been carried out. A numerical computer simulation of the system with input component temperatures, refrigerant concentration/mass flow rate and effectiveness of the heat exchangers has been made to evaluate the relative heat transfer rates (i.e. coefficients of performance) and the mass flow rates for the cooling/heating modes. It is found that unlike the low generator temperature behaviour the coefficients of performance for both cooling and heating modes are reduced at higher generator temperatures. However, an increase of condenser temperature for each mode of operation improves the performance of the systems at higher generator temperatures. A choice for keeping the absorber temperature equal to/lower than that of the condenser is also predicted at lower/higher generator temperatures, respectively. In general the results are more pronounced for the refrigeration mode than for the heat pump mode and are least effective for the airconditioning mode.     

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.     

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.     

Thermodynamic Optimization of Heat-Driven Refrigerators in the Transient Regime

The present work introduces a transient endoreversible model of a heat-driven refrigeration plant, which is driven by a fuel-burning heater. The model consists of a combustion chamber with negligible heat loss to the ambient, a refrigerator with three finite-size heat exchangers, namely, the evaporator between the refrigeration load and refrigerant, the condenser between the refrigerant and the ambient, and the generator between the combustion chamber and the refrigerant, and finally the refrigerated space. The total thermal conductance of the three heat exchangers is fixed. A thermodynamic optimization of the absorption cycle is then performed, reporting the operating conditions for minimum time to reach a prescribed cold-space temperature, thus maximum refrigeration rate, specifically, the optimal mass fuel flow rate and the optimal way of allocating the thermal conductance inventory. Half of the total supply of thermal conductance has to be divided equally between the generator and evaporator and the other half allocated to the condenser, for optimal operation. A narrow range of fuel flow rates lead to the minimum time to achieve a prescribed cold-space temperature, thus stressing the importance of the transient analysis. Appropriate dimensionless groups were identified and the generalized results are reported in dimensionless charts.     

Prediction of condensation characteristics of alternatives to R-502 inside air–refrigerant enhanced surface tubing

In this paper, an experimental study on the heat transfer characteristics of two-phase flow condensation of alternative azeotropic refrigerant mixtures to R-502, on air/refrigerant horizontal enhanced surface tubing, is presented. The condensation data indicated that the heat transfer coefficient on the blend R-408A has the highest heat transfer rate among the blends under investigation. The condensation data also showed that R-502 and R-407B have similar heat transfer rates when plotted against the refrigerant mass flow rate. It also can be observed that, as the mass flux increases, heat transfer coefficient increases. Correlations were proposed to predict the heat transfer characteristics such as average heat transfer coefficients, as well as pressure drops of alternatives to R-502; such as R507, R404A, R407B and R408A in two-phase flow condensation inside enhanced surface tubing. In addition, proposed correlations were found to fairly predict the two-phase flow heat transfer condensation data.     

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.     

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 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.