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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

Heat transfer enhancement in a small pipe by spinodal decomposition of a low viscosity,liquid–liquid,strongly non-regular mixture

We report experimental evidence of a 20–40 % enhancement of the effective heat transfer coefficient for laminar flow of a partially miscible binary liquid–liquid mixture in a small diameter horizontal tube that obtains when phase separation occurs in the tube. A mixture of acetone–hexadecane is quenched into the two-phase region so as to induce spinodal decomposition. The heat transfer rate is enhanced by self-induced convective effects sustained by the free energy liberated during phase separation. The experimental heat transfer coefficients obtained when separation occurs are compared to the corresponding values predicted for flow of a hypothetic mixture with identical properties but undergoing separation. For such comparison, the energy balance equation must carefully take into account both the sensible heat and the excess enthalpy difference between the inlet and the outlet streams because our liquid–liquid binary mixture is a very asymmetric system with large excess enthalpies. The non-ideal mixture thermodynamic properties needed for the energy balance are obtained by an empirical procedure from the experimental data available in the literature for our mixture. The experimental setup and calculation procedure is tested by experiments performed using single-phase water flow and single-phase mixture flow (above the critical point). The convective heat transfer augmentation that results in the presence of liquid–liquid phase separation may be exploited in the cooling or heating of small scale systems where turbulent convection cannot be achieved.     

Heat and mass transfer of ammonia-water in falling film evaporator

To investigate the performance of heat and mass transfer of ammonia-water during the process of falling film evaporation in vertical tube evaporator, a mathematical model of evaporation process was presented, the solution of which that needed a coordinate transformation was based on stream function. The computational results from the mathematical model were validated with experimental data. Subsequently, a series of parameters, such as velocity, film thickness and concentration, etc., were obtained from the mathematical model. Calculated results show that the average velocity and the film thickness change dramatically at the entrance region when x<100 mm, while they vary slightly with the tube length in the fully developed region when x>100 mm. The average concentration of the solution reduces along the tube length because of evaporation, but the reducing tendency becomes slow. It can be concluded that there is an optimalβrelationship between the tube length and the electricity generated. The reason for the bigger concentration gradient in the y direction is that the smooth tube is chosen in the calculation. It is suggested that the roll-worked enhanced tube or other enhanced tube can reduce the concentration gradient in the film thickness direction and enhance the heat and mass transfer rate.     

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.     

Transport phenomena in the thin-film region of a micro-channel

A mathematical model to predict the flow and heat transfer characteristics for a thin film region of a micro-channel is proposed. Gradient of the vapor pressure and the capillary force are considered. The effects of channel height, heat flux and slip boundary condition at the solid-liquid interface are investigated. The length of the thin film region is calculated by comparing the magnitude of the capillary and disjoining pressures. The length and the thickness of the thin film region decrease exponentially with increasing heat flux. The channel height has no effect on the shape of film thickness. In the case of slip condition, the decreased film thickness causes the capillary and disjoining pressures to increase.     

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.     

The novel use of phase change materials in refrigeration plant. Part 2: Dynamic simulation model for the combined system

A dynamic mathematical model for coupling the refrigeration system and PCMs has been developed in this paper. Overall the model consists of the following basic components: a compressor, a condenser, an expansion valve, an evaporator cooler and a PCM heat exchanger. The model developed here, is based on a lumped-parameter method. The condenser and evaporator were treated as storage tanks at different states, which have a superheat region, a two-phase region and a sub-cooled region. In the single-phase region the parameters are considered homogeneous whereas in the two-phase region, the intensive properties are considered as in thermal equilibrium. The compressor model is considered as an adiabatic process; an isentropic efficiency is employed in this process. The expansion process in the thermostatic expansion valve is considered as an isenthalpic process. The PCM is treated as a one-dimensional heat transfer model. The mathematical simulation in this study predicts the refrigerant states and dynamic coefficient of performance in the system with respect to time. The dynamic validation shows good agreement with the test result.     

气体横掠单管强制对流换热的大涡模拟

应用大涡模拟与二价全展开ETC有限元离散格式相结合的方法对气体横掠单管强制对流换热进行了数值模拟,分别计算了气体横掠团管和方管时的温度场,得到了管壁平均换热系数,数值结果与实验关联式符合较好。同时还表明大涡模拟方法善于捕捉温度场以及流场涡系的时间演化过程,非常适合于具有大尺度涡的绕流运动温度场的分析。     

Application of Heat Transfer Enhancement on Vertical Thermosyphon Reboilers Using Tube Inserts

Vertical thermosyphon reboilers and evaporators are widely used in the process industries. However, increasing the thermal efficiency of these units is very difficult. They are commonly used for about 70% of all evaporation duties in chemical industries. The flow in these units depends on the amount of buoyancy created by vaporization. The flow rate is therefore related not only to heat transfer rate, but also to evaporation, friction, and static pressure loss. The hydrostatic heat present at the base of a vertical thermosyphon reboiler suppresses boiling, creating a sub-cooled region. At the base of the tube bundle, this region length sometimes approaches a significant percent of tube length. Because single-phase convective heat transfer is the dominant heat transfer mechanism in this region, tube inserts can be used to promote heat transfer without blocking flow. In this article, using a simulation model that has been validated against the result of HTFS software, the effect of using different types of tube inserts in a sub-cooled zone of a vertical thermosyphon reboiler on the thermal performance of this unit is discussed.     

Laminar droplet flow in combined hydrodynamically and thermally developing region of circular tubes

Forced convective heat transfer to laminar droplet flow in the combined hydrodynamically and thermally developing region of a circular tube is studied numerically for constant heat flux conditions. The saturated liquid droplets in the vapor flow are considered as equivalent heat sinks distributed in the superheated vapor stream. Numerical calculations are performed for the variations of droplet size, mean vapor velocity, and the local Nusselt number in the streamwise direction until the single-phase fully developed condition is reached. The important roles of the liquid droplets and the developing vapor velocity on the forced convective heat transfer to droplet flow in the combined entrance region of a circular tube are clearly demonstrated.     

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 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.     

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.