Numerical simulation of non-adiabatic capillary tubes 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 behavior of capillary tube–suction line heat exchangers has been carried out. The governing equations (continuity, momentum, energy and entropy) for fluid flows, together with the energy equation in solids, are solved iteratively in a segregated manner. The discretized governing equations in the zones with fluid flow are coupled using a fully implicit step-by-step method. An implicit central difference numerical scheme and a line-by-line solver were used in solids. 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, mass fractions, heat fluxes, etc.) together with the thermophysical and transport 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, critical or non-critical flow conditions, metastable regions and transient cases. Comparison of the numerical simulation with experimental data presented in the technical literature will be shown in Part II of the present paper.     

Momentum transfer of ice slurry flows in tubes, modeling

In this paper we present results of the studies of ice slurry flow in horizontal tubes. The possibility of treating the rheological parameters of ice slurry as being those of Bingham fluid was confirmed. The values of parameters (mass fraction, flow velocity) corresponding to the laminar, intermediate and turbulent flow were determined which permits to optimize the flow in the systems working with this cooling agent. Critical flow velocity and mass fraction of ice values were determined thereby; they correspond to a change in character of an ice slurry flow from a laminar to turbulent motion. Experimental results were compared to the analytical results, based on the Hedström and Tomita algorithms (the laminar and turbulent flow, respectively). The comparison showed a very good agreement between these data.     

A dynamic simulation model for transient absorption chiller performance. Part II: Numerical results and experimental verification

This paper is the second paper out of two which present the development of a dynamic model for single-effect LiBr/water absorption chillers. The first part describes the model in detail with respect to the heat and mass balances as well as the dynamic terms. This second part presents a more detailed investigation of the model performance, including performance analysis, sensitivity checks and a comparison to experimental data. General model functionality is demonstrated.A sensitivity analysis gives results which agree very well to fundamental expectations: it shows that an increase in both external and internal thermal mass results in a slower response to the step change but also in smaller heat flow oscillations during the transient period. Also, the thermal mass has been found to influence the heat flow transients more significantly if allocated internally. The time shift in the solution cycle has been found to influence both the time to reach steady-state and the transients and oscillations of the heat flow. A smaller time shift leads to significantly faster response.A comparison with experimental data shows that the dynamic agreement between experiment and simulation is very good with dynamic temperature deviations between 10 and 25 s. The total time to achieve a new steady-state in hot water temperature after a 10 K input temperature step amounts to approximately 15 min. Compared to this, the present dynamic deviations are in the magnitude of approximately 1–3%.     

A generalized moving-boundary model for transient simulation of dry-expansion evaporators under larger disturbances

A generalized model based on the moving-boundary approach is developed to describe the transient behavior of dry-expansion evaporators in the vapor-compression refrigeration system. To improve the robustness of the traditional moving-boundary model under larger disturbances, the time-variant mean void fraction is employed instead of the constant. Numerical integration is applied to get the mean properties in the two-phase region and the superheated region. The interface wall temperature between the two-phase and the superheated regions is also evaluated by a new weighted mean. Qualitative case study shows that the present model can well predict the transient behaviors of evaporators under larger disturbances and keep the robustness whenever superheated region appears or disappears.     

Dynamic behavior of a direct expansion evaporator under frosting condition. Part I. Distributed model

A general distributed model with two-phase flow for refrigerant coupled with a frost model is developed for studying the dynamic behavior of an evaporator. The equations are derived in non-steady-state manner for the refrigerant and a quasi-steady state model with permeation for the frost. The complex flow and geometry of the finned tube evaporator lead to uneven wall and air temperature distributions, which in turn affect the rate of frost growth and densification along the coil depth. Results include frost accumulation and its effect on energy transfer, air off-coil temperature, refrigerant liquid dry-out position and propagation of frost formation along the coil.     

Numerical simulation of non-adiabatic capillary tubes. Special emphasis on the near-saturation zone

The aim of this article is to present a distributed numerical model that simulates the thermal and fluid-dynamic phenomena inside non-adiabatic capillary tubes. The resolution approach is based on a two-phase flow model where the fluid domain is discretized in a one-dimensional way, and the governing equations (continuity, momentum, and energy) are solved by means of a step-by-step algorithm. The model explained herein consists of an improved and extended version of previous works (Escanes et al., 1995; García-Valladares et al., 2002a,b; Ablanque et al., 2010) including two additional features. On the one hand, it allows the simulation of the two typical geometric arrangements found in capillary-tube/suction-line heat exchangers (i.e. concentric and lateral). On the other hand, it has an enhanced capability to address the convergence difficulties found in distributed models at the near-saturation zone. This document presents the major numerical adaptations done to the model, a comprehensive validation of the two geometric configurations, the model performance when tackling the aforementioned numerical difficulties and finally, some numerical studies.     

Numerical simulation of dehumidifying fin-and-tube heat exchangers: Semi-analytical modelling and experimental comparison

The aim of this paper is to present a developed semi-analytical model for the simulation of dehumidifying air–liquid fin-and-tube heat exchangers. The simulation strategy and the mathematical methodology are described in detail. The model is based on -NTU method, and formulated in a compact way for dry and wet surface situations (temperature or enthalpy driven, respectively). Both rating and design procedures have been developed for fully dry, partially wet, or fully wet surface conditions. The model predictions are compared with experimental data obtained on a wavy and a plain finned heat exchanger, giving reasonably accurate results. The limitations of the empirical information used are clearly identified in the work. The aim of this model is to provide a fast but reliable rating and design numerical tool for air–liquid heat exchanger applications.     

Experimentation and modeling of refrigerant flow through coiled capillary tubes

Air-conditioners use spirally coiled capillary tubes as an expansion device to enhance compactness of the unit. However, most empirical correlations for predicting refrigerant flow rate through capillary tubes were developed for straight capillary tubes without consideration of coiled effects. The objectives of this study are to investigate the flow characteristics of the coiled capillary tubes and to develop a generalized correlation for the mass flow rate through the coiled capillary tubes. The mass flow rate of R22 through the coiled capillary tubes and straight capillary tubes was measured for various operating conditions and tube geometries. The mass flow rates of the coiled capillary tubes decreased by 5–16% more than those of the straight capillary tubes at the same operating conditions. A generalized correlation for predicting refrigerant mass flow rate through coiled capillary tubes was developed by introducing the parameter of capillary equivalent length. The present correlation showed good predictions with the present database for R22, R407C and R410A in the straight and coiled capillary tubes, yielding average and standard deviations of 0.24% and 4.4%, respectively.     

Influences of miscible and immiscible oils on flow characteristics through capillary tube—part I: experimental study

A capillary tube is widely used as an expansion device for small refrigeration cycles. In a practical refrigeration cycle, some amount of refrigeration oil is discharged from a compressor and refrigerant/oil mixture flows through the capillary tube. This study investigated experimentally the influence of mixing of the refrigeration oil with the refrigerant on the flow through the capillary tube. The experiments are carried out with not only a miscible combination of refrigerant and oil but also an immiscible combination. In both cases, the mass flow rate through the capillary tube and temperature and pressure distributions along the tube are measured under several conditions of subcooled degree and oil concentration. In the case of miscible combination, the mass flow rate of refrigerant decreases with increasing the oil concentration because the viscosity of liquid phase increases by the mixing of viscous oil. Even in the case of the immiscible combination, the oil droplet is so small that it mixes homogeneously in the liquid phase in the capillary tube and the refrigerant mass flow rate decreases by the mixing of immiscible oil. There is no significant influence of the oil concentration on the underpressure, which means pressure difference between saturation pressure and flash inception pressure, in both miscible and immiscible combinations.     

A comprehensive design and rating study of evaporative coolers and condensers. Part II. Sensitivity analysis

Sensitivity analysis can be used to identify important model parameters, in particular, normalized sensitivity coefficients; by allowing a one-on-one comparison. Regarding design of evaporative coolers, the sensitivity analysis shows that all sensitivities are unaffected by varying the mass flow ratio and that outlet process fluid temperature is the most important factor. In rating evaporative coolers, effectiveness is found to be most sensitive to the process fluid flow rate. Also, the process fluid outlet temperature is most sensitive to the process fluid inlet temperature. For evaporative condensers, the normalized sensitivity coefficient values indicate that the condensing temperature is the most sensitive parameter and that these are not affected by the value of the mass flow ratio. For evaporative condenser design, it was seen that, for a 53% increase in the inlet relative humidity, the normalized sensitivity of the surface area increased 1.8 times in value and, for a 15 °C increase in the condenser temperature, the sensitivity increased by 3.5 times. The performance study of evaporative condensers show that, for a 72% increase in the inlet relative humidity, the normalized sensitivity coefficient for effectiveness increased 2.4 times and, for a 15 °C increase in the condenser temperature, it doubled in value.     

A dynamic simulation model for transient absorption chiller performance. Part I: The model

This paper is the first of two which presents the development of a dynamic model for single-effect LiBr/water absorption chillers. The model is based on external and internal steady-state enthalpy balances for each main component. Dynamic behaviour is implemented via mass storage terms in the absorber and generator, thermal heat storage terms in all vessels and a delay time in the solution cycle. A special feature is that the thermal capacity is partly connected to external and partly to internal process temperatures.In this paper, the model is presented in detail. For verification, the model has been compared to experimental data. The dynamic agreement between experiment and simulation is very good with dynamic deviations around 10 s. General functionality of the model and a more detailed comparison with experimental data are presented in Part II of this paper.     

Modified neural network correlation of refrigerant mass flow rates through adiabatic capillary and short tubes: Extension to CO2 transcritical flow

This paper presents a modified dimensionless neural network correlation of refrigerant mass flow rates through adiabatic capillary tubes and short tube orifices. In particular, CO₂ transcritical flow is taken into account. The definition of neural network input and output dimensionless parameters is grounded on the homogeneous equilibrium model and extended to supercritical inlet conditions. 2000 sets of experimental mass flow-rate data of R12, R22, R134a, R404A, R407C, R410A, R600a and CO₂ (R744) in the open literature covering capillary and short tube geometries, subcritical and supercritical inlet conditions are collected for neural network training and testing. The comparison between the trained neural network and experimental data reports 0.65% average and 8.2% standard deviations; 85% data fall into ±10% error band. Particularly for CO₂, the average and standard deviations are −2.5% and 6.0%, respectively. 90% data fall into ±10% error band.     

Experimental investigation and numerical simulation on the hysteresis zone of a variable displacement wobble plate compressor

A test system with the variable displacement compressor (VDC) for automotive air conditioning system is built to study the changing rule of piston stroke length (PSL). It is found from our experiments that the critical suction pressure where the PSL starts to decrease is less than that where the PSL starts to increase for the same PSL; between the two critical lines, a hysteresis zone is formed, within which all the steady-state points fall and there is a multiple-valued relationship between VDC parameters; and the PSL is kept invariable when the VDC parameters change within the hysteresis zone. In order to find out the reason causing the hysteresis zone and to analyze the influence of the compressor parameters on the hysteresis zone, a steady-state mathematical model of VDC is developed and verified by our experimental data. The theoretical analysis indicates that the hysteresis zone is caused by the frictional forces among the moving components of VDC, and the greater the frictional forces, the broader the hysteresis zone and the larger the changing range of suction pressure. The influence of the discharge pressure and rotary speed on the hysteresis zone is that the hysteresis zone moves in the direction of the suction pressure decreasing along with the increase of the discharge pressure or rotary speed.     

Instability of automotive air conditioning system with a variable displacement compressor. Part 2. Numerical simulation

A test system is built first in order to investigate the instability of the automotive air conditioning (AAC) system with a variable displacement compressor (VDC), and hunting phenomena caused by the large external disturbance in the AAC system with a VDC and a thermal expansion valve, and in the AAC system with a VDC and a fixed-area throttling device are investigated experimentally in part 1 of this paper. The experimental results indicate that there also exist the hunting phenomena in the AAC system with a fixed-area throttling device. The system stability is found to be dependent on the direction of the external disturbance, and the system is apt to cause hunting when the condensing pressure decreases excessively since it may cause two-phase state at the throttling device inlet and make a large disturbance to the system. The piston stroke length will oscillate only when the oscillation amplitudes of forces acting on the wobble plate are great enough, otherwise the piston stroke length will be kept invariable, and then the system instability rule is also suitable for the AAC system with a fixed displacement compressor. From the experimental results, it is concluded that the two-phase flow at the throttling device inlet or at the evaporator outlet is the necessary condition but not sufficient condition for system hunting. Finally, a new concept, conservative stable region, is proposed based on the experimental results and theoretical analysis.     

Study of a novel silica gel–water adsorption chiller. Part II. Experimental study

The prototype of a novel silica gel–water adsorption chiller is built and its performance is tested in detail. The experimental results show that the refrigerating capacity (RC) and COP of the chiller are 7.15 and 0.38 kW, respectively, when the hot water temperature is 84.8 °C, the cooling water temperature is 30.6 °C, and the chilled water outlet temperature is 11.7 °C. The RC will reach 6 kW under the condition of 65 °C hot water temperature, 30.5 °C cooling water temperature and 17.6 °C chilled water temperature. The results confirm that this kind of adsorption chiller is an effective refrigerating machine though its performance is not as fine as the prediction results. Also it is well effectively driven by a low-grade heat source. Therefore, its applications to the low-grade heat source are much attractive.     

Experimental correlation of pool boiling heat transfer for HFC134a on enhanced tubes: Turbo-E

The objectives of this paper are to study the heat transfer characteristics for enhanced surface tubes in the pool boiling and to provide a guideline for the design conditions for the evaporator using HFC134a. The shape of tube surfaces, the wall superheat, and the saturation temperature are considered as the key parameters. Copper tubes (d_o = 19.05 mm) are treated with different helix angles and the saturation temperatures are controlled from 3 to 16 °C. It is found that the pool boiling heat transfer coefficient decreases with increasing the wall superheat. It is also found that boiling heat transfer coefficients for Turbo-II and Turbo-III are 1.5–3.0 times and 1.2–2.0 times higher than that for Turbo-I without the helix angle, respectively. The higher heat transfer performance from Turbo-II and Turbo-III can be explained by the “bubble detention” phenomenon on the surface without the helix angle for the Turbo-I. The experimental correlations for the pool boiling heat transfer on the present enhanced tubes without (Type I) and with the helix angle (Type II and Type III) are developed with the error bands of ±30%, respectively.     

The impact of fouling on the performance of filter–evaporator combinations

This paper presents results of experiments performed on different combinations of five types of filters of varying efficiencies (MERV4, 6, 8, 11, and 14) and four types of evaporator coils with depths and fin geometries under clean and fouled conditions. The fouled conditions were obtained after injection of 600 g (1612 g/m² of coil face area) of dust upstream of the filter–coil combination, which was meant to simulate a year of operation in the field. The air-side pressure drops of the coils and filters and air-side effective heat transfer coefficients of the coils were determined from the measurements under the clean and fouled conditions. Depending upon the filter and coil, the coil pressure drops increased in the range of 6–30% for an air velocity of 2.54 m/s. The impact was significantly greater for tests performed without an upstream filter (the coil pressure drops increased from 43% to 200%). The largest relative effect of fouling on pressure drop occurs for coils with fewer rows, primarily due to higher fin densities. The impact of fouling on air-side effective heat transfer coefficients was found to be relatively small, which ranged from −14% to 4%. In some cases, heat transfer was actually enhanced due to additional turbulence caused by the presence of dust. However, with large dust deposits, heat transfer is degraded because the dust also acts as insulation and creates an uneven air velocity.     

CO2 flow condensation heat transfer and pressure drop in multi-port microchannels at low temperatures

CO₂ flow condensation heat transfer coefficients and pressure drop are investigated for 0.89 mm microchannels at horizontal flow conditions. They were measured at saturation temperatures of −15 and −25 °C, mass fluxes from 200 to 800 kg m⁻² s⁻¹, and wall subcooling temperatures from 2 to 4 °C. Flow patterns for experimental conditions were predicted by two flow pattern maps, and it could be predicted that annular flow patterns could exist in most of flow conditions except low mass flux and low vapor quality conditions. Measured heat transfer coefficients increased with the increase of mass fluxes and vapor qualities, whereas they were almost independent of wall subcooling temperature changes. Several correlations could predict heat transfer coefficients within acceptable error range, and from this comparison, it could be inferred that the flow condensation mechanism in 0.89 mm channels should be similar to that in large tubes. CO₂ two-phase pressure drop, measured in adiabatic conditions, increased with the increase of mass flux and vapor quality, and it decreased with the increase of saturation temperature. By comparing measured pressure drop with calculated values, it was shown that several correlations could predict the measured values relatively well.     

Experimental study on a new internally cooled/heated dehumidifier/regenerator of liquid desiccant systems

For providing good performance of dehumidifier and regenerator with certain dimensions, a new type of internally cooled/heated dehumidifier/regenerator based on the plate–fin heat exchanger (PFHE) was designed. To investigate the behavior of the new equipment, an experimental setup was established in an environment chamber with regulable temperature and humidity air. By the internally cooled dehumidification testing, effects of the cooling water temperature, the air flow rate and the desiccant temperature on the dehumidification performance and the cooling efficiency were presented. The behavior of internally cooled dehumidification process was compared with that of the adiabatic dehumidification process. The results suggested that the cooling efficiency decreased with the increasing of the cooling water temperature and desiccant with low temperature could bring more mass transfer coefficients. There is an optimal air flow rate to achieve the maximum absolute humidity decrease of the air. By the internally heated regeneration testing, effects of the air flow rate and the desiccant inlet temperature on the regeneration performance and air outlet parameters were discussed and also compared with those of the adiabatic regeneration process. It was concluded that the regeneration efficiency of internally heated regeneration was more than that of the adiabatic regeneration, and the internally heated regenerator could offer better thermal performance.     

A novel special distributed method for dynamic refrigeration system simulation

A novel dynamic mathematical model based on spatially distributed approach has been developed and validated in this paper. This model gives good agreement in predicting the system COP and other parameters. The validated model has been used to enhance the prediction of the micro variations of superheat and sub-cooling. The novel spatial distributed model for the condenser and evaporator in refrigeration system, calculates the two-phase region in gas and liquid field separately since the gas and liquid in the two-phase region have different velocities. Previous researchers have used a pre-defined function of the void fraction in their spatially distributed model, based on experimental results. This approach results in the separate solution of the mass and energy equations, and less calculation is required. However, it is recognized that the mass and energy equations should be coupled during solving for more accurate solution. Based on the energy and mass balance, the spatial distribution model constructed here solves the velocity, pressure, refrigerant temperature, and wall temperature functions in heat exchangers simultaneously. A novel iteration method is developed and reduces the intensive calculations required. Furthermore, the condenser and evaporator models have shown a parametric distribution along the heat exchanger surface, therefore, the spatial distribution parameters in the two heat exchangers can be visualised numerically with a two-phase moving interface clearly shown.