A state-space dynamic model for vapor compression refrigeration system based on moving-boundary formulation

A transient response model for vapor compression refrigeration system has been developed in the paper. The system model contains four sub-models representing condenser, evaporator, compressor and electronic expansion valve (EEV). The condenser and the evaporator are developed based on the moving-boundary formulation. Through linearization, these dynamic models are transformed into state-space representation which is expressed in the form of matrix. The compressor and EEV adopt steady models because their thermal inertia is much smaller compared with the heat exchangers (i.e., condenser and the evaporator). The system model has been validated by experiment in terms of step change of EEV opening degree and heat load as well as ramp increase of inlet temperature of coolant oil of condenser. The results show that the model simulations have a good agreement with the experimental data. The simulation errors compared with the experimental data are mostly less than 10%. Since the model proposed in this study is expressed in the form of state-space matrix, they are featured by strong portability and high computation efficiency. It allows us to investigate the thermal dynamic characteristics of a refrigeration system under any complicated conditions and develop excellent control schemes.     

Heat Capacities and Joule–Thomson Coefficients of HFC Refrigerants

In this report, we have examined the behavior of heat capacities and Joule–Thomson coefficients in low- and moderate-density regions based on recent theoretical studies of the ideal-gas heat capacity and virial coefficients of R-32, R-125, R-134a, R-143a, and R-152a. The results have been compared with those derived from empirical equations of state which have been recently developed, based on a large quantity of experimental data for these refrigerants. Both results are in good agreement. Proper behaviors for these second-derivative properties justify the use of the empirical equations of state in low-temperature and low-density regions where no experimental data are available.     

Dynamic simulation and optimal matching of a small-scale refrigeration system

This paper describes a principle and method of optimal matching to reduce energy consumption in small-scale refrigeration systems, based on systems analysis. A knowledge of the dynamic characteristics of a refrigeration system is important for predicting the performance of the system. A simulation model of a refrigeration system consisting of a compressor, an evaporator, a condenser and a capillary tube has been established to illustrate optimal matching. For each component a mathematical model has been developed, in which the concept of transient and distributive is introduced. On the basis of dynamic simulation, a method of optimal matching to minimize power consumption is recommended. To test the reliability of the theoretical models, an experiment was carried out on a small-scale refrigeration system. The experimental data were compared with the theoretical results and it is shown that the theory is valid.     

Thermodynamic Properties of Mixtures of R-32, R-125, R-134a, and R-152a

A mixture model explicit in Helmholtz energy has been developed that is capable of predicting thermodynamic properties of refrigerant mixtures containing R-32, R-125, R-134a, and R-152a. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single equation that is applied to all mixtures used in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate thermodynamic properties of mixtures, including dew and bubble point properties and critical points, generally within the experimental uncertainties of the available measured properties. It incorporates the most accurate published equation of state for each pure fluid. The estimated uncertainties of calculated properties are ±0.25% in density, ±0.5% in the speed of sound, and ±1% in heat capacities. Calculated bubble point pressures are generally accurate to within ±1%.     

Multivariable control-oriented modeling of a direct expansion (DX) air conditioning (A/C) system

A dynamic mathematical model for a DX A/C system has been developed. The dynamic model, written in state-space representation which was suitable for designing multivariable control, was linearized at steady state operating points. The linearized model has been validated by comparing the model simulation results with the experimental data obtained from an experimental DX A/C system. The simulated results agreed well with the experimental data, suggesting that the model developed was able to capture the transient characteristics of the DX A/C system modeled. It is expected that the model developed can be useful in designing a multi-input multi-output (MIMO) controller to simultaneously control indoor air temperature and humidity in a space served by a DX A/C system.     

A hybrid transient model for simulation of air-cooled refrigeration systems: Description and experimental validation

In this paper are described a hybrid dynamic model for transient simulation of refrigeration systems as well as dynamic experiments that have been performed on an air/water heap pump. The machine under consideration is made of an evaporator, a condenser, an expansion valve, a variable speed scroll compressor and a receiver. The refrigerant and second fluid flows in heat exchangers are approximated by a cascade of Continuous Stirred Tank Reactors (CSTRs). This model is quite flexible since a unique structure is used for the evaporator and the condenser models according to different boundary conditions. This is due to the use of a switching procedure between different configurations based on a phase stability test that is designed to ensure the continuity of the system simulation. An analytical thermodynamic model of the refrigerant based on an equation of state is used. Good agreement between simulation results and experimental data is achieved.     

Thermodynamic Properties for R-404A

An 18-coefficient modified Benedict–Webb–Rubin equation of state has been developed for R-404A, a ternary mixture of 44% by mass of pentafluoroethane (R-125), 52% by mass of 1,1,1-trifluoroethane (R-143a), and 4% by mass of 1,1,1,2-tetrafluoroethane (R-134a). Correlations of bubble point pressures, dew point pressures, saturated liquid densities, and saturated vapor densities are also presented. This equation of state has been developed based on the reported experimental data of PVT properties, saturation properties, and isochoric heat capacities by using least-squares fitting. These correlations are valid in the temperature range from 250 K to the critical temperature. This equation of state is valid at pressures up to 19 MPa, densities to 1300 kg·m^–3, and temperatures from 250 to 400 K. The thermodynamic properties except for the saturation pressures are calculated from this equation of state.     

Distributed steady and dynamic modelling of dry-expansion evaporators: Modèlisation du régime stable et du régime transitoire des évaporateurs à détente sèche

A general distributed parameter model is presented to describe both steady and dynamic behaviors of dry-expansion evaporators. The homogeneous and three different non-homogeneous two-phase flow models are used to evaluate the impact of different flow models on the accuracy of the simulation. The experimental work was carried out on a full-scale refrigeration system with R-134a as the working fluid and without frost formation at the evaporator. Comparison between the modelling and experimental measurements shows that the drift flux flow models give satisfactory predictions. The simulation results indicate that an even air temperature distribution off the evaporator may be obtained by controlling liquid dry-out point at the two ends of the coil. The study also indicates that the counterflow configuration provides a higher heat exchange efficiency with a slower transient response compared with the cocurrent-flow configuration. A general distributed parameter model is presented to describe both steady and dynamic behaviors of dry-expansion evaporators. The homogeneous and three different non-homogeneous two-phase flow models are used to evaluate the impact of different flow models on the accuracy of the simulation. The experimental work was carried out on a full-scale refrigeration system with R-134a as the working fluid and without frost formation at the evaporator. Comparison between the modelling and experimental measurements shows that the drift flux flow models give satisfactory predictions. The simulation results indicate that an even air temperature distribution off the evaporator may be obtained by controlling liquid dry-out point at the two ends of the coil. The study also indicates that the counterflow configuration provides a higher heat exchange efficiency with a slower transient response compared with the cocurrent-flow configuration.     

Exergy maximization of cascade refrigeration cycles and its numerical verification for a transcritical CO2–C3H8 system

Analysis of an endoreversible two-stage cascade cycle has been implemented and optimum intermediate temperature for maximum exergy and refrigeration effect have been obtained analytically. Further, the heat reservoir temperatures has been optimised independently. A comprehensive numerical model of a transcritical CO₂–C₃H₈ cascade system was developed with intent to verify the theoretical results. It is seen that the simulation results agree well for optimal T_L but deviate modestly from the theoretical optimum of T_H. It has also been observed that system performance improves as T_H increases and unlike theoretical predictions, no optimal T_H is present within feasible working temperatures.     

Continuous/discrete simulation of controlled atmosphere (CA) cool storage systems: model development and validation using pilot plant CA cool storage

Simulation of dynamic processes in controlled atmosphere (CA) cool room storage systems has been developed. The model consists of three interacting sub-models for the prediction of the transient behavior of the processes in the three units, namely, the cool room, the refrigeration system and the gas-handling unit. Several modules representing each of the components in these units were developed based on energy and mass balances. The modules were then arranged to form the sub-models, which were interconnected, in turn, into the global CA cool storage system model. The modules were implemented in an object-oriented computational environment, (EcosimPro) which can handle both continuous and discrete events. The model was validated using experimental data from a pilot plant CA cool storage facility. Model predictions of the most important discrete and continuous processes were found to agree to the experimental data with a maximum difference less than the observed spatial variability or at best with the accuracy level as set by the measurement instruments. As product respiration and quality models are incorporated, it is possible to use the model for optimization of plant performance with respect to the final quality of the stored product. Moreover, the handling of discrete/continuous events enables the implementation of practical operational procedures and to investigate their implication directly on the product quality and plant performance/design.     

Second-law-based thermodynamic analysis of two-stage and mechanical-subcooling refrigeration cycles

Thermodynamic analysis of HFC-134a vapor-compression refrigeration cycles is investigated by both the first and second laws of thermodynamics. Second-law analysis is carried out for both two-stage and mechanical-subcooling refrigeration cycles. The analysis is performed on each of the system components to determine their individual contribution to the overall system irreversible losses. It is found that most of the losses are due to a low compressor efficiency. Irreversibilities of expansion valves and condenser are also significant. In addition, it is shown that the optimum inter-stage pressure for two-stage and mechanical-subcooling refrigeration systems is very close to the saturation pressure corresponding to the arithmetic mean of the refrigerant condensation and evaporation temperatures. These results are compared with the existing practice in the industry. Furthermore, theoretical results of a two-stage refrigeration system performance are also compared with experimental values for a CFC-22 system.     

The substitution of R134a with R744: An exergetic analysis based on experimental data

This paper deals with the problem of R314a substitution with a natural refrigerant fluid. A comparison is performed between R134a and R744 (CO₂). R134a is a hydrofluorocarbon with a large direct warming impact (GWP), whereas the R744 contribution is negligible. A comparative exergetic analysis, carried out with experimental tests, has been presented. This paper compares a commercial R134a refrigeration plant and a prototype R744 system working in a trans-critical cycle. Based on the experimental data an exergetic analysis has been carried out on the overall plant and on each device. The overall exergetic performances of the classical vapour compression plant working with R134a are consistently better than that of R744 (from a minimum of 20 to a maximum of 44%). The performance of the individual components of the plant has been analyzed, in order to pinpoint those contributing most to the decrease in the exergetic performance of R744.     

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.     

Thermal stability of R-134a, R-141b, R-13I1, R-7146, R-125 associated with stainless steel as a containing material

An experimental apparatus for assessing the thermal stability threshold of refrigerant working fluids is described and results for R-134a (1,1,1,2-tetrafluoroethane), R141b (1,1-dichloro-1-fluoroethane), R-13I1 (trifluoromethyl iodide), R-7146 (sulphur hexafluoride), R-125 (pentafluoroethane) are presented. The information is a concern for the design of refrigeration systems, high temperature heat pumps and Organic Rankine Cycles (ORC), for which the above refrigerants are proposed. The method aims to identify a maximum temperature for plant operation in contact with stainless steel and involves the evaluation of four indicators: (1) pressure variation while the fluid is maintained at set temperature; (2) saturation pressure comparison after heat treatment; (3) chemical analysis; and (4) vessel visual inspection after the test session. The highest temperatures at which no evident degradation occured are: 368°C for R-134a; 102°C for R-13I1; 90°C for R-141b; 204°C for R-7146; and 396°C for R-125.     

改进的R23/R134a自复叠制冷系统试验台设计

为了研究R23/R134a混合工质自复叠制冷系统在变工况下的运行性能,更深入地了解系统各部件对自复叠循环的影响,设计一套试验装置。该装置对现有循环流程进行改进,增加了电磁阀、膨胀容器等部件。对该系统的运行工况、参数范围以及系统的各部件进行设计或选型,并介绍所搭建的试验台。     

Numerical simulation and experimental validation of vapour compression refrigeration systems. Special emphasis on CO2 trans-critical cycles

A numerical and experimental comparative study of a carbon dioxide trans-critical refrigerating system and a conventional sub-critical refrigerating cycle is presented. Attention is focussed not only on the whole refrigeration cycle, but also on the behaviour of the hermetic reciprocating compressors used in these systems. The comparative cases presented have been specially designed for small cooling capacity units with an evaporation temperature around 0 °C. A detailed numerical simulation model for hermetic reciprocating compressors performance, widely validated under conventional fluid refrigerants, has been extended to numerically obtain the CO₂ compressor prototypes behaviour. Two CO₂ compressor prototypes working with CO₂ have been experimentally tested in a specific unit, specially designed and built to analyse high-pressure single stage vapour compression trans-critical refrigerating equipments. This set-up has allowed validating a detailed numerical simulation code for the thermal and fluid-dynamic behaviour of single stage vapour compression refrigeration system working with CO₂ as fluid refrigerant. The numerical results and the experimental data obtained to validate compressors, heat exchangers and whole cycle behaviour have shown a really good agreement. Finally, the numerical and experimental comparison between the carbon dioxide system and the sub-critical conventional cycle has shown the possibility of CO₂ as fluid refrigerant under the studied working conditions.     

多元混合工质节流制冷机内工质组分浓度变化特征的实验研究

建立了专门实验系统来研究多元混合工质闭式循环节流制冷机内工质组元浓度动态变化特征，针对三个典型制冷温区的三种混合物工质进行了实验研究，研究结果表明，混合物工质浓度在不同运行时期发生变化，最大变化会达到6％，另外系统内浓度不均匀更会高达12％，甚至更高，实验研究对修正理论模拟模型以及制冷机设计具有帮助。     

Simulation of the transient response of heat driven refrigerators with continuous temperature control Simulation de la réponse transitoire des réfrigérateurs utilisant une source de chaleur avec maîtrise de la température en continu

A theoretical and experimental study is presented and a mathematical model is introduced for a heat driven refrigeration system operating with continuous temperature control. The model consists of a refrigerated space, an absorption refrigerator, operating irreversibly, a temperature sensor and a reference signal, and a power law control action. The steady-state behavior of the absorption refrigerator model is validated by direct comparison between theoretical results and experimental data. The model is then used to identify an optimal thermal conductance allocation, for a fixed total thermal conductance inventory, such that the refrigeration rate is maximized and the ‘pull-down' time is minimized. A simulation of the system operating in a transient mode is carried out to show that closed-loop operation results in a large reduction of fuel consumption, with respect to the ‘on–off' operation. Appropriate dimensionless groups are identified and the generalized results reported in charts using dimensionless variables.     

Ejector design and theoretical study of R134a ejector refrigeration cycle

In the present paper, a mathematical model is developed to design R134a ejector and to predict the performance characteristics of a vapor jet refrigeration system over a wide range of the investigated parameters. These parameters include boiling temperature (65–85 °C), condensing temperature (25–40 °C), evaporating temperature (0–10 °C), degrees of superheat (0–15 °C), nozzle efficiency (0.75–0.95) and diffuser efficiency (0.75–0.95). Simulated results showed that the present model data are in good agreement with experimental data in the literature with an average error of 6%. It is found that the ejector area ratio at boiling temperature of 85 °C is about double that at boiling temperature of 65 °C for various evaporating and condensing temperatures. The present results confirm that waste heat sources of temperature ranging from 65 to 85 °C are adequate to operate vapor jet refrigeration system for air-conditioning applications.     

Thermodynamic properties of 1,1,1,2-tetrafluoroethane (R-134a) + 2,3,3,3-tetrafluoropropene (R-1234yf) mixtures: Measurements of the critical parameters and a mixture model based on the multi-fluid approximation

Thermodynamic properties are discussed for 1,1,1,2-tetrafluoroethane (R-134a) + 2,3,3,3-tetrafluoropropene (R-1234yf) mixtures. The critical temperatures, densities, and pressures experimentally determined are first presented with their uncertainties. Subsequently a mixture model for calculations of thermodynamic properties is formulated using the multi-fluid approximation. Comparisons to experimental data show that the mixture model calculates the vapor–liquid equilibrium and densities of the mixtures with reasonable accuracies. The critical parameters are also well represented by the mixture model.