Development and validation of “grey-box” models for refrigeration applications: A review of key concepts

“Grey-box” modelling combines the use of first-principle based “white-box” models and empirical “black-box” models, offering particular benefits when: (a) there is a lack of fundamental theory to describe the system or process modelled; (b) there is a scarcity of suitable experimental data for validation or (c) there is a need to decrease the complexity of the model. The grey-box approach has been used, for example, to create mathematical models to predict the shelf life of chilled products or the thermal behaviour of imperfectly mixed fluids, or to create models that combine artificial neural networks and dynamic differential equations for control-related applications. This paper discusses the main characteristics of white-box, black-box and their integration into grey-box models, the requirements and sourcing of accurate data for model development and important validation concepts and measures.     

Modeling absorption of pure refrigerants and refrigerant mixtures in lubricant oil

This paper addresses the problem of absorption of refrigerant vapor in a stagnant layer of lubricant oil. The bulk motion of the solute is described in terms of apparent diffusion coefficients that encompass both molecular diffusion and possible macroscopic motion induced by liquid density instability and surface tension. In absorption of refrigerant mixtures, diffusion in the vapor and liquid phases are coupled with a thermodynamic model for interfacial equilibrium. Results are compared with experimental data available in the literature for absorption of several refrigerants in polyol ester oil (POE68). The adequacy of the formulation is assessed in the light of its basic assumptions and performance of the model.     

Real-time measurement of mixing ratio of refrigerant/refrigeration oil mixture

The mixing of refrigeration oil with refrigerant in a refrigeration cycle has great influence on cycle performance. A sampling method is the most general way to measure the mixing ratio of refrigerant and refrigeration oil. Since the sampling method is time-consuming and reduces the amount of refrigerant and oil in the cycle, a real-time measurement is desirable. In this study, a refractive index measurement was applied to measure the mixing ratio of refrigerant/oil mixture. A laser displacement sensor was used to detect any change in optical path which results from changes of the refractive index of refrigerant/oil mixture. For the practical application of real-time measurement of the oil circulation ratio (OCR) in the refrigeration cycle, a correlation between the refractive index and the mixing ratio was developed. In addition, the changes of the refractive index in a range of a few percentages of the oil concentration and under subcooled conditions were measured. Finally, a transient measurement of the OCR in a practically operating refrigeration cycle was carried out successfully.     

An experimental investigation and modelling of the thermodynamic properties of isobutane–compressor oil solutions: Some aspects of experimental methodology

This paper presents experimental data for the solubility, density and capillary constant for solutions of natural refrigerant isobutane with commercial mineral compressor oil Azmol over a wide range of temperatures and concentrations. Based on information for the capillary constant, the surface tension of the solutions isobutane/Azmol is determined. The experimental data were obtained in the temperature range from 303 K to 363 K and at pressures up to 1.7 MPa using static methods. The experimental data obtained for the solutions of the natural refrigerant isobutane with the commercial mineral compressor oil Azmol are sufficiently described with the help of correlations based on the theory of thermodynamic similarity. The paper reports variation of the vapor pressure, density, capillary constant and surface tension as a function of concentration for the isobutane/Azmol solutions. The enthalpy of liquid phase of the isobutane/Azmol solutions is calculated. The analysis of the behaviour of the excess thermodynamic functions is carried out. The paper examines experimental and methodical uncertainties in the investigation of thermodynamic properties of the refrigerant/oil solutions (ROS). The influence of the time taken to establish thermodynamic equilibrium in the experimental cell on the uncertainty of the experimental data for gas-saturated mixtures such as ROS is discussed. Information about the changing concentration of refrigerant in the liquid phase of the ROS and in the surface layer of the liquid phase of the ROS at increasing temperature is presented. In addition, the experimental data for the density, surface tension and refractive index of the mineral compressor oil Azmol are reported.     

Recent developments in simulation techniques for vapour-compression refrigeration systems

Simulation has been widely used for performance prediction and optimum design of refrigeration systems. A brief review on history of simulation for vapour-compression refrigeration systems is done. The models for evaporator, condenser, compressor, capillary tube and envelop structure are summarized. Some developing simulation techniques, including implicit regression and explicit calculation method for refrigerant thermodynamic properties, model-based intelligent simulation methodology and graph-theory based simulation method, are presented. Prospective methods for future simulation of refrigeration systems, such as noise-field simulation, simulation with knowledge engineering methodology and calculation methods for nanofluid properties, are introduced briefly.     

Use of ejectors in a multi-evaporator refrigeration system for performance enhancement

In this study, an improved cooling cycle for a conventional multi-evaporators simple compression system utilizing ejector for vapour precompression is analyzed. The ejector-enhanced refrigeration cycle consists of multi-evaporators that operate at different pressure and temperature levels. A one-dimensional mathematical model of the ejector was developed using the equations governing the flow and thermodynamics based on the constant-area ejector flow model. The model includes effects of friction at the constant-area mixing chamber. The energy efficiency and the performance characteristics of the novel cycle are theoretically investigated. The comparison between the novel and conventional system was made under the same operating conditions. Also, a comparison of the system performances with environment friendly refrigerants (R290, R600a, R717, R134a, R152a, and R141b) is made. The theoretical results show that the COP of the novel cycle is better than the conventional system.     

Stress corrosion cracking in refrigeration systems

It is generally understood that stress corrosion cracking can occasionally affect the high pressure vessels in ammonia refrigeration systems, but the nature of the problem is often mis-represented in design codes, safety standards and textbooks and ways in which the initiation of stress corrosion can be prevented are ignored. It is also not appreciated that stress corrosion can also affect low pressure vessels and pipework in ammonia systems, and copper pipework in fluorocarbon refrigeration systems.This paper provides an overview of published literature on stress corrosion cracking and then presents some recent case study material illustrating various ways in which stress corrosion has arisen in practice. The conclusions will provide guidance for design engineers and equipment owners on eliminating stress corrosion cracking and on dealing with it if it arises.     

Modelling of food transportation systems – a review

In 2002, over a million refrigerated road vehicles, 400,000 refrigerated containers and many thousands of other forms of refrigerated transport systems are used to distribute chilled and frozen foods throughout the world. All these transportation systems are expected to maintain the temperature of the food within close limits to ensure its optimum safety and high quality shelf life.Increasingly, modelling is being used to aid the design and optimisation of food refrigeration systems. Much of this effort has concentrated on the modelling of refrigeration processes that change the temperature of the food such as chilling, freezing and thawing. The purpose of a refrigerated transport system is to maintain the temperature of the food and appears to have attracted less attention from modellers. This paper reviews the work that has been carried out specifically on the modelling of food temperature, microbial growth and other parameters in the transportation of food.     

Comprehensive investigation of numerical methods in simulating a steady-state vapor compression system

Computer simulation has become a required tool in the design phase of vapor compression systems; however with relatively few exceptions most simulations focus on the basic four component systems. With an increasing focus being placed on energy efficiency, the simulation of multi-component vapor compression systems (having multiple evaporators, condenser or compressors) will become essential to assist in the design of these more complicated systems. The implementation of a component-based framework will facilitate the simulation of multi-component systems. This paper describes three algorithms used to simulate a component-based vapor compression system. A test matrix of 6174 sample runs covering a wide range of operating conditions was constructed to determine the robustness and speed of each method when using three different types of nonlinear equation solvers. Each method was tested by simulating a basic four component cycle and a more advanced multiple evaporator system. The results are presented in such a format as to describe the reasons that contribute to any instability of the solvers and the computational efficiency of each method is discussed.     

Review on research of room temperature magnetic refrigeration

Room temperature magnetic refrigeration is a new highly efficient and environmentally protective technology. Although it has not been maturely developed, it shows great applicable prosperity and seems to be a substitute for the traditional vapor compression technology. In this paper, the concept of magnetocaloric effect is explained. The development of the magnetic material, magnetic refrigeration cycles, magnetic field and the regenerator of room temperature magnetic refrigeration is introduced. Finally some typical room temperature magnetic refrigeration prototypes are reviewed.     

Hydrocarbons as refrigerants in small heat pump and refrigeration systems – A review

Due to the concern for the effects of the release of HFC refrigerants on the global environment caused by the high global warming potential of these substances, there is a large interest in Europe and elsewhere for the use of hydrocarbons as refrigerants. This article presents a comparison of the properties and performance of hydrocarbons as refrigerants in small-size heat pump and refrigeration systems (<20 kW cooling). A listing of several commercially available systems is also presented. The designs, safety precautions and performances of some of these systems are described.As a general conclusion, it is shown that using hydrocarbons will result in COPs equal to, or higher than, those of similar HFC systems. It is also shown that components suitable for hydrocarbon systems are available on the market, even though the number of large-size hermetic compressors is limited. A major concern, which should not be taken lightly, is the safety issue. Reduced charge through indirect systems and compact heat exchangers, outdoor placing of the unit, hydrocarbon sensors and alarms and forced ventilation are all steps which may be applied to reduce the risks under normal operation.     

Numerical simulation of a variable speed refrigeration system

This work presents two numerical models to simulate the transient and steady state behavior of a vapor compression refrigeration system. The condenser and the evaporator were divided into a number of control volumes. Time dependent partial differential equations system was obtained from the mass, energy and momentum balances for each control volume. As the expansion valve and the compressor both have very small thermal inertia, the steady state models were applied for these components. Transient and steady state models numerical predictions were compared and good agreement was found. Further simulations were performed with the objective of verifying the possibility of controlling the refrigeration system and the superheating of the refrigerant in the evaporator outlet by varying the compressor speed and the throttling valve sectional area. The results indicate that the proposed models can be used to formulate an algorithm for controlling a refrigeration system.     

A general thermodynamic framework for understanding the behaviour of absorption chillersCadre thermodynamique facilitant la compréhension du comportement des refroidisseurs à absorption

In this article, a general definition of the process average temperature has been developed, and the impact of the various dissipative mechanisms on 1/COP of the chiller evaluated. The present component-by-component black box analysis removes the assumptions regarding the generator outlet temperature(s) and the component effective thermal conductances. Mass transfer resistance is also incorporated into the absorber analysis to arrive at a more realistic upper limit to the cooling capacity. Finally, the theoretical foundation for the absorption chiller T–s diagram is derived. This diagrammatic approach only requires the inlet and outlet conditions of the chiller components and can be employed as a practical tool for system analysis and comparison.     

Experimental investigation on R134a vapour ejector refrigeration system

The experimental investigation of the performance of a vapour ejector refrigeration system is described. The system uses R134a as working fluid and has a rated cooling capacity of 0.5 kW. The influence of generator, evaporator and condenser temperatures on the system performance is studied. This kind of system can be operated with low grade thermal energy such as solar energy, waste heat, etc. The operating conditions are chosen accordingly as, generator temperature between 338 K and 363 K, condenser temperature between 299 K and 310.5 K, and evaporator temperature between 275 K and 285.5 K. Six configurations of ejectors of different geometrical dimensions are selected for the parametric study. The performance of the refrigeration system at different operating temperatures is presented.     

Solar refrigeration options – a state-of-the-art review

A state-of-the-art review is presented of the different technologies that are available to deliver refrigeration from solar energy. The review covers solar electric, solar thermal and some new emerging technologies. The solar thermal systems include thermo-mechanical, absorption, adsorption and desiccant solutions. A comparison is made between the different solutions both from the point of view of energy efficiency and economic feasibility. Solar electric and thermo-mechanical systems appear to be more expensive than thermal sorption systems. Absorption and adsorption are comparable in terms of performance but adsorption chillers are more expensive and bulkier than absorption chillers. The total cost of a single-effect LiBr–water absorption system is estimated to be the lowest.     

Application of an ejector in autocascade refrigeration cycle for the performance improvement

This paper presented a novel autocascade refrigeration cycle (NARC) with an ejector. In the NARC, the ejector is used to recover some available work to increase the compressor suction pressure. The NARC enables the compressor to operate at lower pressure ratio, which in turn improves the cycle performance. Theoretical computation model based on the constant pressure-mixing model for the ejector is used to perform a thermodynamic cycle analysis for the NARC with the refrigerant mixture of R23/R134a. The effects of some main parameters on cycle performance were investigated. The results show the NARC has an outstanding merit in decreasing the pressure ratio of compressor as well as increasing the COP. For NARC operated at the condenser outlet temperature of 40 °C, the evaporator inlet temperature of −40.3 °C, and the mass fraction of R23 is 0.15, the pressure ratio of the ejector reaches to 1.35, the pressure ratio of compressor is reduced by 25.8% and the COP is improved by 19.1% over the conventional autocascade refrigeration cycle.     

Optimising the refrigeration cycle with a two-stage centrifugal compressor and a flash intercooler

The optimisation of a refrigeration process with a two-stage centrifugal compressor and flash intercooler is presented in this paper. The two-stage centrifugal compressor stages are on the same shaft and the electric motor is cooled with the refrigerant. The performance of the centrifugal compressor is evaluated based on semi-empirical specific-speed curves and the effect of the Reynolds number, surface roughness and tip clearance have also been taken into account. The thermodynamic and transport properties of the working fluids are modelled with a real-gas model. The condensing and evaporation temperatures, the temperature after the flash intercooler, and cooling power have been chosen as fixed values in the process. The aim is to gain a maximum coefficient of performance (COP). The method of optimisation, the operation of the compressor and flash intercooler, and the method for estimating the electric motor cooling are also discussed in the article.     

Simulation results of triple-effect absorption cycles

A simulation analysis was carried out for three kinds of triple-effect absorption cycles of parallel-flow, series-flow and reverse-flow using a newly developed simulation program. The cycles investigated in this paper are similar to the alternate double-condenser coupled cycles of Grossman. The coefficient of performance, the maximum pressure and the maximum temperature of each cycle were calculated. The sensitivity analysis of UA of each component was also carried out. The results show that the parallel-flow cycle yields the highest coefficient of performance among the cycles, while the maximum pressure and temperature in the reverse-flow cycle are lower than those of other cycles.     

Detailed thermodynamic characterization of hermetic reciprocating compressors

The aim of this paper is the detailed analysis of different well-known thermodynamic efficiencies usually used to characterize hermetic compressors. Attention is focussed on the volumetric efficiency, the isentropic efficiency, and the combined mechanical–electrical efficiency. A procedure is presented to detach these efficiencies into their main components (physical sub-processes) to get deeper insight on the overall behavior.The volumetric efficiency is split into partial efficiencies related to pressure drop and heat transfer effects, supercharging effects, superdischarging effects, leakages, etc. The isentropic efficiency is detached using two different points of view: the work associated to the individual sub-processes (compression, discharge, expansion, suction), and the work associated to the underpressures, overpressures, and between the inlet and outlet mean compressor pressures. Finally, the combined mechanical–electrical efficiency is related to the heat transfer losses/gains, and to the exergy transfers and exergy destroyed.Even though some of the concepts introduced in the paper can be applied to different kinds of compressors, the discussion is specially focussed on hermetic reciprocating compressors. An advanced simulation model developed by the authors has been used to generate data to illustrate the possibilities of the detailed thermodynamic characterization proposed. The criteria developed are useful tools for comparison purposes, to characterize compressors, and to assist designers during the optimization process.     

Experimental investigation of oil retention in air conditioning systems

In air conditioning and refrigeration systems a small amount of oil is carried with the refrigerant and is retained in the system components. Oil retention characteristics in the condenser, evaporator, liquid and suction lines were measured and are presented and discussed here. Refrigerants R22, R410A, and R134a with miscible and non-miscible lubricants were considered to investigate oil retention physics in the widest possible range of transport properties. A parametric analysis in the suction line showed that oil retention depends on the oil mass fraction, vapor refrigerant mass flux, mixture viscosity ratio and orientation of the pipe. In the suction line, an increase in mixture viscosity of about 55% caused a rise in oil retention in the range of 50%, depending on the oil mass fraction. Oil retention in the upward vertical suction line is about 50% higher than in the horizontal line at similar conditions.