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• A three-phase CO 2 /lubricant swirl ejector with swirl motive nozzle. • Heterogeneous mixture model developed for ejector with swirl motive nozzle. • Helical pitch and oil circulation ratio affect ejector performances. • Empirical correlation of entrainment ratio with swirl number. At present, most simulations of ejectors ignore the presence of lubricating oil, which may affect the accuracy of the results. Additionally, there has been less research conducted on the influence of motive nozzles with swirl generators on the performance of ejectors. In this study, a heterogeneous mixture model was developed for a three-phase swirl ejector equipped with a motive nozzle featuring a swirl generator. This article examines the performance of swirl ejectors under supercritical conditions using three-dimensional numerical simulations conducted in ANSYS. The study explores swirl ejectors with varying helical angles of 77°, 64°, 58°, 50°, 37°. The study also takes into account the influence of lubricating oil to enhance the practicality of the research. Firstly, lubricating oil with a volume fraction of 2 % was introduced into both the motive and suction streams, followed by conducting an ejection analysis. The results indicate that the swirl enhances the entrainment ratio, and the swirl strength can be modified by changing the helical angle. A smaller helical angle results in greater swirl strength and a higher entrainment ratio. When the helical angle is 37° and the helical pitch is 20 mm, a swirl number of 0.42, an entrainment ratio of 0.998, and an effective entrainment ratio of 0.863 is achieved. However, when the oil circulation ratio in the suction stream is increased from 2 % to 10 % while keeping the oil circulation ratio of the motive stream constant, the entrainment ratio decreases. [ABSTRACT FROM AUTHOR]

• A comprehensive numeric model of a condensation-driven dilution refrigerator is established. • Systematical simulations are carried out to analyze the system performances. • T-S and P-T figures of the cold cycle at typical operating conditions are given. • The influence of the key operating parameters such as 3He flowrate are investigated. The dilution refrigerator is the most popular subkelvin refrigerator and important for research fields such as condensed matter physics, astronomical observation, and quantum computing. For applications requiring small cooling powers as well as small footprints, the cold-cycle dilution refrigerators without ambient mechanical pumps and complex connecting gas circuits have become a new research frontier. In this paper, a condensation-driven dilution refrigerator, as a kind of cold-cycle dilution refrigerator, is studied numerically. A comprehensive model covering the thermodynamics, heat transfer and fluid dynamics is established and systematical simulations are carried out to analyze the system performance and the influence of key operating parameters. Through simulations, the T - S and P - T figures of the cold cycle at typical operating conditions are given, and the thermodynamic processes and irreversibility are analyzed. Typically, a COP of 0.025 with the corresponding thermodynamic second-law efficiency of 7.5% can be obtained at 100 mK with the still temperature being 450 mK and the condensation pump temperature being 400 mK. The results reveal the mechanism of the condensation-driven dilution refrigerators and provide useful guidance to the design and operation of experimental setup. [ABSTRACT FROM AUTHOR]

• A methodology for fan efficiency deployment was proposed. • The axial flow maldistribution drops the overall fan efficiency by 14%. • A sensitivity analysis of seven fan parameters was carried out. • Comparisons against the predictions of the fan laws were conducted. • The pitch angle is the most influencing parameter on the fan performance. This paper advances a methodology for axial fan efficiency mapping followed by a design optimization exercise of a low-pressure axial fan for small capacity refrigeration applications. For these purposes, a tailor-made first-principles simulation model based on the so-called blade element theory (BET) was put forward. First, the fan efficiency was deployed into two terms – namely, electric motor and blade efficiency, which in turn was split into two other terms that account not only for the irreversible losses but also for flow maldistribution – in order to identify opportunities for blade optimization. Later, a sensitivity analysis was performed to find out the optimum values of key operating and design parameters of the fan, namely motor speed, blade size and number, chord length, pitch angle, and airfoil characteristics, such as thickness and maximum camber values. Among those, the pitch angle stood out as the most influencing parameter affecting the fan characteristics, including the airflow rate, the power consumption, and the blade efficiency. Comparisons with results obtained by means of the so-called fan laws are also reported for the blade size and speed. [ABSTRACT FROM AUTHOR]

• Existing two-phase ejector analysis does not take oil into account. • 1D simulation to consider the impact of oil in two-phase ejector. • Two-phase ejector internal oil obstructs flow and affects mass flow rate. • Ejector flow analysis according to OCR with varying external conditions. • Validation of simulation study through experiment with uncertainty analysis. The use of traditional refrigerants such as HCFCs and HFCs has a significant impact on global warming. On the other hand, natural refrigerants have little environmental impact with essential characteristics such as low global warming potential (GWP) and zero ozone depletion potential (ODP). Among various natural refrigerants, carbon dioxide is used as an alternative natural refrigerant due to its excellent heat transfer efficiency in a supercritical state. However, its COP is low due to its inherent high compressor work. To reduce this high compressor work, additional components such as ejectors are used for carbon dioxide cycles. In this study, a two-phase ejector was investigated. In particular, ejector analysis was performed in consideration of the influence of lubricant oil. In vapor compression cycle, lubrication is essential. This lubricant oil is discharged to the system through a compressor. When oil flows to system and enters the ejector, it forms a layer that can obstruct the flow inside the ejector. Oil circulation ratio (OCR) change can affect the mass flow rate of the ejector as if the inner diameter of the ejector is reduced. Therefore, it is essential to consider effects of OCR in a two-phase ejector analysis. As a result of the simulation, considering the effect of oil, a lower mass flow rate was predicted compared to existing analysis. Compared to previous studies without considering oil, there was an average mass flow rate difference of 13.6%. This simulation result was validated through experiments. [ABSTRACT FROM AUTHOR]

In this work the relative impacts that different boundary conditions have on the temperature separation predictions of 3D Computational Fluid Dynamics (CFD) models of the Ranque-Hilsch Vortex Tube (RHVT) are explored. Concurrently, in the interest of comparing to experimental results, the impact of including the exit plenums and inlet shroud in the computational models of temperature separation are examined. Simulations of the 3D model using the k − ε , k − ω , k − ω SST and Scale-Adaptive-Simulation SST turbulence models are presented and their relative impacts on flow structure and energy separation are discussed. The results of this study show that imposition of the inlet mass flow combined with mass flow rate at one outlet and pressure at the other leads to reasonable predictions, whereas multiple pressure conditions at RHVT boundaries leads to errors in inlet flow or mass flow split. It is also shown that each turbulence model predicts a unique eddy viscosity distribution inside the vortex tube and that the length of the stagnation stream surface is negatively correlated to the (average) eddy viscosity. By this observation, it is noted that the integral results for energy separation are not sufficient to determine which turbulence model is best. [ABSTRACT FROM AUTHOR]

The back-pressure mechanism plays an important role in the performance and efficiency of the scroll compressor. In this work, the level of back pressure of an asymmetrical algebraic scroll compressor is experimentally measured and it is shown that the back pressure decreases with the increase of compressor frequency under all tested operating conditions. The mathematical model of the scroll compressor is also developed in order to further investigate other influence factors of back pressure. The predicted back pressure is compared with experiment result, showing a similar trend to them. The pressures in each working chamber and back-pressure chamber are studied to identify the effect of leakage through flank and radial leakage gaps. The influences of compressor frequency, leakage gap size, back-pressure volume on back pressure are discussed in detail based on developed model. The axial forces and stability of the orbiting scroll are also evaluated under these operating conditions by using interpolation method to calculate the pressure distribution on tips. [ABSTRACT FROM AUTHOR]

Helical condenser coiled tube is widely used in refrigeration machines for water heating due to its higher heat transfer, compact structure, high energy efficiency, ease of manufacture and arrangement. In addition, developing and optimizing the helical condenser coil designs are considered a sustainable solution for improving the performance of the system. Based on this vision, a particular difference of this study with other studies performed on similar researches is the influence of different shapes of condenser coil designs on heat transfer and temperature distribution during heating process. Therefore, the main objective of this paper is to improve the thermal performance of a helical coil by modifying the coil shape. Based on the results, the average heat transfer coefficient and average COP of variable pitch coil were increased by 36.48% and 16.17%, respectively, compared with normal coil. Moreover, the obtained results indicated that the water temperature, the water velocity, the heat transfer and the performance of the helical condenser with variable pitch coil were improved in comparison with that of normal coil. However, this investigation could provide some guidance to obtain the optimum coil structure of refrigeration machines for domestic hot water production. [ABSTRACT FROM AUTHOR]

Numerous novel devices have already utilized desiccant coating to implement various functions, such as atmospheric water harvesting, energy storage, and thermal/humidity management. The mathematical models employed in former literature, for instance the finite-element or finite-volume models usually suffer significant drawbacks such as extreme complexity and time-consuming. To solve this problem, this paper outlines a general strategy to develop dynamic compact thermal models of the quasi-one-dimensional sorption-based systems in the virtue of the thermal resistance-capacitance network. To be specific, the mass transfer process induced by the adsorption/desorption process is equivalent to a heat/cooling source, therefore the coupled heat and mass transfer kinetics in the corresponding device can be evaluated simultaneously. Two comprehensive experimental prototypes in our previous literature are employed to validate the effectiveness of the proposed model. The results show that our model can forecast the transient thermal behavior of the devices accurately within a few seconds. The dynamic deviation of the system output, for instance the material temperature and outlet air humidity, between simulation and experiment is within 7%. Furthermore, a parametric study is conducted based on the proposed model to analyze the influence of key parameters on system performance, showing great potential for guiding the system design and optimization. [ABSTRACT FROM AUTHOR]

• Hollow fiber and flat membrane energy accumulators are designed and simulated. • Dynamic mathematic models of heat and mass transfer in full-scale MEAs were built. • Influence of membrane to membrane and the boundary of the MEAs were considered • The reliability of mathematic models has been verified by the experimental results. • Triangular arrangement of the fibers is more conducive to the mass transfer process. The hollow fiber membrane energy accumulator (HFMEA) and the flat membrane energy accumulator (FMEA) were designed. Dynamic mathematic models of the heat and mass transfer in the full-scale membrane energy accumulators (MEAs) were built in order to consider the membrane-to-membrane interactions and boundary effect in MEAs. The reliability of mathematic models has been verified by the experimental results. The maximum relative deviations of the mass transfer flux and solution temperature were 14.9 % and 14.6 %, respectively. The change rate of LiBr mass fraction in the FMEA was 1.38 times of that in the HFMEA. The hollow fiber membrane bundle in HFMEA is more conducive to the mass transfer process when the arrangement of the fibers is triangular. When the length of the membrane channel increased from 50 mm to 160 mm in HFMEA, the mass transfer per membrane surface area decreased by about 5 %. With increasing the vapor inlet pressure from 700 Pa to 1500 Pa, the mass transfer flux was tripled. And the average temperature of the solution increased by more than 3.75°C in 10 minutes. If the membrane filled density increased from 1.4 % to 2.1 %, the mass transfer flux increased to 2.04 times in FMEA. [ABSTRACT FROM AUTHOR]

• The performance of the GCHP and SAHP systems under cold climates is studied. • The use of a solar thermal collector in the system heat pump is evaluated. • The two systems were compared in terms of thermal performance. • The combined heat pump with a solar system is adequate for heating greenhouse. This work presents a comparative investigation of a heating system of a solar-assisted and a conventional heat pump using numerical and experimental studies. The heating system includes a tempered glass greenhouse connected with a water-to-water heat pump of a power of 10 kW, a solar collector, and a capillary tube mat as a heat distribution system. Furthermore, a comparative analysis of the system performance operating at the same condition with and without the solar energy was conducted. The system was optimized using the software TRNSYS to obtain the appropriate boundary conditions for the real system, and its best efficiency. The impact of climatic conditions on system performance is discussed. The Tunisian weather data were used to simulate heating systems by considering a 100 m2 glass greenhouse and 2 m2 as the collector area. The numerical simulations were validated by the experimental results. It was concluded that the proposed heating system could be adequate for greenhouse heating in winter. An area of a 2 m2 collector was found to match the heating load of a 10-kW power heat pump. The heat supplied by the solar collector at noon is between 1.5 and 4 kW in Tunisia and the heat pump with a power of 10 kW can supply the required amount of heating. The solar collector highly affects the performance of the water-water heat pump. [ABSTRACT FROM AUTHOR]

In warm and humid climates, a primary source of building energy consumption is dehumidification of conditioned air supplied to the building spaces. The system analyzed utilizes a selective membrane to remove water vapor from ambient air instead of a vapor compression cycle or a desiccant. This work analyzed a membrane dehumidification system with a focus on the system energy performance. A system performance goal was set by the project sponsor for an inlet air condition of 32.2 °C and 90% relative humidity, an outlet condition of 12.8 °C and 50% relative humidity and a total cooling load of 3.52 kW resulting in a target COP latent for the system of 3.34. Models of the basic system components were used to develop the system, analyze operating parameters and predict performance. The results indicate that the system requires two optimizations to meet the target performance: condenser pressure optimization and the use of multiple membrane segments operating at different pressures. Subsequently, a model was developed to analyze the performance of the final system configuration under a variety of operating conditions and yielded a maximum COP latent of 4.37 for membrane properties comparable to those of the earliest membrane module tested. This may be compared with a COP of about 3.5 for current refrigeration technology at these conditions. The best small membrane sample produced to date would increase the COP latent of the membrane system to well above 8, suggesting that the membrane system has high promise. Uncertainty analysis was also performed to assess the simulation results. [ABSTRACT FROM AUTHOR]

• Thermodynamic analysis of a two bed solar adsorption refrigeration system is presented. • Activated carbon-ethanol is the best adsorbent-adsorbate pair for the continuous operating adsorption cooling cycle. • The maximum C O P S Y of the system is 0.68 for the desorption temperature of 95 °C. • Dependency of performance parameters with desorption temperature is studied. • Isothermal adsorption is thermodynamically efficient as compared to isobaric adsorption. In this study, a thermodynamic model for analysing the performance of a two-bed solar adsorption cooling system (SAC) has been presented. It projects isothermal adsorption instead of isobaric to reduce the heat of adsorption and hence improve the performance of SAC system. An adsorption chiller of 500 W capacity operating at an evaporator temperature of 5 °C and a condenser temperature of 45 °C is selected for the present research. The proposed adsorption chiller uses activated carbon/ethanol as the working pair. The refrigeration cycle operates between an evaporator pressure of 2.01 kPa and a condenser pressure of 23.1 kPa. The input heat distribution in the bed component, followed by, assessing the effect of maximum desorption temperature on the performance of the system is also carried out. The maximum coefficient of performance of 0.68 is observed for a desorption temperature of 95 °C.The thermal performance of the system is also studied for adsorbate fraction, adsorbent bed pressure and effect of desorption temperature on various parameters. It has been found that the isothermal adsorption process increases the thermal performance of the SAC and it is estimated that coefficient of performance of the system with isothermal adsorption is 13.23% times more when compared with conventional isobaric adsorption. The study aims at providing a formidable solution to the low performance of adsorption cooling systems. [ABSTRACT FROM AUTHOR]

• The first prototype of the second type absorption heat exchanger was completed. • The second type absorption heat exchanger process was realized through experiments. • A simulation model for the second type absorption heat exchanger is established. • Tested the performance of the prototype under different working conditions. • The temperature efficiency of the prototype has been tested between 1.25 and 1.34. Absorption heat exchanger(AHE), as a kind of heat transformation device, is widely used in long-distance heat transportation system, waste heat recovery and other heat exchange processes s with large flow ratio on both sides. A second type of absorption heat exchanger was first designed, manufactured, and tested to get the performance in this research. The falling-film prototype absorption heat exchanger is consisting of a multi-section absorption heat transformer and a plate heat exchanger, using LiBr-H2O as working fluid. Under different working conditions, the tested results showed that the outlet temperature of the heat sink water was 916 K higher than the inlet temperature of the water on the heat source side. The coefficient of performance (COP) of the absorption heat transformer (AHT) was between 0.33 and 0.42. The temperature efficiency of the absorption heat exchanger was 1.24–1.35. Finally, the simulation model used to design the prototype machine was verified by the test results. [ABSTRACT FROM AUTHOR]

• Single-effect absorption refrigeration system is simulated using aspen HYSYS. • Commercial butane as refrigerant and commercial hydrocarbons as absorbents are used. • Optimal working fluid is found to be butane/heavy naphtha. • Performance changes marginally with butane recovery unlike reboiler temperature. • Butane/heavy naphtha system competes effectively with current commercial chillers. A heat-powered single-effect absorption refrigeration system operating with commercial n-butane as a refrigerant and six commercial hydrocarbons (stabilized condensate, light naphtha, heavy naphtha, reformate, light reformate and heavy reformate) as absorbents was studied. The main target of the study was actuating these systems to the available waste heat. Simulation models were created using Aspen HYSYS process simulator. The main parameters of an absorption refrigeration system, using the proposed working fluids, were compared at different evaporator, condenser and absorber temperatures to select the best working fluid. Moreover, a focused interpretation was given to the behavior of the best system at different operating conditions. Furthermore, the effect of both butane recovery and purity, in the generator, on the performance of the best system was investigated. Results revealed that, among the proposed working fluids, the best performance was achieved by butane/heavy naphtha. It could achieve a Coefficient of Performance (COP) of 0.78 at evaporator temperature of 20 °C and both condenser and absorber temperatures of 30 °C. The COP passed through a different maximum value at certain recovery for each evaporator temperature and condenser and absorber temperatures and similar behavior was observed for purity. Low reboiler temperatures were feasible at low butane recoveries with almost the same COP of the high butane recoveries. Generally, Butane/heavy naphtha system could compete effectively with the commercial absorption refrigeration systems, within their range of operating conditions, without experiencing their limitations. [ABSTRACT FROM AUTHOR]

Desiccant coated heat exchangers (DCHEs), utilizing an inner cooling source to remove sorption heat, are promising alternatives for evaporators and condensers (DCEs/DCCs) in vapor compression (VC) heat pumps. A mathematical model is necessary to facilitate the design, analysis and performance prediction of the component and the relevant systems. In this study, a three-dimensional model of DCEs/DCCs is proposed, accounting for the two-phase phenomena, the periodical switchover, the solid-side resistance, the fluid transport in multiple directions and the coupled heat and mass transfer. Study reveals that, high latent load (inlet humidity) reduces the sensible heat handling capacity of the DCEs, while the dehumidification capacity is almost independent of its sensible heat load. DCEs possess a satisfying effect of dehumidification above the dew point, thus it is unnecessary to employ low evaporation temperature. Meanwhile, the adsorption-desorption temperature difference of 30°C seems to be the optimal value for the commonly adopted evaporation temperatures (10°C-20°C). For a specific coating thickness, there is a critical switchover period where the best performance of dehumidification is obtained. Switchover period shorter than the critical time should be avoided, and elongating the switchover cycle helps balance the ability of the system to handle the sensible and latent heat loads at the same time. [ABSTRACT FROM AUTHOR]

• Larger heat transfer coefficient and pressure drop are captured in wavy channels. • Increase amplitude or decrease wavelength can achieve heat transfer enhancement. • Wavy channels with opposite crests and troughs show better heat transfer performance. • Channel structure and parameter have great effect on buoyancy force and flow fields. A numerical study on cooling heat transfer and pressure drop of supercritical CO 2 in horizontal wavy microchannels with consistent crests and troughs (WMCCT) and wavy microchannels with opposite crests and troughs (WMOCT) was conducted. The aim is to provide reference for optimal design in trans-critical CO 2 gas cooler equipment. The influence of the channel structure on heat transfer coefficient, pressure drop, buoyancy effect, flow fields and overall thermal performance was analyzed. WMOCT and WMCCT show great advantages in heat transfer performance, while get slightly larger pressure loss punishment when compared with straight microchannel (SM). It is worthy to note that both heat transfer coefficient and pressure drop increase with increased amplitude or decreased wavelength in both WMOCT and WMCCT, which is particularly evident in WMOCT. Furthermore, the analyses carried out identified an optimal channel structure that could improve the overall thermal performance of microchannel gas coolers. [ABSTRACT FROM AUTHOR]

• Performance deterioration of CO 2 heat pump water heaters in Shanghai was revealed. • Annual performance factor of heat pump water heaters was proposed and predicted. • Suggestions on system design and control of CO 2 HPWH for long-term operation were made. CO 2 heat pump water heating is an energy-efficient technology and being widely applied in Shanghai. However, its energy efficiency after long-term operation has not been well evaluated so far. In this paper, the energy efficiency and potential issues of CO 2 heat pump water heater after multi-year service are in-depth investigated. In-situ study of CO 2 heat pump water heating systems in Shanghai was carried out. Operating data were collected and field test was conducted. A typical case was chosen for comprehensive analysis. The results show that the annual performance factor (APF) of the actual system is 2.57, relative to 4.12 in its perfect shape. To find out what happened to this system, a simulation model was developed, calibrated and validated with field test data and operating data. In terms of simulations, suggestions were made on the system design and control for long-term performance improvement. [ABSTRACT FROM AUTHOR]

• Thermodynamic performance of a cascade refrigeration system was investigated. • Three mixed refrigerants (R744/R1270, R744/RE170, R744/R717) were tested in both subcycles. • Mixed refrigerants allow a better thermodynamic performance than pure fluids. • R744/RE170 presented the greatest global COP, 2.34, for a fixed cooling rate of 100 kW. • Exergetic efficiency increased up to 30% and refrigerant mass flow rate was reduced up to 34%. This work evaluates the thermodynamic performance of three different mixed refrigerants: R744/R1270, R744/R717 and R744/RE170 in a cascade refrigeration system composed of two vapor compression cycles. Mixture composition and condensation temperature of the cascade heat exchanger were used as inputs in a parametric analysis, while outputs considered were: compressor power, refrigerant mass flow rate in both cycles, exergy destruction rate, exergetic efficiency and coefficient of performance. Systems were optimized for COP maximization, considering a fixed cooling rate of 100 kW in the evaporator. After optimization, COP increased from 18% to 32% when compared to the values obtained for pure refrigerants. R744/RE170 mixture showed the best results with a COP of 2.34, increasing exergetic efficiency up to 30% and reducing refrigerant mass flow rate in the range from 6% to 34%, compressor power between 20% to 23% and exergy destruction rate was decreased around 31% to 36%. [ABSTRACT FROM AUTHOR]

• A model of a CO 2 heat pump is described. • A first model simulates a heat pump for simultaneous heating and cooling. • A second model simulates a heat pump for simultaneous cooling and desalination. • CO 2 proposes new interesting applications for multi-function heat pumps. This article presents the numerical model of a heat pump using CO 2 in a transcritical cycle. Two systems are envisaged in this work: a heat pump for simultaneous heating, cooling and domestic hot water (HPS1) and a heat pump for simultaneous cooling and desalination (using heat) (HPS2). The simulation study uses EES and TRNSYS to assess the performance of two heat pumps in different applications and operating conditions. The simulations show interesting performance indicators: the seasonal COP for heating and cooling and the exergy efficiency for both systems. HPS2 producing cooling and desalination has a higher seasonal process exergy efficiency than HPS1 due to the interesting use of energy for the desalination application. The performance analysis presents a seasonal Coefficient of Performance (COP) between 2 and 3. [ABSTRACT FROM AUTHOR]

• Universal model for a caloric refrigerator based on thermal diodes or switches. • Lumped elements representation enables an analogy to a low pass filter. • Analytical model verified with simulations and measurements from literature. • Thin caloric material and excellent heat transfer are key for high cycle frequency. Solid state cooling based on caloric materials has a large potential, because there is no need for fluid refrigerants. The state of the art system approach relies on a heat transfer fluid, which is pumped back and forth through a regenerator of caloric material. This system approach has fundamental limitations regarding the cycle frequency. Different system approaches are considered. One is the utilization of fast thermal diodes or switches. The aim of this work is to provide a universal model to describe a cooling system based on caloric materials using thermal diodes or switches. The heat capacitance of the caloric material is defined to be constant, allowing a lumped elements representation. An analytical model based on an analogy to an electrical low pass filter is introduced. The analytical model is compared with good agreement to lumped elements simulations and measurement data from the literature. It is shown, that the newly introduced cut-off frequency as merit for the potential cycle frequency is proportional to the heat transfer coefficient of the diodes/switches in flux direction and inverse proportional to the length scale of the caloric material in heat flux direction. Different heat transfer mechanisms are discussed as basis for such thermal diodes and switches in combination with different caloric effects. To increase the cycle frequency compared to state of the art systems, latent heat transfer is a promising candidate for all caloric effects, whereas for example a dry press contact for a magnetocaloric system presents many challenges. [ABSTRACT FROM AUTHOR]

• Modeling of vapor compression systems under on-off conditions. • Detailed compressor modeling to estimate its temperature distribution and p-V diagram. • Compressor model predictions validated with transient measurements. • System energy consumption in different on-off conditions is compared to measurements. • Effect of different compressor designs on COP is discussed. This paper presents a simulation model for the transient behavior of vapor compression refrigerating appliances subjected to on-off control patterns focusing on the reciprocating compressor. A detailed compressor model is adopted, which can predict the valve dynamics, pressure pulsations in mufflers, and temperature of different components. The remaining components of the single-door frost-free refrigerator considered in this work are modeled based on mass and energy balances considering each component as an even lump. The overall system simulation model was validated by comparing predictions for the compressor temperatures and mass flow rate, indicated power, power consumption and overall energy consumption with the experimental counterparts measured in a household refrigerator, whose components – including the compressor – were carefully instrumented with thermocouples and pressure transducers, and tested in a climate chamber. Finally, sensitivity analyses were conducted to assess the effect of the compressor design parameters on its performance under calorimeter and actual system conditions. [ABSTRACT FROM AUTHOR]

Highlights • A novel modeling approach of feature-recognition was proposed. • The chiller models were developed based on feature-recognition. • The models were validated by comparisons between simulations and experiments. • Relative errors of simulations and experiments are all within 10%. Abstract With the absence of structure parameters of chillers, it is difficult to simulate the chiller performance by the conventional precise modeling approach. Thus, a novel modeling approach is proposed, which makes unknown structure parameters lumped and obtains them (i.e. the characteristic parameters, which are unique for each chiller) based on measured data of chillers. The modeling principle of feature recognition is described, based on which then the chiller models were developed. An experimental platform of chiller was established, and the relevant chiller models were established on basis of measured data. Moreover, to verify the chiller models, simulations and experiments were compared under variable water flow rate and variable water temperature conditions respectively. Results show that with the feature recognition method, the chiller models can function quickly and efficiently, and achieve a high accuracy. Compared with experimental results, relative errors of simulated performance parameters, such as refrigerating capacity and COP (coefficient of performance), are all within 10%. This study provides a new and efficient approach for chiller modeling. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a detailed analysis on the leakage characteristics of R410A in the swing compressor with no valves. Leakage losses through all clearances have been studied by using the present method. Simulation results show that the leakage loss through the clearances between rotor faces and the head walls of the cylinder becomes the most important one and the second one is the leakage loss through the radial clearance. Additionally, refrigerant mass flow rate is used as an important parameter to verify the accuracy of the theoretical formulas. Calculation results of the theoretical refrigerant mass flow rate are compared with the experimental results and the results are satisfactory. Furthermore, an optimization measure has been provided for the design of the swing compressor with no valves. [ABSTRACT FROM AUTHOR]

Highlights • Thermodynamic model of membrane based heat pump developed to provide 3 t of cooling. • Membrane system COP more sensitive to outdoor wet-bulb than dry-bulb. • Membrane system more efficient than vapor compression in different US climate zones. Abstract Membrane based heat pumps systems have attracted the attention of many research groups as a potentially more environmentally friendly alternative to vapor compression systems for space cooling. Several prototype systems have been developed, with reported claims of Energy Efficiency Ratios (EER) approaching 26. At present, no detailed analysis is publicly available which simulates the capability of these systems in different climate zones. In this work, a thermodynamic cycle model of a representative membrane heat pump system is developed and heat and mass transfer components are sized to provide 3 t of cooling at nominal rating conditions. The performance of the 3 t system is then simulated in various climate regions using representative cooling loads calculated from a building energy modeling software. The simulated membrane heat pump system had an EER of 16–20. Compared with the performance of a commercial vapor compression system, the membrane system performs better at higher dry-bulb temperature and shows energy saving potential in all climate regions examined. While the membrane system shows potential from a thermodynamic perspective, there are many practical challenges that must be addressed prior to commercialization including the design of an efficient vacuum pump, mitigating membrane fouling and reliability issues, and developing advanced controls to maintain desired sensible and latent heating capacities. [ABSTRACT FROM AUTHOR]

Highlight • Our developing numerical simulation model can reproduce static and dynamic characteristics of variable refrigerant flow (VRF) systems precisely. • Our simulation model can be estimated dynamic characteristics quantitatively and can be analyzed the cause of response time difference of manipulated variables. • Interference from mutual indoor units affects the supply air temperature and superheating temperature largely, in case of manipulated each expansion valves especially. • This simulation results is expected to be applied to another VRF systems. Abstract In commercial and office buildings, it has recently become popular to install variable refrigerant flow (VRF) compression-type heat pump systems. In particular, VRF systems with multiple indoor units are being installed in large buildings because such systems have large adjustment capacity. On the other hand, because users of VRF systems can freely choose the number of indoor units to install and can turn indoor units on and off independently, operating conditions are not predictable and it is difficult to find adequate control parameters under wide changes in load. With this background, we are developing a new numerical simulation model based on the laws of physics. Because this model can easily add and delete system elements, we believe that it will be useful for VRF system analysis. In this study, we utilize a numerical simulation model to evaluate both steady and unsteady conditions in VRF systems. In this paper, we focus on the connection between manipulated variables (the expansion valve's open pulse and fan rotational speed) and controlled variables (supply air temperature and the degree of superheating at the evaporator outlet). Moreover, we compare the difference between the performance of a single indoor unit and that of multiple indoor units operating simultaneously. As a result, we can evaluate the dynamic characteristics of manipulated variables and the effect of changing the number of active indoor units, each of which has their own VRF characteristics. [ABSTRACT FROM AUTHOR]

Highlights • Thermodynamic performance of a FTVI refrigeration cycle was investigated. • Binary mixtures of hydrocarbon refrigerants were used in simulations of a FTVI cycle. • Mixed refrigerants allow a better thermodynamic performance than pure fluids. • Mixed refrigerant R290/R600 60/40 wt% presented the greatest COP. • R170/R290 and R290/R600 presented the best temperature glide matching in the evaporator. Abstract Refrigeration systems are major consumers of electrical energy in many process industries. Hydrocarbons have regained interest as refrigerants because of the increasing restrictions applied to halogenated fluids. In this work, the use of hydrocarbons mixed refrigerants and an alternative flash tank with vapor injection (FTVI) refrigeration cycle were combined. Five different binary mixed refrigerants involving R170 (ethane), R290 (propane), R600 (n-butane) and R600a (isobutane) were studied. Using different refrigerant compositions, the cycle was simulated and optimized for maximum COP, considering a fixed refrigeration capacity in the evaporator to reduce the temperature of a secondary thermal fluid from 281.55 K to 269.15 K. Parameters analyzed were: coefficient of performance, temperature glide in the evaporator and refrigerant mass flow rate. The use of a FTVI led to a COP improvement from 4% to 36% when compared to the traditional vapor compression cycle (VCC). The pair R290/R600 with 60/40 wt% presented the maximum COP of 4.88. [ABSTRACT FROM AUTHOR]

Highlights • Heat rejection control strategies that increase chillers efficiency are presented. • Different cooling towers sequencing approaches are investigated theoretically. • A cooling water set-point as a function of the wet-bulb temperature is proposed. • Both simulation and monitoring results show up to 15% electricity savings. Abstract Energy efficient cooling systems are urgently required in order to face the increasing cooling demand of the building and industry sectors and comply with the ambitious EU target of greenhouse gas emission reductions. The present work aims to show that simple heat rejection control strategies can lead to significant energy savings. Different approaches of sequencing the operation of several cooling towers and a method to adapt the cooling water temperature set-point to the actual ambient conditions are proposed. These strategies are first investigated theoretically for an existing chilled-water plant of 13.7 MW installed cooling capacity. Up to 20% energy savings are theoretically possible depending on the used control strategy and the weather conditions. A variable cooling water set-point as a function of the wet bulb temperature allows for the most significant savings. After implementation of this measure in the existing cooling plant, 2 years monitoring results show that the overall system efficiency of the chilled water plant could be increased by 15% compared to the initial status confirming the results of the theoretical study. [ABSTRACT FROM AUTHOR]

Highlights • Improvements to the ABSIM software code were implemented and demonstrated. • Improvements include an algorithm to automate the initial guess selection for the solver. • The algorithm improves reliability and reduces manual user work. • The algorithm made possible the implementation of a genetic global optimization feature. Abstract ABSIM (an acronym for ABsorption SIMulation) is a computer code for simulation of absorption systems in flexible and modular form. It may be applied to closed and/or open absorption cycles operating at steady state, as well as to vapor compression and other thermodynamic cycles. This modular code is based on unit subroutines containing the governing equations for the system's units/components and on property subroutines containing thermodynamic properties of the working fluids. The units are linked together by a main program which calls the unit subroutines according to the user's specifications to form the complete cycle. When all the equations for the entire cycle have been established, a mathematical solver routine is employed to solve them simultaneously. As the simulated system becomes more complex, it is increasingly difficult to find a suitable initial guess. If the user obtains one, there is no guarantee that this guess will be adequate for simulating a different system state, even with but a slight change in its parameters (small change in temperature, and/or flow rate, heat transfer coefficients, etc.). To deal with this problem, an automatic initial guess generating algorithm was developed. This algorithm aids the user by automatically selecting the initial guess for the solver to work with. This is to achieve convergence for different operating conditions, given that at least one good initial guess was already obtained for a certain operating point. An additional new feature of the ABSIM software is the implementation of a genetic optimization algorithm. It is enabled by the above automated initial guess algorithm. [ABSTRACT FROM AUTHOR]

Highlights • A dynamic grey box thermodynamic model is used to model the heat pump components. • A zonal model allows to model convection and thermal stratification in the tank. • An experimental set up is used to evaluate the model accuracy in various conditions. • The developed model allows to accurately predict the energy performance and comfort. Abstract Air Source Heat Pump Water Heaters (ASHPWHs) are efficient and fast-developing sanitary hot water production systems for the building sector. However, it was shown that their energy performance can still be improved. Therefore, a dynamic grey box Modelica based model is developed representing a split type ASHPWH with a mantle heat exchanger. The thermal storage model includes a zonal model to model convection during heat-ups and the heat pump is modeled using the TIL® thermal component library. The model is first compared to dynamic experimental data during 9 heat-up tests under various operating conditions, including low temperature defrosting stages. On such heating periods, the overall mean relative error reached is of 2% for the COP and the maximum temperature error over the height of the tank is less than 1°C. The model is reproducible and can be used to conduct further design based optimization studies. [ABSTRACT FROM AUTHOR]

The steady-state mathematical modelling of advanced absorption cycles can be time-consuming and error-prone. In this work, a computer tool based on a modular approach and supported by a comprehensive methodology is described. The solver automatically eliminates redundant mass and species balance equations, detects the existence of paired interconnections, and identifies the nature of the missing auxiliary conditions. To illustrate the tool's capabilities, two advanced refrigeration cycles are modelled, double-lift and resorption. For each cycle, two different embodiments are discussed in consideration of the volatility of the absorbent. With reference to cooling applications driven by low temperature heat, the performance of three cycles are compared: NH 3 -LiNO 3 double lift (DL1), NH3-H2O double lift (DL2), NH 3 -H 2 O resorption (R2). DL1 and DL2, despite their lower thermal COP c can achieve a maximum value of EER (about 7.7) only slightly lower than that achieved by R2 (about 7.9) with a much lower driving temperature. [ABSTRACT FROM AUTHOR]

The current study examines different arrangements of vortex tubes (VTs) to get higher performances for cooling and heating. The effects of thermo-physical parameters such as inlet feed temperature and inlet/outlet vortex tube pressure on generated temperature gradient are investigated. To estimate the cold outlet temperatures, the available equations in the literature are verified against our experimental data. Moreover, we propose a new equation to estimate the hot outlet temperature based on the upper limit of hot temperature (ULHT) and the lower limit of cold temperature (LLCT), verified with experimental data as well. Further, several arrangements are simulated to obtain the minimum cold and the maximum hot temperatures for the outlet streams. Finally, the optimal arrangement of the three vortex tubes and a double-pipe helical heat exchanger that gives the highest performance is proposed. [ABSTRACT FROM AUTHOR]

A new way to evaluate the performance of the active magnetocaloric regenerator (AMR) was developed based on a few critical parameters proposed in this study. The critical parameters were derived from the energy equations that have been used to describe the transient energy transfer processes in the AMR for both the magnetocaloric materials and the heat transfer fluid. Each parameter is corresponding to a specific energy transfer mechanism in the AMR and can be easily implemented to evaluate the contribution from each term, including axial conduction and remnant energy storage in the magnetocaloric materials, axial conduction, remnant energy storage and fluid dissipation in the heat transfer fluid, and internally regenerated energy. Parametric studies were carried out to explore the impact of geometric and operating parameters and to determine whether or not a certain heat transfer mechanism is significant to the overall system performance. [ABSTRACT FROM AUTHOR]

For predicting the performance of variable refrigerant flow multi-split air conditioning (VRF) systems with arbitrary layouts under various operating conditions, a general simulation model for VRF systems based on graph theory was proposed. In the present study, the directed graphs and adjacent matrixes were established to describe the systems with arbitrary layouts under cooling and heating modes, and a diagonal matrix was developed to describe the operating number of indoor units; the general description matrix of VRF systems under various operating conditions was expressed as the multiplication of the adjacent matrixes and the diagonal matrix. The component models meeting the simulation accuracy requirement were presented. A tailor-made iteration algorithm using graph-based traversal method was developed to solve the system model. The proposed simulation model for VRF systems was validated experimentally, and the model deviations of the heat capacity, temperature and pressure are within 3%, ±3 °C and ±5%, respectively. [ABSTRACT FROM AUTHOR]

This paper presents the experimental testing results of a novel triple-state sorption chiller with integrated cold storage. The performance of the chiller was measured for hot water inlet temperatures between 65 °C and 95 °C, heat rejection inlet temperatures between 15 °C and 35 °C, and chilled water inlet temperatures between 10 °C and 25 °C. An empirical model was developed for implementation in the TRaNsient SYstem Simulation (TRNSYS) software. To validate the model, a five-hour experimental charge test was conducted during which the hot water and heat rejection inlet temperatures were continuously varied. The model was able to predict the total heat input and heat rejection energy to within 0.7% and 1.3% of the experimentally measured values, respectively. [ABSTRACT FROM AUTHOR]

This study deals with a frost-free refrigerated display cabinet, in which frosting can be retarded by dehumidifying the air before it enters the evaporator of the display cabinet via a desiccant-coated heat exchanger. Because the desiccant can be regenerated via the condensation heat of the refrigerant (which is exhausted into ambient air in conventional refrigerated display cabinets), the proposed system can achieve high energy efficiency. Calculation shows that the coefficient of performance (COP) of this system is 3.1 and the daily electricity consumption of the compressor is 10.5 kWh when the temperature ( T RA ) and relative humidity ( RH RA ) of the return air entering the evaporator are 12 °C and 0.6, respectively. Furthermore, it is found that T RA and RH RA significantly affect the COP: COP increases by about 115% when T RA varies from 8 to 14 °C, and increases by 35% when RH RA varies from 0.5 to 0.8. [ABSTRACT FROM AUTHOR]

This work presents a new dynamic lumped parameter model that is able to simulate the oscillation of electronic expansion valve (EEV) controlled refrigeration system due to unsuitable control or abrupt change of external parameters. Based on bubble dynamics theory, the heat transfer characteristic is used to divide the evaporator into the stable and unstable conditions, and a matching switch criteria is presented. Together with the model of main components, the dynamic behavior of oscillation of system parameters is simulated successfully. Model validation against experimental data demonstrates the capabilities of the modeling approach in predicting the instability of system control loop. This study provides the basis for further developing advanced control algorithm which will ensure that an EEV-controlled system refrigeration system has better stability. [ABSTRACT FROM AUTHOR]

Desiccant wheel based air handling units are of great interest in drying processes, such as in the pharmaceutical and food industries, due to the significant energy savings that can be achieved compared to conventional systems. Units based on desiccant wheels are usually optimized in peak conditions, while little attention is given to operation at part load and off design conditions. The aim of this work is to analyze the effects of different control strategies of desiccant wheels on regeneration heat consumption. The analysis is performed through a phenomenological desiccant wheel model, which is validated with experimental data collected in typical working conditions of the drying room investigated in this work. Five control strategies are proposed, highlighting that each one leads to significantly different heat consumption. Finally, an additional simplified control is introduced, showing that it can effectively reduce thermal power consumption compared to conventional control strategies. [ABSTRACT FROM AUTHOR]

This work gives insight in the development and the application of a semi-implicit transient cycle simulation tool. The model consists of subcomponents that are independently validated and coupled in order to shape a fully functional cycle simulation. The methods used comprise empirical models, artificial neural networks or more complicated, transient 1d finite volume formulations for two-phase flow. The validation of the cycle simulation is carried out using data from a specially equipped domestic freezer. The model is calibrated to one operating point and afterwards tested under varying ambient temperatures and thermostat settings. The agreement compared to measurements is 6.9% mean and 5.5% standard deviation of the total electric energy consumption. Furthermore, parameters like refrigerant distribution, pressure drop, temperature or mass flow rate can be monitored. [ABSTRACT FROM AUTHOR]

Plate Heat Exchangers (PHEs) are used in a wide variety of applications including heating, ventilation, air-conditioning, and refrigeration. PHEs are characterized by compactness, flexible thermal sizing, close approach temperature, and enhanced heat transfer performance. Due to their desirable characteristics, they are increasingly utilized in two-phase flow applications. Detailed research on heat transfer and fluid flow characteristics in these types of exchangers is required to design and use plate heat exchangers in an optimal manner. This paper reviews the available literature on the correlations for heat transfer and pressure drop calculations for two-phase flow in PHEs as an initial process step in order to understand the current research status. Comparative evaluations for some of the existing correlations are presented in the light of their applicability to different refrigerants. Overall, there is a significant gap in the literature regarding two-phase heat transfer and fluid flow characteristics of these types of exchangers. [ABSTRACT FROM AUTHOR]

This work presents a performance evaluation of a vapor injection refrigeration system using a mixture refrigerant R290/R600a, through steady-state simulations used to accomplish a parametric analysis considering the influence of the refrigerant composition over the following parameters: COP; compressor power; refrigerant mass flow rate; refrigerant temperature glide; mass flow ratio between vapor and feed streams in the flash tank; liquid and vapor composition of flash tank outlet streams and compression ratio. Two cases, denominated A and B, considering different fixed temperatures at the refrigeration system were studied and their performances were compared with the one of a basic vapor compression cycle. A maximum COP was obtained for a mixture containing 40 wt% of R290. COP of vapor injection refrigeration cycle is 16–32% greater than the one of a vapor compression cycle, depending on the composition of the mixture refrigerant and pressure drop at the cycle upper-stage expansion valve. [ABSTRACT FROM AUTHOR]

The air conditioning (A/C) system of the cabin is one of the most energy consuming auxiliaries in a vehicle and its optimization is a technological option suitable for achieving fuel consumption reduction in automotive sector. Hence, in this paper, the Authors present a mathematical model of the A/C system, starting from its single components: compressors, condenser, expansion valve and evaporator. The model considers off-design behavior of components, being this system often at partial load operating conditions. Therefore, considering fixed orifice as expansion device, performance of the whole system has been evaluated and an optimization of the components was derived. Their design influence has been assessed and, moreover, the opportunity to have an A/C condenser cooled by a liquid circuit in place of external air is discussed, considering the opportunity to integrate it into the main engine cooling system. The performances outlined using R1234yf showed a 22% reduction of compressor shaft power with respect to the air cooled condenser case and significant COP increase. [ABSTRACT FROM AUTHOR]

Previous reviews on ejectors for expansion work recovery have provided detailed discussions of operating characteristics and control of ejector cycles, zero-dimensional ejector modeling, ejector geometry effects, and alternate ejector cycles. However, important advances in the field of ejector technology have occurred since previous reviews were written. Several focuses of recent ejector research are the development of multi-dimensional CFD ejector models, investigation of alternate ejector cycles and uses of the work recovered by the ejector, implementation of effective control strategies for ejector cycles, and application of ejectors in real systems. The objective of this paper is to present a review of developments in the use of ejectors for expansion work recovery in vapor-compression systems focusing on the past several years. Although the first commercial applications are being introduced to the market, it is suggested that future works continue in these areas in order to make ejectors more suitable for additional applications. [ABSTRACT FROM AUTHOR]

The aim of the study presented in this paper is the comparison of different possibilities to reduce the power consumption and environmental impact of barrack buildings of the US army. For this purpose different building standards, different heating and cooling appliances and a cold storage concept are compared using annual building simulations. These simulations are carried out for central and northern locations in the US. The focus of this paper is the applicability of cold climate heat pumps in these climates. A coupled building and appliance model has been established to allow a fair comparison based on first energy usage and CO 2 emissions. Altogether seven different building configurations in six different locations have been investigated. Simulation results show the most significant energy savings (up to 90%) can be achieved by improving building insulation and heat recovery of the ventilation system. Second major improvement is the usage of two-stage heat pump systems, which drastically reduces the need for backup heating systems and lead to seasonal efficiencies (SCOPs) in the area of 3.0, or in other words an energy saving of 20–35%. Thermal storage and control concepts such as night setback in comparison show little effect. The simulation results also showed that primary energy demand or greenhouse gas emissions are better measures for the comparison of environmental impact than COP and SCOP. [ABSTRACT FROM AUTHOR]

A semi-empirical characterization and simulation model for automotive air-conditioning open piston compressor is developed. The model is based on fundamental conservation principles and takes into account pressure drop and heat transfer in suction and discharge passages. Fundamental conservation principles equations, as well as volumetric and isentropic efficiencies, pressure drop, heat transfer and property equations are combined to form a system of non-linear algebraic equations. They are worked out so as to identify constants that are sole characteristics of the compressor and should not vary with different operating conditions or refrigerants. A numerical method determines such constants from existing experimental data, thus characterizing the compressor. Experimental data were obtained from tests carried out by Navarro et al. (2013) for an open piston compressor running with fluids R134a, R1234yf and R290. First, the experimental data were employed to determine the characterization parameters of the compressor. Then, the simulation model, with the R134a-based parameters, was applied to simulate the compressor operation with R1234yf and R290. Good agreement was obtained between predicted and experimental values, proving the suitability of the model for the study of new refrigerants. [ABSTRACT FROM AUTHOR]

The cooling energy consumption of data centers is increasing rapidly and free cooling attracts growing concern. To achieve the independent running of free cooling system all the year round, integrated system of mechanical refrigeration and thermosyphon (ISMT) is an ideal method. In this study, a distributed-parameter simulation model of an ISMT is built and validated by experimental data. The simulation results show that for thermosyphon mode, the cooling capacity increases with increasing air flow rate, temperature difference and pipe diameter, while decreases with increasing pipe length. For refrigeration mode, decreasing outdoor air temperature or increasing indoor air flow rate will improve the cooling capacity and reduce the input power of the compressor. For dual mode, applicable outdoor temperature range and indoor air flow rate range exist and the cooling capacity drops below that of refrigeration mode beyond these ranges. The critical values are 19 °C and 0.5 m 3  s −1 , respectively. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical study of a combined thermal system, which combines the Rankine cycle and the ejector refrigeration cycle. This combined cycle produces power and refrigeration simultaneously. The thermal system could use low temperature heat sources. A simulation was carried out to evaluate the cycle performance using several working fluids as R123, R141b, R245fa, R601a and R600a. 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 ejector is studied in optimal operating regime. The influence of thermodynamic parameters on system performance is studied. The results show that the condenser temperature, the evaporation temperature, the extraction ratio, the fluid nature and the generating temperature have significant effects on the system performances (the coefficient of performance of the combined cycle and the entrainment ratio of the ejector). [ABSTRACT FROM AUTHOR]

A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally combines explicit and implicit techniques in order to solve the one-dimensional conjugate heat transfer problem in an accurate and fast manner while ensuring energy conservation. The present model has been thoroughly validated against passive regenerator cases with an analytical solution. Compared to the fully implicit scheme, the proposed scheme achieves more accurate results, prevents numerical errors and requires less computational effort. In AMR simulations the new scheme can reduce the computational time by 89%. [ABSTRACT FROM AUTHOR]

Resistance heating with PTC elements to cover the heat demand of electric vehicles reduces significantly the cruising range at low outside temperatures. Reversible heat pump systems are one of the most promising solutions for this problem. However, in heat pump mode the frost formation on the exterior heat exchanger reduces the performance and efficiency of the system. Therefore, an efficient defrost method is crucial to benefit from the heat pump also under frosting conditions. In the present paper, a transient Modelica simulation model of a reversible CO 2 -heat pump system with hot gas defrost was set up in order to assess the impact of different defrost start times. The model is able to handle frost growth on the exterior heat exchanger as well as defrosting. The simulation results showed an optimal point of time to conduct defrost at chosen operating conditions in order to maximize the average COP including the frosting and defrost period. [ABSTRACT FROM AUTHOR]