Pump Cycle

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Gang Yan - One of the best experts on this subject based on the ideXlab platform.

  • thermodynamic assessment of a condenser outlet split ejector based high temperature heat Pump Cycle using various low gwp refrigerants
    Energy, 2019
    Co-Authors: Tao Bai, Gang Yan
    Abstract:

    Abstract This paper presents a condenser outlet split ejector based Cycle for high temperature heat Pump. The thermodynamic behaviors of the Cycle are investigated with energetic and exergetic methods. The condenser outlet split ejector-based Cycle and ejector outlet split Cycle are compared at various low GWP refrigerants suitable for high temperature heat Pump applications, and results indicate that R600, R1224yd(Z), R1234ze(Z) and R1233zd(E) are proposed due to low GWP, high coefficient of performance (COP) and small compressor size. The condenser outlet split ejector-based Cycle could provide dual-temperature evaporation with an ejector between two evaporators. In comparison with the basic heat Pump Cycle and the ejector outlet split Cycle, the condenser outlet split-based Cycle presents 14.1–17.5% and 5.4–11.9% higher COP, respectively. The ejector pressure lift ratio of the condenser outlet split ejector Cycle is 6.5–12.5% higher than that in the ejector outlet split-based Cycle. The exergy destruction of the evaporator can be effectively reduced by the dual-temperature evaporation in the condenser outlet split ejector-based Cycle. The performance characteristics of the ejector outlet split Cycle show its potential advantages in high-temperature heat Pump applications.

  • theoretical study on a modified heat Pump Cycle with zeotropic mixture r32 r290 for district heating in cold region
    Applied Thermal Engineering, 2019
    Co-Authors: Chaochao Fan, Gang Yan
    Abstract:

    Abstract This paper proposes an ejector enhanced internal auto-cascade heat Pump Cycle (EIHP) with zeotropic mixture R32/R290 for district heating in cold region. The internal auto-cascade and ejector techniques are applied for enhancing the system performance. Performances of the EIHP are investigated by using a developed thermodynamic model. The simulation results indicate that as the evaporator outlet temperature ranges −25 °C to 5 °C, EIHP yields 19–9% higher COP and 37–12% higher volumetric heating capacity over the conventional heat Pump Cycle (CHP) at a fixed condenser outlet temperature of 60 °C. Moreover, to evaluate the system performance in detail, the other critical parameters are investigated including condenser outlet temperature, refrigerant mass fraction of R32, ejector performance and so on. Generally, the EIHP system can obtain a significant performance enhancement for district heating applications.

  • Theoretical study on a modified heat Pump Cycle with zeotropic mixture R32/R290 for district heating in cold region
    Applied Thermal Engineering, 2019
    Co-Authors: Fan Chaochao, Gang Yan
    Abstract:

    Abstract This paper proposes an ejector enhanced internal auto-cascade heat Pump Cycle (EIHP) with zeotropic mixture R32/R290 for district heating in cold region. The internal auto-cascade and ejector techniques are applied for enhancing the system performance. Performances of the EIHP are investigated by using a developed thermodynamic model. The simulation results indicate that as the evaporator outlet temperature ranges −25 °C to 5 °C, EIHP yields 19–9% higher COP and 37–12% higher volumetric heating capacity over the conventional heat Pump Cycle (CHP) at a fixed condenser outlet temperature of 60 °C. Moreover, to evaluate the system performance in detail, the other critical parameters are investigated including condenser outlet temperature, refrigerant mass fraction of R32, ejector performance and so on. Generally, the EIHP system can obtain a significant performance enhancement for district heating applications.

  • Thermodynamic analysis of a modified solar assisted ejector-compression heat Pump Cycle with zeotropic mixture R290/R600a
    Applied Thermal Engineering, 2019
    Co-Authors: Fan Chaochao, Gang Yan
    Abstract:

    Abstract This paper proposes a modified solar assisted ejector-compression heat Pump Cycle with zeotropic mixture R290/R600a (MHP) for water heater applications, which could efficiently utilize both the air source energy and solar energy. Depending on the solar radiation intensity, MHP contains two operation modes, i.e., Mode-A/-B for high/low solar radiation intensity conditions, respectively. In MHP, the use of zeotropic mixture ensures a better matching characteristic between the temperature variations of the refrigerant and water in the condenser due to its temperature glide feature. The simulation results show that compared with the conventional heat Pump Cycle (CHP), as the condenser inlet saturated temperature ranges 45–80  °C, MHP-A yields 28–33% higher COP and 22–47% higher volumetric heating capacity at a fixed evaporator outlet temperature of 10 °C. And increasing the solar radiation intensity is beneficial to the performance improvement of MHP-A. Additionally, in order to display the Cycle characteristic, the effects of other critical parameters are studied in detail, including the evaporator outlet temperature, mixture composition, heat source capacity ratio, etc.

  • energy and exergy efficiency analysis of solar driven ejector compressor heat Pump Cycle
    Solar Energy, 2016
    Co-Authors: Gang Yan, Tao Bai
    Abstract:

    Abstract This study presents a solar driven ejector compression heat Pump Cycle (SEHPC) for air-source heat Pump water heater application. The proposed Cycle utilizing solar radiation to drive an ejector could effectively lift the suction pressure of the compressor and enhance the system heating performance. The thermodynamic investigations on the performance characteristics of the SEHPC using R134a and R1234yf as the refrigerant are performed with energetic and exegetic methods, and the comparative analyses with the conventional compression heat Pump Cycle (CHPC) are conducted. The simulation results show that SEHPC system yields a remarkable improvement of heating performance over the CHPC system. It is found that under the operating conditions considered, the system COP, heating capacity and heating exergy output could be improved by 15.3%, 38.1% and 52.8% over the conventional heat Pump system, respectively. The largest exergy destruction is generated in the ejector, which could amount to 25.7% of the total system exergy input, followed by condenser and evaporator. The performance characteristics of the proposed Cycle show its application potential in air-source heat Pump water heater.

Fengrui Sun - One of the best experts on this subject based on the ideXlab platform.

  • thermodynamic optimization principle for open inverse brayton Cycle refrigeration heat Pump Cycle
    Scientia Iranica, 2012
    Co-Authors: W. Zhang, Lingen Chen, Fengrui Sun
    Abstract:

    Abstract A thermodynamic model for an open inverse Brayton Cycle (refrigeration or heat Pump Cycle) with pressure drop irreversibilities is established. There are seven flow resistances (or pressure drops) encountered by the working fluid stream for the inverse Brayton Cycle. Two of these, the friction through the blades and vanes of the compressor and the expander, are related to the isentropic efficiencies. The remaining flow resistances are always present because of the changes in flow cross-section at the compressor inlet and outlet, heat exchanger inlets and outlets and expander inlet and outlet. The analytical formulae about the cooling load of refrigeration Cycle, the heating load of heat Pump Cycle and other coefficients are derived, which indicate that the thermodynamic performance for open inverse Brayton Cycle can be optimized by adjusting the mass flow rate (or the distribution of pressure losses along the flow path). It is shown that there are optimal air mass flow rates (or the distribution of pressure losses along the flow path) which maximize the cooling load of refrigeration Cycle, and the optimal air mass flow rates are smaller than the one at the maximum power output of the direct Brayton Cycle.

  • thermodynamic optimisation for open regenerated inverse brayton Cycle refrigeration heat Pump Cycle
    Journal of The Energy Institute, 2012
    Co-Authors: W. Zhang, Lingen Chen, Fengrui Sun
    Abstract:

    A thermodynamic model for an open regenerated inverse Brayton Cycle with pressure drop irreversibilities is established using finite time thermodynamics considering the size constraints of real plant in Part 1 of this paper. The analytical formulae about the cooling load and coefficient of performance of refrigeration Cycle, the heating load and coefficient of performance of heat Pump Cycle are derived, which indicate that the thermodynamic performance for open regenerated inverse Brayton Cycle can be optimised by adjusting the mass flowrate. It is shown that the cooling load, heating load and the power input increase with the increase in the compressor inlet relative pressure drops, the coefficient of performance reaches its maximum at the optimal compressor ratio and the exhaust temperature is higher than that of the ambient, which is lower than that of the ambient only at small effectiveness of the regenerator.

  • Thermodynamic optimisation for open regenerated inverse Brayton Cycle (refrigeration/heat Pump Cycle)
    Journal of the Energy Institute, 2012
    Co-Authors: W. Zhang, Lingen Chen, Fengrui Sun
    Abstract:

    A thermodynamic model for an open regenerated inverse Brayton Cycle with pressure drop irreversibilities is established using finite time thermodynamics considering the size constraints of real plant in Part 1 of this paper. The analytical formulae about the cooling load and coefficient of performance of refrigeration Cycle, the heating load and coefficient of performance of heat Pump Cycle are derived, which indicate that the thermodynamic performance for open regenerated inverse Brayton Cycle can be optimised by adjusting the mass flowrate. It is shown that the cooling load, heating load and the power input increase with the increase in the compressor inlet relative pressure drops, the coefficient of performance reaches its maximum at the optimal compressor ratio and the exhaust temperature is higher than that of the ambient, which is lower than that of the ambient only at small effectiveness of the regenerator.

  • Optimal piston speed ratio analyses for irreversible Carnot refrigerator and heat Pump using finite time thermodynamics, finite speed thermodynamics and direct method
    Journal of the Energy Institute, 2011
    Co-Authors: Leida Chen, Huijun Feng, Fengrui Sun
    Abstract:

    AbstractAn irreversible Carnot refrigeration and heat Pump Cycle model with external irreversibilities caused by finite rate of heat transfer, heat leakage from heat sink to heat source and internal irreversibilities caused by finite piston speed, friction and gas throttling is established by using the combination of finite time thermodynamics, finite speed thermodynamics and direct method. Different from the model of constant speed of the piston on the four branches, the piston speeds on the four branches in this model are assumed to be unequal. Expressions of cooling load and coefficient of performance (COP) of the Carnot refrigeration Cycle as well as heating load and COP of the heat Pump Cycle are derived for a fixed Cycle period. Numerical examples show that the curves of COP versus cooling load and COP versus heating load are parabolic like ones, and there exist optimal finite piston speed ratios on the four branches, which lead to the maximum COPs. Moreover, the effects of the heat leakage coeffici...

  • Finite-time exergoeconomic performance analysis and optimisation for generalised irreversible combined heat Pump Cycles
    International Journal of Ambient Energy, 2011
    Co-Authors: Lingen Chen, Fengrui Sun
    Abstract:

    Finite-time exergoeconomic performance of a Newtonian heat transfer law system generalised irreversible combined heat Pump Cycle model with irreversibility of finite-rate heat transfer, heat leakage and internal irreversibility is studied in this article. The operation of the generalised irreversible combined heat Pump Cycle is viewed as a production process with exergy as its output. The performance optimisation of the Cycle is performed by taking profit as the objective. The optimal profit rate, optimal coefficient of performance (COP), as well as the relation between the optimal profit rate and COP of the Cycle are derived. The focus of this article is to obtain the compromise optimisation between economics (profit rate) and the energy utilisation factor (COP) for the Cycle, by searching the optimum COP at maximum profit rate, which is termed as the finite-time exergoeconomic performance bound. Moreover, the effects of various factors, including heat leakage, internal irreversibility and the price rati...

Shigeru Koyama - One of the best experts on this subject based on the ideXlab platform.

  • thermodynamic analysis of vapor compression heat Pump Cycle for tap water heating and development of co2 heat Pump water heater for residential use
    Applied Thermal Engineering, 2016
    Co-Authors: Michiyuki Saikawa, Shigeru Koyama
    Abstract:

    Abstract The ideal vapor compression Cycle for tap water heating and its coefficient of performance (COP) have been studied theoretically at first. The ideal Cycle is defined as the Cycle whose high temperature heat source varies temperature with constant specific heat and other processes are same as the reverse Carnot Cycle. The COP upper limit of single stage compression heat Pump Cycle for tap water heating with various refrigerants such as fluorocarbons and natural refrigerants was calculated. The refrigerant which achieves the highest COP for supplying hot water is CO2. Next, the prototype of CO2 heat Pump water heater for residential use has been developed. Its outline and experimental results are described. Finally its further possibility of COP improvement has been studied. The COP considered a limit from a technical point of view was estimated about 6.0 at the Japanese shoulder season (spring and autumn) test condition of heating water from 17 °C to 65 °C at 16 °C heat source air temperature (dry bulb)/12 °C (wet bulb).

  • The Circulation Composition Characteristic of the Zeotropic Mixture R1234ze(E)/R32 in a Heat Pump Cycle
    2012
    Co-Authors: Sho Fukuda, Nobuo Takata, Shigeru Koyama
    Abstract:

    This study presents an experimental investigation of the circulation composition in a heat Pump Cycle for considering the effect of its difference from the charged composition on the Cycle performance prediction. The experiment was conducted with a vapor compression heat Pump Cycle using a compressor developed for R410A. The tested refrigerants are R1234ze(E)/R32 (20/80 mass%),R1234ze(E)/R32 (50/50 mass%), and R1234ze(E)/R32 (80/20 mass%). Compared with the charged composition, the measured mass fraction of the more volatile component R1234ze(E)increases at inlet of the expansion valve. When the difference between vapor and liquid composition is large in the two-phase flow, the difference between circulation and changed composition is large enough to affect the COP evaluation. The circulation composition depends on the velocity ratio of vapor and liquid, the operating pressure of heat Pump Cycle, and the degree of subcool at condenser outlet.

  • Analysis of Heat Pump Cycle Using CO2/DME Mixture Refrigerant
    2008
    Co-Authors: Yoji Onaka, Akio Miyara, Koutaro Tsubaki, Shigeru Koyama
    Abstract:

    In this study, the performance analysis of heat Pump Cycle using carbon dioxide (CO2) and dimethyl ether (DME) zeotropic mixture has been carried out by Cycle calculation in order to clarify the characteristics and coefficient of performance (COP) of CO2/DME heat Pump Cycle. The calculation conditions were established as a hot-water supply system and the calculations were conducted by considering the heat transfer between the refrigerant and heat source/sink water. The heat Pump Cycle is formed around the critical point for high CO2 concentration mixtures and it is formed under the critical point for low CO2 concentration mixtures. The COP has the maximum at a certain pressure for each mixture and the COPs of the mixture and pure DME are higher than that of pure CO2. Operating pressure and refrigerant mass flow rate decreases with increase of DME concentration. The effects of concentration on characteristics of the Cycle have also been discussed.

  • Performance evaluation of a vapor compression heat Pump Cycle using binary zeotropic refrigerant mixtures
    1999
    Co-Authors: Shigeru Koyama, Tomoyasu Yara
    Abstract:

    The HCFC refrigerants such as R22 have been used widely as working fluids in refrigeration and air-conditioning systems until now. These refrigerants, however, should be phased out early in the next century to prevent the depletion of the ozone layer. In this situation, binary and/or ternary mixtures composed of HFC and/or natural refrigerants have attracted a great deal of attention due to the following possibilities: (1) to improve the coefficient of performance, COP, by utilizing the temperature glide during phase change processes; (2) to keep the system in more suitable condition for given temperature levels of heat source and heat sink by selecting the combination and composition of refrigerants, etc. From this point of view, in the present study, the performance prediction of a vapor compression heat Pump Cycle using binary zeotropic refrigerant mixtures is carried out to clarify the effects of the combination of refrigerants, the composition of refrigerants and the size of heat exchangers on COP. In the prediction calculation, a vapor compression heat Pump Cycle, which consists of a compressor, a vertical plate-fin condenser, an expansion valve, a liquid-vapor separator and a vertical plate-fin evaporator is treated, and the following assumptions are employed: (1) the compression processmore » is isentropic, (2) the expansion process is isenthalpic, (3) the refrigerant is a saturated liquid at the condenser outlet and a superheated vapor at the evaporator outlet, (4) the pressure drop in the condenser is negligible, while that in the evaporator is considered, (5) the local heat transfer characteristics in heat exchangers are considered. The prediction calculation is done for the binary zeotropic refrigerant mixtures of HFC134a/HCFC123 on condition that the heat source water temperature at the condenser outlet, the heat sink water temperature at the evaporator inlet, the water temperature change through condenser and evaporator, the heat load of condenser, the superheat of refrigerant vapor at the evaporator outlet and the size of heat exchangers are given as known parameters.« less

  • Performance evaluation of a heat Pump Cycle using NARMs by a simulation with equations of heat transfer and pressure drop
    International Journal of Refrigeration, 1993
    Co-Authors: Akio Miyara, Shigeru Koyama, Tetsu Fujii
    Abstract:

    Abstract Simulation analyses for a vapour compression heat Pump Cycle using nonazeotropic refrigerant mixtures (NARMs) of R22 and R114 are conducted under the condition that the heat Pump thermal output and the flow rate and inlet temperatures of the heat sink and source water are given. The heat transfer coefficients of the condensation and evaporation are calculated with empirical correlations proposed by the authors. The validity of the evaluation method and the correlations is demonstrated by comparison with experimental data. The relations between the coefficient of performance (COP) and composition are shown under two conditions: (1) the constant heat transfer length of the condenser and evaporator; and (2) the constant temperature of refrigerant at the heat exchanger inlet. The COP of the NARMs is higher than that of pure refrigerant when the heat transfer lengths of the condenser and evaporator are sufficiently long.

Lingen Chen - One of the best experts on this subject based on the ideXlab platform.

  • thermodynamic optimization principle for open inverse brayton Cycle refrigeration heat Pump Cycle
    Scientia Iranica, 2012
    Co-Authors: W. Zhang, Lingen Chen, Fengrui Sun
    Abstract:

    Abstract A thermodynamic model for an open inverse Brayton Cycle (refrigeration or heat Pump Cycle) with pressure drop irreversibilities is established. There are seven flow resistances (or pressure drops) encountered by the working fluid stream for the inverse Brayton Cycle. Two of these, the friction through the blades and vanes of the compressor and the expander, are related to the isentropic efficiencies. The remaining flow resistances are always present because of the changes in flow cross-section at the compressor inlet and outlet, heat exchanger inlets and outlets and expander inlet and outlet. The analytical formulae about the cooling load of refrigeration Cycle, the heating load of heat Pump Cycle and other coefficients are derived, which indicate that the thermodynamic performance for open inverse Brayton Cycle can be optimized by adjusting the mass flow rate (or the distribution of pressure losses along the flow path). It is shown that there are optimal air mass flow rates (or the distribution of pressure losses along the flow path) which maximize the cooling load of refrigeration Cycle, and the optimal air mass flow rates are smaller than the one at the maximum power output of the direct Brayton Cycle.

  • thermodynamic optimisation for open regenerated inverse brayton Cycle refrigeration heat Pump Cycle
    Journal of The Energy Institute, 2012
    Co-Authors: W. Zhang, Lingen Chen, Fengrui Sun
    Abstract:

    A thermodynamic model for an open regenerated inverse Brayton Cycle with pressure drop irreversibilities is established using finite time thermodynamics considering the size constraints of real plant in Part 1 of this paper. The analytical formulae about the cooling load and coefficient of performance of refrigeration Cycle, the heating load and coefficient of performance of heat Pump Cycle are derived, which indicate that the thermodynamic performance for open regenerated inverse Brayton Cycle can be optimised by adjusting the mass flowrate. It is shown that the cooling load, heating load and the power input increase with the increase in the compressor inlet relative pressure drops, the coefficient of performance reaches its maximum at the optimal compressor ratio and the exhaust temperature is higher than that of the ambient, which is lower than that of the ambient only at small effectiveness of the regenerator.

  • Thermodynamic optimisation for open regenerated inverse Brayton Cycle (refrigeration/heat Pump Cycle)
    Journal of the Energy Institute, 2012
    Co-Authors: W. Zhang, Lingen Chen, Fengrui Sun
    Abstract:

    A thermodynamic model for an open regenerated inverse Brayton Cycle with pressure drop irreversibilities is established using finite time thermodynamics considering the size constraints of real plant in Part 1 of this paper. The analytical formulae about the cooling load and coefficient of performance of refrigeration Cycle, the heating load and coefficient of performance of heat Pump Cycle are derived, which indicate that the thermodynamic performance for open regenerated inverse Brayton Cycle can be optimised by adjusting the mass flowrate. It is shown that the cooling load, heating load and the power input increase with the increase in the compressor inlet relative pressure drops, the coefficient of performance reaches its maximum at the optimal compressor ratio and the exhaust temperature is higher than that of the ambient, which is lower than that of the ambient only at small effectiveness of the regenerator.

  • Finite-time exergoeconomic performance analysis and optimisation for generalised irreversible combined heat Pump Cycles
    International Journal of Ambient Energy, 2011
    Co-Authors: Lingen Chen, Fengrui Sun
    Abstract:

    Finite-time exergoeconomic performance of a Newtonian heat transfer law system generalised irreversible combined heat Pump Cycle model with irreversibility of finite-rate heat transfer, heat leakage and internal irreversibility is studied in this article. The operation of the generalised irreversible combined heat Pump Cycle is viewed as a production process with exergy as its output. The performance optimisation of the Cycle is performed by taking profit as the objective. The optimal profit rate, optimal coefficient of performance (COP), as well as the relation between the optimal profit rate and COP of the Cycle are derived. The focus of this article is to obtain the compromise optimisation between economics (profit rate) and the energy utilisation factor (COP) for the Cycle, by searching the optimum COP at maximum profit rate, which is termed as the finite-time exergoeconomic performance bound. Moreover, the effects of various factors, including heat leakage, internal irreversibility and the price rati...

  • heating load cop exergy loss rate exergy output rate and ecological optimizations for a class of generalized irreversible universal heat Pump Cycles
    Revista Mexicana De Fisica, 2010
    Co-Authors: Lingen Chen, Huijun Feng
    Abstract:

    The optimal performance of a class of generalized irreversible universal steady flow heat Pump Cycle model, which consists of two heatabsorbing branches, two heat-releasing branches and two irreversible adiabatic branches with the losses of heat-resistance, heat leakage and internal irreversibility is analyzed by using finite time thermodynamics. The analytical formulae about heating load, coefficient of performance (COP), exergy loss rate, exergy output rate and ecological function of the universal heat Pump Cycle are derived. Moreover, performance comparisons among maximum COP condition, a given exergy output rate condition and maximum ecological function condition are carried out by using numerical examples. It is shown that the ecological function objective is an excellent candidate objective with the ideal of an ecological and long-term goal. The effects of heat leakage and internal irreversibility on the Cycle performance are discussed. The universal Cycle model gives a unified description of seven heat Pump Cycles, and the results obtained include the performance characteristics of Brayton, Otto, Diesel, Atkinson, Dual, Miller and Carnot heat Pump Cycles with the losses of heat-resistance, heat leakage and internal irreversibility.

Meibo Xing - One of the best experts on this subject based on the ideXlab platform.

  • performance analysis of a new ejector enhanced vapor injection heat Pump Cycle
    Energy Conversion and Management, 2015
    Co-Authors: Xiao Wang, Meibo Xing
    Abstract:

    Abstract This paper proposes a novel ejector enhanced vapor injection Cycle (EVIC) for air-source heat Pumps. In the EVIC system, an ejector associated with an additional flash tank is introduced to enhance the overall system performance at low ambient temperature. The performances of the EVIC using R22, R290 and R32 are evaluated using the developed mathematical model, and then compared with those of the basic vapor injection Cycle (BVIC). According to the simulation results, the EVIC with R22, R290 and R32 have 2.6–3.1%, 3.2–3.7% and 2.9–3.1% improvement in coefficient of performance (COP), 6.0–8.4%, 7.3–10.2% and 6.7–8.2% improvement in volumetric heating capacity compared with those of the BVIC under the same given operating conditions. Simultaneously, the EVIC also shows a good performance in reduction of the compressor discharge temperature at the given operating conditions. The performance characteristics of the EVIC may show its promise in heat Pump applications.

  • thermodynamic analysis on a two stage transcritical co2 heat Pump Cycle with double ejectors
    Energy Conversion and Management, 2014
    Co-Authors: Meibo Xing, Jianlin Yu
    Abstract:

    Abstract In this study, two ejectors are proposed as expansion devices for a two-stage transcritical CO 2 heat Pump Cycle to enhance the Cycle performance. The two ejectors are arranged at the low- and high-pressure stages, respectively, to recover more available expansion work, and significantly reduce the throttling loss at each stage. The performance of the improved two-stage Cycle is evaluated by using the developed mathematical model, and then compared with those of the basic two-stage Cycle with a flash tank. The simulation results show that the improved two-stage Cycle exhibits higher heating COP and volumetric heating capacity compared to the basic two-stage Cycle. By further incorporating an internal heat exchanger, the heating COP can be increased by 10.5–30.6% above that of the baseline Cycle when the subcooling degree varied from 0 to 15 °C under given operation conditions of −15 °C evaporating temperature, 10 MPa gas cooler pressure and 35 °C outlet temperature. Additionally, the effects of the gas cooler pressure and intermediate pressure on the maximal heating COP are also discussed.