A correlation of optimal heat rejection pressures in transcritical carbon dioxide cycles

In this work, a cycle simulation model has been developed to optimize the coefficient of performance (COP) of transcritical carbon dioxide air-conditioning cycles. The analysis shows that the COP of the transcritical carbon dioxide cycle varies nonmonotonically with the heat rejection pressure; a maximum COP occurs at an optimal heat rejection pressure. It is further revealed that the values of the optimal heat rejection pressure mainly depend on the outlet temperature of the gas cooler, the evaporation temperature, and the performance of the compressor. Based on the cycle simulations, correlations of the optimal heat rejection pressure in terms of appropriate parameters are obtained for specific conditions. The results are of significance for the design and control of the transcritical carbon dioxide air-conditioning and heat pump systems     

Theoretical and experimental studies on optimum heat rejection pressure for a CO2 heat pump system

The experimental and simulation researches have been conducted to investigate the relationships between optimum heat rejection pressure and other related operating parameters for a transcritical CO₂ heat pump system with two throttle valves. It proved that it is relatively reliable to control the heat rejection pressure of the CO₂ system with two expansion valves in series. The experimental results also show similar trends with those from simulation, under widely different operating conditions. Thus both the simulation and experimental results meet here: for a transcritical CO₂ cycle, there exists an optimal heat rejection pressure, under which the system can reach the maximum heating coefficient of performance (COP). Furthermore, the research also reveals that the optimal heat rejection pressure mainly depends on the refrigerant outlet temperature of gas cooler whereas the evaporating temperature and the performance of the given compressor have smaller effect on the optimum heat rejection pressure. Based on the experimental data, a correlation of the optimal heat rejection pressure with respect to mainly involved parameters is obtained for specific conditions.     

A comparative study of the carbon dioxide transcritical power cycle compared with an organic rankine cycle with R123 as working fluid in waste heat recovery

The organic rankine cycle (ORC) as a bottoming cycle¹ to convert low-grade waste heat into useful work has been widely investigated for many years. The CO₂ transcritical power cycle, on the other hand, is scarcely treated in the open literature. A CO₂ transcritical power cycle (CO₂ TPC) shows a higher potential than an ORC when taking the behavior of the heat source and the heat transfer between heat source and working fluid in the main heat exchanger into account. This is mainly due to better temperature glide matching between heat source and working fluid. The CO₂ cycle also shows no pinch limitation in the heat exchanger. This study treats the performance of the CO₂ transcritical power cycle utilizing energy from low-grade waste heat to produce useful work in comparison to an ORC using R123 as working fluid.Due to the temperature gradients for the heat source and heat sink the thermodynamic mean temperature has been used as a reference temperature when comparing both cycles. The thermodynamic models have been developed in EES² The relative efficiencies have been calculated for both cycles. The results obtained show that when utilizing the low-grade waste heat with the same thermodynamic mean heat rejection temperature, a transcritical carbon dioxide power system gives a slightly higher power output than the organic rankine cycle.     

Transcritical CO2 heat pump systems: exergy analysis including heat transfer and fluid flow effects

This paper presents the exergetic analysis and optimization of a transcritical carbon dioxide based heat pump cycle for simultaneous heating and cooling applications. A computer model has been developed first to simulate the system at steady state for different operating conditions and then to evaluate the system performance based on COP as well as exergetic efficiency, including component wise irreversibility. The chosen system includes the secondary fluids to supply the heating and cooling services, and the analyses also comprise heat transfer and fluid flow effects in detail. The optimal COP and the exergetic efficiency were found to be functions of compressor speed, ambient temperature and secondary fluid temperature at the inlets to the evaporator and gas cooler and the compressor discharge pressure. An optimization study for the best allocation of the fixed total heat exchanger inventory between the evaporator and the gas cooler based on heat transfer area has been conducted. The exergy flow diagram (Grassmann diagram) shows that all the components except the internal heat exchanger contribute significantly to the irreversibilities of the system. Unlike a conventional system, the expansion device contributes significantly to system irreversibility. Finally, suggestions for various improvement measures with resulting gains have been presented to attain superior system performance through reduced component irreversibilities. This study is expected to offer useful guidelines for system design and its optimisation and help toward energy conservation in heat pump systems based on transcritical CO₂ cycles.     

Exergy analysis of transcritical carbon dioxide refrigeration cycle with an expander

In this paper, a comparative study is performed for the transcritical carbon dioxide refrigeration cycles with a throttling valve and with an expander, based on the first and second laws of thermodynamics. The effects of evaporating temperature and outlet temperature of gas cooler on the optimal heat rejection pressure, the coefficients of performance (COP), the exergy losses, and the exergy efficiencies are investigated. In order to identify the amounts and locations of irreversibility within the two cycles, exergy analysis is employed to study the thermodynamics process in each component. It is found that in the throttling valve cycle, the largest exergy loss occurs in the throttling valve, about 38% of the total cycle irreversibility. In the expander cycle, the irreversibility mainly comes from the gas cooler and the compressor, approximately 38% and 35%, respectively. The COP and exergy efficiency of the expander cycle are on average 33% and 30% higher than those of the throttling valve cycle, respectively. It is also concluded that an optimal heat rejection pressure can be obtained for all the operating conditions to maximize the COP. The analysis results are of significance to provide theoretical basis for optimization design and operation control of the transcritical carbon dioxide cycle with an expander.     

Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source

In order to compare the power output of the carbon dioxide transcritical cycle and the R125 transcritical cycle for a low-grade heat source of about 100 °C, the two cycles were optimized for power output using a simulation method. In contrast to conventional approaches, each working fluid’s heat transfer and pressure drop characteristics within the heat exchangers were taken into account by using a discretized heat exchanger model. To fairly compare the power output of the cycles by using different working fluids, the inlet temperatures and the flow rates of both the heat source and the heat sink were fixed. The cycle minimum temperature was not given, but was determined by the heat sink conditions and the working fluid’s heat transfer and pressure drop characteristics, as it is in actual practice. The total heat transfer area was fixed, whereas the allocation of the heat-exchanger area between the vapor generator and the condenser was optimized in the simulation. The R125 transcritical cycle produced 14% more power than did the carbon dioxide transcritical cycle. Even though the carbon dioxide cycle shows better heat transfer and pressure drop characteristics in the heat exchangers, the high pumping power required to manage the large pressure head degrades the cycle’s power output. Based on this study, the R125 transcritical cycle is recommended for heat sources of about 100 °C.     

Wellbore temperature and pressure calculation model for coiled tubing drilling with supercritical carbon dioxide

To better control the state of carbon dioxide during supercritical carbon dioxide drilling, a mathematical model is established to analyze the wellbore carbon dioxide temperature and pressure influencing factors. In this model, the influences of formation temperature change and fluid-friction-generated heat on wellbore temperature distribution are considered. Additionally, the impact of casing, tubing, and cement sheath thermal resistance on heat transfer are considered. The model is validated by comparing the wellbore temperature data calculated from this model with data from previous models. Based on the model, the factors that may affect the wellbore carbon dioxide temperature and pressure are analyzed. The results show that the downhole temperature decreases with the decrease in nozzle diameter and geothermal gradient, and with the increase in injection rate. The injection temperature significantly affects the wellbore temperature near the wellhead, but it does not affect the downhole temperature. Therefore, for low geothermal gradient formation, reducing the injection rate and increasing the nozzle diameter are two effective methods to maintain the CO₂ at the downhole in the supercritical state. The pressure inside the coiled tubing increases with the increase in injection rate and decrease in nozzle diameter, but the injection temperature and geothermal gradient has little effect on the pressure inside both the coiled tubing and annulus.     

Investigation of convection‐based energy systems using supercritical carbon dioxide as a working fluid

Carbon dioxide is the best retrofit to meet the future demand on long‐term environmental friendly working fluids. The volumetric efficiency of supercritical carbon dioxide is very high, which makes it a promising working fluid in convection‐based energy systems with high efficiency and small volume. Here, the natural convection of supercritical carbon dioxide driven only by temperature difference is studied in circulation loops. The Reynolds number of the flow is about 10⁴ when the temperature difference is only 20 K, about two orders of magnitude greater than that of water. Furthermore, the heat transfer rate is about 3 times as great as that of water. These results demonstrate the potential of carbon dioxide as a working fluid in solar thermal conversion, nuclear power and waste heat utilization, etc. The influence of the tube diameter on the flow and heat transfer characteristics is discussed. Both the velocity and the Nusselt number are greater in the loop with a larger tube diameter where flow reversal occurs periodically. It is found that flow reversal degrades the system efficiency of the natural circulation loop. Therefore, the optimization about the geometric configuration of convection‐based energy systems using carbon dioxide as a working fluid does exist and is very important for their safe and effective operation. Copyright © 2010 John Wiley & Sons, Ltd.     

Thermoeconomic optimization and exergy analysis of CO2/NH3 cascade refrigeration systems

In this paper, thermoeconomic optimization and exergy analysis are applied to a CO₂/NH₃ cascade refrigeration cycle. Cooling capacity, ambient temperature and cold space temperature are constraints of the optimization procedure. Four parameters including condensing temperature of ammonia, evaporating temperature of carbon dioxide, condensing temperature of carbon dioxide and temperature difference in the cascade condenser are chosen as decision variables. The objective function is the total annual cost of the system which includes costs of input exergy to the system and annualized capital cost of the system. Input exergy to the system is the electricity consumption of compressors and fans, and the capital cost includes purchase costs of components. Results show that, optimum values of decision variables may be found by trade-off between the input exergy cost and capital cost. Results of the exergy analysis for each of the system components in the optimum state are also given.     

Theoretical performance analysis of heat pump water heaters using carbon dioxide as refrigerant

The aim of this paper is to simulate the performance of an air source heat pump water heater using carbon dioxide (CO₂) as a working fluid. The heat pump water heating system consists of a compressor, a gas cooler, an expansion device and an evaporator. The computer simulation model has been developed by using the heat transfer data and the thermodynamic properties of CO₂. The effects on the heat pump performance by the operating parameters such as the compressor rotational speed, the inlet water temperature at the gas cooler, the inlet air temperature at the evaporator and the mass flow rate ratio of water to refrigerant were presented. For rated capacities of a 4 kW compressor with a 10 kW gas cooler and a 6 kW evaporator, the coefficient of performance is found to be between 2.0 and 3.0. The mass flow rate ratio of water and CO₂ between 1.2 and 2.2 is the most suitable value for generating hot water temperature above 60°C at 15–25°C ambient air temperature. Copyright © 2007 John Wiley & Sons, Ltd.     

Exergy assessment of an optimized capillary tube‐based transcritical CO2 heat pump system

A capillary tube‐based CO₂ heat pump is unique because of the transcritical nature of the system. The transcritical cycle has two independent parameters, pressure and temperature, unlike the subcritical cycle. A comparative study for various operating conditions, based on system COP and exergetic efficiency, of a capillary tube and a controllable expansion valve‐based transcritical carbon dioxide heat pump systems for simultaneous heating and cooling at 73 and 4°C, respectively, is presented here. Two optimized capillary tubes having diameter of 1.5 and 1.6 mm are compared with an equivalent controllable throttle valve. Heat transfer and fluid flow effects are included in the gas cooler and evaporator model and capillary tube employs the homogeneous flow model to simulate two‐phase flow. Subcritical and supercritical thermodynamic and transport properties of CO₂ are calculated employing a precision in‐house property code. Optimization of effective distribution of total heat exchanger area ratio between gas cooler and evaporator is investigated. The exergetic efficiency is better in case of the capillary tube than that of a controllable throttle valve‐based system. Capillary tube‐based system is shown to be quite flexible regarding changes in ambient temperature, almost behaving to offer an optimal pressure control just like the controllable expansion valve yielding both, maximum system COP and maximum exergetic efficiency. Relatively at a smaller diameter, the capillary tube exhibits better exergetic efficiency. Capillary tube length is the critical parameter that influences system optimum conditions. The exergy flow diagram exhibits that compressor, gas cooler and capillary tube contribute a larger share, in that order, to system irreversibility. It is fairly established in this study that a capillary tube can be a good engineering option for small capacity systems in lieu of an expansion valve, which has been thought of as the only possible solution to attain the pressure optimization, an important feature of all transcritical CO₂ systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical Investigation of Jet Impingement Cooling of a Flat Plate with Carbon Dioxide at Supercritical Pressures

Confined round jet impingement cooling of a flat plate at constant heat flux with carbon dioxide at supercritical pressures was investigated numerically. The pressure ranged from 7.8 to 10.0 MPa, which is greater than the critical pressure of carbon dioxide, 7.38 MPa. The inlet temperature varied from 270 to 320 K and the heat flux ranged from 0.6 to 1.6 MW/m². The shear-stress transport turbulence model was used and the numerical model was validated by comparison with experimental results for jet impingement heating with hot water at supercritical pressures. Radial conduction in the jet impingement plate was also considered. The sharp variations of the thermal-physical properties of the fluid near the pseudocritical point significantly influence heat transfer on the target wall. For a given heat flux, the high specific heat near the wall for the proper inlet temperature and pressure maximizes the average heat transfer coefficient. For a given inlet temperature, the heat transfer coefficient remains almost unchanged with increasing surface heat flux at first and then decreases rapidly as the heat flux becomes higher due to the combined effects of the thinner high specific heat layer and the smaller thermal conductivity at higher temperature.     

Modeling and simulating the transcritical CO2 heat pump system

In this paper, a mathematical model for steady-state simulation of transcritical CO₂ water-to-water heat pump system with an expander has been developed. It is used to simulate the performance of transcritical CO₂ system with CO₂ expander prototype. Simulated results are compared with experimental data to verify the accuracy of the simulation model. The comparison results show the average deviation of about 15% for COP_c(cooling coefficient of performance) and COP_h(heating coefficient of performance), about 17% for cooling and heating capacity at experimental high pressure ranges. With this model, which has been validated in a limited high pressure range, the influence of water mass flow rate and water inlet temperature of both evaporator and gas cooler on the performance of transcritical CO₂ expander system is analyzed. The results show that decreasing inlet temperature and increasing mass flow rate of cooling water cannot only increase the system performance but also reduce the optimal heat rejection pressure, at which the maximum COP (coefficient of performance) can be obtained. For chilling water, increasing its inlet temperature and mass flow rate is favorable for increasing the system performance, while the optimal heat rejection pressure does not vary very much.     

Cooling load density characteristics of an endoreversible variable‐temperature heat reservoir air refrigerator

The performance optimization of an endoreversible air refrigerator with variable‐temperature heat reservoirs is carried out by taking the cooling load density, i.e. the ratio of cooling load density to the maximum specific volume in the cycle, as the optimization objective in this paper. The analytical relations of cooling load, cooling load density and coefficient of performance are derived with the heat resistance losses in the hot‐ and cold‐side heat exchangers. The maximum cooling load density optimization is performed by searching the optimum pressure ratio of the compressor, the optimum distribution of heat conductance of the hot‐ and cold‐side heat exchangers for the fixed total heat exchanger inventory, and the heat capacity rate matching between the working fluid and the heat reservoirs. The influences of some design parameters, including the heat capacitance rate of the working fluid, the inlet temperature ratio of heat reservoirs and the total heat exchanger inventory on the maximum cooling load density, the optimum heat conductance distribution, the optimum pressure ratio and the heat capacity rate matching between the working fluid and the heat reservoirs are provided by numerical examples. The refrigeration plant design with optimization leads to a smaller size including the compressor, expander and the hot‐ and cold‐side heat exchangers. Copyright © 2002 John Wiley & Sons, Ltd.     

变工况下直接空冷机组最佳真空的分析

为了提高直接空冷机组运行经济性,以冷端系统的变工况模型为基础,通过计算空冷凝汽器风机送风量增大时空冷机组发电功率与对应风机耗功功率的增量,得到直接空冷机组凝汽器最佳真空的确定方法．根据相似定律确定迎面风速对风机耗功的影响,并通过冷端系统数学模型的分析和简化得到机组背压与发电功率的关系,最终导出了不同环境温度和排汽热负荷下迎面风速对应的最佳真空．根据模型对某330Mw机组在变工况下的最佳真空进行了计算,结果表明：随着排汽量的增加或环境温度的升高,最佳真空及对应的风量都增加;当环境温度高于20℃时,环境温度对最佳真空的影响更加突出．     

Performance of an air-cooled looped thermoacoustic engine capable of recovering low-grade thermal energy

An air-cooled looped thermoacoustic engine is designed and constructed, where an air-cooled cold heat exchanger (consisting of copper heat transfer block, aluminum flange, and aluminum fin plate) is adopted to extract heat and the resonant tube is spiraled and shaped to fit to the available space. Experiments have been conducted to observe how onset temperature difference and resonant frequency are affected by mean pressure, working fluid, and diameter of compliance tube. Besides, the influences of temperature difference, mean pressure, working fluid and diameter of compliance tube on pressure amplitude, output acoustic power, and thermal efficiency of the system have been investigated. The air-cooled looped thermoacoustic engine can start to oscillate at a lowest temperature difference of 46°C, with the working fluid of carbon dioxide at 2.34 MPa. A highest output acoustic power obtained is 6.65 W at a temperature difference of 199°C, with the working gas of helium at 2.58 MPa, and the thermal efficiency is 2.21%. This work verifies the feasibility of utilizing low-grade thermal energy to drive an air-cooled looped thermoacoustic engine and extends its application in the water deficient areas.     

Steady-State Behavior of Natural Circulation Loops Operating With Supercritical Fluids for Open and Closed Loop Boundary Conditions

Supercritical water (SCW) exhibits excellent heat transfer characteristics and a high volumetric expansion coefficient (hence high mass flow rates in natural circulation systems) near the critical temperature. SCW is being considered as a coolant in some advanced nuclear reactor designs on account of its potential to offer high thermal efficiency, compact size, and elimination of steam generator, separator, and dryer, making it economically competitive. The elimination of phase change results in elimination of the critical heat flux phenomenon. Cooling a reactor at full power with natural instead of forced circulation is generally considered an enhancement of passive safety. In view of this, it is essential to study natural circulation behavior at supercritical conditions. Carbon dioxide can be considered to be a good simulant of water for natural circulation at supercritical conditions, since the density and viscosity variation of carbon dioxide follows a curve parallel to that of water at supercritical conditions. Hence, experiments were conducted in a closed supercritical pressure natural circulation loop (SPNCL) with supercritical carbon dioxide as working fluid. A nonlinear stability analysis code (NOLSTA) has been developed to carry out steady-state and stability analysis of open and closed loop natural circulation at supercritical conditions. The code has been validated for steady-state predictions with experimental data available in open literature and experiments conducted in SPNCL.     

Electrochemical performance characteristics and optimum design strategies of a solid oxide electrolysis cell system for carbon dioxide reduction

An analytical model is developed to study the electrochemical characteristics of a solid oxide electrolysis cell (SOEC) for carbon dioxide reduction, in which the activation overpotential, concentration overpotential, and ohmic overpotential are considered as the main sources of voltage losses. The Bulter-Volmer equation, DGM model, and Ohm's law are employed to characterize the three overpotentials, respectively. The theoretical model is validated by comparing the simulation results with the experimental data from the literature. The anode-supported configuration SOEC is found to be the most favorable design. The effects of the cathode inlet gas molar fraction on the cathode overpotential and the cell potential are discussed in detail. It is found that there exists an optimum molar fraction for the cathode inlet gas at which the cathode concentration overpotential attains its minimum for given operation conditions. Moreover, the effects of some importantly operating parameters such as the current density, temperature and pressure on the cell potential are discussed. Thermal-electrochemical analysis shows that the Joule heat generated from the irreversibilities in the SOEC may be larger than, equal to, or smaller than the thermal energy needed for the carbon dioxide reduction reaction, and consequently, a system layout with five different design strategies to implement the carbon dioxide electrolysis is put forward.     

Tethered methanol droplet combustion in carbon-dioxide enriched environment under microgravity conditions

Tethered methanol droplet combustion in carbon dioxide enriched environment is simulated using a transient one-dimensional spherosymmetric droplet combustion model that includes the effects of tethering. A priori numerical predictions are compared against recent experimental data. The numerical predictions compare favorably with the experimental results and show significant effects of tethering on the experimental observations. The presence of a relatively large quartz fiber tether increases the burning rate significantly and hence decreases the extinction diameter. The simulations further show that the extinction diameter depends on both the initial droplet diameter and the ambient concentration of carbon dioxide. Increasing the droplet diameter and ambient carbon dioxide concentration both of them lead to a decrease in the burning rate and increase in the extinction diameter. The influence of ambient carbon dioxide concentration on extinction shows a sharp transition in extinction for larger size droplets (d_o > 1.5 mm) due to a change in the mode of extinction from diffusive to radiative control. In addition predictions from the numerical model is compared against a recently developed simplified theoretical model for predicting extinction diameter for methanol droplets, where the presence and heat transfer contribution of the tether is not taken into account implicitly. The numerical results suggest some limitation in the theoretical modeling assumptions for favorable comparisons with the experimental data.     

热虹吸管传热过程中的熵增分析

以热力学理论为基础，对稳定操作条件下的热虹吸管的重要操作参数、工作特点及其内部工质循环过程进行详细分析，导出了由于存在温度差、工质流动摩擦损失、蒸气温度／压力降等因素而引起的熵增的表达式，并由此得到相应的最小熵增优化准则。所得到的热虹吸管重要操作条件，即蒸发段和冷凝段温度匹配关系以及其它重要影响参数的关系，可以为热管实际设计和应用提供重要的理论参考。