Performance evaluation of a low-grade power generation system with CO2 transcritical power cycles

Globally, there are vast amounts of low-grade heat sources from industrial waste and renewables that can be converted into electricity through advanced thermodynamic power cycles and appropriate working fluids. In terms of the working fluid’s environmental impact, temperature match of cycle heat processes and system compactness, CO2 transcritical power cycles (T-CO2) were deemed more applicable for low-grade heat to power conversion. However, the system thermal efficiency of a T-CO2 requires further improvement. Subsequently, a test rig of the small-scale power generation system with T-CO2 power cycles was developed with essential connected components. These include a plate thermal coil CO2 supercritical heater, a CO2 transcritical turbine, a plate recuperator, an air-cooled finned-tube CO2 condenser and a CO2 liquid pump. Various preliminary test results from the system measurements are demonstrated in this paper. Meanwhile, the system model has been developed and applied to predict system performance at different operating conditions. The simulation results can therefore instruct further design and optimisation of system and components.


Introduction
The extensive consumption of fossil fuels worldwide in power generation has been increasingly contributing towards global warming, air pollution and the imminent energy crisis. One of the challenges of the 21st century is to tackle the risks arising from excessive CO 2 emissions by replacing fossil fuels with recovered waste heat and renewable energy. Waste heat sources can be divided into three main categories according to their temperature ranges: high temperature (> 650°C), medium temperature (230-650°C) and low temperature (< 230°C) [1]. However, statistics have shown that more than 50% of industrial waste heat and renewables are within the low-grade range [2]. These include heat from manufacturing and process industries, solar energy, geothermal energy, and from internal combustion engine exhausts and coolants used in commercial, institutional or automotive applications. Therefore, low-grade waste heat recovery for power generation is a significant and highly recommended strategy to tackle global warming, utilising advanced thermodynamic power cycles and appropriate working fluids [3,4].
Organic Rankine Cycles (ORC) are a known feasible option for the application of low-grade heat sources in terms of operating parameters, system sizes, thermal and exergy efficiencies. The ORC functions similarly to a Clausius-Rankine steam power plant, but instead uses an organic working fluid such as R245fa, which is able to condense at a lower pressure (compared to evaporator pressure) and evaporate at a higher pressure (compared to condenser pressure). However, one important limitation of the ORC is its constant evaporation temperature, which increases irreversibly during the heat addition process when using sensible heat sources such as waste heat [5]. In addition, a hydrofluorocarbon (HFC) working fluid is conventionally applied in an ORC, which has zero Ozone Depletion Potential (ODP) but a relatively high Global Warming Potential (GWP). This will affect the future application of ORCs in low-grade waste heat recovery.
On the other hand, as a natural working fluid, CO 2 has been widely applied in refrigeration [6] and heat pump [7] systems owing to its zero ODP, negligible GWP and superb thermophysical properties, despite its high critical pressure and low critical temperature. The high operating pressures of a CO 2 energy system require special designs for system components and controls, while the low critical temperature will turn a CO 2 low-grade power generation system into a transcritical Rankine cycle (T-CO 2 ) or even a supercritical CO 2 Brayton cycle. Of these CO 2 power cycles, the T-CO 2 is most effective at harvesting low-grade heat sources when a low temperature heat sink is accessible [8,9]. The supercritical heat-addition process of a T-CO 2 can produce high-efficiency temperature matching between the sensible heat source and the working fluid, leading to no pinch limitations. In addition, the superb thermophysical properties of CO 2 can create a more compact T-CO 2 system than those of ORCs. These include a higher density, latent heat, specific heat, thermal conductivity, volumetric cooling capacity, and lower viscosity. Therefore, the T-CO 2 has considerable potential for low-grade power generation. Nevertheless, the performance of such a system requires thorough investigation in order to understand operational mechanisms for optimising system efficiency.
Due to the high critical pressures of CO 2 , the pressure of heating processes in CO 2 transcritical power cycles would also be high (typically above 90 bar), such that conventional heat exchangers, gas turbines or expanders and power cycles cannot be directly applied. Consequently, up to now, investigations on low temperature heat source energy conversion systems with CO 2 transcritical power cycles have been limited to small-scale laboratory work and theoretical analyses. A solar-powered test rig with a CO 2 transcritical power cycle was set up to examine system performance at designated operating states [10]. As this test rig used a throttling valve to simulate expansion device, power generation could not be measured directly. A highly promising solution to the CO 2 turbine market problem is to use a CO 2 scroll expander for the test rig or practical installation. The expander works as the corresponding compressor in reverse, which is a positive displacement machine. CO 2 scroll expanders and compressors have already been implemented in refrigeration and air conditioning [11]; however, its application in transcritical power cycles needs to be explored as it plays an important role in the power system. A steady-state thermodynamic model for the above solar-CO 2 power system showed that the power and heat outputs and efficiencies varied remarkably in different seasons of the year, due to the periodical change of solar radiation [12]. Therefore, a transient mathematical model would be more suitable in simulating the real performance of the solar system. In the application of waste heat with a maximum heat source temperature of 150°C, the performance of a CO 2 transcritical power cycle with optimised supercritical pressure was compared thermodynamically to a R123 ORC subcritical cycle [13]. The total system efficiency of the CO 2 transcritical cycle was proven to be higher than that of a R123 subcritical cycle due to better matching of the CO 2 flow temperature variation to its heat source temperature glide. In addition, the CO 2 power system is more compact and the cycle also shows no pinch limitation in the heat exchanger. This result is encouraging since the R123 subcritical cycle was formerly recognised to harbour a higher system performance [14]. Significantly, this research demonstrates the importance of the design and selection of the high side supercritical CO 2 gas heater and optimal supercritical pressure control in order to determine overall system efficiency [15]. However, comprehensive experimental and theoretical analyses for a low-grade T-CO 2 system are necessary to gain full understanding of system operations and achieve optimal designs and controls. So far, to the authors' acknowledges, very few experimental investigations have been carried comprehensively on low-grade power generation with T-CO 2 systems in which actual power generations were measured. On the other hand, some theoretical analyses including energy and exergy were conducted on the T-CO2 systems but mostly were limited to thermodynamics bases [16][17][18][19]. Nevertheless, to fully understand and model the system performance and controls, the detailed system component models need to be involved. These issues will be addressed in the paper in terms of comprehensive experimental investigation and detailed model development.
In this paper, a test rig of a low temperature power generation system with the T-CO 2 power cycle is described and measurements demonstrated for the effect of CO 2 mass flow rates and heat source flow rates on system performance. In the meantime, a mathematic model of the tested system was developed and validated with measurements from current and previous research projects. The model predicts the effect of heat sink and source parameters and CO 2 pressures at the turbine inlet on system performance, which aids in the understanding of system operations towards the eventual optimisation of system design and controls.

Test facilities
A test rig of a small-scale low-grade power generation system with T-CO 2 power cycles was purposefully built on the top floor of an 80 kW e micro-turbine CHP unit, as shown schematically in Fig. 1.
To clearly understand the flow process of the T-CO 2 power cycles, the system layout and its corresponding T-S diagram are depicted in Fig. 2. The test rig consisted of a number of essential components including a CO 2 turbine/expander, electricity generator, recuperator, aircooled condenser, receiver, liquid pump and thermal oil-heated CO 2 gas generator. The CO 2 turbine is an axial type with single stage. The turbine stage is reaction type with a reaction degree or reaction ratio of 0.5. The turbine designed power generation, pressure ratio, CO 2 mass flow rate and diameter are 5 kWe, 1.5, 0.281 kg/s and 144 mm respectively. The turbine power generation was connected directly to grid and there was no load connected to the turbine. An automatic generation control was therefore applied to control turbine rotational speed. However, the turbine rotational speed was not measured by this project. The CO 2 liquid pump was a type of triplex plunger pump with a minimum power consumption of 3 kW flexibly coupled with an 11 kW motor most suitable for the frequency inverter. The heat source of the test rig was hot thermal oil flow heated by exhaust flue gases from the 80 kW e CHP unit. The thermal oil parameters, temperature and flow rate were respectively modulated by the CHP power output and a variable-speed thermal oil pump. On the condenser side, the air flow (heat sink) parameters, flow rate and temperature were respectively controlled by a variable-speed condenser fan and a purposely-built electric heater installed underneath the heat exchanger. Inside the T-CO 2 Rankine cycle, the supercritical CO 2 pressure and temperature were varied and controlled by thermal oil side flow rate and temperature respectively, and the CO 2 condensing pressure by heat sink parameters particularly air flow rate. In addition, the CO 2 mass flow rate was modulated by means of a variable speed CO 2 liquid pump which concurrently affected the CO 2 supercritical pressure. Furthermore, four two-way valves were installed at the CO 2 turbine exit and high-pressure liquid line to allow the CO 2 working fluid to either flow through or bypass the recuperator. The system performance with and without the recuperator could therefore be measured and compared.
The test rig was fully instrumented with a temperature sensor and pressure transducer between any two main components in the system. The inlet and outlet temperatures and flow rates of the thermal oil and condenser air flows were all measured. In addition, a CO 2 mass flow meter and electricity power meter were also installed to respectively measure the CO 2 mass flow rate and turbine power generation. These instruments or sensors were completely calibrated before installation to ensure acceptable accuracy, with each thermocouple uncertainty at less than ± 0.5°C, pressure transducer ± 0.3%, air velocity meter ± 3.0%, CO 2 mass flow rate ± 0.1% and power meter ± 0.8%.
As listed in Table 1, a series of measurements were carried out on the developed test rig at different heat source and sink parameters. For the heat source parameters, temperatures varied between 142.4°C and 144.4°C, and the flow rate from 0.25 kg/s to 0.5 kg/s. As for the heat sink parameters, temperatures varied from 22.5°C to 23.5°C which can be treated as constant but flow rate remained unchanged. In addition, the CO 2 mass flow rate was controlled by the CO 2 liquid pump in the range of 0.2 kg/s and 0.3 kg/s. The test results can be used to validate the system and component models to be developed. Table 1 demonstrates that for heat source parameters, thermal oil temperatures do not significantly vary; moreover, at the heat sink side, both condenser inlet air temperatures and flow rates remained approximately constant. Therefore, from the test results, only the effects of thermal oil flow rate and CO 2 mass flow rate on system performance have been selected and demonstrated in this paper. It is understandable that CO 2 mass flow rates increased linearly with higher CO 2 liquid pump speeds, and decreased slightly at higher thermal oil flow rates. The test results verify that CO 2 mass flow rates in the T-CO 2 power cycle can be effectively controlled by the modulation of CO 2 pump speeds. Subsequently, the effect of the CO 2 pump speed on system performance can be represented by the CO 2 mass flow rate. As depicted in Fig. 3, both CO 2 pressures at the turbine inlet and outlet increased at higher CO 2 mass flow rates, providing starting pressures were not too low. Moreover, higher thermal oil flow rates could also augment both CO 2 Fig. 1. Test facility of CO 2 transcritical power generation system and its integration with an 80 kW microturbine CHP unit. pressures. The CO 2 mass flow rate and thermal oil flow rate also exerts an effect on the power generation of the CO 2 turbine, as shown in Fig. 4. There are two groups of results in the figure; the solid lines are derived from turbine generator measurements and the dotted lines represent actual cycle power generations calculated individually from the product of measured CO 2 mass flow rate and the enthalpy difference between the turbine inlet and outlet. The enthalpy at either turbine inlet or outlet is calculated from corresponding measurements of temperature and pressure. The ratio of turbine power generation to actual cycle power generation is a product of turbine mechanical efficiency and electrical efficiency, both of which need to be significantly improved. As seen from the measurements, power generation increases with both higher CO 2 mass flow rates and higher thermal oil flow rates. Accordingly, the turbine isentropic efficiency and overall efficiency are calculated at different CO 2 and thermal oil mass flow rates, as depicted in Fig. 5. The turbine overall efficiency is defined as the product of turbine isentropic efficiency, mechanical efficiency and electrical efficiency. Higher CO 2 mass flow rates have shown to enhance overall turbine efficiency but does not benefit isentropic efficiency, which in turn should be significantly affected by turbine pressure ratio and speed. In addition, higher thermal oil flow rates can reinforce both turbine isentropic and overall efficiencies.

Model development and simulation
As seen from Section 2.2, the test results of the T-CO 2 power system are limited because of high operating pressures at the turbine inlet and regular leakage of the CO 2 liquid pump. To fully understand the operations and controls of the tested system, a comprehensive system model for the T-CO 2 power cycle has been developed under the TRNSYS software platform by integrating all of the essential component models, as shown in Fig. 6. These include a CO 2 gas generator, turbine, recuperator, air cooled condenser and liquid pump. It should be noted that the CO 2 finned-tube air cooled condenser model has been previously developed, validated and comprehensively explained by the authors [20]. In brief, the model was developed based on lumped method in which the condenser was divided into three sections: superheat, saturated and subcooled. The calculations of energy balances and pressure drops were applied into each section of the heat   exchanger. For the models of turbine and liquid pump, conventional thermodynamic models were applied for actual expansion and compression processes. In each of these models, the efficiencies of isentropic, mechanical and electrical are assumed to be constant although certain effective parameters could be considered [21]. Therefore, in this paper, only the component models of CO 2 gas generator and recuperator are described.

Models of CO 2 gas generator and recuperator
A plate CO 2 gas generator was used in the T-CO 2 test rig in which thermal oil and supercritical CO 2 were respectively positioned on the hot and cold sides of the heat exchanger. The thermal oil was used as a high-temperature heat transfer fluid and heat source for the CO 2 gas generator with a working temperature ranging from 0 to 340°C. Based on the manufacturer's data, various important thermophysical properties of the thermal oil are correlated and presented respectively in Eqs. (1)-(4).
For density (kg/m 3 ) at temperature range 0-340°C: For specific heat capacity (kJ/kg K) at temperature range 0-340°C: For thermal conductivity (W/m K) at temperature range 0-340°C: For kinematic viscosity (mm 2 /s) at temperature range 0-340°C: These properties are important parameters for the heat transfer calculation and analysis of the CO 2 gas generator. On the other hand, a plate recuperator was installed in the rig to evaluate its effect on system performance. As shown in Figs. 1 and 2, the hot and cold sides of the recuperater respectively constitute low pressure CO 2 superheated gas from the turbine exit and high pressure subcooled liquid from the pump outlet. Since there is no phase change for either the CO 2 gas generator and recuperator, the same model may be applied to both heat exchangers and as such, they are described together in this paper.
As shown in Fig. 7, internally, for each plate heat exchanger, many Chevron plates are installed in parallel with a fixed pitch between two neighbour plates. Certain structural parameters describing the heat exchanger are required for the model development [22]. These include the total number of plates (N), channel numbers per pass for both hot and cold fluids, distance between the head plates, horizontal length of the plates (W), vertical length of the fluid path between the upper and lower ports (L p ), plate thickness (δ p ), the ratio of the developed length to the projected length (ϕ) and chevron angle (β), etc.
For the plate heat exchanger, as shown in Fig. 7, counter flow profiles for hot and cold fluids are assumed and the effectiveness ε for the heat transfer is calculated: The correlations from literature reference are used to calculate the fluid heat transfer coefficients on both hot and cold sides [23].
The heat capacity and fluid outlet temperatures of both hot and cold sides can therefore be calculated.

Model validation
The developed gas generator model is then used to predict the heat exchanger's hot and cold-side outlet parameters and heat capacity when corresponding inlet parameters from measurements are given, as listed in Table 2. The simulation results compared with measurements including thermal oil outlet temperature, CO 2 outlet temperature and the heat exchanger capacity are shown in Figs. 8-10 respectively. The results reveal that thermal oil outlet temperatures tend to be over-predicted by the model while CO 2 outlet temperatures are under-predicted. One of the reasons may stem from the assumption of constant specific heat capacity on the CO 2 side which actually changes significantly during the supercritical heating process in the heat exchanger. However, the predicted temperature errors are mostly within 5 K, which are generally acceptable considering the high temperature ranges of both hot and cold fluids. The temperature prediction errors lead to model under-prediction for the heat exchanger heat capacity compared to measurements, as shown in Fig. 10. Nonetheless, these relative errors are mostly within 5% and again are acceptable. Since the overall test results were achieved under a T-CO 2 power generation system without the recuperator, the validation of the recuperator model could not be carried out. However, considering the similarity between recuperator and gas generator models, the recuperator model is assumed to be reasonable. As explained previously, these can therefore demonstrate the acceptability of the T-CO 2 system model.

Simulation of the T-CO 2 power generation system
The model of the test system with fixed components can thus be used to predict the effects of heat source and sink parameters and CO 2 pressures at the turbine inlet with large scales on system performance. The variations of these parameters are specified in Table 3, in which thermal oil inlet temperatures vary between 200°C and 280°C, its flow rate between 0.8 kg/s and 1.6 kg/s, and condenser incoming air temperatures from 5°C to 25°C. The temperature difference between CO 2 Geometrical parameters of a Chevron plate [17] A counter flow mode Fig. 7. Plate parameters and flow mode of the plate heat exchanger.

Table 2
The test parameter ranges for the hot and cold side inlets of CO 2 gas generator.
Thermal oil inlet parameter range condensing and condenser incoming air is assumed constant at 5 K and the CO 2 liquid subcooling at the condenser outlet is controlled at 2 K by modulating the condenser fan speed or condenser air flow rate. The system power generation is designed and specified to 5 kW e , and can be controlled by the variable speed CO 2 liquid pump or CO 2 mass flow rate in the system at different conditions, while CO 2 pressures at the turbine inlet can be modulated from 80 bar to 120 bar. In a similar strain to the experimental measurement, for each model simulation, only one parameter is changed with all others kept constant at 240°C thermal oil side temperature, 1.2 kg/s oil flow rate and 120 bar turbine inlet pressure. Figs. 12 and 13 respectively show the effects of condenser incoming air temperature, thermal oil inlet temperature and flow rate on the CO 2 mass flow rate so as to generate 5 kW power in different conditions. Fig. 11 furthermore demonstrates that at fixed thermal oil side parameters (temperature and flow rate), the CO 2 mass flow rate should be     11. Variation of CO 2 mass flow rate with thermal oil temperature and condenser inlet air Temperature.      controlled to increase with ascending condenser air side temperatures but decrease with higher thermal oil temperatures when other parameters are unchanged. On the other hand, the simulation results from Fig. 12 show that thermal oil flow rates exert almost zero effect on the CO 2 mass flow rate. Moreover, in order to maintain constant power generation when the CO 2 pressure decreases from 120 bar to 80 bar, CO 2 mass flow rate should also be controlled to increase in order to maintain constant power generation, as shown in Fig. 13. In addition, if the CO 2 pressure at the turbine inlet drops to 80 bar and the condenser air inlet temperature is higher than 20°C, a significant rise in CO 2 mass flow rate is required.
Since the CO 2 mass flow rate can be controlled by pump motor frequency or speed, this directly affects pump power consumption, as shown in Fig. 14. Subsequently, similar effects can be found for heat source parameters and condenser air temperatures on CO 2 pump power consumption. Additionally, the CO 2 pump power consumption is mainly affected by CO 2 mass flow rate and CO 2 pump pressure ratio. In this case, as shown in Fig. 15, higher CO 2 pressures at the turbine inlet require a higher CO2 pump power input when the condenser air inlet temperature is less than 20°C. When the CO 2 mass flow rate increases abruptly at a higher air temperature and lower CO 2 pressure, a greater CO 2 pump power input is needed.
The CO 2 gas generator capacity is mainly determined by the maximum fluid temperature difference between hot and cold sides and also the CO 2 mass flow rate. In some cases, such as with low thermal oil temperatures, the effect of large temperature shifts in heat capacity can overwhelm CO 2 mass flow rates. For example, in Fig. 16, when the condenser air temperature is lower than 15°C and thermal oil temperature is 200°C, the heat capacity decreases at higher condenser air temperatures or higher CO 2 mass flow rates. Otherwise, at a constant thermal oil temperature, the heat capacity generally increases with higher condenser air temperatures and CO 2 mass flow rates. In the meantime, at a constant condenser air temperature, the heat capacity increases with lower thermal oil temperatures due to the requisite high CO 2 mass flow rate. On the other hand, as shown in Fig. 17, the effects of CO 2 pressure at the turbine inlet and condenser air inlet temperature on gas heater capacity are very similar to those same parameters on the CO 2 mass flow rate. At the same condenser air inlet temperature, the CO 2 gas heater heat capacity increases with lower CO 2 pressures at the turbine inlet, and the gap increases with higher condenser air inlet temperatures.
The overall system thermal efficiency is a ratio of net power generation (CO 2 power generation minus pump power consumption) to gas generator heat capacity. Since the system power generation is fixed at 5 kW, thermal efficiency is determined solely by CO 2 pump power consumption and gas generator capacity. As shown in Fig. 18, at a constant thermal oil temperature of greater than 240°C, overall thermal efficiency generally decreases with higher condenser air temperatures. But when a thermal oil temperature is lower than 240°C, a maximum overall thermal efficiency can be obtained due to its effect on the generator heat capacity. In addition, as shown in Fig. 19, overall efficiency increases with higher CO 2 pressures at the turbine inlet when condenser air inlet temperatures are above 15°C. However, with condenser air inlet temperatures of below 15°C, overall efficiency tends to decrease with higher CO 2 pressures at the turbine inlet due to the increased pump power consumption.
The experimental and simulation results are beneficial to aid understanding of system performance at different applicable operating conditions and can therefore lead to optimal controls of system operation once turbine power generation is specified. The safety and efficient operations can also be controlled for the T-CO 2 systems if the research outcomes from this paper can be applied.

Conclusions
A transcritical CO 2 Rankine cycle (T-CO 2 ) is a prospective option for low temperature heat source power generation, considering its natural working fluid properties and lower footprint compared with conventional ORC systems. A small-scale test rig of the T-CO 2 Rankine cycle was developed and measurements were carried out to investigate the effects of heat source and sink parameters on system performance. Preliminary test results showed that the CO 2 mass flow rate could be directly controlled by variable CO 2 liquid pump speeds. The CO 2 pressures at the turbine inlet and outlet and turbine power generations all increased with higher CO 2 mass flow rates. In addition, the tested turbine overall efficiency proved to be smaller than its isentropic efficiency, indicating that the turbine's mechanical and electrical efficiencies need to be further improved. The heat source flow rate was also found to confer almost negligible impact on system performance. On the other hand, a model of the tested T-CO 2 power generation system has been developed by integrating all the system component models, and validated against both current measurements and previous test results. The validated model is therefore used to predict the effects of heat source and sink parameters and CO 2 pressures at the turbine inlet with larger scales on the system performance. The simulation results show that heat source, heat sink temperatures and CO 2 pressures at the turbine inlet all have significant effects on system performance. A maximum system thermal efficacy exists when the system works at certain conditions such as high pressure at the turbine inlet or low heat source temperature. In addition, the effect of heat source flow rate on system performance is relatively small. This system model can be an efficient and useful tool in the investigation of alternative system designs, efficient controls, performance evaluation and optimisation. research project.