This is an excerpt from a technical paper, presented at the ASME Turbo Expo 2020 online conference and written by Leonid Moroz, Maksym Burlaka, Tishun Zhang, and Olga Altukhova. Follow the link at the end of the post to read the full study!
The attempts to simulate transient and steady-state sCO2 cycles off-design performance were performed by numerous authors , , , , and . Some of them studied the dynamic behavior of regulators, some studied different control strategies or off-design behavior in different scenarios, which definitely has certain utility in the development of the reliable technology of sCO2 cycle simulation. Nevertheless, they used rather simplified models of components, especially turbomachinery and heat exchangers, which are of crucial importance to correctly simulate cycle performance.
The authors of this paper attempted to apply the digital twin concept to a simulation of off-design and part-load modes of the sCO2 bottoming cycle considering real machine characteristics and performance, which nobody tried to apply in this area.
On IGTC Japan 2015, SoftInWay Inc. has published a paper “Evaluation of Gas Turbine Exhaust Heat Recovery Utilizing Composite Supercritical CO2 Cycle”. The paper considered combinations of different bottoming sCO2 cycles for a specific middle power gas turbine. It mainly studied the advantages of different types of sCO2 cycles to increase the power production utilizing GTU waste heat.
The present paper is a further study based on that so the Cycle 2  from that previous paper was selected as the sCO2 bottoming PGU layout in the present paper for subsequent analysis. The cycle is a combination of recompression cycle and simple cycle which offers 16.13 MW as output. GE LM6000-PH DLE gas turbine, was used as the heat source for bottoming PGU. According to GE official brochure , the GE LM6000 offers 40 MW to over 50 MW with up to 42% efficiency and 99% fleet reliability in a flexible, compact package design for utility, industrial and oil and gas applications. GE LM6000-PH DLE provides 53.26 MW output with exhaust temperature at 471 ℃ and exhaust flow at 138.8 kg/s. (This information came from GE products specification from 2015. It appears that GE continuously modifying the parameters of its turbines along with the naming of different modifications. Therefore, today’s parameters and configuration names might be slightly different comparing to 2015) Exhaust gas pressure was assumed to be 0.15 MPa. These parameters were taken to analyze the bottoming PGU and are presented below in TABLE 1.
The digital twin (DT) concept is the developing technology that allows simulation of object behavior during its life cycle or in specified time due to changing ambient conditions, for example. The DT is applicable for performance tuning, digital machine building, healthcare, smart cities, etc  that allows decreasing the time and costs of development and optimize the object on the developing stage. GE has raised DT concepts for power plants to continually improves its ability to model and track the state of the plants .
In the context of this paper, DT is a simulation system comprised of physicist-based models organized in a special algorithmic structure that allows simulating the behavior of sCO2 PGU under alternating ambient conditions and grid demands.
The DT in this study was created utilizing AxSTREAM® Platform, which includes multiple software tools. The following software tools were utilized in this study: AxCYCLE™ was used to perform cycle thermodynamic calculation; solution generator in AxSTREAM® helped with finding possible machine geometry with given boundary conditions when performing preliminary design for compressors and turbines at design point; parameters and performance of turbomachinery including mass flow rate, pressure, power, efficiencies, etc. were calculated by Meanline/Streamline solver in AxSTREAM® for design and off-design conditions; AxSTREAM NET™ is a 1D system modeling solver and it was introduced here to simulate performance of heat exchangers (HEX) and pressure drop in the pipes involved in the cycle; AxSTREAM ION™ was used to integrate all modules and tools together in one simulation system.
CO2 thermodynamic and transport properties were determined utilizing NIST RefProp .
1 Cycle Initial Parameterization and Simulation
The layout and preliminary parameters that were used for modeling the 16.13 MW PGU have been chosen exactly the same as Cycle 2  as mentioned in the introduction. The simulated cycle of 16.13 MW PGU configuration implemented in the cycle simulation tool using NIST database property is presented in Figure 1.
This is a combination of a recompression sCO2 cycle (high temperature) and a simple sCO2 cycle (low temperature). The foundation for this combination creation was an idea to use the highly efficient recompression cycle for the high-temperature exhaust gas utilization while taking into account the rather high flue gas residual temperature after the Intermediate Heat Exchanger (IHX) of this cycle. Moreover, the recuperated cycle was installed to utilize the low-temperature exhaust fuel gas residual heat and increase the total power production. The designations which are used in Figure 1 and in further figures are presented in TABLE 2. Preliminary parameters taken from Cycle 2  analysis are shown in TABLE 3. Values of HEX efficiency and recuperator pinch were taken from our previous paper . In this study, these values were set as initial values. They were substituted with accurate values once respective components were designed. It is well known that cooler outlet temperature strongly depends on ambient conditions and even year averaged value could be different for different climates. The cooler outlet temperature was set to 33 °C as a design point and for part-load simulations. This value (or very close) is often taken as a design point value in many papers. The temperature could be set to other values depending on the climate of the anticipated location of the power system. Recompression ratio value and other cycle parameters were optimized in . The optimization process and comparison with other cycles are described in .
Although the whole layout of the combination sCO2 cycle was chosen to keep the same in this paper, some parameters were still under careful consideration in the next section and the cycle performance was recalculated and updated due to those changed parameters in the cycle simulation tool.* Ratio of the mass flow rate that goes to a cooler to the mass flow rate that goes to a recompressor
2 Turbomachinery Preliminary Design and Updated Cycle Results at Design Point
The Cycle 2  performance with 16.13 MW output based on some initial guess of parameters was selected as the design point of the cycle. The efficiencies for compressors and turbines were general guesses as input for Cycle 2 in the previous paper because at that stage the focus was on the performance of different configurations of SCO2 cycles at the design point. Details of performance for turbomachinery such as efficiencies were not considered. Besides, the pressure drop in HEXs and pipelines were ignored. In the present paper, off-design performances of the cycle at different part-load were analyzed. In order to get accurate off-design condition performance of the cycle, preliminary design for compressors and turbines were implemented. From the GTU parameters and other cycle parameters listed above, boundary conditions for compressors and turbines at design point were achieved. However, during the design process for turbomachinery, efficiency for Compressor 1 and Compressor 2 was found can’t reach the value of 85 % at the same time on the same shaft. With the help of a solution generator searching for 6000 random points to get possible machine geometry solution, for constant boundary conditions, Compressor 1 is more likely to reach 80 % efficiency at a rotational speed lower than 40000 rpm. In contrast, Compressor 2 can reach higher efficiency at a rotational speed higher than 45000 rpm. The results are shown in FIGURE 2 and FIGURE 3. Each point showed in the figures refers to a different individual design and applied points are the preliminary designs of two compressors that were chosen for further study (FIGURE 4, TABLE 4 and FIGURE 5, TABLE 5).
The same rotational speed was used as a design speed for both turbines. For Turbine 2, efficiency even a little higher than 90 % can be reached. Efficiency for Turbine 1 was observed slightly lower than 90 %. Nozzle restaggering was not considered for both turbines because in the approach currently, the mass flow rate was found by given outlet pressure and the new mass flow rate was iterated back to the next iteration of calculation for cycle performance at the off-design condition. However, in later analysis, they were used to study the operation of control strategies. Preliminary design results for Turbine 1 and Turbine 2 are shown in FIGURE 6, FIGURE 7, TABLE 6 and TABLE 7.