초임계 이산화탄소 발전사이클 및 유기랭킨사이클을 위한 외측 방사형 흐름 터빈의 예비설계 및 성능해석에 관한 연구. 개발된 예비설계 프로그램을 이용하여 초임계 이산화탄소 발전사이클 및 유기랭킨사이클용 외향 방사형 흐름 터빈의 설계를 수행하였다.
Introduction
Radial outflow turbine
Radial outlet turbines can be used to compensate for the shortcomings of axial and radial inlet turbines. In other words, radial outlet turbines are easier to design and manufacture compared to axial turbines.
Research background
Among them, the turbine is relatively more important in the efficiency and cost of the organic Rankine cycle (Bao & Zhao, 2013). 2017b) also designed axial turbines, radial inlet turbines, and radial outlet turbines for organic Rankine cycles.
Research objective
Finally, I identify the range of specific speed, load and flow coefficients for a radial outflow turbine that apply to high efficiency in each cycle. I also propose the optimal range of dimensionless variables that can be used universally for radial outflow turbines.
Basic theory
A distinguishing feature of radial outlet turbines, compared to axial turbines, is that there is a difference in the peripheral speed of the rotor inlet and outlet. The rotor inlet peripheral speed can be determined through the ratio of the speed and the outlet speed.
Algorithm of preliminary design
However, the efficiency of the turbine is closely related to the efficiency of the thermodynamic cycle. Therefore, a pressure loss model was used in this study to accurately predict the blade shape and nozzle exit condition quantities. In this chapter, I present a case study on radial outlet turbine design for a CO2 supercritical power cycle using the developed preliminary design program.
To calculate the main turbine specifications, the turbine design conditions must be entered into the preliminary design program. In addition, as mentioned earlier, it is necessary to clearly specify the target efficiency of the turbine.
Results of preliminary design
Results of CFD analysis
The rotational speed of the rotor domain was 6,000 RPM with the same preliminary design condition. A frozen rotor model was used for the interface between the nozzle and the rotor domain. Meanwhile, the preliminary design program of this study ignored the deviation angles of the nozzle and rotor blades according to the assumption (5).
It was assumed that for the velocity triangle implemented in the preliminary design, each exit angle of the nozzle blade () and rotor blade () was equal to the absolute velocity angle of the nozzle exit () and the relative velocity angle of the rotor exit () respectively ). However, the results in Table 4 indicate that the deviation angle should be considered in the design of the radial outflow turbine to meet the target performance and speed triangle at each point.
Optimization of velocity triangles
- Optimization procedure
- Optimization of nozzle velocity triangle
- Optimization of rotor velocity triangle
The velocity triangle of the rotor inlet and outlet is closely related to the nozzle. Therefore, the nozzle blade, whose exit angle is adjusted to 74° by the nozzle optimization, should be included in the CFD analysis for the rotor optimization. The setting of the boundary conditions and the CFD analysis method are the same as described in section 3.3.
The rotor blade () inlet angle was changed to -21.05° by optimizing the nozzle blade. To optimize the rotor blade, the exit angle of the rotor blade () was adjusted to remove
Performance evaluation of final geometry
- Final geometry
- Convergence test
- Final performance
CFD analysis results show that the performance of this radial outlet turbine is in good agreement with the design conditions. Although the pressure and temperature ratios match the design conditions well, the CFD numerical results show that the efficiency of the radial outlet turbine designed in this study exceeds the target design efficiency. Sauret and Gu (2014) found that CFX predicts higher than actual turbine efficiency due to inherent errors in the enthalpy and entropy prediction models used by CFX.
More specifically, inherent errors are caused by the characteristics of the actual gas in which enthalpy and entropy react sensitively to slight temperature changes. In other words, the predicted efficiency of the radial outlet turbine designed in this study exceeds 5.30% of the design condition, but in practice this error is expected to be somewhat reduced.
Performance analysis of off-design conditions
At other revolutions, turbine efficiency varies greatly with changes in mass flow rate. At design RPM, turbine efficiency continues to increase up to a pressure ratio range of 1.62 and then decreases. At other revolutions, the turbine efficiency varies greatly depending on changes in the pressure ratio.
Typically, when the rotational speed was lower than the design RPM, the turbine efficiency tended to decrease as each independent variable increased. Conversely, when the rotational speed was higher than the design RPM, the turbine efficiency tended to increase with an increase to each independent variable.
Performance curve based on dimensionless variables
- Performance curve
- Analysis of CFD results
In addition, the pressure side is always higher than the suction side in all areas of the rotor blades. At point B, the stagnation point is formed relatively wide on a certain pressure side on the leading edge of the rotor blade. At point C, a very small stagnation point appears on the suction side of the leading edge of the rotor blade.
28 illustrates the streamline at each point, which varies at the leading edges of the rotor blade. At point B, the streamline is directed toward the pressure side at approximately 20.33° from the rotor blade angle.
Radial outflow turbine for an organic Rankine cycle
Design condition
Results of preliminary design
Results of CFD analysis
The outlet boundary condition was set to static pressure (3.4 MPa) as a result of preliminary design. The rotation speed of the rotor domain was 4100 RPM with the same preliminary design condition. It indicates that the pre-designed radial output turbine does not meet the target power () and the designed efficiency.
The CFD analysis results show that the values of and are slightly different from the preliminary design results. In this case study, it was also assumed that for the velocity triangle completed in the preliminary design, each nozzle blade exit angle () and impeller blade () was equal to the absolute nozzle exit velocity angle ( ) and the relative velocity angle of the rotor output (), respectively.
Optimization of velocity triangles
- Optimization procedure
- Optimization of nozzle velocity triangle
- Optimization of rotor velocity triangle
The inlet angle of the rotor blade () was modified to -22.01° by optimizing the nozzle blade. Therefore, to avoid directing the inlet flow from the rotor to the suction side of the rotor blades, the angle of incidence was also taken into account during optimization. When is -75°, the result is very close to the design condition, and the inlet flow of the rotor blade is directed to the pressure side.
A positive value of the angle of attack means that the inlet flow of the rotor blades is directed towards the pressure side. 32 CFD results according to the rotor outlet blade angle () of the radial outflow turbine ( & Incidence angle).
Performance evaluation of final geometry
- Final geometry
- Convergence test
- Final performance
The CFD analysis results show that the performance of the designed radial outlet turbine is in good agreement with the design conditions.
Performance analysis of off-design conditions
The off-design performance analysis of the radial discharge turbine for the organic Rankine cycle was similar to that of the CO2 supercritical power cycle turbine. For the organic Rankine cycle turbine, the change in efficiency was relatively small and a high efficiency range was maintained with respect to the change in each independent variable even at 90% RPM. The difference between a supercritical CO2 turbine and an organic Rankine cycle turbine is that the efficiency of the latter changes relatively quickly as the independent variable changes.
The efficiency of the supercritical CO2 power cycle turbine varies within, whereas the efficiency of the organic Rankine cycle turbine varies between 82.82−. This indicates that the organic liquid is more sensitive to the operating conditions of the radial outflow turbine than the supercritical CO2.
Performance curve based on dimensionless variables
- Performance curve
- Analysis of CFD results
Looking at points A and B, the pressure drops accordingly from entering the nozzle blade to exiting the rotor blade. At point A, a small stagnation point forms at the beginning of the leading edge of the rotor blade. 44 shows the flow at each point varying on the leading edges of the rotor blades.
At point B, the streamline is directed towards the pressure side at approximately 30.10° from the angle of the rotor blades. At point C, the streamline is directed towards the suction side at approximately -20.85° from the angle of the rotor blades.
Results and Discussion
The preliminary design program suggests the turbine shape to meet the cycle design requirements. The initial shape of the turbine requires an optimization process due to the lack of a yaw angle model. In Table 21, the dimensionless variables at each point clearly show different values, and the efficiency of the turbine in each cycle can be evaluated according to the specific speed, load and flow coefficients.
In other words, the radial outflow turbine efficiency was found to be more sensitive to changes in operating conditions when using organic fluid than supercritical CO2. Figures 45-47 show the performance curves of the radial outflow turbine for each cycle according to specific speed, load and flow coefficients.
Conclusions
Second, a preliminary design program has shown that it is possible to design radial discharge turbines for the supercritical CO2 power cycle and the organic Rankine cycle. There are currently no radial discharge turbine performance curves for supercritical CO2 and R143a with respect to dimensionless variables. In this study, the performance curves of radial outlet turbines were proposed with respect to specified speed, load and flow coefficients using the results of the off-design performance analysis of each turbine.
This study proposed a set of dimensionless variables that can be used universally for the optimal design of radial outlet turbines that require high efficiency. Modeling and Parametric Analysis of Small Scale Axial and Radial Turbines for Organic Rankine Cycle Applications.
