In the context of advancing renewable energy technologies, we focus on enhancing the efficiency of solar power systems through innovative turbine design. This study explores the aerodynamic optimization of a radial inflow turbine operating with supercritical carbon dioxide (S-CO₂) within a Brayton cycle, tailored for tower-based solar power systems. The integration of S-CO₂ as a working fluid leverages its high power density and superior heat transfer properties, which are critical for maximizing the performance of concentrated solar power systems. Our objective is to design and analyze a turbine that achieves high efficiency under the demanding conditions typical of solar power systems, where temperature fluctuations and variable loads pose significant challenges.
We begin by outlining the thermodynamic and aerodynamic design principles applied to the S-CO₂ radial inflow turbine. The design process incorporates real fluid properties from the NIST database, ensuring accuracy in predicting behavior under supercritical conditions. The turbine’s initial parameters are summarized in Table 1, which includes key operational values such as inlet pressure, temperature, and mass flow rate. These parameters are foundational to our computational modeling and subsequent analysis of the turbine’s performance within a solar power system framework.
| Parameter | Value |
|---|---|
| Inlet Pressure (MPa) | 13.53 |
| Inlet Temperature (K) | 833 |
| Outlet Pressure (MPa) | 8.2 |
| Mass Flow Rate (kg/s) | 25.8 |
| Rotational Speed (r/min) | 31000 |
The efficiency of the turbine is evaluated using key performance metrics, such as isentropic efficiency and power output. The wheel efficiency equation is central to our analysis:
$$\eta_u = 2X_\alpha \left( \phi \cos \alpha_2 \sqrt{1 – \Omega} – \mu^2 X_\alpha + \mu\psi \cos \beta_2 \sqrt{\Omega + \phi^2 (1 – \Omega) + \mu^2 X_\alpha^2 – 2X_\alpha \phi \cos \alpha_2 \sqrt{1 – \Omega}} \right)$$
where $\eta_u$ represents the wheel efficiency, $X_\alpha$ is the velocity ratio, $\Omega$ denotes the reaction degree, $\mu$ is the diameter ratio, $\alpha_2$ and $\beta_2$ are flow angles, and $\phi$ and $\psi$ are velocity coefficients. This formula allows us to quantify the energy conversion efficiency in the context of a solar power system, where minimizing losses is crucial for overall system performance.
Leakage and friction losses are significant factors in turbine efficiency, particularly for high-pressure applications in solar power systems. The leakage loss is calculated as:
$$\Delta h_j = \frac{U_1^3 Z_2}{8\pi} \left( 0.4 \Delta_z V_z + 0.75 \Delta_r V_r + 0.3 \sqrt{\Delta_z \Delta_r V_z V_r} \right)$$
with $V_z$ and $V_r$ defined as:
$$V_z = 1 – \left( \frac{r_{2s}}{r_1} \right) \frac{C_{20}}{l_1}, \quad V_r = \left( \frac{r_{2s}}{r_1} \right) \frac{b_z – l_1}{C_{20} l_2 r_2}$$
Here, $\Delta h_j$ is the leakage loss, $U_1$ is the wheel speed, $Z_2$ is the number of blades, and $\Delta_z$ and $\Delta_r$ are axial and radial clearances. The loss coefficient $\xi_j$ is derived as $\xi_j = \Delta h_j / \Delta h_s$, where $\Delta h_s$ is the ideal enthalpy drop. Friction loss is given by:
$$\xi_f = \frac{4 f \rho_1 r_1^2 U_1^3}{360 G \Delta h_s}$$
where $f$ is the friction coefficient, $\rho_1$ is the inlet density, and $G$ is the mass flow rate. The overall isentropic efficiency is then:
$$\eta_s = \eta_u – \xi_j – \xi_f$$
and the power output is $P = G \eta_s \Delta h_s$. These equations form the basis for our optimization efforts in the solar power system turbine design.
We developed a three-dimensional model of the turbine using Bladgen for the rotor blades and TC-4P profiles for the stator blades. The mesh independence study ensured computational accuracy, with final grid sizes of 262,816 elements per stator passage and 341,455 per rotor passage. The simulation setup included boundary conditions of total inlet temperature and pressure, static outlet pressure, and stage interfaces for fluid domain coupling. The SST turbulence model and real CO₂ properties from NIST were employed to capture the complex flow dynamics inherent in solar power system applications.
The internal flow characteristics reveal critical insights into loss mechanisms. In the rotor passage, leakage vortices form due to pressure differences between the pressure and suction sides, leading to secondary flows that reduce efficiency. The total pressure loss coefficient $C_p$ is defined as:
$$C_p = \frac{p_{1s} – p_{2s}}{p_{1s} – p_2}$$
where $p_{1s}$ and $p_{2s}$ are total pressures at inlet and outlet. Analysis shows that losses are concentrated in the upper axial region of the rotor, where leakage flows interact with the mainstream, creating spiral vortices. This phenomenon is particularly relevant in solar power systems, where maintaining stable flow under varying thermal conditions is essential.
To optimize performance, we investigated the effect of rotor blade wrap angle on turbine efficiency. Wrap angles ranging from 25° to 75° were analyzed, with results summarized in Table 2. As the wrap angle increases, flow separation diminishes, but leakage and friction losses rise. At 45°, the turbine achieves peak efficiency, balancing these opposing factors effectively for solar power system requirements.
| Wrap Angle (°) | Isentropic Efficiency (%) | Power Output (MW) | Mass Flow Rate (kg/s) |
|---|---|---|---|
| 25 | 81.54 | 1.64 | 25.80 |
| 35 | 81.92 | 1.64 | 25.75 |
| 45 | 82.18 | 1.65 | 25.70 |
| 55 | 81.34 | 1.59 | 25.60 |
| 65 | 81.30 | 1.57 | 25.50 |
| 75 | 81.28 | 1.56 | 25.40 |
The variation in reaction degree and enthalpy drop with wrap angle is critical for understanding turbine behavior in a solar power system. The reaction degree $\Omega$ increases with wrap angle, leading to higher rotor enthalpy drops but reduced overall turbine enthalpy drop. This relationship is expressed as:
$$\Delta h_{\text{rotor}} = \Omega \Delta h_s, \quad \Delta h_{\text{actual}} = \eta_s \Delta h_s$$
where $\Delta h_{\text{rotor}}$ is the enthalpy drop across the rotor, and $\Delta h_{\text{actual}}$ is the actual enthalpy drop. The mass flow rate decreases slightly with larger wrap angles due to increased flow resistance, impacting the solar power system’s operational stability.
Velocity and entropy distributions further illustrate the optimization effects. At lower wrap angles, flow separation and vortex formation are prominent, whereas at 45°, the flow is more organized, reducing entropy generation. The absolute velocity at the rotor outlet $C_2$ decreases with wrap angle, lowering exit kinetic energy losses, which is beneficial for solar power system efficiency. The leakage vortex development is suppressed at optimal wrap angles, minimizing secondary flow losses. The entropy $s$ is calculated from thermodynamic relations, and its minimization is key to enhancing performance in solar power systems.
In conclusion, our design and analysis demonstrate that optimizing the rotor blade wrap angle significantly improves the aerodynamic performance of S-CO₂ radial inflow turbines in solar power systems. The 45° wrap angle yields the highest isentropic efficiency of 82.18% and power output of 1.65 MW, achieved by balancing leakage, friction, and exit losses. This optimization approach provides a reliable foundation for advancing turbine technology in renewable energy applications, particularly for tower-based solar power systems where efficiency and durability are paramount. Future work could explore adaptive control strategies to maintain performance under dynamic solar conditions, further solidifying the role of S-CO₂ turbines in sustainable energy infrastructure.
The integration of such turbines into solar power systems not only enhances energy conversion but also supports grid stability through efficient power generation. By continuously refining aerodynamic designs, we can contribute to the scalability and affordability of solar power systems worldwide, addressing global energy demands while minimizing environmental impact. The equations and tables presented here serve as a reference for engineers and researchers aiming to implement similar optimizations in their solar power system projects.