#
Design of a 130 MW Axial Turbine Operating with a Supercritical Carbon Dioxide Mixture for the SCARABEUS Project^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

_{2}) can be mixed with dopants such as titanium tetrachloride (TiCl

_{4}), hexafluoro-benzene (C

_{6}F

_{6}), and sulphur dioxide (SO

_{2}) to raise the critical temperature of the working fluid, allowing it to condense at ambient temperatures in dry solar field locations. The resulting transcritical power cycles have lower compression work and higher thermal efficiency. This paper presents the aerodynamic flow path design of a utility-scale axial turbine operating with an 80–20% molar mix of CO

_{2}and SO

_{2}. The preliminary design is obtained using a mean line turbine design method based on the Aungier loss model, which considers both mechanical and rotor dynamic criteria. Furthermore, steady-state 3D computational fluid dynamic (CFD) simulations are set up using the k-ω SST turbulence model, and blade shape optimisation is carried out to improve the preliminary design while maintaining acceptable stress levels. It was found that increasing the number of stages from 4 to 14 increased the total-to-total efficiency by 6.3% due to the higher blade aspect ratio, which reduced the influence of secondary flow losses, as well as the smaller tip diameter, which minimised the tip clearance losses. The final turbine design had a total-to-total efficiency of 92.9%, as predicted by the CFD results, with a maximum stress of less than 260 MPa and a mass flow rate within 1% of the intended cycle’s mass flow rate. Optimum aerodynamic performance was achieved with a 14-stage design where the hub radius and the flow path length are 310 mm and 1800 mm, respectively. Off-design analysis showed that the turbine could operate down to 88% of the design reduced mass flow rate with a total-to-total efficiency of 80%.

## 1. Introduction

_{2}) are promising candidates for concentrated solar power (CSP) plants [1,2,3]. Supercritical CO

_{2}power cycles operate between two pressure limits where both the heat addition and heat rejection pressures are higher than the critical point of the working fluid. Consequently, the compression process takes place in the supercritical phase using a compressor. The EU-funded SCARABEUS project [4] is investigating the applicability of transcritical power cycles operating with CO

_{2}mixtures, where the working fluid is compressed in the liquid phase. This could result in enhanced power generation efficiency and bring the levelised cost of electricity (LCoE) of CSP plants to a competitive level within the renewable energy market [5]. Therefore, several sCO

_{2}-based mixtures have been proposed to increase the mixture’s critical temperature and hence allow for air condensation in a transcritical power cycle for dry regions where water cooling is not available [4,6].

_{2}with carbonyl sulfide (COS) increased the efficiency of the cycle to 45.05%, compared to 41.25% for pure CO

_{2}, while the specific investment cost decreased to 2621$/kWe for the blended CO

_{2}cycle compared to 2811$/kWe for the pure CO

_{2}cycle. The SCARABEUS consortium proposed hexafluorobenzene (C

_{6}F

_{6}), sulfur dioxide (SO

_{2}), and titanium tetrachloride (TiCl

_{4}) as possible candidate mixtures [8,9]. The effects of changing C

_{6}F

_{6}and TiCl

_{4}molar fractions on cycle performance were presented, considering safety and health characteristics [10,11]. The study revealed an absolute efficiency gain of 3% compared to pure CO

_{2}cycles, whilst the optimum mixture molar fraction ranged from 10% to 20%. The cycle layouts were also simpler when using mixtures compared to pure CO

_{2}cycles. Doping pure CO

_{2}with 20% to 30% SO

_{2}was investigated by Crespi et al. [9], which resulted in an optimised recompression cycle with an efficiency of 51% at 700 °C inlet temperature. This corresponds to an efficiency gain of 2% compared to the recompression cycle operating with pure carbon dioxide.

_{4}) did not thermally degrade at 700 °C. On the contrary, C

_{6}F

_{6}showed signs of thermal degradation for temperatures above 600–625 °C. Unfortunately, the thermal stability of CO

_{2}/SO

_{2}has not yet been confirmed after long exposure times, but the experimental investigation is currently underway. Previous studies in the literature have indicated that CO

_{2}/SO

_{2}is thermally stable at temperatures above 700 °C [12]. In addition to thermal stability, environmental hazards were considered for the selected mixtures. TiCl

_{4}has potential limitations due to its high reactivity with moisture in the air and the formation of HCl and TiO

_{2}, which are both hazardous to human health. For these reasons, and considering the cycle optimisation analysis, the current study aims to design the turbine flow path for a CO

_{2}-SO

_{2}precompression cycle layout, which has demonstrated a superior performance compared to the other mixtures. It is worth mentioning that these mixtures are to be implemented for closed cycles developed for CSP applications. These power plants are strategically located in dry regions which are well-ventilated, effectively mitigating various threats, including the toxicity of SO

_{2}.

_{2}cycles considerably [13,14,15]. A study by Novales et al. [13] estimated that sCO

_{2}cycles can only compete with state-of-the-art steam cycles if turbine efficiencies are above 92%. They also estimated that a 1% efficiency change in the turbine could result in a 0.31–0.38% change in cycle efficiency. According to Brun et al. [15], a 1% decrease in turbine efficiency decreased cycle efficiency by 0.5%. Therefore, it is evident that the path to commercialisation of sCO

_{2}cycles entails a better understanding of turbine design, yet it remains to be seen what effect CO

_{2}mixtures have on the achievable performance.

_{2}turbines at different scales to reveal the critical design considerations and the expected efficiency ranges. Zhang et al. [16] conducted a CFD analysis on a 15 MW single-stage axial turbine, predicting a total-to-static efficiency of 83.96%. The study also demonstrated the significance of gas bending stresses on the turbine blades. However, the impact of adding additional stages to the turbine on the performance was not investigated. On the other hand, Shi et al. [17] predicted a total-to-total efficiency of 92.12% for a three-stage design for a 10 MW axial turbine. Moreover, they showed that the turbine can maintain 85% to 92% efficiency while operating at off-design conditions in the range of mass flow rate from 115 kg/s to 201.3 kg/s. Total-to-total efficiency above 90% was also predicted by Bidkar et al. [18] for four-stage and six-stage 50 MW and 450 MW axial turbines, respectively. Kalra et al. [19] designed a four-stage axial turbine for a 10 MW CSP plant. The study focused on practical considerations such as mechanical integrity, vibrational damping, sealing, shaft assembly, and operational transients. It highlighted the unique challenges imposed by sCO

_{2}turbines, such as high torque requirements, small aerofoil fabrication, aero-design optimisation with mechanically safe blade design, and high cycle fatigue life of the rotor.

_{2}axial turbine by mean line design and 3D design using a STAR-CCM+ CFD package. They observed that both methods predict similar vane geometries, but mean line design overestimates the efficiency of the stage when compared to the CFD analysis. The reason for the discrepancy was attributed to the inadequacy of the Soderberg loss model to capture all primary losses. They also observed that the fluid’s high density at the turbine inlet results in short blades relative to the blade chord length, which promotes secondary flow and tip clearance losses.

_{2}mixtures, Aqel et al. [21] investigated the effect of the choice of the equation of state (EoS) and its calibration on the turbine design accuracy. The uncertainty in mean diameter and blade height when using the Peng–Robinson EoS was 2.6% and 4.3%, respectively. However, most of the deviations stemmed from variations in the turbine boundary conditions as defined by the cycle model. This indicates that turbine designs for CO

_{2}/SO

_{2}can be designed with reasonable accuracy, even with uncertainty in the fluid model. It is worth noting that the mixture modelling is most critical when modelling the thermodynamic cycle, and there is not a large sensitivity when considering the turbine in isolation because the turbine operates quite far from the critical point of the fluid where non-ideal effects are most significant. Specifically, the compressibility factor of pure CO

_{2}at the turbine inlet conditions of 700 °C and 239 bar is 1.054, which indicates a behaviour close to ideal gas with less dependency on the equation of state and binary interaction parameters [11].

_{2}expander by generating a mean line flow path followed by a 3D numerical simulation and detailed rotor dynamic analysis.

_{2}/SO

_{2}is presented. This design is initiated utilising mean line design and further refined using CFD simulation. Design constraints are introduced based on industrial experience to ensure design feasibility in terms of aerodynamic–mechanical integration. The proposed turbine design is evaluated under various operating conditions to enhance understanding of the aerodynamic performance at both design and off-design conditions. More details about the aerodynamic–mechanical design and integration of this turbine have been published in another publication [23].

## 2. Design Process

#### 2.1. Meanline Design Model

_{2}axial turbine design [25]. The mean line design tool has been previously verified against multiple cases from the literature. This includes cases involving air, CO

_{2}and organic fluids as the working medium. A good agreement was obtained for both the geometric parameters as well as the total-to-total efficiency. A maximum percentage difference of 1.5% and 1.2% in the total-to-total and total-to-static efficiencies, respectively, was observed [30].

#### 2.2. CFD Model Definition

_{2}mixtures are evaluated using SIMULIS [33]. The selected equation of state is Peng–Robinson in both mean line design and CFD simulations for its simplicity and accuracy [21]. The binary interaction parameters for the selected EoS were selected to match those used for the cycle analysis to ensure consistency in the thermodynamic properties obtained by both models [21,34]. The properties are introduced to the CFD models using look-up tables that cover the expected pressure and temperature ranges with the size of 500 × 500 points. The pressure range is set between 10 bar and 300 bar, while the temperature range is set between 400 K and 1200 K. The CFD model results have been checked to ensure that the property tables cover the global minimum and maximum values of the pressure and temperature within the solution domain.

_{2}turbine, the calculated deviation in the total-to-static efficiency was 0.2% [22]. Compared to the experimental results of a 140 kW axial air turbine, the obtained deviation in the total-to-total efficiency was 1% [35].

#### 2.3. Blade Shape Optimisation

## 3. Results and Discussion

#### 3.1. Flow Path Design

_{2}mixtures have been found to be promising to elevate the critical temperature of the mixture. According to design optimisation results previously obtained by the authors for the three proposed CO

_{2}mixtures, it has been found that similar flow path geometries are achieved, regardless of the working fluid, although it was found that the chord length is larger for the TiCl

_{4}designs compared to the SO

_{2}and C

_{6}F

_{6}designs due to higher bending stresses [22]. However, no significant impact of the working fluid was observed on the design process or the applied methodology. Among the mixtures, the CO

_{2}-SO

_{2}mixture has been selected for further analysis based on considerations of thermal stability, health, and environmental factors, as discussed in the introduction.

#### 3.2. Evaluation of Design-Point Performance

_{2}[25]. However, near the final turbine stages, where the blades are longer, and the boundary layers occupy a narrower portion of the flow path, the overall losses are lower. Similar to the total-to-total efficiency, the total-to-static efficiency decreases almost in unison with the shift in the total-to-total efficiency, which is because all the stages are designed with identical velocity triangles. To further understand the distribution of losses between the turbine stages, the enthalpy loss coefficients obtained using the CFD model results are plotted over the efficiency curves in Figure 13. Generally, the losses decrease with the stage number, which reflects the efficiency results shown in Figure 13. Moreover, the rotor losses are higher than the stator losses due to the blade rotation and tip clearance, which generates more turbulence. However, the last stator and rotor enthalpy loss coefficients are 39% and 13% lower than the first stage, respectively. This indicates that the rotor losses are more affected by the development of the flow field and cumulative flow angle deviation compared to the stator losses.

#### 3.3. Off-Design Analysis

## 4. Conclusions

_{2}/SO

_{2}mixture. The design process was initiated by defining the aerodynamic and mechanical constraints along with the cycle requirements, which were used to obtain the basic flow path through mean line design.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Geometry of a blade cross-section where C is the absolute velocity, W is the relative velocity, U is the blade linear speed, C

_{a}is the absolute axial velocity, C

_{w}is the absolute tangential velocity, α is the absolute velocity angle and β is the relative velocity angle.

**Figure 2.**Axial flow turbine stage showing the stator (S) and the rotor (R) where r is the radius at hub, tip and mean sections.

**Figure 4.**Mesh study of the first stage out of the 14-stage design. The blue line shows the efficiency variation with the number of grid points while the red dashed line highlights the selected mesh point for the study.

**Figure 5.**Blade aerofoil geometry as defined for the optimisation model. The green dashed line represents the aerofoil chord line.

**Figure 7.**Effect of the number of stages (${n}_{st}$) on (

**a**) the total-to-total efficiency (${\eta}_{tt}$) and hub diameter (${D}_{hub}$), and (

**b**) peripheral speed for the CO

_{2}-SO

_{2}mixture as evaluated by the mean line loss model.

**Figure 8.**The loss breakdown of the 4-, 9-, and 14-stage models obtained using the Aungier loss model.

**Figure 11.**Comparison between the flow field obtained for the 1st and 14th stages at the design point. The red dashed circles highlight the incidence angle for the different stages.

**Figure 13.**Comparison between the MLD and CFD total-to-total and total-to-static efficiencies per stage, along with the enthalpy loss coefficients obtained using the CFD model results.

**Figure 15.**Off-design evaluation per stage. (

**a**) Power developed, (

**b**) enthalpy–entropy diagram, and (

**c**) the rotor inlet incidence angle as obtained at different operating inlet total pressures.

**Figure 16.**Flow field obtained for the five mid-stages: (

**a**) design point and (

**b**) 88% of the design’s reduced mass flow rate.

Design Parameter | Value | Design Parameter | Value |
---|---|---|---|

Surface roughness (mm) | 0.002 | $\mathrm{Degree}\mathrm{of}\mathrm{reaction}\Lambda $ | 0.5 |

$\mathrm{Stage}\mathrm{flow}\mathrm{coefficient}\varphi $ | 0.5 [26] | $\mathrm{Trailing}\mathrm{edge}-\mathrm{to}-\mathrm{throat}\mathrm{ratio}t/o$ | 0.05 [27] |

$\mathrm{Stage}\mathrm{loading}\mathrm{coefficient}\psi $ | 1 [26] | $\mathrm{Pitch}-\mathrm{to}-\mathrm{chord}\mathrm{ratio}s/c$ | 0.85 [28] |

Parameter | Value | Parameter | Value |
---|---|---|---|

Dopant | SO_{2} | Outlet static pressure (bar) | 81.24 |

Dopant molar fraction (%) | 20% | Mass flow rate (kg/s) | 827 |

Turbine inlet total pressure (bar) | 239 | Rotational speed (RPM) | 3000 |

Turbine inlet total temperature (K) | 973 |

Parameter | S1 | R1 | S7 | R7 | S14 | R14 |
---|---|---|---|---|---|---|

Axial chord (mm) | 35.53 | 38.96 | 40.43 | 44.28 | 48.75 | 53.12 |

Hub radius (mm) | 310.61 | |||||

Inlet tip radius (mm) | 365.17 | 366.54 | 386.34 | 387.54 | 423.51 | 425.21 |

Outlet tip radius (mm) | 366.17 | 368.04 | 387.21 | 389.81 | 424.74 | 428.99 |

No. of blades | 58 | 53 | 53 | 48 | 47 | 42 |

Tip gap (mm) | - | 0.515 | - | 0.546 | - | 0.601 |

Parameter | Unit | MLD | CFD | Difference |
---|---|---|---|---|

$\dot{m}$ | kg/s | 827.06 | 822.9 | 0.51% |

$Power$ | MW | 131.9 | 130.1 | 1.38% |

${\eta}_{tt}$ | % | 93.84 | 92.90 | 1.01% |

${\eta}_{ts}$ | % | 93.06 | 91.95 | 1.21% |

Model | $\dot{\mathit{m}}$ (kg/s) | $\mathbf{P}\mathbf{o}\mathbf{w}\mathbf{e}\mathbf{r}\left(\mathbf{M}\mathbf{W}\right)$ | ${\mathit{\eta}}_{\mathit{t}\mathit{t}}$ (%) | ${\mathit{\sigma}}_{\mathit{S}}$ (MPa) | ${\mathit{\sigma}}_{\mathit{R}}$ (MPa) |
---|---|---|---|---|---|

Reference geometry | 898.22 | 10.07 | 93.15 | 445.70 | 310.64 |

Increase outlet wedge angle (decrease throat opening 5%) | 846.46 | 9.60 | 92.98 | 333.28 | 258.38 |

Increase the base aerofoil thickness (around 25%) | 873.38 | 9.76 | 92.77 | 272.13 | 237.99 |

Increase the whole blade thickness (around 25%) | 848.72 | 9.46 | 92.19 | 269.86 | 223.97 |

Increase base fillet radius from 1 mm to 2 mm | 890.15 | 9.85 | 92.86 | 238.36 | 264.22 |

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**MDPI and ACS Style**

Abdeldayem, A.S.; Salah, S.I.; Aqel, O.A.; White, M.T.; Sayma, A.I.
Design of a 130 MW Axial Turbine Operating with a Supercritical Carbon Dioxide Mixture for the SCARABEUS Project. *Int. J. Turbomach. Propuls. Power* **2024**, *9*, 5.
https://doi.org/10.3390/ijtpp9010005

**AMA Style**

Abdeldayem AS, Salah SI, Aqel OA, White MT, Sayma AI.
Design of a 130 MW Axial Turbine Operating with a Supercritical Carbon Dioxide Mixture for the SCARABEUS Project. *International Journal of Turbomachinery, Propulsion and Power*. 2024; 9(1):5.
https://doi.org/10.3390/ijtpp9010005

**Chicago/Turabian Style**

Abdeldayem, Abdelrahman S., Salma I. Salah, Omar A. Aqel, Martin T. White, and Abdulnaser I. Sayma.
2024. "Design of a 130 MW Axial Turbine Operating with a Supercritical Carbon Dioxide Mixture for the SCARABEUS Project" *International Journal of Turbomachinery, Propulsion and Power* 9, no. 1: 5.
https://doi.org/10.3390/ijtpp9010005