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Article

Off-Design Analysis of a Small-Scale Axial Turbine in Organic Rankine Cycle

1
Advanced Energy Conservation Research Group (AECRG), College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2
Collaborative Innovation Center for Advanced Aero-Engine, Beijing 100191, China
3
State Key Laboratory of Clean and Efficient Turbomachinery Power Equipment, Dongfang Electric Corporation Dongfang Turbine Co., Ltd., Deyang 618000, China
*
Authors to whom correspondence should be addressed.
Sustainability 2025, 17(4), 1360; https://doi.org/10.3390/su17041360
Submission received: 30 October 2024 / Revised: 7 January 2025 / Accepted: 20 January 2025 / Published: 7 February 2025
(This article belongs to the Section Waste and Recycling)

Abstract

:
Amidst the global energy crisis and progress in clean energy, this study aims to reduce design costs and improve the adaptability of turbines in small ORC systems. It seeks to offer enhanced renewable energy utilization methods for sustainable development. This paper focuses on the performance of an impulse single-stage turbine with partial admission and analyzes it through numerical simulations using computational fluid dynamics (CFD). The study investigates critical parameters under design and off-design conditions by varying inlet total pressure and rotor speed. The results indicate that the turbine’s isentropic efficiency and power output at design conditions are 64% and 4.78 kW, respectively. The power output ranges from 4.65 kW to 6.81 kW, and the isentropic efficiency ranges from 57% to 62% under off-design conditions. Both experimental and simulation results show good agreement. Furthermore, the velocity triangles under these conditions conform to those of a pure impulse turbine. These findings demonstrate that the turbine could adapt to different conditions and facilitate the design of ORC systems.

1. Introduction

The global energy crisis poses a significant challenge to sustainable development [1]. Fossil fuels are declining due to fluctuating prices and reserves, as well as geopolitical and environmental issues caused by their rapid consumption. To address this challenge, low- and medium-temperature heat sources, such as renewables (solar, geothermal, biomass, and ocean thermal energy) and wasted heat from various industrial processes (such as petrochemical plants, gas turbines, and internal combustion engines), are being widely used [2].
ORC systems, which use organic working fluids, are a flexible and efficient solution for converting low-grade heat sources, such as biomass, waste heat, and solar energy, into electricity [3]. Many types of organic fluids can be used as working fluids in ORC systems, including hydrocarbons, hydrofluorocarbons, hydrochlorofluorocarbons, chlorofluorocarbons, perfluorocarbons, siloxanes, alcohols, aldehydes, ethers amines, and inorganic fluids. ORC systems are widely applicable, secure, and environmentally friendly, making them well-suited to low- and medium-temperature energy conversion technologies [4]. ORC systems could be of significant benefit, both environmentally and economically [5]. However, some components of ORC systems, particularly turbines, can be expensive to design, which is impractical for small-power-load ORC systems that cannot bear the cost of each component’s design. Thus, it is essential to consider the off-design performance of the same component to optimize the system’s overall cost-effectiveness. Similar to the traditional steam Rankine cycle, the ORC expands high-pressure working mediums to low pressure for power output. Also, the components are the same, which include a generator, expander, condenser, pump, etc. However, the main difference between them is the working fluid: the ORC uses an organic compound with an evaporation temperature lower than that of water, which allows for power generation from low-and medium-temperature heat sources [6].
The ORC system is a unique power cycle that is suitable for low-temperature heat sources, and the same equipment can be used with different types of working fluids [7]. ORC applications can be found in a wide range of power outputs, including micro/mini/small/medium/large ORCs (<5 kW, 5–50 kW, 50–500 kW, 500 kW–5 MW, and >5 MW) [8]. The turbine is the primary component responsible for converting heat into power in ORC systems and can be classified into various types, such as axial flow, centripetal, piston, scroll, and screw turbines [9]. Researchers have been focusing on optimizing the performance of the turbine and increasing the efficiency of ORC systems. For example, Zhao et al. [9] reviewed various expansion devices for ORC systems using low-temperature heat recovery, while Kolasinski [10] proposed a method for selecting the most suitable working fluid for ORC systems employing volumetric expanders. Zhang et al. [11] investigated the selection of zeotropic mixtures for ORCs using single-screw expanders. Hou et al. [12] employed the supercritical carbon dioxide cycle and organic Rankine cycle using a mixture of cyclopentane/R365mfc, resulting in high system efficiency and low costs.
Feng et al. [13] found that the use of toluene in dual-source ORC systems can significantly improve fuel economy and reduce carbon dioxide emissions. Additionally, studies have significantly contributed to the development of ORC technology and the optimization of turbine performance [14,15,16,17,18]. While the cost of design for some ORC components can be high, especially for turbines, it is meaningful to consider the off-design performance of the same component for small-power-load ORC systems to bear the design cost of each part.
In the field of ORC turbine research, much attention has been focused on maximizing efficiency through mainline models and predicting turbine performance under off-design conditions. However, many papers propose the design of a new turbine for each specific working condition, which can be costly, especially for small-scale turbines. To address this issue, Fiaschi et al. [19] proposed a method that couples fluid selection and turbine efficiency estimation methods to improve the basic design of the turbine. They also proposed a 0D model to predict the performance of radial turbines for ORCs. Jubori et al. [20] compared the performance of both axial and radial turbines in ORCs and found that the axial turbine performed better. Sauret and Gu [21] used CFD simulations to analyze the performance of a turbine with R143a as the working medium, demonstrating that the efficiency changed significantly with large variations in the fluid. White et al. [22] used similitude theory to adapt an axial turbine to work efficiently with different fluids, improving the economy of scale. CFD simulations have been widely used in many studies to explain the laws of parameter changes, as it is both conventional and effective. For example, Mohammad et al. [23] used the CFD method to evaluate the performance of the micro wind turbine, Michael et al. [24] identified optimal operating conditions based on a given turbine and real gas as the working medium, while Mario et al. [25] used 3D CFD methods and 2D PD calculations to verify the performance of a small multi-stage axial turbine. Dawid et al. [26] optimized ORC turbine design using CFD technology to improve power generation efficiency.
Based on the aforementioned survey, it is apparent that there is a lack of off-design analyses of axial turbines in ORC systems. However, the axial flow turbine in the ORC system requires off-design analysis to assess its adaptability to varying operating conditions and output requirements. This analysis is crucial for reducing design costs and improving the system’s renewable energy utilization efficiency.
To achieve this goal, a 3D model of the turbine was built using physical data. CFD simulations were then used to analyze the turbine’s performance, and the results were analyzed to discuss the characteristics of the turbine and its influencing factors. Moreover, the reliability of the simulation model was verified by the experiment. The contribution of this paper is the analysis of a small-scale ORC turbine to make it more suitable and reduce design costs for different available ORC systems. At present, most of the research on ORC turbines is focused on centripetal turbines. This article mainly studies axial flow turbines and verifies their good off-design characteristics.

2. Description of the Model

The turbine, as one of the most important components in an ORC system, plays a crucial role in converting heat into power. In this study, a 5 kW ORC impulse microturbine with 0.5 partial admissions and R245fa as the working medium was designed and manufactured (Figure 1a). The vanes and blade profiles were obtained from the design manual, while the other geometry data were acquired from the mockup or design parameters. A 3D model of the turbine was built for analysis purposes.
To assess the performance of the turbine, its major parameters, namely the thermal state of the imported working medium and the rotor speed, were analyzed. These parameters have a significant impact on the efficiency and adaptability of the turbine, especially under off-design conditions. Therefore, the analysis of the turbine’s performance and influencing factors is crucial for designing turbines that can operate under a wide range of conditions.

3. CFD Simulations

3.1. Model

The 3D model of the fluid domain and the turbine’s flow passage are shown in Figure 1b, with an average diameter of the vanes and blades of 77 mm. The turbine has 6 vanes for 0.5 partial admissions and 27 blades, with both blades and vanes having a height of 5 mm. Under the design parameters, the turbine mass flow rate is 0.3 kg/s, and the power output of the turbine is 5 kw. The fluid enters from the upper end-face in Figure 1b, while the outlet section’s flow area is extended to promote full liquidity development.

3.2. Mesh

The structured meshes were generated by the multizone method in ANSYS meshing based on the 3D model, with each vane having approximately 32,500 meshes and each blade having approximately 22,000 meshes, and the blade surface boundary was set with a boundary layer. The entire model has around 850,000 hexahedral meshes, with a minimum orthogonality mesh angle of 38.5 degrees. This minimum angle is much larger than that required by conventional computational fluid dynamics calculations, ensuring the stability and reliability of the simulation results. From Table 1, it can be seen that as the number of grids increases from 425,000 to 850,000, the temperature of the working fluid at the outlet of the stationary blade changes significantly. However, as the number of grids increases from 850,000 to 3,400,000, the temperature of the working fluid at the outlet of the stationary blade remains basically unchanged, which shows the reliability of the mesh.

3.3. Numerical Method

Various conservation equations are being followed by the flow in the turbine, including the continuity equation, momentum equation, energy equation, turbulent kinetic energy and turbulent dissipation-rate equation, and k-ε equation. The k-epsilon turbulence model is the most common turbulence model; it boasts high computational efficiency, extensive applicability, and is capable of accurately delineating the flow intricacies of the working fluid within the turbine, while simultaneously providing a comprehensive reflection of the turbine’s overall performance. This belongs to the two-equations model and is suitable for fully developed turbulence. By coupling the transport equations of k and ε, as well as the momentum equation of average velocity, the continuity equation, the thermal equilibrium equation, etc., both k and ε can be solved.
The conservation equation is expressed with the following equation:
ρ ϕ t + ρ v x ϕ x + ρ v y ϕ y + ρ v z ϕ z = x Γ ϕ x + y Γ ϕ y + z Γ ϕ z + S
where Φ is the variable in the conservation equation, Γ is the corresponding generalized diffusion coefficient, and S is the source term.
For the continuity equation, there is no diffusion term and source term:
Φ = 1 , Γ = 0 , S = 0
For the energy conservation equation,
Φ = k , Γ = μ + μ t σ k , S = G k ρ ε
For the momentum equation,
x-direction
ϕ = v x , Γ = μ e f f = μ + μ t , S = p x + x μ e f f v x x + y μ e f f v y x + z μ e f f v z x
y-direction
ϕ = v y , Γ = μ e f f = μ + μ t , S = p y + x μ e f f v x y + y μ e f f v y y + z μ e f f v z y
z-direction
ϕ = v z , Γ = μ e f f = μ + μ t , S = p z + x μ e f f v x z + y μ e f f v y z + z μ e f f v z z
ANSYS CFX 2022 software is used for numerical calculations. The finite volume method is used for discrete conservation equations, and the SIMPLE algorithm is applied to simulate the flow field. The purpose is to simulate the flow by the fluid on the turbine in the impeller passage.

3.4. Boundary Conditions

The previous section outlined the design condition and operating conditions of the ORC turbine model. In this section, the off-design conditions are presented. The off-design conditions are listed in Table 2, which includes the total inlet pressure, rotor speed, and inlet total temperature. The total inlet pressure is raised from 0.65 MPa to 0.85 MPa at 0.05 MPa intervals, and the rotor speed is increased from 17,500 rpm to 18,500 rpm at 500 rpm intervals. A superheat is set in the off-design conditions to prevent the medium from undergoing a phase transition due to the different total pressure.
It is important to analyze the off-design conditions of the turbine as it reflects the adaptability of the turbine to different operating conditions and output requirements, which is crucial for designing wide-operating-condition turbines. The off-design analysis can also help in saving the design cost of a turbine for different systems.

3.5. Main Performance Indicators

In order to analyze and evaluate the performance index of the turbine, some main indicators should be acquired through the post-processing of simulation results.
Power output:
P = 2 π ω T 60 × 1000
where ω is the rotor speed (rads/min) and T is the torque of the blades (Nm).
The isentropic efficiency:
η = P m Δ h
where m is the mass flow (kg/s) and Δh is the theoretical isentropic enthalpy drop from the inlet to the outlet of the medium (kJ/kg).
The total pressure recovery:
C p t = P i n * P o u t * P i n * P s , o u t  
where Pt is the total pressure and Ps is the static pressure.
The velocity triangle shows how the medium works in the turbine. To establish this, we must obtain the mass flow average circumferential and radial velocities at the vane outlet and blade outlet from the numerical calculation.
The load factor can be obtained from the velocity triangle:
K = Δ C u U
where ΔCu is the circumferential velocity change and U is the implicated velocity, which depends on the rotor speed.

3.6. Validation

To ensure the accuracy of the numerical calculation, a verification process was conducted by comparing the simulation results with experimental data. The experimental apparatus was obtained from a small-scale ORC experiment system described in reference [27].

4. Results and Discussion

In the previous sections, we presented the structure and parameters of the axial ORC turbine. The performance of the turbine was evaluated through simulation calculations under both the design condition and off-design conditions. The off-design conditions involved increasing the inlet total pressure to prevent the working fluid from undergoing phase transition by changing the inlet total temperature from 346 K to 358 K. Additionally, we conducted post-processing of the simulation to analyze the factors that affect the turbine’s performance.

4.1. Performance Under Design Condition

The performance of the ORC turbine under the design condition was obtained through simulation, which showed a power output of 4.78 kW and an efficiency of 64%. The blade-to-blade plot of temperature and pressure at a span of 0.5 is presented in Figure 2. The pressure gradually decreases during the flow in the vane but remains relatively stable in the blade. This conforms to the pressure change trend of a pure impulse turbine. In the simulation, the blade was divided into a flow part and a non-flow part due to partial admission. The pressure on the pressure surface was greater than that on the suction surface, resulting in blade rotation.
The velocity triangle is illustrated in Figure 3, and the corresponding values can be found in Table 3. The absolute velocity of the vane outlet (C1) is much larger than that of the blade outlet (C2), but the values of both relative velocities to the blade (W1 and W2) are almost the same. This indicates that the power output is mainly generated by the fluid impinging on the turbine blades.

4.2. Performance Under Off-Design Conditions

The small-scale ORC turbine (<10 kW) is designed to use standard components, making it suitable for use in different working conditions. However, its performance is influenced by the inlet total pressure and rotor speed (with 10K superheat to prevent the fluid from condensing). The relationship between power output and total inlet pressure is positive, while the relationship between efficiency and total inlet pressure is negative. The maximum power output is 6.81 kW under condition 15, while the efficiency variation range is small, ranging from 57% to 64%. This is effective as the efficiency under design conditions is 64%. Therefore, it can adapt to different heat sources or changing power output demands. Figure 4b shows the isentropic efficiency, which is the ratio of the enthalpy drop of blades to isentropic enthalpy drop. The isentropic enthalpy drop increases steadily with total inlet pressure. Based on the changes in mass flow rate in Table 4, at speeds of 18,000 rpm and 18,500 rpm, the growth rate of the mass flow rate significantly decreases as the total inlet pressure increases from 0.8 MPa to 0.85 MPa, but the isentropic enthalpy drop and output power remain stable, resulting in an increase in efficiency under corresponding operating conditions.
Figure 5 shows the meridional total enthalpy nephogram. The total enthalpy in front of the blades decreases, while the one at the end increases with an increase in inlet pressure. The total enthalpy change decreases significantly from conditions 11 to 14. From conditions 14 to 15, the inlet total enthalpy in blades changes little, but the one at the outlet decreases significantly. This indicates that the total enthalpy drop almost does not reduce from condition 14 to 15.

4.3. Total Pressure Recovery in Vanes

The recovery of total pressure in the vanes indicates the pressure loss of the cascade section, as illustrated in Figure 6. The graph shows a negative correlation between the recovery and the inlet pressure range and a positive correlation with rotor speed. The maximum and minimum values are 0.82 and 0.41, respectively. The steep slope of the curve is due to the stable geometric dimensions of the compressor and diffuser of the vane, which are not well-adapted to varying inlet total pressure. The nozzle design, based on operating conditions, has a significant influence on the cascade loss under changing conditions. Therefore, keeping the total inlet pressure within an applicable range or designing the vane to be more adaptable to changing pressure could reduce the total pressure recovery in variable working conditions.
Figure 7a,b shows the total pressure under condition 5 and condition 1, respectively. The total pressure losses are concentrated at the end of the passage. The total pressure gradient in Figure 7b is more uniform than in Figure 7a, as the latter deviates further from the nozzle’s design condition, causing the straight blade to create a more uneven pressure at the end of the passage under inlet condition changes. This results in a decrease in total pressure recovery as the total inlet pressure increases.

4.4. Velocity Triangle

In order to analyze the pneumatic state, it is not enough to only look at the total pressure recovery in the vane. The velocity triangle provides a more comprehensive understanding of the expansion of fluid passing through the vane and the blade, as well as the mass flow and power output. The velocity triangles with the most significant changes obtained from the simulation results are shown in Figure 8 under condition 1 and condition 15, and the values are shown in Table 5. The axial velocities at the outlet of the vane and blade should be the same as in an impulse turbine. However, C1a′ is slightly higher than C2a′, which indicates that the fluid is compressed slightly in the blade. C1a″ is approximately equal to C2a″, which indicates that the turbine is pure impulse. The velocities remain close in changing conditions, maintaining the turbine’s power output ability.
The load factor, which shows the circumferential impact of fluid on the blade, can be obtained from the velocity triangle, as shown in Figure 9. It increases as the total inlet pressure rises but decreases as the angular velocity increases. This is because higher total inlet pressure leads to higher entangled velocity and lower angular velocity leads to lower U. The load factor reaches its highest value of 3.66 under condition 5.

4.5. Thermodynamic Curves (H-S)

The thermodynamic curves in Figure 10a represent the design condition, while Figure 10b shows the curves under varying inlet conditions, from 11 to 15. In Figure 10a, the curve starts with the total pressure P0 due to the no-speed inlet. The static enthalpy drops from zero points to one point and remains close to the isobaric curve from one point to two points. This is due to the pure impulse turbine, where the expansion process occurs entirely in the vanes, resulting in all impulse work in the blades. This leads to a significant drop in static enthalpy in the vanes and its recovery along the isobaric curve in the blades. The ideal isentropic enthalpy drop, represented by Δht, is obtained from the intersection point of the constant pressure curve and isentropic line, and the isentropic efficiency is evident in the curve. The exit loss is Δhl, which accounts for 5.5% of the isentropic enthalpy.
In Figure 10b, it is evident that the static enthalpy drops further with an increase in the inlet total pressure, while the entropy increment decreases. This leads to increased power output. A higher inlet total pressure implies a more ideal isentropic enthalpy drop, and a smaller entropy increase suggests greater isentropic efficiency.

4.6. Experimental Results

The initial parameters of the experiment are presented in Table 6, and the simulation was conducted under the same working condition. The results of both the experiment and simulation are summarized in Table 7. The error rate of pressure and isentropic efficiency under these conditions was found to be 3.5%. This indicates that the numerical method used in this study is capable of accurately predicting the operating performance of the turbine, thus providing a reliable foundation and support for the performance prediction and optimization of the design of the turbine.

5. Conclusions

In this study, the performance of a small-scale turbine in an ORC system has been investigated under design and off-design conditions using CFD methods. Experimental data validated the simulation results. Under the design condition, the turbine had a power output of 4.78 kW and an isentropic efficiency of 64%. The turbine’s off-design performance was evaluated by raising the total inlet pressure from 0.65 MPa to 0.85 MPa at 0.05 MPa intervals and increasing the rotor speed from 17,500 RPM to 18,500 RPM at 500 RPM intervals with 10 K superheat. The power output ranged from 4.65 kW to 6.81 kW, and the isentropic efficiency ranged from 57% to 62%. The results showed that the turbine maintained good performance under various off-design conditions, indicating its adaptability to different power demands and waste heat-recovery scenarios. It can adapt to various working conditions under corresponding heat sources in different environments and can be used for the recovery of industrial low-temperature waste heat, low-grade geothermal energy, and waste flue-gas heat energy, thereby improving energy utilization efficiency. The methods developed in this study can be applied to analyze the off-design performance of a given turbine and guide the design of small-scale turbines for a wide range of off-design conditions. This makes the turbine more suitable and reduces the design costs of different available ORC systems. This study helps in the development of sustainable energy solutions by conducting in-depth research on the aerodynamic characteristics of turbine components in ORC systems. Further research should evaluate the impact of the off-design performance of a single turbine on the overall performance of the system, and more work is needed to delve deeper into the specific mechanisms of organic working fluids working in turbines.

Author Contributions

Conceptualization, W.H.; methodology, W.H. and Z.L.; software, W.H. and Z.L.; validation, Z.L.; formal analysis, Z.L.; resources, W.H.; data curation, C.W.; writing—Original draft preparation, Z.L.; writing—Review and editing, W.H., D.H., Z.Y. and P.S.; visualization, Z.L.; funding acquisition, W.H. and Z.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by [the financial support from the fund of State Key Laboratory of Long-life High Temperature Materials] grand number [DEC8300CG202210279EE280285] and [the Fundamental Research Funds for the Central Universities] grand number [ 501XTCX2023146001].

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Owing to the necessity of safeguarding privacy and ensuring data security, we are unable to provide the raw data.

Conflicts of Interest

The authors declare no conflicts of interest.

Nomenclature

aaxial
Cabsolute velocity (m/s)
Cpttotal pressure recovery
henthalpy
ininlet
Ppressure (MPa)
Kload factor
lloss
mmass flow rate (kg/s)
nreal
outoutlet
Ppressure (MPa)
RPMrevolutions per minute
Sentropy (kJ/(kg·K))
sisentropic
aaxial
Uimplicated velocity(m/s)
ucircumferential
Wrelative velocity(m/s)
αinlet flow angle (°)
βoutlet flow angle (°)
ωrotor speed (rads/min)
ηefficiency (%)
Δdifference
*total

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Figure 1. The physical model and three-dimensional model of the turbine. (a) The turbine in the organic Rankine cycle. (b) The 3D model built from the design parameters.
Figure 1. The physical model and three-dimensional model of the turbine. (a) The turbine in the organic Rankine cycle. (b) The 3D model built from the design parameters.
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Figure 2. The blade-to-blade plot under design conditions. (a) Temperature field. (b) Pressure field.
Figure 2. The blade-to-blade plot under design conditions. (a) Temperature field. (b) Pressure field.
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Figure 3. The velocity triangle under design conditions.
Figure 3. The velocity triangle under design conditions.
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Figure 4. Power output and efficiency under off-design conditions. (a) Power output. (b) Efficiency and isentropic enthalpy drop.
Figure 4. Power output and efficiency under off-design conditions. (a) Power output. (b) Efficiency and isentropic enthalpy drop.
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Figure 5. Meridional total enthalpy nephogram under conditions 11, 12, 13, 14, and 15.
Figure 5. Meridional total enthalpy nephogram under conditions 11, 12, 13, 14, and 15.
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Figure 6. Total pressure recovery in vanes under off-design conditions.
Figure 6. Total pressure recovery in vanes under off-design conditions.
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Figure 7. Meridional total pressure nephogram in vanes.
Figure 7. Meridional total pressure nephogram in vanes.
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Figure 8. Velocity triangles under off-design conditions. (a) Velocity triangle under condition 1. (b) Velocity triangle under condition 15.
Figure 8. Velocity triangles under off-design conditions. (a) Velocity triangle under condition 1. (b) Velocity triangle under condition 15.
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Figure 9. Load factor under off-design conditions.
Figure 9. Load factor under off-design conditions.
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Figure 10. The thermodynamic curves. (a) H-S curves under design condition. (b) ΔH-S curves under off-design conditions.
Figure 10. The thermodynamic curves. (a) H-S curves under design condition. (b) ΔH-S curves under off-design conditions.
Sustainability 17 01360 g010
Table 1. Mesh validation.
Table 1. Mesh validation.
Number of Meshes425,000850,0001,700,0003,400,000
Temperature at outlet of blade (K)303.2308.9308.7308.9
Table 2. The off-design conditions. “*”means “total”.
Table 2. The off-design conditions. “*”means “total”.
Serial NumberP*inT*inRPM
10.65 MPa358 K17,500
20.70 MPa358 K17,500
30.75 MPa358 K17,500
40.80 MPa358 K17,500
50.85 MPa358 K17,500
60.65 MPa358 K18,000
70.70 MPa358 K18,000
80.75 MPa358 K18,000
90.80 MPa358 K18,000
100.85 MPa358 K18,000
110.65 MPa358 K18,500
120.70 MPa358 K18,500
130.75 MPa358 K18,500
140.80 MPa358 K18,500
150.85 MPa358 K18,500
Table 3. Values of the velocity triangle for design conditions.
Table 3. Values of the velocity triangle for design conditions.
VariableUnitValue
C1m/s209.1
W1m/s138.9
C2m/s61.5
W2m/s117.7
C1am/s59.7
C2am/s52.7
C1um/s200.4
C2um/s31.7
α1°16.6
α2°58.9
β1°25.5
β2°26.2
Table 4. Mass flow under off-design conditions.
Table 4. Mass flow under off-design conditions.
Mass Flow (kg/s)0.65 MPa0.7 MPa0.75 MPa0.8 MPa0.85 MPa
17,500 rpm0.2640.2810.3000.3250.350
18,000 rpm0.2620.2810.3060.3350.351
18,500 rpm0.2610.2860.3140.3370.351
Table 5. Values of the velocity triangle for off-design condition.
Table 5. Values of the velocity triangle for off-design condition.
VariableUnitValue Under Condition 1Value Under Condition 15
C1m/s216.3210.6
W1m/s149.8138.8
C2m/s65.861.5
W2m/s121.3142.3
C1am/s62.961.1
C2am/s54.363.3
C1um/s206.9201.6
C2um/s54.351.9
α1°16.916.8
α2°55.650.6
β1°24.825.7
β2°26.626.4
Table 6. Initial parameters of the experiment. “*”means “total”.
Table 6. Initial parameters of the experiment. “*”means “total”.
VariableT*in (K)P*in (MPa)Tout (K)Pout (MPa)RPM
Value348.30.62323.30.1616,000
Table 7. Experimental data and simulation results.
Table 7. Experimental data and simulation results.
m (kg/s)Δh (kJ/kg)P (kW)ηs
Experimental result0.26514.083.7356.6%
Simulation result0.25415.193.8658.6%
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Lou, Z.; He, W.; Yao, Z.; Wang, C.; Su, P.; Han, D. Off-Design Analysis of a Small-Scale Axial Turbine in Organic Rankine Cycle. Sustainability 2025, 17, 1360. https://doi.org/10.3390/su17041360

AMA Style

Lou Z, He W, Yao Z, Wang C, Su P, Han D. Off-Design Analysis of a Small-Scale Axial Turbine in Organic Rankine Cycle. Sustainability. 2025; 17(4):1360. https://doi.org/10.3390/su17041360

Chicago/Turabian Style

Lou, Zeyu, Weifeng He, Zhaohui Yao, Chen Wang, Pengfei Su, and Dong Han. 2025. "Off-Design Analysis of a Small-Scale Axial Turbine in Organic Rankine Cycle" Sustainability 17, no. 4: 1360. https://doi.org/10.3390/su17041360

APA Style

Lou, Z., He, W., Yao, Z., Wang, C., Su, P., & Han, D. (2025). Off-Design Analysis of a Small-Scale Axial Turbine in Organic Rankine Cycle. Sustainability, 17(4), 1360. https://doi.org/10.3390/su17041360

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