# Unidimensional and 3D Analyses of a Radial Inflow Turbine for an Organic Rankine Cycle under Design and Off-Design Conditions

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^{2}

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## Abstract

**:**

## 1. Introduction

_{2}H

_{5}-OH). The parameters of the preliminary turbine design were analyzed and calculated in MATLAB, while the 3D analysis of the turbine rotor and nozzle passage was performed in MATLAB ANSYS-CFX 14.5. The K-ω and k-ϵ shear stress transport (SST) turbulence models were implemented in this study. Miranda [31] presented a preliminary design of a subsonic radial turbine that works with organic fluids, such as R-123, R-134a, R-141b, and R-152a, that considered the real properties of these fluids. For these tests, the author used Fortran to develop the parameter calculation algorithm and CFD to perform the 3D analysis of the turbine. The program developed in Fortran for the one-dimensional analysis of the turbine determined the characteristics of the flow along the mean streamline for the point of operation under steady-state conditions. The parameters calculated by the one-dimensional analysis were used as inputs for the 3D design of the turbine in ANSYS. Under such conditions, the author ultimately found that R-141b enabled the largest turbine, with a rotor of 114.144 mm in radius and with a total efficiency of 70.504%. The analysis of turbine efficiency as a function of blade tip clearance and rotor backplate showed that the latter had a stronger effect on turbine operation and power output.

## 2. One-Dimensional Model of the Radial Turbine

## 3. Rotor Model

_{b4}), outlet blade tip thickness (t

_{6t}), outlet blade root thickness (t

_{6h}), outlet blade root radius (r

_{h6}), the axial length of the rotor (L

_{R}), and the number of blades (${\mathrm{Z}}_{\mathrm{R}}$) are determined using the following equations [42,47]:

_{6}) is calculated using Equation (30).

## 4. Nozzle Model

_{s}is a nozzle design parameter [1.0–2.8] [50] and ${C}_{s}$ is the nozzle blade chord. The nozzle blade chord (${C}_{s}$) is calculated using Equation (43) [50].

## 5. Volute Model

## 6. Radial Turbine Losses

#### 6.1. Rotor Losses

#### 6.1.1. Friction Losses

#### 6.1.2. Outlet Losses

#### 6.1.3. Aerodynamic Load Losses

#### 6.1.4. Trailing Edge Loss

#### 6.2. Nozzle Losses

#### 6.3. Volute Losses

## 7. 3D Radial Turbine Design

^{®}, the meshes were generated and configured in ANSYS Turbogrid

^{®}, and the boundary conditions of each case analyzed and simulated in this study were defined using the tool CFX-Pre

^{®}. In addition, the simulation control conditions were set in CFX-Pre

^{®}for each case developed in this study. After all the steps shown in Figure 7, the 3D geometries of the ORC turbine nozzle and radial rotor were obtained based on the working fluid and operating conditions defined for each project. The simulations performed in the module CFX-Pre

^{®}yielded pressure, velocity, and Mach number profiles across turbine components.

## 8. Validation of One-Dimensional Mathematical Models of the Radial Turbine

## 9. Radial Turbine Design Results

## 10. Efficiency Characteristics of the Radial Turbine Nozzle-Rotor Set

## 11. Characteristic Curves of Radial Turbines

## 12. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$A$ | Area (m^{2}) |

b | Normal, interaction coefficient, base, nozzle blade |

C | Specific heat (kJ/kg·K), Absolute velocity |

${C}_{s}$ | Nozzle Chord |

d | Diffuse |

$D$ | Diameter (m) |

eva | Evaporator |

$f$ | Friction factor, fluid |

F_{t} | Correction factor |

$h$ | hub |

${k}_{volute}$ | Pressure loss coefficient |

L | Length (m) |

m | Meridional plane |

${\dot{m}}_{}$ | Mass flow (kg/s) |

p | Constant pressure, loss, projection |

R | Rotor blade |

r | Radius (m) |

rms | Root mean square radius |

$T$ | Temperature (K) |

s | shroud, storage, dry section |

${S}_{s}$ | Nozzle design parameter |

U | Circumferential rotation speed (m/s) |

v | Volute, Volume (m^{3}) |

W | Relative velocity (m/s) |

$\mathrm{Z}$ | Nozzle blades number |

$\omega $ | Rotation speed (rad/s) |

Greek symbols | |

$\alpha $ | Absolute flow angle (°) |

β | Relative flow angle (°) |

$\epsilon $ | Rotor radius ratio |

$\theta $ | Tangential plane |

γ_{fi} | Interception factor |

ξ | Meridional speed ratio |

$\psi $ | Loading coefficient |

Φ | Flow coefficient |

Subscribed | |

0 | Total, Volute input |

1 | Receiver side one, Nozzle inlet |

2 | Receiver side two |

3 | Nozzle outlet |

4 | Rotor inlet |

6 | Rotor outlet |

in | Inlet |

$ise$ | Isentropic |

$out$ | Outlet |

orc | Organic Rankine Cycle |

PTC | Parabolic Trough Collectors |

wf | Working fluid |

$sur$ | Surroundings |

## References

- Wang, H.; Wang, G.; Qi, J.; Schandl, H.; Li, Y.; Feng, C.; Yang, X.; Wang, Y.; Wang, X.; Liang, S. Scarcity-weighted fossil fuel footprint of China at the provincial level. Appl. Energy
**2020**, 258, 114081. [Google Scholar] [CrossRef] - Curtin, J.; McInerney, C.; Gallachóir, B.Ó.; Hickey, C.; Deane, P.; Deeney, P. Quantifying stranding risk for fossil fuel assets and implications for renewable energy investment: A review of the literature. Renew. Sustain. Energy Rev.
**2019**, 116, 109402. [Google Scholar] [CrossRef] - Gaete-Morales, C.; Gallego-Schmid, A.; Stamford, L.; Azapagic, A. Life cycle environmental impacts of electricity from fossil fuels in Chile over a ten-year period. J. Clean. Prod.
**2019**, 232, 1499–1512. [Google Scholar] [CrossRef] - Carrillo Caballero, G. Estudo E Modelagem Dos Componentes de Um Sistema Dish Stirling Visando à Otimização Da Potência E a Eficiência Do Sistema. Dissertação de Mestrado, Universidade Federal de Itajubá, Itajubá, Brazil, 2013. [Google Scholar]
- Woodland, B.J.; Ziviani, D.; Braun, J.E.; Groll, E.A. Considerations on alternative organic Rankine Cycle congurations for low-grade waste heat recovery. Energy
**2020**, 193, 116810. [Google Scholar] [CrossRef] - Abrosimov, K.A.; Baccioli, A.; Bischi, A. Techno-economic analysis of combined inverted Brayton—Organic Rankine cycle for high-temperature waste heat recovery. Energy Convers. Manag.
**2020**, 207, 112336. [Google Scholar] [CrossRef] - Liu, X.; Nguyen, M.Q.; Chu, J.; Lan, T.; He, M. A novel waste heat recovery system combing steam Rankine cycle and organic Rankine cycle for marine engine. J. Clean. Prod.
**2020**, 265, 121502. [Google Scholar] [CrossRef] - Xu, B.; Rathod, D.; Yebi, A.; Filipi, Z. A comparative analysis of real-time power optimization for organic Rankine cycle waste heat recovery systems. Appl. Therm. Eng.
**2020**, 164, 114442. [Google Scholar] [CrossRef] - Elakhdar, M.; Landoulsi, H.; Tashtoush, B.; Nehdi, E.; Kairouani, L. A combined thermal system of ejector refrigeration and Organic Rankine cycles for power generation using a solar parabolic trough. Energy Convers. Manag.
**2019**, 199, 111947. [Google Scholar] [CrossRef] - Arteconi, A.; Del Zotto, L.; Tascioni, R.; Cioccolanti, L. Modelling system integration of a micro solar organic Rankine Cycle plant into a residential building. Appl. Energy
**2019**, 251, 113408. [Google Scholar] [CrossRef] - Khanmohammadi, S.; Saadat-Targhi, M.; Ahmed, F.W.; Afrand, M. Potential of thermoelectric waste heat recovery in a combined geothermal, fuel cell and organic Rankine flash cycle (thermodynamic and economic evaluation). Int. J. Hydrogen Energy
**2020**, 45, 6934–6948. [Google Scholar] [CrossRef] - Han, J.; Wang, X.; Xu, J.; Yi, N.; Talesh, S.S.A. Thermodynamic analysis and optimization of an innovative geothermal-based organic Rankine cycle using zeotropic mixtures for power and hydrogen production. Int. J. Hydrogen Energy
**2020**, 45, 8282–8299. [Google Scholar] [CrossRef] - Simpson, M.C.; Chatzopoulou, M.A.; Oyewunmi, O.A.; Le Brun, N.; Sapin, P.; Markides, C.N. Technoeconomic analysis of internal combustion engine—Organic Rankine cycle systems for combined heat and power in energy-intensive buildings. Appl. Energy
**2019**, 253, 113462. [Google Scholar] [CrossRef] - Shi, L.; Shu, G.; Tian, H.; Deng, S. A review of modified Organic Rankine cycles (ORCs) for internal combustion engine waste heat recovery (ICE-WHR). Renew. Sustain. Energy Rev.
**2018**, 92, 95–110. [Google Scholar] [CrossRef] - Kim, D.K.; Choi, H.W.; Kim, M.S. Design of a rotary expander as an expansion device integrated into organic Rankine cycle (ORC) to recover low-grade waste heat. Appl. Therm. Eng.
**2019**, 163, 114326. [Google Scholar] [CrossRef] - Liao, G.; Jiaqiang, E.; Zhang, F.; Chen, J.; Leng, E. Advanced exergy analysis for organic Rankine Cycle-based layout to recover waste heat of flue gas. Appl. Energy
**2020**, 266, 114891. [Google Scholar] [CrossRef] - Lin, Y.-P.; Wang, W.-H.; Pan, S.-Y.; Ho, C.-C.; Hou, C.-J.; Chiang, P.-C. Environmental impacts and benefits of organic Rankine cycle power generation technology and wood pellet fuel exemplified by electric arc furnace steel industry. Appl. Energy
**2016**, 183, 369–379. [Google Scholar] [CrossRef] - Yang, H.; Xu, C.; Yang, B.; Yu, X.; Zhang, Y.; Mu, Y. Performance analysis of an organic Rankine Cycle system using evaporative condenser for sewage heat recovery in the petrochemical industry. Energy Convers. Manag.
**2020**, 205, 112402. [Google Scholar] [CrossRef] - de Campos, G.B.; Bringhenti, C.; Traverso, A.; Tomita, J.T. Thermoeconomic optimization of organic Rankine bottoming cycles for micro gas turbines. Appl. Therm. Eng.
**2020**, 164, 114477. [Google Scholar] [CrossRef] - Zhai, L.; Xu, G.; Wen, J.; Quan, Y.; Fu, J.; Wu, H.; Li, T. An improved modeling for low-grade organic Rankine cycle coupled with optimization design of radial-inflow turbine. Energy Convers. Manag.
**2017**, 153, 60–70. [Google Scholar] [CrossRef][Green Version] - Li, Y.-R.; Du, M.-T.; Wu, C.-M.; Wu, S.-Y.; Liu, C. Potential of organic Rankine cycle using zeotropic mixtures as working fluids for waste heat recovery. Energy
**2014**, 77, 509–519. [Google Scholar] [CrossRef] - Rayegan, R.; Tao, Y.X. A procedure to select working fluids for solar Organic Rankine Cycles (ORCs). Renew. Energy
**2011**, 36, 659–670. [Google Scholar] [CrossRef] - Li, Y.; Ren, X.-d. Investigation of the organic Rankine cycle (ORC) system and the radial-inflow turbine design. Appl. Therm. Eng.
**2016**, 96, 547–554. [Google Scholar] [CrossRef] - Kang, S.H. Design and preliminary tests of ORC (organic Rankine cycle) with two-stage radial turbine. Energy
**2016**, 96, 142–154. [Google Scholar] [CrossRef] - Al Jubori, A.M.; Al-Dadah, R.; Mahmoud, S. An innovative small-scale two-stage axial turbine for low-temperature organic Rankine cycle. Energy Convers. Manag.
**2017**, 144, 18–33. [Google Scholar] [CrossRef] - Wang, Z.; Zhang, Z.; Xia, X.; Zhao, B.; He, N.; Peng, D. Preliminary design and numerical analysis of a radial inflow turbine in organic Rankine cycle using zeotropic mixtures. Appl. Therm. Eng.
**2019**, 162, 114266. [Google Scholar] [CrossRef] - Bao, J.; Zhao, L. A review of working fluid and expander selections for organic Rankine cycle. Renew. Sustain. Energy Rev.
**2013**, 24, 325–342. [Google Scholar] [CrossRef] - Sauret, E.; Rowlands, A.S. Candidate radial-inflow turbines and high-density working fluids for geothermal power systems. Energy
**2011**, 36, 4460–4467. [Google Scholar] [CrossRef] - Atkinson, M.J. The Design of Efficient Radial Turbines for Low Power Applications. Ph.D. Thesis, University of Sussex, Falmer, UK, 1998. [Google Scholar]
- Salih, U.M. Numerical Simulation, Design and Optimization of Radial Inflow Turbine for Energy Recovery Usage of Automobile. Ph.D. Thesis, Technical University of Munich, Munich, Germany, 2015. [Google Scholar]
- Miranda, R. Projeto de Turbinas Radiais Operadas Com Fluidos Orgânicos Para Baixas Potências. Ph.D. Thesis, Universidade Federal de Itajubá, Itajubá, Brazil, 2015. [Google Scholar]
- Song, J.; Gu, C.-W.; Ren, X. Influence of the radial-inflow turbine efficiency prediction on the design and analysis of the Organic Rankine Cycle (ORC) system. Energy Convers. Manag.
**2016**, 123, 308–316. [Google Scholar] [CrossRef] - Song, Y.; Sun, X.; Huang, D. Preliminary design and performance analysis of a centrifugal turbine for Organic Rankine Cycle (ORC) applications. Energy
**2017**, 140, 1239–1251. [Google Scholar] [CrossRef] - Da Lio, L.; Manente, G.; Lazzaretto, A. A mean-line model to predict the design efficiency of radial inflow turbines in organic Rankine cycle (ORC) systems. Appl. Energy
**2017**, 205, 187–209. [Google Scholar] [CrossRef] - Zheng, Y.; Hu, D.; Cao, Y.; Dai, Y. Preliminary design and off-design performance analysis of an organic Rankine Cycle radial-inflow turbine based on mathematic method and CFD method. Appl. Therm. Eng.
**2017**, 112, 25–37. [Google Scholar] [CrossRef] - Han, Z.; Jia, X.; Li, P. Preliminary design of radial inflow turbine and working fluid selection based on particle swarm optimization. Energy Convers. Manag.
**2019**, 199, 111933. [Google Scholar] [CrossRef] - Li, Y.; Li, W.; Gao, X.; Ling, X. Thermodynamic analysis and optimization of organic Rankine cycles based on radial-inflow turbine design. Appl. Therm. Eng.
**2021**, 184, 116277. [Google Scholar] [CrossRef] - Carrillo Caballero, G.; Escorcia, Y.C.; Mendoza Castellanos, L.S.; Galindo Noguera, A.L.; Venturini, O.J.; Silva Lora, E.E.; Gutiérrez Velásquez, E.I.; Alviz Meza, A. Thermal Analysis of a Parabolic Trough Collectors System Coupled to an Organic Rankine Cycle and a Two-Tank Thermal Storage System: Case Study of Itajubá-MG Brazil. Energies
**2022**, 15, 8261. [Google Scholar] [CrossRef] - Carrillo Caballero, G. Modelagem Do Comportamento Integrado de Um Sistema de Coletor Cilíndrico Parabólico Operando com Ciclo Rankine Orgânico E Armazenamento Térmico de Dois Tanques. Ph.D. Thesis, Universidade Federal de Itajubá, Itajubá, Brazil, 2018. [Google Scholar]
- Bell, I.H.; Wronski, J.; Quoilin, S.; Lemort, V. Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library coolprop. Ind. Eng. Chem. Res.
**2014**, 53, 2498–2508. [Google Scholar] [CrossRef] [PubMed][Green Version] - Moustapha, H.; Zelesky, M.F.; Baines, N.C.; Japikse, D. Axial and Radial Turbines; Concepts NREC: White River Junction, VT, USA, 2003. [Google Scholar]
- Aungier, R.H. Turbine Aerodynamics: Axial-Flow and Radial-Inflow Trubine Design and Analysis; ASME Press: New York, NY, USA, 2006. [Google Scholar]
- Japikse, D.; Baines, N. Introduction to Turbomachinery; Concepts ETI: Oxfordshire, UK, 1997. [Google Scholar]
- Dixon, S. Fluid Mechanics and Thermodynamics of Turbomachinery; Elsevier: Oxford, UK, 1998; pp. 1–27. [Google Scholar]
- Rahbar, K.; Mahmoud, S.; Al-Dadah, R.K.; Moazami, N. Modelling and optimization of organic Rankine cycle based on a small-scale radial inflow turbine. Energy Convers. Manag.
**2015**, 91, 186–198. [Google Scholar] [CrossRef] - Benson, R.S. A review of methods for assessing loss coefficients in radial gas turbines. Int. J. Mech. Sci.
**1970**, 12, 905–932. [Google Scholar] [CrossRef] - Glassman, A.J. Turbine Design and Application; Technical Report; Scientific and Technical Information Office, National Aeronautics and and Space Administration: Washington, DC, USA, 1990; Volume 1. [Google Scholar]
- Balje, O.E. Turbomachines: A Guide to Design Selection and Theory; John Wiley & Sons: Hoboken, NJ, USA, 1981. [Google Scholar]
- Ventura, C.A.M.; Jacobs, P.A.; Rowlands, A.S.; Petrie-Repar, P.; Sauret, E. Preliminary design and performance estimation of radial inflow turbines: An automated approach. J. Fluids Eng.
**2012**, 134, 031102. [Google Scholar] [CrossRef] - Al Jubori, A.; Al-Dadah, R.K.; Mahmoud, S.; Bahr Ennil, A.S.; Rahbar, K. Three dimensional optimization of small-scale axial turbine for low temperature heat source driven organic Rankine cycle. Energy Convers. Manag.
**2017**, 133, 411–426. [Google Scholar] [CrossRef] - Watanabe, I.; Ariga, I.; Mashimo, T. Effect of dimensional parameters of impellers on performance characteristics of a radial-inflow turbine. J. Eng. Power
**1971**, 93, 81–102. [Google Scholar] [CrossRef] - Paltrinieri, A. A Mean-Line Model to Predict the Design Performance of Radial Inflow Turbines in Organic Rankine Cycles. Master’s Thesis, Università Degli Studi Di Padova, Technische Universität Berlin, Berlin, Germany, 2014. [Google Scholar]
- Baloni, B.D.; Channiwala, S.A.; Mayavanshi, V.K. Pressure recovery and loss coefficient variations in the two different centrifugal blower volute designs. Appl. Energy
**2012**, 90, 335–343. [Google Scholar] [CrossRef] - Suhrmann, J.F.; Peitsch, D.; Gugau, M.; Heuer, T.; Tomm, U. Validation and development of loss models for small size radial turbines. Turbo Expo Power Land Sea Air
**2010**, 44021, 1937–1949. [Google Scholar] - Churchill, S.W. Friction factor equation spans all fluid flow regimes. Chem. Eng. J.
**1977**, 84, 91–92. [Google Scholar] - Wasserbauer, C.A.; Glassman, A.J. FORTRAN Program for Predicting the Off-Design Performance of Radial Inflow Turbines; NASA Technical Note TN D-8063; NASA: Cleveland, OH, USA, 1975. [Google Scholar]
- Rudinger, G. Chamber dimension effects on induced flow and frictional resistance of enclosed rotating disks. J. Basic Eng.
**1960**, 82, 230. [Google Scholar] [CrossRef] - Erbas, M.; Sofuoglu, M.A.; Biyikoglu, A.; Uslan, I. Design and optimization of a low temperature organic rankine cycle and turbine. In ASME 2013 International Mechanical Engineering Congress and Exposition; American Society of Mechanical Engineers: New York, NY, USA, 2013; pp. 1–7. [Google Scholar]
- Glassman, A.J. Computer Program for Design Analysis of Radial-Inflow Turbines; Technical Report; NASA: Washington, DC, USA, 1976. [Google Scholar]
- Abas, N.; Kalair, A.R.; Khan, N.; Haider, A.; Saleem, Z.; Saleem, M.S. Natural and synthetic refrigerants, global warming: A review. Renew. Sustain. Energy Rev.
**2018**, 90, 557–569. [Google Scholar] [CrossRef] - Long, R.; Bao, Y.J.; Huang, X.M.; Liu, W. Exergy analysis and working fluid selection of organic Rankine cycle for low grade waste heat recovery. Energy
**2014**, 73, 475–483. [Google Scholar] [CrossRef] - Lim, T.-W.; Choi, Y.-S.; Hwang, D.-H. Optimal working fluids and economic estimation for both double stage organic Rankine cycle and added double stage organic Rankine cycle used for waste heat recovery from liquefied natural gas fueled ships. Energy Convers. Manag.
**2021**, 242, 114323. [Google Scholar] [CrossRef] - Wei, Z. Meanline Analisis of Radial Inflow Turbines. Master’s Thesis, Carleton University, Ottawa, ON, Canada, 2014. [Google Scholar]
- Sauret, E.; Gu, Y. 3D CFD simulations of a candidate R143A radial-inflow turbine for geothermal power applications. In Proceedings of the ASME Power 2014, 32158; American Society of Mechanical Engineers: Baltimore, MD, USA, 2014. [Google Scholar]
- Al Jubori, A.; Daabo, A.; Al-Dadah, R.K.; Mahmoud, S.; Ennil, A.B. Development of micro-scale axial and radial turbines for low-temperature heat source driven organic Rankine cycle. Energy Convers. Manag.
**2016**, 130, 141–155. [Google Scholar] [CrossRef]

**Figure 2.**Meridional view of the radial inflow turbine, indicating different components and main dimensions, adapted from [41].

**Figure 3.**Velocity triangle at the rotor inlet of a radial turbine, adapted from [45].

**Figure 4.**Velocity triangle at the rotor outlet of a radial turbine, adapted from [44].

**Figure 5.**Simplified diagram of the nozzle adapted from [29].

**Figure 13.**Variation in the total isentropic efficiency and power of the turbine operating with R-245fa, as a function of pressure ratio.

**Figure 14.**Variation in the total isentropic efficiency and power of the turbine operating with R-245fa, as a function of rotation speed.

**Figure 15.**Variation in the total isentropic efficiency and power of the turbine operating with R-141b, as a function of pressure ratio.

**Figure 16.**Variation in the total isentropic efficiency and power of the turbine operating with R-141b, as a function of rotation speed.

**Figure 17.**Variation in the total isentropic efficiency and power of the turbine operating with R-123, as a function of pressure ratio.

**Figure 18.**Variation in the total isentropic efficiency and power of the turbine operating with R-123, as a function of rotation speed.

Radial Turbine Parameters | |
---|---|

Fluid | R-245fa |

Flow coefficient (ϕ) | 0.215 |

Pressure coefficient (ψ) | 0.918 |

Inlet total pressure (kPa) | 1000 |

Condenser working temperature (K) | 303.15 |

Rotation (rpm) | 9000 |

Mass flow rate (kg/s) | 10.92 |

Parameter | Paltrinieri [52] | NEST Model | Difference (%) |
---|---|---|---|

Rotor | |||

Inlet radius, r4 (m) | 0.1796 | 0.1709 | 4.8 |

Inlet blade height, b4 (m) | 0.0114 | 0.0106 | 7.0 |

Inlet absolute flow angle, α4 (°) | 76.8186 | 76.8186 | 0 |

Inlet relative flow angle, β4 (°) | −43.4682 | −42.5484 | 2.1 |

Inlet static temperature, T4 (K) | 354.62 | 353.7832 | 0.24 |

Inlet static pressure, p4 (kPa) | 585.37 | 590.7688 | 0.92 |

Inlet absolute Mach number, Ma4 | 1.0369 | 1.0479 | 1.06 |

Inlet relative Mach number, Ma4′ | 0.3258 | 0.2788 | 14.4 |

Outlet hub radius, r6h (m) | 0.0539 | 0.053 | 1.7 |

Outlet shroud radius, r6s (m) | 0.1169 | 0.1182 | 1.1 |

Outlet blade height, b6 (m) | 0.063 | 0.0653 | 3.7 |

Outlet absolute flow angle, α6 (°) | −0.4018 | −0.4018 | 0 |

Outlet relative flow angle, β6_rms | −64.0532 | −65.0962 | 1.6 |

Outlet static temperature, T6 (K) | 325.74 | 323.8017 | 0.59 |

Outlet static pressure, p6 (kPa) | 171.81 | 175.12 | 1.92 |

Outlet absolute Mach number, Ma6 | 0.2582 | 0.2434 | 5.7 |

Outlet relative Mach number, Ma6´ | 0.59 | 0.6277 | 4.7 |

Number of blades, Z_{R} (−) | * | 18 | |

Nozzle | |||

Inlet radius, r1 (m) | 0.2335 | 0.2222 | 4.8 |

Inlet blade height, b1 (m) | 0.0114 | 0.0106 | 7.0 |

Inlet static temperature, T1 (K) | 369.75 | 369.89 | 0.04 |

Inlet static pressure, p1 (kPa) | 995.88 | 999.9 | 0.4 |

Inlet absolute Mach number, Ma1 | 0.095 | 0.1100 | 15.7 |

Outlet radius, r2 (m) | 0.1811 | 0.1734 | 4.3 |

Outlet blade height, b2 (m) | 0.0114 | 0.0106 | 4.38 |

Outlet absolute flow angle, α2 (°) | 76.8186 | 76.8186 | 4.14 |

Inlet static temperature, T2 (K) | 354.62 | 353.7832 | 0.174 |

Outlet static pressure, p2 (kPa) | 585.37 | 590.7688 | 0.107 |

Outlet absolute Mach number, Ma2 | 1.0369 | 1.0479 | 1.06 |

Number of blades, Z_{B} (−) | 25 | 25 | 0 |

Total to static efficiency, η_{ts} (%) | 74.1 | 71.85 | 3.0 |

Net Power, P (kW) | 267 | 260.5 | 2.4 |

Parameter/Fluid | R-245fa | R-141b | R-123b |
---|---|---|---|

Turbine nozzle inlet total temperature (°C) | 79.9 | 94.3 | 96.6 |

Mass flow rate of the working fluid (kg/s) | 0.61 | 0.45 | 0.62 |

Flow coefficient (ϕ) | 0.215 | 0.215 | 0.215 |

Load coefficient (ψ) | 0.918 | 0.918 | 0.918 |

Pressure ratio | 5.71 | 4.71 | 4.71 |

Rotation speed, ω (rpm) | 25,800 | 22,000 | 24,000 |

Parameter | R-245fa | R-141b | R-123 |
---|---|---|---|

Rotor | |||

Inlet radius, r_{4} (m) | 0.0568 | 0.0592 | 0.0531 |

Inlet blade height, b_{4} (m) | 0.0036 | 0.0039 | 0.0041 |

Inlet absolute flow angle, α_{4} (°) | 76.8186 | 76.8186 | 76.8186 |

Inlet relative flow angle, β_{4} (°) | −45.718 | −46.0327 | −40.3337 |

Inlet static temperature, T_{4} (°C) | 66.5 | 80.3 | 81.5 |

Inlet static pressure, p_{4} (kPa) | 394.8306 | 325.7557 | 371.049 |

Inlet absolute Mach number, Ma_{4} | 0.9591 | 0.8798 | 0.9586 |

Inlet relative Mach number, Ma_{4}′ | 0.2618 | 0.2392 | 0.2541 |

Outlet hub radius, r_{6h} (m) | 0.0222 | 0.0231 | 0.0207 |

Outlet shroud radius, r_{6s} (m) | 0.037 | 0.0376 | 0.0357 |

Outlet blade height, b_{6} (m) | 0.0148 | 0.0145 | 0.015 |

Outlet absolute flow angle, α_{6} (°) | 0 | 0 | 0 |

Outlet relative flow angle, β_{6_rms} (°) | −66.8922 | −66.6462 | −67.2171 |

Outlet relative flow angle, β_{6_h} (°) | −61.1328 | −61.1328 | −61.1328 |

Outlet relative flow angle, β_{6_t} (°) | −71.7233 | −71.3152 | −72.2554 |

Outlet static temperature, T_{6} (°C) | 37.5 | 47.4 | 53.5 |

Outlet static pressure, p_{6} (kPa) | 116.4663 | 107.3252 | 131.6736 |

Outlet absolute Mach number, Ma_{6} | 0.2357 | 0.2219 | 0.2299 |

Outlet relative Mach number, Ma_{6}′ | 0.5967 | 0.5617 | 0.5819 |

Number of blades, Z_{R} (−) | 18 | 18 | 18 |

Nozzle | |||

Inlet radius, r_{1} (m) | 0.0739 | 0.0769 | 0.0691 |

Inlet blade height, b_{1} (m) | 0.0036 | 0.0039 | 0.0041 |

Inlet static temperature, T_{1} (°C) | 79.9 | 94.4 | 96.7 |

Inlet static pressure, p_{1} (kPa) | 659.1412 | 505.5017 | 620.1825 |

Inlet absolute Mach number, Ma1 | 0.1955 | 0.1796 | 0.1891 |

Inlet absolute flow angle, α_{1} (°) | 49.1958 | 49.3194 | 49.4424 |

Outlet radius, r_{2} (m) | 0.0575 | 0.0599 | 0.0539 |

Outlet blade height, b_{2} (m) | 0.0026 | 0.0039 | 0.0041 |

Outlet absolute flow angle, α_{2} (°) | 76.8186 | 76.8186 | 76.8186 |

Outlet static temperature, T_{2} (°C) | 66.5 | 80.3 | 81.5 |

Outlet static pressure, p_{2} (kPa) | 394.8306 | 325.7557 | 371.049 |

Outlet absolute Mach number, Ma_{2} | 0.9591 | 0.8798 | 0.9586 |

Blade thickness (mm) | 0.59171 | 0.58982 | 0.57152 |

Number of blades, Z_{B} (−) | 25 | 25 | 25 |

Working Fluid | Number of Elements | ${\mathsf{\eta}}_{\mathit{t}}$ (%) | ${\mathit{P}}_{\mathit{t}}$ (kW) | $\mathbf{Difference}\text{}(\%)\text{}{\mathsf{\eta}}_{\mathit{t}}$ | $\mathbf{Difference}\text{}(\%)\text{}{\mathit{P}}_{\mathit{t}}$ |
---|---|---|---|---|---|

R-245fa | 413,845 | 76.12 | 8.76 | - | - |

629,391 | 76.73 | 8.71 | 0.8 | 0.57 | |

R-141b | 510,330 | 80.30 | 9.41 | - | - |

782,506 | 80.47 | 9.37 | 0.21 | 0.42 | |

R-123 | 418,276 | 77.60 | 7.37 | - | - |

627,414 | 78.20 | 7.40 | 0.77 | 0.40 |

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## Share and Cite

**MDPI and ACS Style**

Carrillo Caballero, G.; Cardenas Escorcia, Y.; Venturini, O.J.; Silva Lora, E.E.; Alviz Meza, A.; Mendoza Castellanos, L.S.
Unidimensional and 3D Analyses of a Radial Inflow Turbine for an Organic Rankine Cycle under Design and Off-Design Conditions. *Energies* **2023**, *16*, 3383.
https://doi.org/10.3390/en16083383

**AMA Style**

Carrillo Caballero G, Cardenas Escorcia Y, Venturini OJ, Silva Lora EE, Alviz Meza A, Mendoza Castellanos LS.
Unidimensional and 3D Analyses of a Radial Inflow Turbine for an Organic Rankine Cycle under Design and Off-Design Conditions. *Energies*. 2023; 16(8):3383.
https://doi.org/10.3390/en16083383

**Chicago/Turabian Style**

Carrillo Caballero, Gaylord, Yulineth Cardenas Escorcia, Osvaldo José Venturini, Electo Eduardo Silva Lora, Anibal Alviz Meza, and Luis Sebastián Mendoza Castellanos.
2023. "Unidimensional and 3D Analyses of a Radial Inflow Turbine for an Organic Rankine Cycle under Design and Off-Design Conditions" *Energies* 16, no. 8: 3383.
https://doi.org/10.3390/en16083383