# Performance Analysis of Organic Rankine Cycle with the Turbine Embedded in a Generator (TEG)

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Thermodynamic Analysis of the ORC

- The system operates under steady-state conditions.
- The system is adiabatic with negligible heat losses.
- The pressure drop in the pipes is neglected.
- The mechanical efficiency of the system is neglected.

## 3. Design of the Turbine for the TEG

#### 3.1. Concept of TEG

#### 3.2. Turbine Design Procedure

#### 3.2.1. Mean-Line Design Method

#### 3.2.2. Velocity Triangle and Dimensionless Parameters

#### 3.2.3. Turbine Loss Model

#### 3.2.4. Flow Chart of the Turbine Design

## 4. Results and Discussion

#### 4.1. Mean-Line Design Validation

#### 4.2. Parametric Analysis

#### 4.3. Thermal Efficiency of ORC

#### 4.4. 3D Turbine Generator Assembly

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$C$ | Blade chord length, m |

${C}_{x}$ | Blade axial chord length, m |

$h$ | Specific total enthalpy, kJ/kg |

$H$ | Blade height, m |

$\dot{m}$ | Mass flow rate (MFR), kg/s |

P | Pressure, Pa |

$\dot{Q}$ | Heat transfer rate, kW |

$r$ | Blade radius, m |

S | Blade pitch, m |

T | Temperature, K |

$U$ | Tangential velocity, m/s |

$V$ | Absolute velocity, m/s |

${V}_{x}$ | Meridional velocity, m/s |

W | Relative velocity, m/s |

W | Power, kW |

Y | Total pressure loss coefficient |

Greek Symbols | |

α | Absolute flow angle |

β | Relative flow angle |

η | Efficiency |

ξ | Degree of reaction |

σ | Blade solidity (C/S) |

τ | Tip clearance height, m |

φ | Flow coefficient |

ψ | Loading (work) coefficient |

ω | Angular velocity, 1/s |

Subscrips | |

1−4 | state point in ORC |

$\mathrm{car}$ | Carnot |

$e$ | Evaporation |

$ex$ | Exergy |

$\mathrm{H}$ | High |

L | Low |

$\mathrm{m}$ | Mean value of the blade |

$\mathrm{p}$ | Pump, profile loss |

s | Isentropic, secondary loss |

t | Turbine |

TC | Tip clearance loss |

TE | Trailing edge |

th | Thermal |

0 | total |

1 | Inlet of the stator |

2 | Inlet of the rotor |

3 | Outlet of the rotor |

## References

- Hung, T.C. Waste heat recovery of organic Rankine cycle using dry fluids. Energy Convers Manag.
**2001**, 42, 539–553. [Google Scholar] [CrossRef] - Quoilin, S.; Lemort, V.; Lebrun, J. Experimental study and modeling of an Organic Rankine Cycle using scroll expander. Appl. Energy
**2010**, 87, 1260–1268. [Google Scholar] [CrossRef] - Barse, K.A.; Mann, M.D. Maximizing ORC performance with optimal match of working fluid with system design. Appl. Eng.
**2016**, 100, 11–19. [Google Scholar] [CrossRef] [Green Version] - Wei, D.; Lu, X.; Lu, Z.; Gu, J. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Manag.
**2007**, 48, 1113–1119. [Google Scholar] [CrossRef] - Li, Y.R.; Wang, J.N.; Du, M.T. Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle. Energy
**2012**, 42, 503–509. [Google Scholar] [CrossRef] - Wang, J.; Yan, Z.; Wang, M.; Li, M.; Dai, Y. Multi-objective optimization of an organic Rankine cycle (ORC) for low grade waste heat recovery using evolutionary algorithm. Energy Convers Manag.
**2013**, 71, 146–158. [Google Scholar] [CrossRef] - Kang, S.H. Design and experimental study of ORC (organic Rankine cycle) and radial turbine using R245fa working fluid. Energy
**2012**, 41, 514–524. [Google Scholar] [CrossRef] - Declaye, S.; Quoilin, S.; Guillaume, L.; Lemort, V. Experimental study on an open-drive scroll expander integrated into an ORC (Organic Rankine Cycle) system with R245fa as working fluid. Energy
**2013**, 55, 173–183. [Google Scholar] [CrossRef] - Lazzaretto, A.; Manente, G. A new criterion to optimize ORC design performance using efficiency correlations for axial and radial turbines. Int. J. Thermo.
**2014**, 17, 192–200. [Google Scholar] [CrossRef] [Green Version] - 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] - Al Jubori, A.M.; Al-Mousawi, F.N.; Rahbar, K.; Al-Dadah, R.; Mahmoud, S. Design and manufacturing a small-scale radial-inflow turbine for clean organic Rankine power system. J. Clean. Prod.
**2020**, 257, 120488. [Google Scholar] [CrossRef] - Giovannelli, A.; Archilei, E.M.; Salvini, C. Two-Stage Radial Turbine for a Small Waste Heat Recovery Organic Rankine Cycle (ORC) Plant. Energies
**2020**, 13, 1054. [Google Scholar] [CrossRef] [Green Version] - Peng, N.; Wang, E.; Zhang, H. Preliminary Design of an Axial-Flow Turbine for Small-Scale Supercritical Organic Rankine Cycle. Energies
**2021**, 14, 5277. [Google Scholar] [CrossRef] - Hu, S.; Yang, Z.; Li, J.; Duan, Y. A Review of Multi-Objective Optimization in Organic Rankine Cycle (ORC) System Design. Energies
**2021**, 14, 6492. [Google Scholar] [CrossRef] - Wang, E.H.; Zhang, H.G.; Fan, B.Y.; Ouyang, M.G.; Zhao, Y.; Mu, Q.H. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy
**2011**, 36, 3406–3418. [Google Scholar] [CrossRef] - Fernández-Guillamón, A.; Molina-García, Á.; Vera-García, F.; Almendros-Ibáñez, J.A. Organic Rankine Cycle Optimization Performance Analysis Based on Super-Heater Pressure: Comparison of Working Fluids. Energies
**2021**, 14, 2548. [Google Scholar] [CrossRef] - Tournier, J.M.; El-Genk, M.S. Axial flow, multi-stage turbine and compressor models. Energy Convers Manag.
**2010**, 51, 16–29. [Google Scholar] [CrossRef] - Da Lio, L.; Manente, G.; Lazzaretto, A. New efficiency charts for the optimum design of axial flow turbines for organic Rankine cycles. Energy
**2014**, 77, 447–459. [Google Scholar] [CrossRef] - Da Lio, L.; Manente, G.; Lazzaretto, A. Predicting the optimum design of single stage axial expanders in ORC systems: Is there a single efficiency map for different working fluids? Appl. Energy
**2016**, 167, 44–58. [Google Scholar] [CrossRef] - Moustapha, H.; Zelesky, M.F.; Baines, N.C.; Japikse, D. Axial and Radial Turbines; Concepts NREC: White River Junction, VT, USA, 2003. [Google Scholar]
- Wilson, D.G.; Korakianitis, T. The Design of High-Efficiency Turbomachinery and Gas Turbines; MIT Press: Cambridge, MA, USA, 2014. [Google Scholar]
- Ainley, D.G.; Mathieson, G.C.R. A Method of Performance Estimation for Axial-Flow Turbines; Aeronautical Research Council: London, UK, 1951. [Google Scholar]
- Dunham, J.; Came, P.M. Improvements to the Ainley-Mathieson method of turbine performance prediction. J. Eng. Power
**1970**, 92, 252–256. [Google Scholar] [CrossRef] - Craig, H.R.M.; Cox, H.J.A. Performance estimation of axial flow turbines. Proc. Inst. Mech. Eng.
**1970**, 185, 407–424. [Google Scholar] [CrossRef] - Zhu, J.; Sjolander, S.A. Improved profile loss and deviation correlations for axial-turbine blade rows. In Proceedings of the Turbo Expo: Power for Land, Sea, and Air; ASME: Reno, NV, USA, 2005; Volume 47306, pp. 783–792. [Google Scholar]
- Kacker, S.C.; Okapuu, U. A mean-line prediction method for axial flow turbine efficiency. J. Eng. Power
**1982**, 104, 111–119. [Google Scholar] [CrossRef] - Patdiwala, U.J.; Patel, H.C.; Parmar, P.K. A review on tip clearance flow and secondary flow losses in linear turbine cascade. J. Mech. Civ. Eng.
**2014**, 11, 33–37. [Google Scholar] [CrossRef] - Dixon, S.L.; Hall, C. Fluid Mechanics and Thermodynamics of Turbomachinery; Butterworth-Heinemann: Oxford, UK, 2013. [Google Scholar]
- Rist, D. Influence of geometric effects on the aspect ratio optimization of axial turbine bladings. In Proceedings of the Turbo Expo: Power for Land, Sea, and Air; ASME: London, UK, 1978; Volume 79726, p. V01BT02A072. [Google Scholar]
- Gao, K.; Xie, Y.; Zhang, D. Effects of rotor solidity and leakage flow on the unsteady flow in axial turbine. Appl. Therm. Eng.
**2018**, 128, 926–939. [Google Scholar] [CrossRef] - Simpson, A.T.; Spence, S.W.T.; Watterson, J.K. Numerical and experimental study of the performance effects of varying vaneless space and vane solidity in radial turbine stators. J. Turbomach.
**2013**, 135, 031001. [Google Scholar] [CrossRef] - Zweifel, O. The spacing of turbomachine blading, especially with large angular deflection. Brown Boveri. Rev.
**1945**, 32, 436–444. [Google Scholar] - Kofskey, M.G.; Nusbaum, W.J. Aerodynamic Evaluation of Two-Stage Axial-Flow Turbine Designed for Brayton-Cycle Space Power System; National Aeronautics and Space Administration: Washington, DC, USA, 1968.
- Smith, S.F. A simple correlation of turbine efficiency. Aeronaut. J.
**1965**, 69, 467–470. [Google Scholar] [CrossRef] - Nagpurwala, Q.H. Hydraulic Turbine; PEMP RMD 2501; M.S. Ramaiah School of Advanced Studies: Bengaluru, India, 2016; pp. 1–70. [Google Scholar]

**Figure 2.**Turbine generator structure in the ORC system. (

**a**) Conventional type: The generator rotor is rotated using the turbine rotor torque through the shaft. (

**b**) Proposed turbine embedded in a generator (TEG) type. The generator rotor is rotated using the rotation of the turbine rotor without a shaft.

**Figure 5.**Comparison of the mean-line design results investigated in the present study and previously reported experimental results [33].

**Figure 6.**Total-to-total pressure ratio (PR) of the turbine when the flow coefficient ($\phi $) ranges from 0.4 to 1.0 and loading coefficient ($\psi $) ranges from 0.8 to 1.4.

**Figure 7.**Absolute Mach number (Ma) at the turbine stator outlet when the flow coefficient ($\phi $) ranges from 0.4 to 1.0 and loading coefficient ($\psi $) ranges from 0.8 to 1.4.

**Figure 8.**Total-to-total isentropic efficiency of the turbine (${\eta}_{t}$) when the flow coefficient ($\phi $) ranges from 0.4 to 1.0 and loading coefficient ($\psi $) ranges from 0.8 to 1.4.

**Figure 9.**Power of the turbine (${\dot{W}}_{t}$) when the flow coefficient ($\phi $) ranges from 0.4 to 1.0 and loading coefficient ($\psi $) ranges from 0.8 to 1.4.

**Figure 10.**Total-to-total isentropic efficiency of the turbine (${\eta}_{t}$) with and without the tip clearance loss coefficient (${Y}_{TC}$) when the total-to-total pressure ratio (PR) ranges from 1.0 to 3.0.

**Figure 11.**Power of the turbine (${\dot{W}}_{t}$) with and without the tip clearance loss coefficient (${Y}_{TC}$) when the total-to-total pressure ratio (PR) ranges from 1.0 to 3.0.

**Figure 12.**Comparison of thermal and exergy efficiency of the ORC based on the application of the proposed TEG.

Working Fluid | Molecular Formula | Mol. Weight (g/mol) | Critical Temperature (K) | Critical Pressure (MPa) | GWP (100 yr) |
---|---|---|---|---|---|

R245fa | CF3CH2CHF2 | 134.05 | 427.16 | 3.651 | 1030 |

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

Working fluid | R245fa |

Mass flow rate [kg/s] | 2.02 |

Turbine inlet temperature [°C] | 80 |

Turbine inlet total pressure [MPa] | 0.7 |

Turbine rotor rotational speed [rpm] | 20,000 |

Heat source temperature [°C] | 90 |

Heat sink temperature [°C] | 20 |

Pump efficiency [-] | 0.75 |

Generator efficiency [-] | 0.95 |

Loss Models | Equation | Ref. |
---|---|---|

$\mathrm{Profile}\mathrm{loss},{Y}_{p}$ | ${Y}_{P}=0.914\left({K}_{in}Y{\u2019}_{P,AM}{K}_{P}+{Y}_{shock}\right)f\left(Re\right)$ $Y{\u2019}_{p,AM}=\left\{{Y}_{p,AM}^{\left({m}_{1}=0\right)}+\left|\frac{{\beta}_{1}}{{\alpha}_{2}}\right|\left(\frac{{\beta}_{1}}{{\alpha}_{2}}\right)\left[{Y}_{p,AM}^{\left({\beta}_{1}={\alpha}_{2}\right)}-{Y}_{p,AM}^{\left({\beta}_{1}=0\right)}\right]\right\}\times {\left(\frac{{t}_{max}/C}{0.2}\right)}^{{K}_{m}{\beta}_{1}/{\alpha}_{2}}$ | [22,25] |

$\mathrm{Sec}\mathrm{ondary}\mathrm{loss},{Y}_{s}$ | ${Y}_{s}=1.2Y{\u2019}_{S,AM}{K}_{s}$ $Y{\u2019}_{S,AM}=0.0334{f}_{\left(AR\right)}\left(\frac{cos({\alpha}_{2})}{cos({\beta}_{1})}\right){\left(\frac{{C}_{L}}{s/c}\right)}^{2}\frac{co{s}^{2}{\alpha}_{2}}{co{s}^{3}{\alpha}_{m}}$ | [25] |

$\mathrm{Trailing}\mathrm{edge}\mathrm{loss},{Y}_{TE}$ | ${Y}_{TE}=\frac{\mathsf{\Delta}{P}_{0}}{0.5\rho {V}_{2}^{2}}={\left(\frac{{t}_{2}}{{o}_{2}-{t}_{2}}\right)}^{2}$ | [18] |

$\mathrm{Tip}\mathrm{clearance}\mathrm{loss},{Y}_{TC}$ | ${Y}_{TC}=B\frac{\mathrm{c}}{h}{\left(\frac{k}{c}\right)}^{0.78}Z$ $\mathrm{Z}=\left({C}_{L}\frac{c}{s}\right)\frac{co{s}^{2}{a}_{2}}{co{s}^{3}{a}_{m}}$ | [22,23] |

Design Parameters | Value |
---|---|

Flow coefficient, φ [-] | 0.70 |

Loading coefficient, ψ [-] | 1.00 |

Degree of reaction, ξ [-] | 0.50 |

Total-to-total pressure ratio, PR [-] | 2.09 |

$\mathrm{Blade}\mathrm{mean}\mathrm{radius},{r}_{m}$ [mm] | 47.70 |

Aspect ratio (H/C), AR [-] | 1.05 |

$\mathrm{Blade}\mathrm{axial}\mathrm{chord},{C}_{x}$ [mm] | 9.51 |

Number of blade [-] | 37 |

Solidity (C/S), σ [-] | 1.20 |

Zeweifel coefficient, Z [-] | 0.78 |

Tip clearance height, τ [mm] | 0.50 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sim, J.-B.; Yook, S.-J.; Kim, Y.W.
Performance Analysis of Organic Rankine Cycle with the Turbine Embedded in a Generator (TEG). *Energies* **2022**, *15*, 309.
https://doi.org/10.3390/en15010309

**AMA Style**

Sim J-B, Yook S-J, Kim YW.
Performance Analysis of Organic Rankine Cycle with the Turbine Embedded in a Generator (TEG). *Energies*. 2022; 15(1):309.
https://doi.org/10.3390/en15010309

**Chicago/Turabian Style**

Sim, Jung-Bo, Se-Jin Yook, and Young Won Kim.
2022. "Performance Analysis of Organic Rankine Cycle with the Turbine Embedded in a Generator (TEG)" *Energies* 15, no. 1: 309.
https://doi.org/10.3390/en15010309