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Design of a supersonic turbine for the organic Rankine cycle system

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Abstract

The aerodynamic design of a hundred-kilowatt class supersonic turbine is presented in this study. Its purpose is to improve organic Rankine cycle (ORC) power systems’ performance. The ORC systems require a higher pressure ratio across the turbine to generate higher power output. It leads some designs to suffer from a choking condition by the higher pressure ratio. A choked flow leads to saturation of the mass flow rate and power, and a supersonic turbine can be an alternative to this problem. We use the meanline analysis, the method of characteristics, case studies, and validation of the 3D computational fluid dynamics simulations to design the supersonic turbine. 3D CFD is used to simulate the performance of the designed turbine. This approach allows us to understand its aerodynamic characteristics, performance in off-design conditions and also to find the recommended operating conditions. For validation of the numerical model, a comparison was carried out using previous literature that utilized supersonic flow with an organic fluid. The compared results are consistent, validating our numerical model. The designed supersonic turbine has 18 blades for the nozzle and 61 blades for the rotor. The predicted power output using R245fa is about 85.12 kW with a mass flow rate of 3.18 kg/s and a rotational speed of 33120 RPM.

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Abbreviations

a :

Speed of sound

C :

Absolute velocity

C l :

Chord length

D :

Diameter

e a :

Approximate relative error

e ext :

Extrapolated relative error

f :

Acentric factor (f = 0.0115)

h :

Enthalpy

H :

Helmholtz energy, throat height

I :

Imaginary number, \(\sqrt { - 1} \)

k :

Polytropic exponent

K :

Total pressure loss coefficient

m :

Mass flow rate

Ma :

Mach number

n :

Coefficients (see Ref. [24])

N :

Number of the rotor blade

P :

Pressure

r :

Grid refinement factor

R :

Ideal gas constant (8.314413 J/mol·K)

Rr :

Rotor blade radius

\(\overline {\rm{R}} \) :

Specific gas constant

s :

Pitch

T :

Temperature

U :

Tangential velocity

v :

Specific volume

W :

Relative velocity

W x :

Shaft power

y + :

Non-dimensional wall distance

Z :

Compressibility factor

α :

Nozzle exit flow angle

β :

Relative angle

δ :

Reduced density (δ = ρ/ρc)

ζ :

Enthalpy loss coefficient

η :

Efficiency

θ :

Rotating angle in the rotor

λ :

Blade angle

τ :

Torque, inverse reduced temperature (τ = Tc/T)

ν :

Prandtl-Meyer angle

ω :

Rotational speed

Φ :

Deviation of the power and efficiency

Φ ext :

Extrapolated value

Ψ :

Zweifel coefficient

CFD :

Computational fluid dynamics

GCI :

Grid convergence index

iPRSV :

Improved Peng-Robinson-Stryjek-Vera

MOC :

Method of characteristics

PREOS :

Peng and Robinson equation of state

RMS :

Root mean square

SWEOS:

Span-Wagner equation of state

1 :

Nozzle inlet

2 :

Rotor inlet

3 :

Rotor outlet

c :

Critical point property

N :

Nozzle property

r :

Rotational frame

R :

Rotor property

s :

Static property, isentropic property

t :

Total property

θ :

Tangential direction

m :

Meridional direction

0 :

Ideal gas property

r :

Real gas property

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Acknowledgments

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20172010105960). This work was financially supported by the National R&D project of “Development of 1 MW OTEC demonstration plant (6/6)” (PMS4730) funded by the Ministry of Oceans and Fisheries of the Republic of Korea. This study was financially supported by Seoul National University of Science & Technology.

Author information

Authors and Affiliations

  1. Korea Research Institute of Ships and Ocean Engineering, Daejeon, 34103, Korea

    J. Seo

  2. Korea Institute of Machinery and Materials, Daejeon, 34104, Korea

    Bum-Seog Choi

  3. Seoul National University of Science and Technology, Seoul, 139-743, Korea

    S. Han

Authors
  1. J. Seo
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  2. Bum-Seog Choi
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  3. S. Han
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Corresponding author

Correspondence to S. Han.

Additional information

J. Seo (Jongbeom Seo) is a Senior Researcher of the Korea Research Institute of Ships and Ocean Engineering. His research interests include turbomachinery, and heat and mass transfer analogy. He obtained a Master’s (2015) and Ph.D. (2019) in Mechanical Engineering from Seoul National University of Science and Technology.

Bum-Seog Choi is a Principal Researcher of Korea Institute of Machinery & Materials, Daejeon, Korea. He received his Ph.D. in Mechanical Engineering from the University of New South Wales. His research interests include ORC turbines, turbo-expanders and energy recovery systems.

S. Han is a Professor of Mechanical Engineering at Seoul National University of Science and Technology in Korea. He obtained a Ph.D. from the University of Minnesota, USA, in 2004. His research interests include heat and mass transfer, thermal process design, gas turbines, and organic Rankine cycle systems.

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Seo, J., Choi, BS. & Han, S. Design of a supersonic turbine for the organic Rankine cycle system. J Mech Sci Technol 35, 4179–4192 (2021). https://doi.org/10.1007/s12206-021-0830-7

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  • DOI: https://doi.org/10.1007/s12206-021-0830-7

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