A methodology for the performance prediction: flow field and thermal analysis of a helium turboexpander

  • Manoj KumarEmail author
  • Debashis Panda
  • Amitesh Kumar
  • Ranjit K. Sahoo
  • Suraj K. Behera
Technical Paper


Helium liquefaction systems are widely used in nuclear fission, superconductivity, space industries, and other scientific instruments. However, the efficiency of these systems is quite low due to the cryogenic operating temperature. In this regard, the one-dimensional design methodology of the helium turbine and nozzle (hereafter, renowned as turboexpander) is important to increase the efficiency of the system. This paper demonstrates the sensitivity analysis and optimal range of non-dimensional design variables on which the radial inflow turbine has maximum efficiency, minimum losses, and maximum power output using artificial intelligence techniques. On this basis, three turboexpander models are developed within the optimal range of predicted non-dimensional variables. After that, a comparative numerical study is carried out to highlight the flow field and thermal characteristics of helium fluid. The standard two equations \(k{-}\omega \) SST model is used to solve the three-dimensional incompressible flow inside the computational domain. The numerical results are validated with the available experimental data from the existing literature. The variation of Mach number, Reynolds number, Prandtl number, static entropy, static enthalpy, temperature, and pressure inside the turboexpander is significantly affected by blade profile which is enormously affected by the design methodology. The study also demonstrates the flow separation region, vortex formation, tip leakage flow, secondary losses, and its reasons along with the spanwise location. The results highlight the importance of the design methodology, sensitivity analysis, the prediction capability of the artificial intelligence network, numerical methodology, and development of the helium turboexpander prototype models.


Helium turboexpander Sobol sensitivity analysis Flow pattern Thermal characteristics Artificial intelligence 

List of symbols


Blade height \(\left( \mathrm{m}\right) \)


Nozzle height \((\mathrm{m})\)


Absolute velocity \(\left( \mathrm{m}/\mathrm{s}\right) \)


Spouting velocity \(\left( \mathrm{m}/\mathrm{s}\right) \)


Chord length \(\left( \mathrm{m}\right) \)


Nozzle throat velocity (Meridional component) \((\mathrm{m})\)

\(C_{_{\theta t}}\)

Nozzle throat velocity (Tangential component) \((\mathrm{m})\)


Specific heat capacity \(\left( \mathrm{J}/\mathrm{kg\,K}\right) \)


Turbine diameter ratio


Hydraulic diameter \(\left( \mathrm{m}\right) \)


Diameter of nozzle ring \(\left( \mathrm{m}\right) \)


Nozzle throat circle diameter \((\mathrm{m})\)

\(D_{i}\left( Y\right) \)

First-order variance

\(D_{ij}\left( Y\right) \)

Second-order variance


Specific diameter


Enthalpy \(\left( \mathrm{kJ}/\mathrm{kg}\right) \)


Thermal conductivity of fluid \(\left( \mathrm{W}/\mathrm{mK}\right) \)


Total loss


Mass flow rate \((\mathrm{kg}/\mathrm{s})\)


Specific speed


Power \(\left( \mathrm{kW}\right) \)


Pressure \(\left( \mathrm{Pa}\right) \)


Turbine inlet radius \(\left( \mathrm{m}\right) \)


Hub radius \(\left( \mathrm{m}\right) \)


Shroud radius \(\left( \mathrm{m}\right) \)


Pressure ratio


First-order sensitivity index


Mean flow velocity \(\left( \mathrm{m}/\mathrm{s}\right) \)


Blade speed \(\left( \mathrm{m}/\mathrm{s}\right) \)

\(\mathrm{Var}\left( Y\right) \)

Total variance of the output


Velocity ratio


Relative velocity \(\left( \mathrm{m}/\mathrm{s}\right) \)


Throat width \(\left( \mathrm{m}\right) \)




Number of inputs


Target function


Number of blades


Rotor axial length \(\left( \mathrm{m}\right) \)

Greek symbols

\(\alpha \)

Absolute flow angle \((\circ )\)

\(\beta \)

Relative flow angle \((\circ )\)

\(\zeta _{\mathrm{b}}\)

Back friction

\(\zeta _{\mathrm{l}}\)

Leakage loss

\(\varepsilon _{\mathrm{x}}\)

Axial clearance \((\mathrm{m})\)

\(\varepsilon _{\mathrm{r}}\)

Radial clearance \((\mathrm{m})\)

\(\lambda \)

Ratio of rotor outlet to inlet

\(\mu \)

Coefficient of viscosity \(\left( \mathrm{Pa}\,\mathrm{s}\right) \)

\(\Omega \)

Degree of reaction

\(\rho \)

Density \(\mathrm{kg}/\mathrm{m}^{3}\)

\(\psi _{\mathrm{z}}\)

Zweifel number

\(\phi \)

Flow coefficient

\(\psi \)

Stage loading coefficient

\(\chi \)

Absolute meridional velocity

\(\eta _{\mathrm{is}}\)

Isentropic efficiency

\(\omega \)

Rotational speed \(\left( \mathrm{rpm}\right) \)



Nozzle inlet


Turbine inlet


Rotor outlet















\(\theta \)




Adaptive neuro-fuzzy inference system


Artificial neural network


Genetic algorithms


Heat exchanger


Mean absolute error


Membership function


Multilayer perceptron


Organic Rankine cycle


Pressure surface


Root-mean-squared error


Suction surface


Shear stress transport


Transfer function


Turbulence kinetic energy



The authors sincerely thank to the Board of Research in Nuclear Sciences (BRNS) (Grant No. 39/23/2015-BRNS/39001), Ministry of Human Resource Development (MHRD), Government of India, and National Institute of Technology, Rourkela for providing the financial support.

Compliance with ethical standards

Conflict of interest

The authors declared that there is no conflict of interest to any person or organization.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.National Institute of Technology RourkelaRourkelaIndia
  2. 2.Indian Institute of Technology VaranasiVaranasiIndia

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