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

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Abstract

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.

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Abbreviations

b :

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

\(b_\mathrm{t}\) :

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

C :

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

\(C_{0}\) :

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

\(\mathrm{Ch}_\mathrm{n}\) :

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

\(C_\mathrm{mt}\) :

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

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

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

\(c_\mathrm{p}\) :

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

D :

Turbine diameter ratio

\(D_{\mathrm{h}}\) :

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

\(D_{\mathrm{n}}\) :

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

\(D_{\mathrm{t}}\) :

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

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

First-order variance

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

Second-order variance

\(d_{\mathrm{s}}\) :

Specific diameter

h :

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

\(k_{0}\) :

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

\(L_{\mathrm{t}}\) :

Total loss

\(\overset{.}{m}\) :

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

\(n_{\mathrm{s}}\) :

Specific speed

P :

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

p :

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

\(R_{2}\) :

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

\(R_{\mathrm{h}}\) :

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

\(R_{\mathrm{s}}\) :

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

\(r_{\mathrm{p}}\) :

Pressure ratio

\(S_{\mathrm{i}}\) :

First-order sensitivity index

U :

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

u :

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

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

Total variance of the output

\(v_{\mathrm{s}}\) :

Velocity ratio

W :

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

\(W_{\mathrm{t}}\) :

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

X :

Parameters

\(x_{\mathrm{i}}\) :

Number of inputs

Y :

Target function

Z :

Number of blades

\(Z_{\mathrm{r}}\) :

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

\(\alpha \) :

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

1:

Nozzle inlet

2:

Turbine inlet

3:

Rotor outlet

\(\mathrm{h}\) :

Hub

\(\mathrm{m}\) :

Meridional

\(\mathrm{n}\) :

Nozzle

\(\mathrm{r}\) :

Radial

\(\mathrm{s}\) :

Shroud

\(\mathrm{t}\) :

Throat

\(\mathrm{z}\) :

Axial

\(\theta \) :

Tangential

ANFIS:

Adaptive neuro-fuzzy inference system

ANN:

Artificial neural network

GA:

Genetic algorithms

HEX:

Heat exchanger

MAE:

Mean absolute error

MF:

Membership function

MLP:

Multilayer perceptron

ORC:

Organic Rankine cycle

PS:

Pressure surface

RMSE:

Root-mean-squared error

SS:

Suction surface

SST:

Shear stress transport

TF:

Transfer function

TKE:

Turbulence kinetic energy

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Acknowledgements

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.

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Authors and Affiliations

  1. National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

    Manoj Kumar, Debashis Panda, Ranjit K. Sahoo & Suraj K. Behera

  2. Indian Institute of Technology Varanasi, Varanasi, U.P, 221005, India

    Amitesh Kumar

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  1. Manoj Kumar
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Correspondence to Manoj Kumar.

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Kumar, M., Panda, D., Kumar, A. et al. A methodology for the performance prediction: flow field and thermal analysis of a helium turboexpander. J Braz. Soc. Mech. Sci. Eng. 41, 484 (2019). https://doi.org/10.1007/s40430-019-1989-z

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