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Performance prediction, numerical and experimental investigation to characterize the flow field and thermal behavior of a cryogenic turboexpander

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Abstract

Radial inflow turbine and nozzle among the other components of the cryogenic turboexpander has a significant effect on the efficiency of the system. This study proposes an effective one-dimensional design approach of a radial turbine by introducing different loss correlations. The methodology also describes the effect of non-dimensional design variables on the performance of the turbine. These variables (blade speed ratio, pressure ratio, hub and shroud to turbine inlet radius ratio) undergo artificial intelligence-based model to predict their optimal range for better efficiency and power output of the turbine. Based on these optimal ranges, two turbine and nozzle models are generated. The results of the optimized configuration show that the turbine total-to-static efficiency and power output are higher by 4% and 18.9% respectively as compared to the existing literature. Thereafter, the three-dimensional computational fluid dynamics (CFD) analysis is carried out to visualize the fluid flow and thermal characteristics at different inlet temperatures in the flow passage using ANSYS CFX®. The study also focuses to identify the flow separation zone, tip leakage flow, vortex formation, secondary losses and its reasons at different spans of the turbine. An experimental platform is also established to validate the CFD results of a case study. The experimental results show that the mass flow rate and rotational speed has major effect on temperature drop and isentropic efficiency of the turboexpander. The study highlights the importance of the design methodology, the estimation capability of artificial intelligence models, the experimental techniques and benchmarking model for numerical analysis at different cryogenic temperature.

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Abbreviations

b :

Blade height \(\left (m\right )\)

b t :

Nozzle height (m)

C :

Absolute velocity \(\left (m/s\right )\)

C 0 :

Spouting velocity \(\left (m/s\right )\)

C h n :

Chord length \(\left (m\right )\)

C m t :

Meridional velocity at throat of the nozzle (m/s)

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

Tangential velocity at throat of the nozzle (m/s)

c :

Turbine blade chord \(\left (m\right )\)

D :

Turbine diameter \(\left (m\right )\)

D n :

Nozzle ring diameter \(\left (m\right )\)

D h :

Mean passage hydraulic diameter \(\left (m\right )\)

D t :

Nozzle throat circle diameter (m)

d :

Diameter \(\left (m\right )\)

d s :

Specific diameter

h :

Enthalpy \(\left (kJ/kg\right )\)

k :

Discharge coefficient

k x r :

Cross coupling coefficient

k p :

Constant

L :

Axial length \(\left (m\right )\)

L t :

Total loss

L h :

Mean passage hydraulic length \(\left (m\right )\)

M :

Mach number

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

Mass flow rate (kg/s)

n s :

Specific speed

P :

Power \(\left (kW\right )\)

P n :

Blade pitch length \(\left (m\right )\)

p :

Pressure \(\left (Pa\right )\)

Q :

Volume flow rate \(\left (m^{3}/s\right )\)

R :

Turbine radius \(\left (m\right )\)

R h :

Hub radius \(\left (m\right )\)

R s :

Shroud radius \(\left (m\right )\)

r :

Radius \(\left (m\right )\)

r p :

Pressure ratio

s :

Meridional streamlength \(\left (m\right )\),

t :

Blade thickness\(\left (m\right )\)

U :

Blade speed \(\left (m/s\right )\)

v s :

Blade speed ratio

W :

Relative velocity \(\left (m/s\right )\)

W t :

Throat width\(\left (m\right )\)

Z :

Number of blades

Z r :

Rotor axial length \(\left (m\right )\)

ANFIS :

Adaptive neuro-fuzzy inference system

ANN :

Artificial neural network

CFD :

Computational fluid dynamics

MAE :

Mean absolute error

MLP :

Multi-layer perceptron

ORC :

Organic Rankine cycle

PFHX :

Plate-fin heat exchanger

RMSE :

Root mean squared error

TF :

Transfer function

α :

Absolute velocity angle (degree),

α t :

Nozzle throat angle (degree),

β :

Absolute flow angle (degree),

β 2, opt :

Incidence angle (degree)

ε x :

Axial clearance (m)

ε r :

Radial clearance (m)

γ :

Specific heat ratio

η t−s :

Total-to-static efficiency

ρ :

Density \(\left (kg/m^{3}\right )\)

η i s :

Isentropic efficiency

ψ z :

Zweifel number

ψ :

Stage head coefficient

λ :

Turbine outlet to inlet radius ratio

λ s :

Stagger angle (degree)

χ :

Ratio of absolute meridional velocity

ϕ :

Flow coefficient

ζ :

Hub ratio

Θ :

Rotor meridional velocity coefficient

ω :

Rotational speed \(\left (rpm\right )\)

BL :

Blade loading loss

C l :

Clearance loss

h :

Hub

I :

Incidence loss

m :

Meridional

n :

Nozzle

o :

Total

r :

Radial

rel :

Relative

s :

Shroud, Isentropic

TEL :

Trailing edge loss

t :

Throat

tip :

Tip (turbine exit)

x :

Axial

0:

Stagnation state

1:

Nozzle inlet

2:

Turbine inlet

3:

Turbine outlet

𝜃 :

Tangential

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Authors and Affiliations

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

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

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  1. Manoj Kumar
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Kumar, M., Panda, D., Sahoo, R.K. et al. Performance prediction, numerical and experimental investigation to characterize the flow field and thermal behavior of a cryogenic turboexpander. Heat Mass Transfer 56, 1015–1036 (2020). https://doi.org/10.1007/s00231-019-02777-w

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