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Design and performance optimization of a very low head turbine with high pitch angle based on two-dimensional optimization

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Abstract

Very low head (VLH) axial hydro turbines are efficient turbomachinery to harness energy from tidal or river currents and increase renewable energy penetration in the world’s electric power generation. In this paper, the initial design of a VLH turbine with high pitch blade is optimized. The class function/shape function transformation method is applied along with a coupling of XFOIL with a MATLAB code to find optimum blade profiles with minimum drag-to-lift ratio. SST k–ω turbulence model is implemented to solve three-dimensional (3D) continuity and RANS equations by considering homogeneous multiphase model with standard free surface flow. The numerical results are validated against available experimental measurements, and the optimization results are discussed. The numerical results indicated that efficiency and power of the VLH turbine at the design point increased by 2.4% and 7.7 kW, respectively. Analyzing pressure distribution on suction and pressure sides of runner blades showed no occurrence of cavitation in operating condition of the turbine.

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Abbreviations

C :

Chord length (m)

C D :

Drag coefficient

C L :

Lift coefficient

C s :

Speed of sound

C θ :

Tangential component of absolute velocity (m s−1)

D :

Drag force (N)

D ω :

Cross-section diffusion term

g :

Acceleration due to gravity (ms−2)

G k :

Generation of k

G ω :

Generation of ω

H :

Head parameter (m)

k :

Turbulence kinetic energy

L :

Lift force (N)

Mach:

Mach number

n :

Rotational speed (rpm)

N b :

Number of blades

N s :

Specific speed

P :

Power (kW)

Δp :

Pressure drop (Pa)

Q :

Discharge (m3 s−1)

r :

Radius (m)

Re:

Reynolds number

S :

Solidity

T :

Torque (N m)

U :

Blade linear velocity (m s−1)

u i :

Velocity components (m s−1)

W :

Flow speed (m s−1)

X :

Horizontal coordinates of airfoil (m)

x i :

x-, y-, and z-directions

y :

Vertical coordinates of airfoil (m)

Y k :

Dissipation of k due to turbulence

Y ω :

Dissipation of ω due to turbulence

α :

Absolute speed angle (°)

β :

Relative speed angle (°)

μ t :

Turbulent viscosity

ξ :

y/c

η :

Efficiency (%)

ρ :

Density (kg m−3)

Ψ :

x/c

ω :

Rotational speed or specific turbulence dissipation

Γ k :

Effective diffusivity for k

Γ ω :

Effective diffusivity for ω

0:

Stagnation condition

1, (3):

Runner inlet (validation case)

2, (4):

Runner exit (validation case)

∞:

Average vector

l:

Lower surface

u:

Upper surface

H:

Hydraulic

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Authors and Affiliations

  1. Marine and Hydrokinetic Energy Laboratory, School of Mechanical Engineering, College of Engineering, University of Tehran, P. O. Box 11155/4563, Tehran, Iran

    Mokhtar Mohammadi, Alireza Riasi & Ali Rezghi

Authors
  1. Mokhtar Mohammadi
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  2. Alireza Riasi
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  3. Ali Rezghi
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Correspondence to Alireza Riasi.

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Mohammadi, M., Riasi, A. & Rezghi, A. Design and performance optimization of a very low head turbine with high pitch angle based on two-dimensional optimization. J Braz. Soc. Mech. Sci. Eng. 42, 9 (2020). https://doi.org/10.1007/s40430-019-2084-1

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