Vol.:(0123456789) 1 3
Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:9
https://doi.org/10.1007/s40430-019-2084-1
TECHNICAL PAPER
Design and performance optimization of a very low head turbine
with high pitch angle based on two‑dimensional optimization
Mokhtar Mohammadi
1
· Alireza Riasi
1
· Ali Rezghi
1
Received: 18 June 2019 / Accepted: 15 November 2019
© The Brazilian Society of Mechanical Sciences and Engineering 2019
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 tur-
bulence model is implemented to solve three-dimensional (3D) continuity and RANS equations by considering homogene-
ous 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.
Keywords Turbine · Very low head · Airfoil · Optimization · CST
List of symbols
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 (m
3
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
Greek symbols
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
Technical Editor: Erick de Moraes Franklin.
* Alireza Riasi
ariasi@ut.ac.ir
1
Marine and Hydrokinetic Energy Laboratory, School
of Mechanical Engineering, College of Engineering,
University of Tehran, P. O. Box 11155/4563, Tehran, Iran