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

  • Mokhtar Mohammadi
  • Alireza RiasiEmail author
  • Ali Rezghi
Technical Paper


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 kω 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.


Turbine Very low head Airfoil Optimization CST 

List of symbols


Chord length (m)


Drag coefficient


Lift coefficient


Speed of sound


Tangential component of absolute velocity (m s−1)


Drag force (N)


Cross-section diffusion term


Acceleration due to gravity (ms−2)


Generation of k


Generation of ω


Head parameter (m)


Turbulence kinetic energy


Lift force (N)


Mach number


Rotational speed (rpm)


Number of blades


Specific speed


Power (kW)


Pressure drop (Pa)


Discharge (m3 s−1)


Radius (m)


Reynolds number




Torque (N m)


Blade linear velocity (m s−1)


Velocity components (m s−1)


Flow speed (m s−1)


Horizontal coordinates of airfoil (m)


x-, y-, and z-directions


Vertical coordinates of airfoil (m)


Dissipation of k due to turbulence


Dissipation of ω due to turbulence

Greek symbols


Absolute speed angle (°)


Relative speed angle (°)


Turbulent viscosity




Efficiency (%)


Density (kg m−3)




Rotational speed or specific turbulence dissipation


Effective diffusivity for k


Effective diffusivity for ω



Stagnation condition

1, (3)

Runner inlet (validation case)

2, (4)

Runner exit (validation case)

Average vector


Lower surface


Upper surface




Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Marine and Hydrokinetic Energy Laboratory, School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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