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Application of Smoothed Particle Hydrodynamics Method for the Analysis of the Flow Past Vertical Vortex Turbine of a Micro Hydropower

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KSCE Journal of Civil Engineering Aims and scope

Abstract

The Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) has been applied to simulate the flow through a Gravitational Vertical Turbine (GVT) configuration and the motion of the turbine of a small hydropower system. The turbine blades are assumed to be rigid bodies moving with one-degree of freedom, which is the rotation about its shaft due the hydrodynamic forces of the flow. The intake flow is an open channel flow which falls into a cylindrical basin which houses the turbine and impinges on the turbine blades. The method of simulation is the Weakly Compressible Smoothed Hydrodynamics (WCSPH) with the turbulence models in the equations of motion and the boundary conditions. The results are compared with a laboratory experiments conducted for the same dimension and the configuration. The flow features agree well and the motion of the turbine with a representative mass and a load agrees reasonably with the laboratory experiments

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Abbreviations

A :

Constant in log-law of turbulent wall flow

a :

Particle of which motion is calculated

B :

Constant in log-law of turbulent wall flow

b :

Particles near particle a

c :

Particle just outside wall layer of particle a when a is within wall layer

C D :

Resistance coefficient of turbine

C T :

Wall shear coefficient

D :

Rotational resistance of turbine

h :

Smoothing length

h b :

Thickness of the inflow and outflow bugger regions

h w :

Wall layer thickness

I :

Angular moment of inertia of turbine

j :

Unit vector in y direction

m :

Mass of a particle

n :

Unit vector normal to solid boundary

P :

Power

p :

Pressure

Q :

Transformation matrix for rotation about y axis

r :

Position vector of a particle

T :

Torque about axis of turbine rotation

t :

Time

t :

Unit vector tangent to solid boundary

u τ :

Friction velocity associated with wall shear

v :

Velocity vector

w :

Particles representing solid boundary closest to particle a

y :

Vertical coordinate

ρ :

Density

θ :

Angular position

θ′:

Principal value of θ in (0, 2π)

ω :

Rotational velocity

∇a :

Gradient operator with respect to coordinated of position of particle a

a :

Quantity associated with particle a

b :

Quantity associated with particle b

n :

Component of vector normal to boundary

t :

Component of vector tangent to boundary

w :

Quantity associated with boundary particle w

0 :

Quantity at initial time t = 0

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Acknowledgments

The present work was partly supported by Malaysian Ministry of Higher Education Fundamental Research Grant System FRGS/1/2019/TK01/UTAR/01/1 and Universiti Tunku Abdul Rahman Research Fund (UTARRF/2022-C1/A03).

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Authors and Affiliations

  1. Division of Advanced Science and Engineering, Hiroshima University, Higashihiroshima, 739-0046, Hiroshima, Japan

    Shu Kai Ng

  2. Dept. of Environmental Engineering, Universiti Tunku Abdul Rahman, Kampar, Perak, 31900, Malaysia

    Akihiko Nakayama & Wei Xuan Ng

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  1. Shu Kai Ng
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  2. Akihiko Nakayama
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Correspondence to Akihiko Nakayama.

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Ng, S.K., Nakayama, A. & Ng, W.X. Application of Smoothed Particle Hydrodynamics Method for the Analysis of the Flow Past Vertical Vortex Turbine of a Micro Hydropower. KSCE J Civ Eng 28, 1132–1139 (2024). https://doi.org/10.1007/s12205-024-1732-x

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  • DOI: https://doi.org/10.1007/s12205-024-1732-x

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