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Improvement of flow behavior in the spiral casing of Francis hydro turbine model by shape optimization

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Abstract

A spiral casing is an important component of Francis hydro turbine for the even distribution of kinetic energy along the stay and guide vanes. The fluid flow around the runner is dependent on the flow condition of a spiral casing. The shape of the casing plays an important role in proper flow distribution. In this study, the optimization of the shape of a spiral casing is based on a steady-state flow analysis. Numerical optimization is performed using response surface methodology (RSM) and multiobjective genetic algorithm (MOGA). The flow uniformity and head loss in the spiral casing are selected as objectives for the optimal design of the spiral casing. The optimal design is selected from the solution acquired by RSM and MOGA. Moreover, the flow characteristics in the initial and optimal designs of the spiral casing are compared. The flow conditions in the optimal design improve significantly with the optimal design of the spiral casing. Thus, the inlet conditions for the stay vane are improved with the optimal design of the spiral casing.

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Abbreviations

A :

Cross-sectional area

B :

Height of guide vane

B y :

Height of casing cross section

C :

Circulation

d :

Inlet diameter of spiral casing

\(\overline d \) :

Design variable

g :

Acceleration due to gravity

H :

Total head

H loss :

Head loss

J nABS :

Secondary vortex intensity

k :

Flow constant

l :

Length of casing inlet

N :

Rotational speed

n :

Normal direction

p :

Pressure

p 0 :

Inlet static pressure of spiral casing

p T0 :

Inlet total pressure of spiral casing

Q :

Flow rate

q i :

Discharge through ith cross section

R :

Radius from the central axis

R e :

Radius of circle formed by the trailing edge of SV

R 0 :

Outlet radius of casing

R t :

Radius at the center of the spiral cross section

Re :

Reynolds number

r :

Casing cross-sectional radius

r i :

Radius of spiral casing ith cross section

r 0 :

Casing cross-sectional radius at inlet

u, v, w :

Velocity in the x-, y-, and z-directions

ū :

Average velocity

V 0 :

Inlet velocity at casing

v r :

Radial velocity

v θ :

Tangential velocity

y :

Vertical distance

y i :

Value of output parameter at the ith sample

ŷ i :

Value of response surface model at the ith sample

ȳ :

Arithmetic mean of value yi

Y :

Flow uniformity index

θ u :

Flow angle

v :

Kinematic viscosity of water

ρ :

Density of water

ϕ c :

Central angle

ϕ i :

Central angle for the ith cross section

ω n :

Vorticity in n-direction

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Acknowledgments

This research (work) was supported by the long-term oversea training program of Mokpo National University in 2019.

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Authors and Affiliations

  1. Graduate School of Mechanical Engineering, Mokpo National University, Muan, 58554, Korea

    Ujjwal Shrestha

  2. Department of Mechanical Engineering, Institute of New and Renewable Energy Technology Research, Mokpo National University, Muan, 58554, Korea

    Young-Do Choi

Authors
  1. Ujjwal Shrestha
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Correspondence to Young-Do Choi.

Additional information

Ujjwal Shrestha received his B.E. Tech. degree from Kathmandu University, Nepal and his M.S. degree from Mokpo National University, Korea. He is currently a doctorate candidate in the Graduate School, Department of Mechanical Engineering, Mokpo National University. His research interest includes fluid machinery and new and renewable energy.

Young-Do Choi received his B.S. and M.S. degrees from Korea Maritime University and his Ph.D. in Mechanical Engineering from Yokohama National University, Japan. Since 2009, he has been a Professor at the Department of Mechanical Engineering of Mokpo National University, Korea. His research interests include fluid machinery and new and renewable energies, such as hydro power, ocean energy, and wind power.

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Shrestha, U., Choi, YD. Improvement of flow behavior in the spiral casing of Francis hydro turbine model by shape optimization. J Mech Sci Technol 34, 3647–3656 (2020). https://doi.org/10.1007/s12206-020-0817-9

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  • DOI: https://doi.org/10.1007/s12206-020-0817-9

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