Numerical Investigation of the “Tandem Cascade” Effects for the Flow Through Stay and Guide Vanes of a Francis Turbine

Technical Note
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Abstract

In the open literature and recent publications, many explorations were done on the flow in axial two-dimensional tandem cascades whereby examining each cascade parameter separately it has been shown that the performance strongly depends on the interference effects of the front and aft blade profiles. Governed by the fact that very limited research is done and published on the influence and the effects of separate parameters in a radial tandem cascade for water turbines, this paper presents an initial research in that area. In order to achieve high efficiency for water turbines, the working medium has to be pre-conditioned for entering the runner of the turbine. Despite the role of the spiral casing of the turbine, the stay and guide vanes also play a huge role in these requirements. The flow in the zone of the stay and guide vanes of an existing Francis turbine has been numerically analyzed, emphasizing the effects of the relative angular position between the stay and guide vanes forming a tandem cascade. By varying the relative angular position as a parameter, the total loss, acting forces and the flow distribution of the configurations have been examined. The specialized grid generation software GAMBIT and the solver FLUENT by ANSYS, employing the finite volume method, are used to solve the governing equations for turbulent flows, and conclusions and insights are being made on the basis of the obtained results.

Keywords

Tandem cascades Francis turbine Stay and guide vanes Numerical simulation 

List of symbols

Sm

Mass source or sink

\(\vec{g}\)

Acceleration of gravity

\(\vec{v}\)

Velocity vector

t

Time, angular spacing between guide vanes

p

Static pressure

\(\vec{F}\)

External body force

s

Angle between the leading edges of the profiles in the cascade

Cμ

Turbulence model constant

A0

Normalized guide vanes opening

a0

Absolute guide vanes opening

Q

Discharge

N

Frequency of rotation

I

Unit tensor

D

Runner diameter

E

Delivered energy

zvl

Amount of guide vanes

H

Head

cr

Radial velocity component

cu

Tangential velocity component

Qφ

Volumetric flow in spiral casing sections

K

Free-vortex constant

b

Tandem cascade channel width

r

Radius

Jφ

Characteristic integral

\(\bar{c}\)

Mean velocity

ci

Absolute velocity

A

Control surface

x

Discrete control grid spacing

y

Discrete control grid spacing

Z

Flow distribution criteria

Greek symbols

ρ

Density

k

Kinetic energy of the turbulence

φ

Discharge coefficient

ϵ

Dissipation rate of the kinetic energy of turbulence

μ

Molecular viscosity

μt

Turbulent viscosity

\(\bar{\bar{\tau }}\)

Stress tensor

ψ

Head coefficient

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Copyright information

© Shiraz University 2016

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering“Ss. Cyril and Methodius” University in SkopjeSkopjeRepublic of Macedonia

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