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Design Analysis of Francis Turbine

Runner

P M V Subbarao

Professor

Mechanical Engineering Department

Provision of Features to Reaction Muscle.

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Velocity triangles

rri

rre

UriVwi

VriV

fi

Vai

Ure

Vwe

VreVfe

Vae

bi

ai

beae

rU

UU

r

rire

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Inlet Velocity Triangles VsNs

Low Specific Speed : Slow Francis Runner

Vwi

VaiVfi

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Low Specific Speed : Normal Francis Runner

Vwi

Vai

Vfi

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High Specific Speed : Fast Francis Runner

Vwi

Vai

Vfi

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Specifications of Runner

Slow Runner:Ns=60 to 120

ai 150to 250 Kui= 0.62 to 0.68

bi 900to1200

B0/Dp=0.040.033

Normal Runner: Ns= 120180

ai 120

to 32.50

Kui= 0.68 to 0.72

bi 900

B0/Dp=0.125 to 0.25

Fast Runner: Ns= 180 to 300

ai 32.50to 37.50

Kui= 0.72 to 0.76

bi 600to900

B0/Dp=0.25to 0.5

min

hpin

s

H

PNN

4/5

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Selection of Exit Velocity Triangle

Exploitation of Reaction Character..

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Energy of Water Leaving a Francis Runner

RE

TEZreZte

VteVare

HTW

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Hydraulic Energy of Exiting Fluid

TE

teTERE

areRE gzVpQgzVpQ

22

22

For frictionless flow through exit tube

For frictional flow through exit tube

draftfTE

te

TERE

are

RE pQgz

V

pQgz

V

pQ ,

22

22

For maximum energy recovery

arete VV

tere pp

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draftfTEte

TEREare

RE pgzV

pgzV

p ,

22

22

draftfTEtetwatmREareRE pgzV

gHpgzV

p ,

22

22

draftfTEtwRE

teareREatm pzHzg

VVpp

,

22

2

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Components of Draft Tube

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Geometric Ratios for Draft Tube

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Rsiteat NPSHNPSH

NPSH required

g

Ub

g

VaNPSH refreR 22

22

15.005.0

15.105.1

b

aTurbines

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Dimensions of the outlet

g

UbUa

g

Ub

g

VaNPSH reerere

fre

R2

tan

22

2222

b

13o < be < 22

o

1,05 < a < 1,15

0,05 < b < 0,15

Highest value for highest head

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Internal Anatomy of Runner

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Blade Velocity Vs Tangential Component of Fluid Velocity

Ub

UbVw

Va

Vf

gzUUVVVhI bladebladerx 22222

1

Vr

In maridional plane at mean radius of rotor

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Runner Design

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Runner Design

The main procedure in design of a new runner includes;

Use of Classical theory for shaping the blade geometry

CFD analysis for the tuning of runner geometry

The classical method;

Design the meridional plan of runner based on availablemethods

Obtain the perpendicular view of runner using conformal

Mapping.

Modify using model testing or CFD.

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Runner Design

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Shape of Francis Channel : Meridional Plan

Rr1i

Rr2e

L/Dri

Rr2i

Rr1e

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Real values of Radii

The real value of the outlet tip radius3

1

2

2

e

er

QR

The real value of the intlet root radius31

2

1

1

2

iir

h

gHR

28.024.0 2 e 8.165.1 1

ihRr2eandRr1iare only fix two points of the leading and trailing

edges and the rest of these curves should be drawn to lead to

better efficiency of runner.

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Determination of Inlet & exit edges runner

1i

2i

1e

2e

The form of these edges is two

parabolic curves.

Define the non-dimensional

specific speed

Q

gH

NN NDs 75.0

260

2

For

275.0088.0 NDsN

the leading edge form is a parabolic arc

with the peak in the point by radius of

2.Rr1i-Rr2iwhich passes through the

points 1i and 2i,

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1i

2i

1e

2e

and for specific speeds between

its form is also a parabolic arc but with

the minimum point in the 1i

and the axis is parallel to runner axis.

89.0275.0 NDsN

In the exit area, trailing edge is a parabolic

curve which has a minimum point in 1e and

also passes through a point such as 2i with a

radius of Rr1i/3.

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