Design Analysis of Francis Turbine Runner

P M V SubbaraoProfessor

Mechanical Engineering Department

Provision of Features to Reaction Muscle.…

Velocity trianglesrri

rre

Uri

Vwi

Vri

Vfi

Vai

Ure

Vwe

Vre

Vfe

Vae

i

i

ee

rU

UU

r

rire

Inlet Velocity Triangles Vs Ns

Low Specific Speed : Slow Francis Runner

Vwi

Vai

Vfi

Inlet Velocity Triangles Vs Ns

Low Specific Speed : Normal Francis Runner

Vwi

Vai

Vfi

Inlet Velocity Triangles Vs Ns

High Specific Speed : Fast Francis Runner

Vwi

Vai

Vfi

Specifications of Runner

• Slow Runner: Ns=60 to 120 to 250

– Kui = 0.62 to 0.68 to

– B0/Dp=0.04 – 0.033• Normal Runner: Ns = 120 – 180

to 32.50

– Kui = 0.68 to 0.72 – B0/Dp=0.125 to 0.25

• Fast Runner: Ns = 180 to 300 to 37.50

– Kui = 0.72 to 0.76 to

– B0/Dp=0.25to 0.5

min

hpin

s

H

PNN

4/5

Selection of Exit Velocity Triangle

Exploitation of Reaction Character…..

Energy of Water Leaving a Francis Runner

RE

TEZreZte

Vte

Vare

HTW

Hydraulic Energy of Exiting Fluid

TEte

TEREare

RE gzV

pQgzV

pQ 22

22

For frictionless flow through exit tube

For frictional flow through exit tube

draftfTEte

TEREare

RE pQgzV

pQgzV

pQ ,

22

22

For maximum energy recovery

arete VV

tere pp

draftfTEte

TEREare

RE pgzV

pgzV

p ,

22

22

draftfTEte

twatmREare

RE pgzV

gHpgzV

p ,

22

22

draftfTEtwREteare

REatm pzHzgVV

pp ,

22

2

Components of Draft Tube

Geometric Ratios for Draft Tube

Rsiteat NPSHNPSH

NPSH required

g

Ub

g

VaNPSH refre

R

22

22

15.005.0

15.105.1

b

a

Turbines

Dimensions of the outlet

g

UbUa

g

Ub

g

VaNPSH reererefre

R 2

tan

22

2222

13o < e < 22o

1,05 < a < 1,150,05 < b < 0,15

Highest value for highest head

Internal Anatomy of Runner

Blade Velocity Vs Tangential Component of Fluid Velocity

Ub

UbVw

Va

Vf

gzUUVVVhI bladebladerx 2222

2

1

Vr

In maridional plane at mean radius of rotor

Runner Design

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 available methods

• Obtain the perpendicular view of runner using conformal Mapping.

• Modify using model testing or CFD.

Runner Design

Shape of Francis Channel : Meridional Plan

Rr1i

Rr2e

L/Dri

Rr2i

Rr1e

Real values of Radii

The real value of the outlet tip radius3

1

22

eer

QR

The real value of the intlet root radius3

1

21

1

2

iir h

gHR

28.024.0 2 e 8.165.1 1 ih

Rr2e and Rr1i are 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.

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 75.0260

2

For 275.0088.0 NDsN

the leading edge form is a parabolic arcwith the peak in the point by radius of 2.Rr1i-Rr2iwhich passes through the points 1i and 2i,

1i

2i

1e

2e

and for specific speeds between

its form is also a parabolic arc but with the minimum point in the 1iand 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.