Design of Kaplan Turbine

P M V SubbaraoProfessor

Mechanical Engineering Department

Pure Axial Flow with Aerofoil Theory….

Selection of Kaplan Turbine

MORE ADAPTED TYPE OF TURBINA IN FUNCTION OF THE  SPECIFIC SPEED.

Specific Speed in r.p.m.

Turbine type Jump height in m

From 270 to 500 Slow Kaplan 50 to 15

From 500 to 800 Quick Kaplan 15 to 5

From 800 to 1100 Extra-quick Kaplan Less than 5

45

H

PNN s P in hp and H in meters.

Design of A Kaplan Turbine

Specific Speed of Kaplan Turbine

• Using statistical studies of schemes, F. Schweiger and J. Gregory established the following correlation between the specific speed and the net head for Kaplan turbines:

486.0

827.39

HN s

45

H

PNN s

P in watts.

The Schematic of Kaplan Turbine

Major Parts of A Kaplan Turbine

45

H

PNN s

P, in hp and H in meters.

Design of Guide WheelDegv

N

gHkD ug

egv 260

gHkV fgfgv 2

fgvgvegv VBDQ

Kug

KfgKug

Kfg

Flow & Geometric Details of Guid Wheel Exit

Outlines of Kaplan Runner

Whirl ChamberGuide Vanes

a

b

The space between guide wheel outlet and kaplan runner is known as Whirl Chamber.

a=0.13 Drunner & b=0.16 to 0.2 Drunner.

Design of Kaplan Runner

Drunner

Dhub

Testing of Runner diameter selection

The runner diameter De can be calculated by the following equation:

n

HnD QErunner

60

602.179.05.84

43

294.2

HnQE n in rps

runnerQE

hub Dn

D

0951.025.0

Runner diameter section

22hubrunnerfactor DDHQQ

• The hub diameter Dhub can be calculated with the following equation:

runnerhub DD 0.6 to35.0

Qfactor

Kug

Number of runner Vanes Vs Guide Wheel Diameter

Z 8 10 12 14 16 18 20 24

Dge,mm

<300 300 – 450

450 – 750

750 – 1200

1200 – 1600

1600

-

2200

2200 4000

>4000

DESIGN OF THE BLADE

Two different views of a blade

Hydrodynamics of Kaplan Blade

Distortion of the blade under ideal circumstances

• The velocity triangles, which occur on the blade, play a significant role in determining its distortion.

Uwheel

V ri

Vai

Vfi

1 < 900

Uwheel

V ri

Vai

Vfi

Uwheel

V re

Vae

Vfe

Details of Blade Arrangement

e = 900

Hydraulic Energy Diagram

Hs

Htotal

HriHre

Hm

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

– Bgv/Dmgv=0.04 – 0.033• Normal Runner: Ns = 120 – 180

to 32.50

– Kui = 0.68 to 0.72 – Bgv/Dmgv=0.125 to 0.25

• Fast Runner: Ns = 180 to 300 to 37.50

– Kui = 0.72 to 0.76 to

– Bgv/Dmgv=0.25to 0.5

Design for Maximum Power Retrieval

Uwheel

V ri

Vai

Vfi

Inlet Velocity Triangle

Specifications of the Runner

Velocity Triangles at Mean Runner Diameter

Radial Equilibrium

0

1 0 dr

rVd

r

V

dr

dVV

dr

dp wwff

Radial Equilibrium Equation for Incompressible Fluid Machine

To define the distortion of the blade, the velocity triangles of at least six different radiuses of the blade are to be determined. The angle β of each radius gives conclusions on the distortion of the blade.The angles should be corrected for real hydraulics.

•Free Vortex Whirl:

•Forced Vortex Whirl :

General Rules for Selection of Whirl Component

r

CV

constantfV

rCV

221C rCV f

0

fV

r

rV

Inlet Blade Distortion

Inlet Blade Distortion

Method for Real Kaplan

Vfi=Vfe

VriVre V∞

2rwerwi VV

Define Half Travel Point of a fluid particle as

The “Tragflügeltheorie”V∞

Fideal liftFactual lift

Vri

Characteristics of A Single Blade

• Ideal Blade lift coefficient:

2

22

min22

22

KV

gVV

hHhgVV deaedraftsatmre

blade

draft: Efficiency of draft tube: 0.88 to 0.91K : Profile characteristic number: 2.6 to 3.0hmin=Head equivalent to minimum allowable pressure atRunner exit.

The suction head

• The suction head Hs is the head where the turbine is installed; • if the suction head is positive, the turbine is located above the trail

water; • if it is negative, the turbine is located under the trail water. • To avoid cavitation, the range of the suction head is limited. • The maximum allowed suction head can be calculated using the

following equation:

netdevapatm

s Hg

V

g

ppH

2

2

net

deQE gH

Vn

25241.1

246.1

43

294.2

HnQE

sin

cos12

bladeblade

flowturbine

U

V

V

Hg

t

l

When the lifting coefficient is known, the sufficiency of ratio l/t can be established as follows:

2.5°-- 3°Allowable values of angle of slip

The actual Lifting Coefficient

cascadeb

blade

,

lt

Drag Coefficient

cascadeb,

drag

Actual Angle of Attack

ab,

Calculation of Actual Angle of Slip

ab

dragblade

,arctan

Uwheel

V ri

Vai

Vfi

Uwheel

V re

Vae

Vfe

Speed Specific toalProportion

24 to8 :blades ofNumber :

1.05 9.0)allowed maximum(

ZZ

Dt

tot

l

runner

Details of Blade Arrangement

e = 900

Power Developed by the Runner

wewiblade VVUmddP

Power developed by a differential blade surface

bladeA

wewibladebladetotal VVUmdnP