Design Analysis of Parts of Pelton Wheel Turbine

P M V SubbaraoProfessor

Mechanical Engineering Department

Selection of right parts and right geometry to execute Pure Impulse…..

HEPP with Pelton Wheel

Parts of Pelton Turbine

• The main components of a Pelton turbine are:• (i) water distributor and casing, • (ii) nozzle and deflector with their operating mechanism, • (iii) runner with buckets, • (iv) shaft with bearing, • (v) auxiliary nozzle. • Auxiliary nozzle is used as brake for reducing the speed

during shut down. • The runner is located above maximum tail water to permit

operation at atmospheric pressure.

Key Parts of Pelton Turbine

Runner with Buckets• The runner consists of a circular disc with a number (usually more

than 15) of buckets evenly spaced around its periphery.

• Each bucket is divided vertically into two parts by a splitter that has a sharp edge at the centre and the buckets look like a double hemispherical cup.

• The striking jet of water is divided into two parts by the splitter.

• A notch made near the edge of the outer rim of each bucket is carefully sharpened to ensure a loss-free entry of the jet into the buckets,

• i.e., the path of the jet is not obstructed by the incoming buckets.

Bucket Displacement Diagram

Design of Nozzle is of Prime importance in Pelton Wheel

Nozzle used in 62.5 MW Pelton Wheel

Mechanism of Control of Jet dimensions

The Nozzle and Jet : A Key Step in Design

d0djet,VC

Velocity of the jet at VC:

gHV idealVCjet 2:,

gHKV vactualVCjet 21:, 99.098.0 1 vK

Jet carrying a discharge of Q to deliver a power P

gHKdQ vVCjet 24 1

2,

To generate a discharge of Q, we need a least jet diameter of

gHK

Qd

v

VCjet2

4

1

,

QgHP turbine

Diameter of the Jet at the outlet, do

gHKdQ voo 24

2

83.081.0 vOK

It is important to find out the VC and outlet jet diameters/areas

CFD Analysis of Free Jets & Flows In Air

P M V SubbaraoProfessor

Mechanical Engineering Department

A Consultancy Project Sponsored ByBHEL, Bhopal

The set of governing equations solved were primarily the continuity and the momentum equations.

These basic equations in Cartesian coordinate system for incompressible flows are given below,

( ) 0ii

ux

( )ij

i jj i j

Pu u

x x x

, ,

2

3ji

ij k k i jj i

uuu

x x

Turbulent Viscosity

Computational Grid : Nozzle

Contours of Volume Fractions : Nozzle Air Domain : 0.15m

Contours of Static Pressure : Nozzle Air Domain : 0.15m

Contours of Velocity Magnitude : Nozzle Air Domain : 0.15m

Contours of Volume Fractions : Air Domain : 0.3m

Contours of Volume Fractions : Air Domain : 1.0 m

Industrial Correlations for Jet Area

Optimal value of Outlet jet area, ao

2BsAsao

s is the displacement of spear

sin

sin2 orA

2

2

sin

sinsinsinB

Pelton Wheel Distributor - CFD Analysis • The distributor to the Pelton wheel for the given geometry has

been simulated using Fluent in a 3-d viscous incompressible flow simulation.

• The set of governing equations solved were primarily the continuity and the momentum equations.

• The given geometry was meshed using the unstructured tetrahedral meshes due to geometrical complexity.

• An optimized tetrahedral mesh size of 25 was employed resulting in a a total of 62583 tetrahedral elements.

CAD Model of Distributor

Pelton Wheel Flow Distributor

Static Pressure Distribution

Distribution of Velocity Magnitude

Mean Diameter of Pelton Runner

Mean diameter or Pitch circle diameter:Dwheel

Circumferential velocity of the wheel, Uwheel

gHUwheel 2

gHKUwheeluwheel 2

602 wheelwheel

uwheel

NDgHKU

wheel

wheel

uwheel N

gHKD wheel

260

4 5gH

PN

Nwheel

s

gHKdQ vVCjet 2

4 12

,

turbinevVCjetturbine gHKdgHQgHP 24 1

2,

4 5

12

, 24260

gH

gHKdgH

D

gHK

N

vVCjetturbine

wheel

u

s

wheel

12

,42

260vVCjetturbine

wheel

us Kd

D

KN wheel

wheel

VCjetvturbine

us D

dK

KN wheel ,

14 52

60

Experimental values of Wheel diameter to jet diameter

Dwheel /djet,VC 6.5 7.5 10 20

Ns (rpm) 35 32 24 10

turbine 0.82 0.86 0.89 0.90

45

H

PNN s P in hp, H in meters and N in rpm

For maximum efficiency, the ratio should be from 11 to 14.

The highest ratio used in the world is 110 (Kt. Glauraus Power House in Switzerland).

Specifications of this Pelton wheel are:

Power 3000HP (2.24MW) Speed: 500 rpmDwheel= 5.36m djet,VC=48.77mmHead =1,650 m

6.2

1650

30005004 54 5

gH

PN

Nwheel

s

Path Lines of Jet

D wheel

D pelton

dOVj,O

Number of buckets

• The number of buckets for a given runner must be determined so that no water particle is lost.

• Minimize the risks of detrimental interactions between the out flowing water particles and the adjacent buckets.

• The runner pitch is determined by the paths of; • the bucket tip (diameter Dpelton), the Wheel diameter (DWheel).• and the relative paths of the water particles stemming from the

upper and lower generators of the jet.• The bucket pitch must be selected so that no particle stemming

from the lower generator of the jet can escape the runner without encountering any bucket.

Bucket Duty Cycle

Reference Position

Zones of Bucket Duty Cycle

• i) Approach of the tip to the jet (θj < −40◦).

• ii) Initial feeding process : (θj = −40◦...−10◦).

• iii) Entire separation of the jet (θj = −10◦...0◦)

• iv) Last stage of inflow (θj = 0◦...15◦)

• v) Last stage of outflow (θj = 15◦...50◦).

• vi) Series of droplets (θj = −50◦...∞).

Start of Jet Bucket Interactions

Sequence of Jet Bucket Interactions

Minimum Number of Buckets

1B 1C

Rwheel

Rpelton

Dj,O, Vj,O

1A

1D

The axis of the jet falls on Pitch Circle

Minimum Number of Buckets

1B 1C1E

RwheelR

Pelton

dj,O, Vj,O

Minimum Number of Buckets

RW

heelRPelton

dO, Vj,O

lj

tj : Time taken bye the jet to travel lj

tb: Time taken by first bucket to travel

RWRP

dO, Vj,O

lj

sinpeltonj Dl

wheel

wheel

R

U

• tj = lj/Vjet,O

• tb =

For better working tj < tb

Oj

j

V

l

,

wheel

wheel

Oj

pelton

U

R

V

D

,

sin

Ojwheel

peltonwheel

VR

DU

,

sin

The minimum allowable value of

sin12sin ,

,

wheelvO

wheelu

wheel

pelton

Oj

wheel

Rk

k

R

D

V

U

RWRP

dO, Vj,O

lj

pelton

Ojetwheel

R

dR

2cos

,

wheel

Ojetwheel

R

dR

2cos

,

wheel

wheel

Ojet

D

D

d

2

1

1

cos

,

wheel

VCjetvturbine

us D

dK

KN wheel ,

14

260

wheel

wheel

Ojet

D

D

d

2

1

1

cos

,

Maximum allowable angle between two successive buckets

2

Minimum number of buckets 360

z

Dr Taygun has suggested an empirical relation for z

155.0,

VCjet

wheel

d

Dz

Bucket Power Distribution

P(j)

1

2

34

5

Total

Bucket Energy Distribution

Ej,k

gHm

E

bucketthebyenergyWater

EnergyBucket

water

kk

h

dinterscpet

Geometric Details of Bucket

The hydraulic efficiency depends more on the main bucket dimensions (length (A), width (B) and depth (C)).The shape of the outer part of its rim or on the lateral surface curvature also has marginal effect on hydraulic efficiency.

Shape variations of Buckets

Design 1Design 2

Empirical Geometry of Bucket Shape

A

B

C

2i

e

S

I

IVII

III

V

DW

Empirical Relations for Bucket Geometry

• A = 2.8 djet,VC to 3.2 djet,VC

• B = 2.3 djet,VC to 2.8 djet,VC

• C= 0.6 djet,VC to 0.9 djet,VC

i = 50 to 80

e is varied from section I to section V

• I: 300 to 460

• II: 200 to 300

• III: 100 to 200

• IV: 50 to 160

• V: 00 to 50