Dr. Ir. Harinaldi, M.EngMechanical Engineering Department

Faculty of Engineering University of Indonesia

Reaction tuRbines

Radial Flow Radial Flow –– Francis TurbineFrancis Turbine

Construction of Francis TurbineConstruction of Francis Turbine

Velocity TriangleVelocity TriangleEuler Equation:

g

CUCUmgWE xx 2211

Flow velocities:

111 2 br

QCr

222 2 br

QCr

heightrunnerb

Axial Flow Axial Flow –– Kaplan TurbineKaplan Turbine

Construction of Kaplan TurbineConstruction of Kaplan Turbine

Velocity TriangleVelocity TriangleEuler Equation:

g

CCUmgWE xx 21

For zero whirl at exit:gUCE x1

1

11

cot 180cot

a

oax

CUCUC

g

UCUE a 12 cot

arr CCC 21

22114

dDQCCC arr

Flow velocities:

diameterhubdtipbladetodiameterD

)(diameter mean at evaluate is mDUNote:

2dDDm 60NDU m

InstallationInstallation

Net Head Across TurbineNet Head Across Turbine Net head (H) is the different in the

total head between the inlet flange and the tail water level

Net head (H) is not equal to Gross head (H1)

Total head across turbine

gVZgVgpH

ZgaugepZZgVVgppH22

0 ; )( 0 ; 22

302

00

33302

32

030

gVhHH fp 2231

Relation: net head and gross head

Energy given to the runner

rgd hhhHmgWE

energy kinetic residual2

runnerin loss head frictionaldraft tubein loss head frictional

vanesguidein loss head frictional

pipelinein loss head frictional

23

gVhhhh

r

d

g

fp

Losses and EfficiencyLosses and EfficiencyEnergy balance through the turbine

slcrm PPPPPP Ps = shaft power output Pc = casing and draft tube lossPm= mechanical loss Pl = leakage lossPr = runner loss P = water power available

Runner Loss

rrr hgQP qQQr

runner through rate flowrQleakage rate flowq

runnerin loss head frictionalrh

Leakage Loss

rl gqHP runner theacross head totalrH

Casing and draft tube Loss

cc gQhP draft tube and casingin loss headch

Energy balance becomes: srcrrm PqHQhQhgPgQH

Losses and EfficiencyLosses and EfficiencyOverall Efficiency

gQHPs

o

flangeinlet at availablepower fluidpoweroutput shaft

gQH

PP msH

flangeinlet at availablepower fluidrunnerby receivedpower

Hydraulic efficiency

For maximum efficiency

gQHCU x

H 11

Characteristics CurvesCharacteristics Curves

Characteristics CurvesCharacteristics Curves

Comparison of hydraulic turbine efficiencies

Draft TubeDraft Tube Bring the water pressure back to the pressure of the tailrace Remove the kinetic energy still existing at the runner outlet

adsa

da

a

d

pphgVVHgpgphgVVZygpgp

ygpgpZhZgVgpZgVgp

22

32

22

23

2222

33

32

3322

22

2

2

; 0 22

Energy Equation between runner outlet and tailrace

Efficiency of draft tube

gV

hgVV

d

d

2

2

draft tube of entranceat headvelocity head pressurein gain net

22

23

22

Cavitation in TurbineCavitation in Turbine

ExampleExampleA Francis turbine has an inlet diameter of 1.4 m and rotates at 430 rpm. Water enters the runner without shocks with a flow velocity of 9.5 m/s and leaves the runner without whirl with an absolute velocity of 7 m/s. The difference between the sum of the static and potential heads at entrance to the runner and at the exit from the runner is 62 m. If the turbine develops 12 250 kW and has a flow rate of 12 m3/s of water when the net head is 115 m, find(a) The absolute velocity at entry to the runner and angle of inlet guide vane(b) Runner blade entry angle(c) Head loss in runnerSolution:Given: D1= 1.4 m; N = 430 rpm; Cr1= 9.5 m/s; C2 = 7 m/s; P = 12250 kW; H = 115 m; Q = 12 m3/s ; Cx2 = 0(a) Inlet velocity and inlet guide vane angle

m/s 5.31604304.16011 NDURunner tip speed

Power given to runner

m/s 4.325.311210

10.122503

3

11

112211

QUPC

CQUg

CUCUgQP

x

xxx

ExampleExample

m/s 8.334.325.9 2221

211 xr CCC

(b) Runner blade entry angle

Absolute inlet velocity

Inlet guide vane angle

o

x

r

CC 3.16

4.325.9arctanarctan

1

11

o

x

r

UCC 6.84

5.314.325.9arctanarctan

11

11

(c) Head loss in runner

Head loss in runner = total head across runner – head transferred to runner

Total head across runner = 21

22

2121

2ZZ

gCC

gpp

Head transferred to runner = gCU x11

ExampleExample

m 622121

ZZg

pp

However,

gCUZZ

gCC

gpph x

r11

21

22

2121

2

Head loss in runner

Thus,

m 69.13

81.94.325.31

81.9278.3362

262

22

1122

21

gCU

gCCh x

r