HydroHydroHydroHydro----power plants and hydraulic turbinespower plants and hydraulic turbinespower plants and hydraulic turbinespower plants and hydraulic turbines

Alessandro Corsini

Department of Mechanical & Aerospace EngineeringSapienza University of Rome, Italy

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Energy conversion cascade

Thermal energy

“potential” energy

Electric energy

chemicalgravitational

Mechanical energy

nuclear

Hydro-power conversion

Direct energy conversione process mechanical-to-

mechanical

High overall efficiencies nearly independent from the peculiar

hydro-power tech

Remark: it can be assimilated to a steam power plant

water evaporation is an effect of solar radiation

potential mechanical power is renewed because of evaporation-condensation-precipitation water

cycle

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Hydro-power plants

Hydro-power plants

Terms are measured in m of water gauge [m]:

• z is giving the flow trajectory,

• (z+p/ρg) is the piezometric line,

• (z+p/ρg +v2/2g), is the line of total hydraulic head

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Definitions, total hydraulic head

According to Bernoulli’s theorem, in a perfect liquid, at steady regime, the hydraulic head

is the sum of three components

Such a trinomial is constant as it refers to the specific energy of the liquid in view of its position, velocity and pressure

2v p

z2g gρ

+ +

Hydraulic head difference between two sections reads:

2 22 1 2 1 2 1

2 22 1 2 1 2 1

1 1H ( z z ) ( v v ) ( p p )

2g g

1 1W gQH gQ[( z z ) ( v v ) ( p p )]

2g g

ρ

ρ ρρ

= − + − + −

= = − + − + −

Hydraulic power W is then

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Hydro-power plant energy diagram

• gross head Hu,gross: is the difference of water levels measured between up and down-stream basins (after the power-house)

• net head (or motor) Hu,net : is the share of gross head input to the turbines; as such it is the

hydraulic head different I/O the turbine

useful head H is in general a function of water level given by basins or traverses

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• max derivable flow rate (in m3/sec): is the water flow rate to the set of turbine impellers

• useful runoff in a given time interval T: is the amount (volume) of water in m3 relative to the max derivale runoff

• mean useful runoff or flow rate in a given time interval T (in m3/sec): is the ratio of useful run-off and T

( )e c t e u ,lordo

g c t e

W gQHη η η ρ

η η η η

=

=

Hydro-power We

Remark Noteworthy the overall efficiency is in the range 0.7 – 0.9

Flow rate

Hydro-power plant energy diagram

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Typical hydro-power plants

Hydro-electric power plants,

Val d’Ultimo basin, Bolzano, IT

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Hydro-power plants, Valle Brembana basin (BG), IT

Components

Distributor or stator (1),

Wheel or impeller (2).

Up-stream the bladed stator typically a spiral distributor

(3), down-stream draft tube (4)

generator (5)

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Hydro-power turbines

(3)

(3)

(4)

(2)

(1)

(4)

(2)(2)

(1)(1)

(5)

(3)(3)

(3)

(1)

(2)

Components

volute (3) and pre-distributor (4) distribute the water

along the wheel periphery by controlling the inflow

direction

distributor (1), then, plays three roles

i. Kinematic interface between the spiral feeder and the impeller (with a control on fluid angle)

ii. By changing the stagger angle it does control the distributor opening and as such it modulates turbine flow rate and power

iii. It does contribute to fluid energy evolution by converting totally or partially the hydraulic head in kinetic energy

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(1)

(2)

(3)

(4)

Hydro-power turbines

distributor

distributor

wheel

open closed

Distributor and turbine degree of reaction R

21 1

u ,distributore

v pH

2g gρ= +

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(1)

, with p1 = patm

Zero reaction turbine

Reaction turbine, pressure p1 (distributor outlet) is higher than atmospheric pressure, as such

degree of reaction

21

u,distributore 1 u

vH , v 2gH

2g= =

21

u

u

vH

2gR

H

−

= 1 uv 2g(1 R )H= −

Hydro-power turbines

distributor

wheel

Specific speed

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Hydro-power turbines

High hydraulic head (H>500 m) and low flow rate

es. Pelton turbine (R=0) ns low

Medium hydraulic head (500 m>H>20 m) and medium high flow rate

es. Francis turbine (0.4<R<0.8) ns medium

Low hydraulic head (H<20 m) high flow rate

es. Kaplan turbine (R>0.8) ns high

Turbine R

Hydro-power turbine selection

Correlation among specific speed and impeller geometries

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Hydro-power turbine selection

Ch

ara

cte

ristic s

pe

ed

Head (m)

Pelton turbine, patented L. A. Pelton, 1880, USA

Turgo turbine

Ossberger, or Banki-Mitchell or cross-flow turbine

Zero reaction turbines

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Distributor duct has a nozzle at the outlet where the flow

is accelerated by transforming the available hydraulic head

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Zero reaction turbines, Pelton

1,ideale utile

1,reale utile

v 2gH

v 0.98 2gH

=

= ⋅

Flow rate modulation based on passage area at constant

v1

Doble needle has a deflector to control start and stop

transient

Runner/impeller blades 20 - 24

Vertical or horizontal axis wheel

Distributors (nozzles) 1 - 8

Wheel spun within the housing

Escape velocity is twice the nominal velocity

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Pelton turbine (iii), wheel

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v2

v1

v2Blade width is 3-4 times

the water jet d

( )2 2 21 2 1v v / vη = − Peak efficiency is at v2 = 0

Efficiency zeros at u = 0 (stop) e v1 = u (escape velocity)

D/d ratio 8 to 15-20

according to head

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Turgo turbine

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Hydraulic head 50 to 250 m

Also called inclined impulse turbine (water jet angle approx 20°)

Typically higher rpm

Lower efficiency wrt Pelton turbines

Axial trust bearings

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Reaction turbines

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Turbine families

Francis, and Kaplan

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Turbine families

Kaplan (Tubular)

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Turbine families

Kaplan (Bulb)

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Turbine families

Kaplan (S-type)

Francis turbine (i)

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Invented by James Bickens Francis (1815-1892).

R is equal to 0.4 – 0.6 according

to specific speed

Draft tube is needed to recover

the head available between

impeller outlet section and down-

stream basin level

Water flows centripetally

A Fink distributor ring is used with

variable pitch to control passage

area and volume flow rate

Head up to 500 m

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Francis turbine (ii)

Views of stator and rotor blades

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Francis turbine (iii)

Impeller blade number 8 to 20

Increasing specific speed:

- blade count diminishes

- radial path increases

- inter-distance stator-to-rotor

increases

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Propeller turbine

Reaction turbine, high flow-low head

H = 2 – 25 m

Q = 1 m3/s to 150 m3/s

R = 0.5 – 0.7

Blade count 3 – 5

Stator in the radial passage

Similar to Francis turbines

Kaplan turbine

Invented by V. Kaplan in 1912

Kaplan turbine

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