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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