2 1 2 Basic Principles
-
Upload
nishith316 -
Category
Documents
-
view
214 -
download
0
Transcript of 2 1 2 Basic Principles
-
7/29/2019 2 1 2 Basic Principles
1/17
Workshop on Renewable Energies
November 14-25, 2005
Nadi, Republic of the Fiji Islands
Module 2.1Module 2.1--22
WIND ENERGYWIND ENERGY -- BASIC PRINCIPLESBASIC PRINCIPLESGerhard J. Gerdes
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
2
ContentsContents
J calculate the power in the wind
J power coefficient
J efficiency of wind wheel
J drag devices
J lift devices
J comparison of lift and drag devices
J utilizing wind energyJ maximum power extraction according to Betz
J thrust according to Betz
J airfoil theory:
X drag
X lift
X laminar vs. turbulent flow
-
7/29/2019 2 1 2 Basic Principles
2/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
3
Utilizing wind energyUtilizing wind energy
J conversion of kinetic energy into mechanical or electricenergy
32
wind Av2
1vm
2
1EP === && Pmech = M = M 2 n
- mass flow rate M - torque
v - wind speed n - rotational number - air density - angular velocityA - control area
m&
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
4
Theoretical maximum powerTheoretical maximum power
J by reducing the speed of an air mass, wind power is
converted into mechanical energy
J to reduce the wind speed to zero, obviously would
mean maximum power (hypothesis!)
J not possible - since stopping an air flow completely at
one given spot (rotor) violates the law of energy
continuity
J question: at what speed reduction the maximum wind
power can be extracted?
J answer was given by Betz and Glauert 1926 by a
simple calculation
-
7/29/2019 2 1 2 Basic Principles
3/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
5
Mass flow m through an area AMass flow m through an area A
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
6
J Rotor 54m diameter
J Rotor swept area 1500m
J Disk of 1 m thickness:
X Weight of air: 2.8to
-
7/29/2019 2 1 2 Basic Principles
4/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
7
Betz maximumBetz maximum
J if energy is extracted, wind speed v2 behind the rotor
must be lower than v1
A1 v1 A2 v2
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
8
ContinuityContinuity
J assumption: homogeneous air flow
J product of density, velocity and area is constant
according to continuity
332211 AvAvAv ==
air density, v wind speed, A area
-
7/29/2019 2 1 2 Basic Principles
5/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
9
Maximum Power Extraction by BetzMaximum Power Extraction by Betz
J the theoretical maximum power coefficient cp accordingto Betz is
J this means that a theoretical maximum of 59.3 % of the
power in the wind can be extracted
J in practice, modern electricity producing wind turbines
reach efficiencies of more than 50 % in maximum
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
10
cpcp-- valuevalue
J The cp-value is the efficiency of power production by
wind turbines
J cp gives the relation between power in the wind (Pwind)
to the mechanical power extracted by the turbine rotor
(Pturbine):
J Usually cp electric is used to indicated the total efficiency
of power production by a wind turbine, referring to the
electrical output of the wind turbine generator (Pelectric):
Wind
Turbinep
P
Pc =
Wind
electricelectricp
P
Pc =
-
7/29/2019 2 1 2 Basic Principles
6/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
11
Power in the wind 1Power in the wind 1
J power in the wind with the velocity v and an area A
J Pwind is proportional to the air density , area A and the
third power of the wind velocity v
J the power output of a WTG follows up to a wind speed
of approx. 12 m/s wind speed the v energy curve
J then the power limitation comes into action, to preventthe generator from overload
air density, v wind speed, A area
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
12
Power in the windPower in the wind power outputpower outputcharacteristicscharacteristics
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 2 4 6 8 10 12 14Wind speed [m/s]
Powe
r[kW]
Pwind
PBetz
PWT
Pwind
PBetz
PWT
-
7/29/2019 2 1 2 Basic Principles
7/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
13
Practical consequencesPractical consequences
J first of all, the power in the wind is proportional to the
third power of wind speedJ this has important practical implications
X calculating or estimating the power output of turbines
from wind speed measurements has a high error margin
X doubling the wind speed results in 8 times the power
output
X ability to withstand gusts is of primary importance for
turbines
J with around 60 % maximum efficiency, wind turbine
compare favourably with other energy conversion
systemsX diesel generator: max. ca. 35 %
X large steam turbine: max. ca. 40 %
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
14
Effect of air densityEffect of air density
J the power output of a wind system is proportional to the
air density thus the power varies
X with temperature: low temperatures result in more power
X with altitude: high altitudes reduce power output
-
7/29/2019 2 1 2 Basic Principles
8/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
15
J all early wind power systems were drag devices
J using the force acting on an area perpendicular to thewind direction
J drag is proportional to the area A, air density and the
square of wind speed v:
J the drag coefficient cD depends on the aerodynamic
quality of the body
Drag devicesDrag devices
2
2AvcD D
=
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
16
Drag coefficient depends on shapeDrag coefficient depends on shapeof bodyof body
-
7/29/2019 2 1 2 Basic Principles
9/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
17
Vertical axis wind wheel 1Vertical axis wind wheel 1
J simplification
J wind velocity at the plate: w = v - u
J blade tip speed u = Rm (rotational speed mean
radius)
principle simplified model
v velocity of wind
u rotor blade tip-speed
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
18
Tip speed ratioTip speed ratio
J blade tip speed ratio is the ratio between the speed ofthe tip of a rotor blade related to the affecting wind
speed
J where: angular velocity, Rm blade tip radius, .
Rm- rotational speed at rotor tip, tip speed ratio
v
Rm=
-
7/29/2019 2 1 2 Basic Principles
10/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
19
Power coefficient of wind wheelPower coefficient of wind wheel
blade tip speed ratio = Rm / v
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
20
InterpretationInterpretation
J obviously, at complete standstill ( = 0) the power is
zero
J also, when the the blade-tip speed is equal to wind
speed ( = 1)
J the maximum power coefficient of cp max = 0.16 occurs
at
opt
= 0.33,
when the blade tip moves at 1/3 of the wind speed
J meaning that only 16 % of the wind power can be
extracted
-
7/29/2019 2 1 2 Basic Principles
11/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
21
Drag devicesDrag devices
J all early wind power systems were drag devices
J using the force acing on an area perpendicular to thewind direction
J drag is proportional to the area a, air density and the
square of rotor speed
J the drag coefficient cD depends on the aerodynamic
quality of the body
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
22
Summary drag devicesSummary drag devices
J drag devices operate at tip speed ratios < 1, i. e. at tip
speeds below wind speeds
J the power coefficient cp of drag devices is below 0.2, i.
e. the maximum efficiency is 20 %
J with only 1/3 of the theoretical maximum (Betz: 59.3
%), drag devices are not suitable for electricity
generation
J due to their simple construction, drag devices can be
used for low power pumping needs etc.
J however, contemporary use of drag devices is
practically non-existent
-
7/29/2019 2 1 2 Basic Principles
12/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
23
Lift devicesLift devices
J many bodies have not only a drag force component,
but also a lift forceL
, perpendicular to the flow
J L attacks at about of the chord length c, as long as
the angel of attack is small (< 10 ), thus: cL = f()
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
24
Lift and drag forces L, DLift and drag forces L, D
angle of attack
-
7/29/2019 2 1 2 Basic Principles
13/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
25
Comparison of lift and drag devicesComparison of lift and drag devices
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
26
Airfoil theory: drag vs. liftAirfoil theory: drag vs. lift
vWind vWind
draglift
-
7/29/2019 2 1 2 Basic Principles
14/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
27
Airfoil theory: lift forceAirfoil theory: lift force
J lift force =v
21AcL 21L
Source: DEWI
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
28
Airfoil theory: lift forceAirfoil theory: lift force
Source: DEWI
-
7/29/2019 2 1 2 Basic Principles
15/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
29
Airfoil theory: streamlines andAirfoil theory: streamlines and
pressure distributionpressure distribution
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
30
( ) ( )bcw2
cL 2AL
= ( ) ( )bcw2cD2
AD
=
Airfoil theory: lift and drag at theAirfoil theory: lift and drag at thebladeblade
X L - lift
X D - drag
X c - chord lengthX b - width
X w - velocity
-
7/29/2019 2 1 2 Basic Principles
16/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
31
Airfoil theory: laminar vs. turbulentAirfoil theory: laminar vs. turbulent
flowflow
Source: DEWI
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
32
Airfoil theory: laminar vs. turbulentAirfoil theory: laminar vs. turbulentflowflow
Source: Schlichting / Truckenbrodt
laminar flow (attached flow) turbulent f low (stall)
-
7/29/2019 2 1 2 Basic Principles
17/17
21-
Nov-0
5
(00:02)
e7/PPAWorksho
ponRenewableEnergies
33
Wind and energyWind and energy
J Wind speed is the essential measure influencing thepower output of a wind turbine
J The power in the wind has to be limited with increasing
wind speed
X E.g. 20 m/s on a 40 m rotor of a 600kW turbine equalsroughly 6 MW wind power
3
21 AvcP pWind =
21-
Nov-
05
(00:02)
e7/PPAWorkshoponRenewableEner
gies
34
cp--Diagram
0 4 8 12 16 20 24
0.5
0.4
0.3
0.2
0.1
0
Tip speed ratio
Rotorpo
wercoefficientcp
Rated power
Grid connection
Constant power
StartupCut off
Power < rated power