Rotor/blade Aerodynamics
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Transcript of Rotor/blade Aerodynamics
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen1
An Investigation of Inboard Rotor/blade Aerodynamicsand its Influence on Blade Design
Helge Aagaard MadsenRisoe National Laboratory
Department of Wind Energy
Co-authors:
Jeppe Johansen
Christian Bak
Niels N. Sørensen
Risoe National Laboratory
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen2
Outline
• Motivation for the work
• The modeling used for the investigation
• Results
• Conclusions
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen3
Motivation for the work
The typical design codes use the BEM model for the aerodynamic modeling
Often the blade design is done by numerical optimization where both energy production and fatigue and extreme loads on a number of turbine components are considered -- lowest cost of kWh is the objective
A tendency to more slender blades and in particular in the root region has been seen
However, recently there has been a new focus on the maximum rotor power coefficient – to some degree initiated by the new Enercon blade design
CHARACTERISTICS OF BLADE DESIGN
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen4
Motivation for the work
It is well-known that a number of assumptions have been made in order to derive the simple formulas in the BEM model
• the pressure field from wake rotation is neglected
• uniform loading is assumed to give uniform axial velocity distribution
• radial independency of stream tubes
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen5
Motivation for the work
de Vries (1979) shows that including the effect of wake expansion together with the deficit of the static pressure in the wake, CP can exceed the Betz limit when λ = rΩ/W → 0.
from de Vries (1979)
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen6
The modeling
Two models are used:
a BEM model
an axisymmetric actuator disc model where the flow field is computed with a CFD code
The rotor loading is directly specified – not the blade design
The approach:
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen7
Modeling -- definition of coefficients
( ) ( )cos siny L DC C Cφ φ= + ( ) ( )sin cosx L DC C Cφ φ= −
Normal to rotor plane Tangential to rotor plane
21 22
dTCTV r drρ π∞
=212 r y BdT v C c N drρ=
Local thrust Local thrust coefficient
vax=V∞(1-a)
vtan + rΩ = rΩ(1 + a´)
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen8
Modelling -- definition of coefficients
( ) ( )cos siny L DC C Cφ φ= + ( ) ( )sin cosx L DC C Cφ φ= −
Normal to rotor plane Tangential to rotor plane
Local torque Local torque coefficient
212 r x BdQ v C c N r drρ=
21 22
dQCQV r r drρ π∞
=
vax=V∞(1-a)
vtan + rΩ = rΩ(1 + a´)
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen9
Ideal rotor – CD=0.0
( ) ( )0
act
zCT r f r dz= ∫
( )tanx
y
dQCCQ r
CT dT Cφ= = =
This means: Specify the rotor load distribution by CT(r) and a tip speed ratio λ
- then CQ(r) can be derived from the above equation
- an iteration is necessary as CQ(r) depends on the flow field
CT(r) and CQ(r) are applied to the flow as volume forces (actuator disc concept)
( ) ( )0
act
tCQ r f r dz= ∫and
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen10
Ideal rotor – Power conversion
ax axCP CT v=
sCP CQ r= ΩShaft power coefficient:
2tan tanaxCP v v=
Power conversion in fluid:
From axial forces (extracted from flow)
From tangential forces (applied to flow)
Equilibrium: tans axCP CP CP= −
Note: all variables are dimensionless
v* = v/V∞ -- r*=r/R -- p* = p/(½ρV2) but * is not shown
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen11
CONSTANT LOADING – CT=0.30
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen12
CONSTANT LOADING – CT=0.95
deviations in two regions
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen13
CONSTANT LOADING – CT=0.95
LOCAL CP DISTRIBUTION AVERAGE CP
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen14
CONSTANT LOADING – CT=0.95
LOCAL CP DISTRIBUTION LOCAL CP DISTRIBUTION
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen15
Influence of wake rotation on pressureAXIAL VELOCITY CONTOURS -- CT=0.95 -- NO WAKE ROTATION
PRESSURE CONTOURS – CT=0.95 -- NO WAKE ROTATION
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen16
Influence of wake rotation on pressure
PRESSURE CONTOURS – CT=0.95 -- NO WAKE ROTATION
PRESSURE CONTOURS – CT=0.95 – WAKE ROTATION -- λ=6
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen17
Influence of wake rotation on pressure and flow
PRESSURE CONTOURS – CT=0.95 – WAKE ROTATION -- λ=6
TANGENTIAL VELOCITY CONTOURS – CT=0.95 -- λ=6
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen18
Influence of wake rotation on pressure and flow
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen19
Correction to the BEM model for pressure variation in the wake due to rotation
2*r twake R
vp drr
∗
∗
∗ ∗∗= ∫
wakep∗
• derive the pressure field from wake rotation
where * denote non-dimensional
• derive Δv*a-wake from based on comparisons with
actuator disc simulations:
* *0.7a wake wakev p−Δ =
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen20
Correction to the BEM model for pressure variation in the wake due to rotation
AVERAGE CPLOCAL CP DISTRIBUTION
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen21
Influence of load distribution on power coefficient – actuator disc simulations
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen22
Influence of load distribution on power coefficient – actuator disc simulations
LOCAL CP DISTRIBUTION AVERAGE CP
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen23
Rotor with spinner --10% of radius
axial velocity contours
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen24
Rotor with spinner --10% of radius
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen25
Rotor with spinner --10% of radius
LOCAL CP DISTRIBUTION AVERAGE CP
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen26
Influence of tip loss and blade minimum drag coefficient – CT=0.95LOCAL CP DISTRIBUTION AVERAGE CP
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen27
Influence of tip loss, blade minimum drag coefficient and tip speed ratio – CT=0.95
AVERAGE CP -- λ = 6 AVERAGE CP -- λ = 8
For rotor: CP=0.581, CPftip=0.537
CPftip+CD=min0.007=0.512
For rotor: CP=0.582, CPftip=0.550
CPftip+CD=min0.007=0.517
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen28
CONCLUSIONS - 1
• The ideal power conversion in a wind turbine rotor has been analyzed with an axi-symmetric actuator disc model and compared with the BEM model
• Considerable under-estimation of local CP inboard on the blade with the BEM model because the pressure from the wake rotation is neglected
• However, in the tip region the actuator simulations show an increased induction at high loadings compared with the BEM model
• A simple correction of the BEM model to take into account the influence on induction from the pressure from wake rotation has been shown
Presentation at Sandia Blade Workshop -- Aberquerque, USA, April 18-19, 2006 --- H.A.Madsen29
CONCLUSIONS - 2
• It has not been possible in the present simulations to increase the maximum rotor power coefficient by increasing the load on the inboard part of the blade in order to obtain constant induction
• No positive effect on the maximum power coefficient of using a spinner equal to 10% of rotor radius has been found in the present simulations
• The present simulations have shown that rather different rotor load forms give almost the same maximum power coefficient
• A maximum rotor power coefficient of around 0.52 for a blade CDmin of 0.007 has been obtained at a tip speed ratio of 6-8