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

[email protected]

Co-authors:

Jeppe Johansen

Christian Bak

Niels N. Sørensen

Risoe National Laboratory

mailto:[email protected]


Outline

• Motivation for the work

• The modeling used for the investigation

• Results

• Conclusions


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



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



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)


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:


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´)


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´)


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


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


CONSTANT LOADING – CT=0.30



deviations in two regions



LOCAL CP DISTRIBUTION AVERAGE CP



LOCAL CP DISTRIBUTION LOCAL CP DISTRIBUTION


Influence of wake rotation on pressureAXIAL VELOCITY CONTOURS -- CT=0.95 -- NO WAKE ROTATION

PRESSURE CONTOURS – CT=0.95 -- NO WAKE ROTATION


Influence of wake rotation on pressure

PRESSURE CONTOURS – CT=0.95 -- NO WAKE ROTATION

PRESSURE CONTOURS – CT=0.95 – WAKE ROTATION -- λ=6


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


Influence of wake rotation on pressure and flow


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 =


Correction to the BEM model for pressure variation in the wake due to rotation

AVERAGE CPLOCAL CP DISTRIBUTION


Influence of load distribution on power coefficient – actuator disc simulations


Influence of load distribution on power coefficient – actuator disc simulations



Rotor with spinner --10% of radius

axial velocity contours







Influence of tip loss and blade minimum drag coefficient – CT=0.95LOCAL CP DISTRIBUTION AVERAGE CP


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


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


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

Documents

Rotor/blade Aerodynamics