Computational Studies of Horizontal Axis Wind Turbines
Quarterly Status Report
Covering the period
December 1, 1998 – February 28, 1999
Contract No. XCX-7-16466-02
Submitted to
National Renewable Energy Laboratory
Attn: Alan Laxson and Scott Schreck
1617 Cole Boulevard
Golden, CO 80401-3393
Sandia National Laboratories
Attn: Walter P. Wolfe
P. O. Box 5800, MS 0836
Albuquerque, NM 87185-0836
Prepared by
Lakshmi N. Sankar
School of Aerospace Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0150
February 22, 1999
INTRODUCTION
A computational research program is underway at Georgia Tech in the
area of horizontal-axis wind turbine aerodynamics. The research focuses on
understanding the flow mechanisms that affect the performance of wind turbines
operating in non-axial and non-uniform inflow, and the development of modern,
efficient computational techniques that complement existing combined blade
element-momentum theory.
The computational effort is based on the extension of a 3-D hybrid NavierStokes/potential flow solver that has been developed at Georgia Tech for
helicopter rotor and propeller applications to horizontal axis wind turbines. In this
approach three-dimensional unsteady compressible Navier-Stokes equations are
solved in a small region, on a body-fitted grid surrounding the rotor blade. Away
from the blades, the potential flow equation is solved. The vorticity shed by the
blades as a result of dynamic stall, and spanwise and azimuthal variation of the
circulation are captured by vortex filaments that are freely convected by the local
flow. Since the costly Navier-Stokes calculations are done only in regions close
to the wind turbine blades, and because much of the vorticity is tracked using
Lagrangean techniques, this method is an order of magnitude more efficient than
full blown Navier-Stokes methods.
The hybrid flow methodology is described in detail in the annual report for the
first year, and may be found at the web site:
http://www.ae.gatech.edu/~lsankar/NREL/
ACTIVITIES DURING THE RESEARCH PERIOD
December 01, 1998 – February 30, 1999
Significant progress was made during the reporting period in modeling wind
turbines from first principles. Specifically, the following tasks were carried out:
I. Validation of two transition prediction models and two turbulence models:
The previous report covering the period August 1, 1998-November 31, 1998
(available at the web site: www.ae.gatech.edu/people/lsankar/NREL/report.7.pdf)
describes in detail Eppler’s transition model and Michel’s transition model, and
how they are used in the wind turbine simulations.
The model proposed by Eppler determines transition location from the
characteristics of the boundary layer, such as momentum thickness , shape
factor H, energy thickness , and the ratio H32 = Transition is predicted to
occur if
u  
log  e   18.4 H 32  21.74  0.34r
  
(1)
Here ‘r’ is the roughness parameter. Transition is assumed to occur at the
laminar boundary layer separation point, should flow separation occur before the
above criterion is satisfied.
In Michel’s model, transition is predicted using a criterion that relates
Reynolds number based on momentum thickness R and the Reynolds number
based on the length of laminar boundary layer Rx.
These two transition models, that operate in conjunction with the BaldwinLomax and the Spalart-Allmaras turbulence models have been fully integrated
into the Georgia Tech hybrid code. The following studies have been done.
-3
0_eqn; Eppler
-2
Leading Edge
1_eqn; Eppler
Root
-1
Tip
WR
0
1
0_eqn; Michel
1_eqn; Michel
2
3
0
2
4
6
8
10
Fig. 1 Transition lines on upper surface of Phase III rotor in 6 m/s
12
-3
0_eqn; Eppler
-2
1_eqn; Eppler
Leading Edge
WR
Root
Tip
-1
0
1
2
0_eqn; Michel
1_eqn;Michel
3
0
2
4
6
8
10
12
Fig. 2 Transition lines on lower surface of Phase III rotor in 6 m/s
Fig. 1 and Fig. 2 show the prediction transition lines on the upper surface and
lower surface, for the CER Phase III rotor blade operating at a wind speed of 6
m/s. The rotor operates at 72 rpm. At this low wind speed condition, the flow
field behaves nicely, with attached flow over most of the rotor. The following
observations may be made.
a) Both on the upper and lower surfaces, Eppler’s model predicts a transition
location that is upstream of Michel’s predictions. This is because Eppler’s
model, as implemented in the present code, first checks to see if laminar
boundary layer has separated. If so, Eppler’s model assumes that transition
has occurred. Note that the inflexion point on the separated flow boundary
layer will cause Tollmien-Schlichting instability to develop, causing transition.
Michel criterion, on the other hand, bases its transition criterion primarily on
the boundary layer thickness. At this wind speed, the boundary layer has to
grow up to 55% chord or so, before Michel’s criterion detects transition.
b) On the lower surface, the pressure gradients tend to be more favorable than
on the upper side. This leads to a thinner boundary layer and separation aft of
the 40% chord. As a consequence, both these criteria predict that transition
will occur aft of the corresponding upper surface locations.
c) The Reynolds number near the root is less than 105. Both models predict that
the flow will remain laminar all the way to the trailing edge, near the root
region.
d) Transition line location appears insensitive to the turbulence model used.
-3
0_eqn;Eppler
-2
1_eqn;Eppler
Leading Edge
WR
Root
-1
Tip
0
1
0_eqn;Michel
2
1_eqn;Michel
3
0
2
4
6
8
10
12
Fig. 3 Transition lines on lower surface of Phase III rotor in 8 m/s
Fig. 3 shows the transition lines on the lower surface of the CER Phase III
rotor at 8m/s. Even though the overall pattern of the transition lines is similar to
the 6m/s case, the following differences may be observed:
a) Michel’s model predicts that the transition phenomenon over much of the
lower surface is delayed, compared to the 6m/s case. This is attributable to
the higher local angle of attack the blade sections operate in, and the
favorable pressure gradients that exist on the windward (i.e. lower) side of the
rotor.
b) The Eppler transition model, on the other hand, predicts transition lines that
are similar at the 8m/s and 6m/s conditions, presumably because laminar
separation is detected in the vicinity of 40% chord at both these wind
conditions. Notice that the maximum thickness location for the S-809 airfoil is
near 40% chord. The pressure gradient tends to be favorable from the
leading edge up to 40% chord, after which it becomes adverse at both these
wind conditions.
c) At the higher wind speed, a larger region near the root on the windward side
remains laminar.
d) The transition line predicted using the Michel’s transition model in conjunction
the Sparlart-Allmaras turbulence model has a kink near 33% radius. The
reason for this behavior is not known at this writing.
-3
-2
0_eqn;Eppler
1_eqn;Eppler
Leading Edge
WR
Root
-1
Tip
0
1
0_eqn;Michel
2
1_eqn;Michel
3
0
2
4
6
8
10
12
Fig. 4 Transition lines on upper surface of Phase III rotor in 8 m/s
Fig.4 show the transition lines on the upper surface at 8m/s. Eppler’s model
predicts that transition will occur near the leading edge, as a result of leading
edge separation. Michel’s model predicts transition, on the other hand, around
50% chord, with a considerable radial variation in the transition location,
especially near the root.
The large difference observed in the upper surface transition pattern of the
rotor between the 8 m/s and the 6 m/s is physically meaningful. For the CER
Phase III rotor at 72 rpm, as the wind speed increase to around 8m/s wind, the
operating state switches from a wind turbine state to a turbulent wake state. The
next section shows what happens to the operation of a wind turbine as the wind
speed is increased.
Phase III Rotor Performance and Flow Physics at Off-Design Conditions:
To understand the behavior of wind turbines at extreme wind conditions, the
Phase III rotor was studied at 17.5 m/s wind conditions. Due to the extensive flow
separation that was present, the Navier-Stokes equations were solved
everywhere at this wind speed. Hybrid method calculations were done at the
lower 13.5 m/s speed. Fig. 5 shows the predicted power and measured power vs.
wind speed. Good agreement is observed with experiments.
Generator Power[kw]
20
NREL experiment
Lifting Line
Hybrid code
Navier-Stokes Simulation
15
10
5
0
0
5
10
15
20
Wind Speed[m/s]
Figure 5. Power Generation vs. Wind Speed for the Phase III Rotor
While generating the data for figure 5 we encountered several interesting
questions:
a) It is seen that the measured data has a distinct break near 10 m/s. Why?
b) Why was the power not measured between 13 m/s and 17 m/s?
c) In what region can the hybrid code reliably predict the power output?
To answer these questions, Mr. Guanpeng Xu, the graduate student working
on this project, undertook the following study on the physics of the rotor
aerodynamics.
The theory and phenomenology of rotor states was first studied by
Glauert(1937) for propellers, and extended by Wilson and Lissaman(1972) to
wind rotors (Eggleston, 1987). As illustrated by Eggleston, several wind rotor
states occur as the blade pitch angle changes from a relatively large positive
value to negative values. These wind rotor states are propeller state, zero-slip
state, windmill state, turbulent windmill state, vortex ring state and propeller
brake state.
In the CER experiment, the wind turbines rotate at a constant speed, and the
blade pitch angle is set to a designer-specified value. This angle is (usually) the
optimum pitch angle at which maximum power will be generated, over a variety
of wind conditions encountered in a wind farm.
r
V0

Lift
vi

Vtotal
Zero-lift line
Figure 6a. Wind Turbine Nomenclature
Figure 6b: Propeller state (left) and Zero-Slip State (Right)
Figure 6 shows some of the possible rotor states. The symbol  represents
local impinging angle, and  is the pitch angle with regard to the zero-lift line.
The propeller-state exists when is greater then . In this state, the rotor
accelerates wind in the same direction it was originally going, adding energy to
the wind. The induced velocity vi is in the same direction as the oncoming wind.
Power must be supplied to maintain the rotor rpm when the rotor operates in the
propeller-state.
When  = , the rotor is in zero-slip state, and the induced velocity is zero.
The rotor does not extract energy from the wind, or supply energy. Propeller
aircraft pilots normally adjust the blade pitch angle so that this condition occurs, if
the engine should fail.
When the wind speed increases further, for  < , the windmill state occurs. It
is the designed operational state of wind turbine. Momentum Theory shows that
0  vi 
V0
, and the rotor extracts power. For this condition, the flow field over the
2
rotor is steady (in a rotating coordinate system).
Lift
 r
V0
vi


Zero-lift line
V total
Fig.7. Windmill State
When the wind speed V0 increases further, vi may be larger than V0/2, but
still small enough, so that  is still less than . Then the rotor is in turbulent
windmill state. Under the turbulent windmill state, the rotor still can generate
power. To an observer, the rotor looks like an opaque disk, and the unsteady
vortex structure looks like a turbulent wake. The flow around the rotor is highly
non-uniform, and unsteady, and can not be studied by momentum theory.
a) Turbulent Windmill
b) Vortex Ring
Fig. 8 Off-design states
c) Propeller Brake
When the wind speed increases further, vi may be of the same order of V0,
and the vortex-ring state occurs. The tip vertices are pushed up by the oncoming
wind, and pushed down by the induced velocity. These vortices, therefore, get
trapped in a vortex ring. As more and more vorticity is captured in a doughnutshaped vortex ring, the ring distends and periodically bursts leading to an
unstable flow near the rotor disk. Whenever the ring “bursts” the trapped vorticity
is released and carried away by the wind, and away from the rotor. The process
of accumulation of vorticity inside the vortex ring begins all over again. Thus, the
vortex-ring-state is an unsteady, periodically recurring state.
When the wind speed increased further, a second turbulent windmill state
occurs. In this state, the vortex ring is blown away by the strong wind. The rotor
blade stalls and acts like a plate at an angle of attack, found on ancient wind
turbines. The positive power output observed is due to drag generated by the
blades, and not due to lift. The ratio of power generated to the wind kinetic
energy is low, and the efficiency is low, because the wind turbine is driven by
drag, as ancient windmills were, hundreds or thousands years ago.
The windmill state and the turbulent windmill state are the only two states of
interest to wind turbine designers. The vortex ring state can cause fatigue and
should be avoided by adjusting the blade pitch angle.
Returning back to figure 5, we can answer the questions previously raised as
follows:
a) Near 10 m/s, the measured power curve has a distinct break. Why?
Answer: From 5 m/s to 10 m/s the windmill-state occurs. Between 10m/s
and 13 m/s the rotor operates in a turbulent windmill state. The induced
velocity vi has two branches near vi = V0/2, which must be correctly
chosen based on physical considerations, i.e. the rotor operating state.
The hybrid code correctly (and automatically) takes the correct branch.
Simple wake theories (e.g. that used in YawDyn) may miss completely this
break in the branch and produce a smooth, incorrect power prediction
curve, as shown in figure 5.
b) Why is the power not measurable between 13 m/s and 17 m/s?
Answer: Above 13m/s, the rotor operates in a strong unsteady of vortexring state. The power generated is highly unsteady, and may fluctuate
wildly from a positive value to negative. Operation of the rotor under these
conditions is not advised due to the fatigue considerations, and the rotor is
usually shut down. The CER experiment reports no quasi-steady
measured data in this region until the rotor is in the second turbulent
windmill state at 17 m/s.
c) In what region can the hybrid code reliably predict the power output?
Answer: Our numerical studies show that the hybrid methodology is not
applicable in the vortex-ring state and the second windmill state. Under
these states the basic assumption, i.e. the division of the flow field in to
potential region, Navier-Stokes region, and tip vortex wake, breaks down.
For example, when the vortex ring bursts, it will spill vorticity into the entire
flow field, which must be modeled using an Eulerian approach. In this
regime, the full Navier-Stokes solver must be used.
However, the Hybrid method can predict the turbulent windmill state well.
The reason is that the vorticity is generally confined to a narrow region,
and the geometry of tip vortex wake may be determined by empirical (e.g.
Glauert) methods.
Calculations to be done during the next reporting period:
The hybrid code is being modified for modeling yaw conditions. The flow is
unsteady, and the tip vortex geometry is skewed with respect to the rotor axis.
The flow field will be different from one blade to the next. Despite these
complications, the hybrid theory can still be formulated to handle yaw conditions,
and may be expected to yield useful results. Preliminary results for the Phase III
rotor operating under yaw conditions will be given in the next progress report.
References
1. Eggleston, D. M. and Stoddard F. S., Wind Turbine Engineering Design. ISBN
0-442-22195-9
2. Glauert, H. ‘Airplane Propellers.’ From Div. L, Aerodynamic Theory, ed. W. F.
Durand. Berlin: Springer Verlag, 1935. (Reprinted by Peter Smith, Glouster,
Mass., 1976)
3. Wilson, R. E. and Lissaman, P. B. S., ‘Applied Aerodynamics of Wind Power
Machines.’ Oregon State University, 1974.