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By Michael R. Ruith, Fluent Inc.; and S. Shashidhar, T. Vishak, Ravi Kumar, Fluent India
View the pdf of this Supplement
Axial velocity distribution on the rotor
disks of a group of closely spaced
turbines with axial inflow conditions
In 2003, the U.S. wind generating capacity
increased by more than 30%, faster
than any other form of electric generation.
Wind power farms of various sizes now
operate in 32 states with a total generating
capacity of 6374 MW, enough to meet the
energy needs of more than 3 million homes.
The goal of the U.S. wind industry is to
increase the installed wind power capacity
to about 100 gigawatts (GW) by 2020. This
would account for nearly 6% of the estimated
total electrical power consumed in the
U.S. – a moderate goal, considering that the
winds that blow across the Great Plains
alone could generate more electricity than
the U.S. currently consumes per year [1].
Across the windy Atlantic, the E.U. pursues
an even loftier goal – 150 GW or about 12%
of the total available power is expected to
be harvested from wind farms by 2020 [2].
2003 U.S. Wind Capacity Map; wind
farms of various sizes now operate in
32 states, generating 6374 MW [1]
The wind farms that have been built in
the U.S. to date primarily take advantage of
the country’s best wind resources (Class 6
or 7, with speeds of 8.0 to 11.1 m/s, 50 m
above the ground). Class 4 (7.0 to 7.5 m/s)
wind resources are much more common,
and are often located close to load centers,
making them especially attractive to develop.
However, their cost in $/kWh has been
higher [1]. Development of those geographical
areas to ensure continued industry
growth is the goal of the Department of
Energy (DOE) Wind Program. In particular,
the National Renewable Energy Laboratory
(NREL) has been tasked to bring together
researchers from industry, academia, and
government to develop technologies that
will render wind farm operation profitable
in low speed environments.
Due to the great potential of wind energy,
more utilities are seriously evaluating its
addition to their electric generation portfolios.
However, because wind is a variable
resource, it raises concerns about how it
can be integrated into the grid, particularly
with regard to its effect on regulation, load
following, scheduling, line voltage, and
reserves. A lack of acceptance by the utilities
can inhibit the increase of installed wind
energy capacity. Thus it is critical to develop
simulation tools that enable the analysis of
wind farm operations under various wind
conditions.
Wind turbines operating in farms experience
wake effects. Each wind turbine slows
down the wind behind it as it pulls energy
out of the wind and converts it to electricity.
Ideally, turbines should be spaced as far
apart as possible in the prevailing wind
direction. Yet land use and the cost of connecting
wind turbines to the local grid favor
spacing them closer together. Typically, turbines
in wind farms are spaced between 5
and 9 rotor diameters apart in the prevailing wind direction, and between 3 and 5
diameters apart in the perpendicular direction.
Wake effects for a typical farm layout
can therefore be very large during offdesign
wind conditions. Environmental
effects originating from the presence of
hills, forests, buildings, power lines, and
wind turbine towers also affect the wind
flow through the farm and, ultimately, the
availability of its power output.
Static pressure distribution on the
rotor disk of the Grumman Wind
Stream 33 downwind turbine under
axial inflow conditions, computed
using the single rotating reference
frame (SRF) model (left) and the
virtual blade model (VBM) (right),
where the influence of the support
pole is evident
Comparison of the power generated by various
models for the test rotor.
While wind farm modeling is still in its
infancy, CFD has been widely adopted to
model flow fields around turbine blades
with various degrees of accuracy. A new virtual
blade model (VBM) has recently been
added to FLUENT’s turbomachinery modeling
capabilities. Initially, the VBM was developed
to approximate a helicopter rotor in a
time-averaged manner to simulate its effect
on the fuselage and other nearby components
during hover and forward flight. It
replaces the rotor blades with variable
momentum sources on an actuator disk,
allowing the pressure jump across the disk
to vary with radius and azimuth. This eliminates
the need to generate individual meshes
over each of the rotor blades, so fewer
cells are needed, and mesh generation time
is reduced. The magnitudes of the momentum
sources are obtained from blade element
theory (BET), allowing for varying
twist, chord and airfoil types along the
span. The non-linear aerodynamic interaction
between the rotor system and other
structural components – and between different
rotor systems – is solved by coupling
the BET with the governing flow field equations.
Airfoil tables required by the BET can
be specified as functions of Mach and
Reynolds number, allowing both incompressible
and compressible flows to be
treated accurately. Coning and flapping, as
well as collective and cyclic pitch can be
taken into account, whereby the blade
pitch can be calculated through a trim routine
to achieve a specified thrust coefficient
and zero moment about the hub. The
method has been validated with experimentally
measured surface pressures on
generic helicopter fuselages [3]. It is currently
implemented via user-defined functions
(UDFs) in FLUENT and is accessible
through the graphical user interface (GUI).
Axial velocity distribution on planes passing through
closely spaced turbines reveals the strong wake effect
on the downstream wind turbine under this worst-case
wind direction
As a test of the VBM for horizontal
axis wind turbines (HAWT), a modified
Grumman Wind Stream 33 was studied
[4, 5]. It consists of a 10m diameter, threebladed
(S809 airfoil, phase II), downwind,
free-yaw, stall-controlled turbine, operating
at a constant speed of 72 rpm. In addition
to the VBM, the turbine was also simulated
using a single rotating reference frame
(SRF) model. While the SRF model incorporates
the full geometry of the turbine blade,
all non-axisymmetric stationary components,
such as the drive-train and tower,
must be ignored. For both numerical
approaches, predictions for the power generated
as a function of wind speed were
found to be in good agreement with experiment
[4] and other numerical methods [5].
While FLUENT’s VBM and SRF models of
a single isolated turbine are similar to traditional
numerical approaches, only the VBM
can take into account added complexities in
a rigorous fashion, while keeping the computational
mesh manageable. In another
example studied, a wind farm consisting of
five modified Grumman Wind Stream 33’s,
distributed over a hilly terrain was simulated.
A cylindrical domain of diameter 160 m
(16D) and average height 40 m (4D)
required fewer than 2 million cells.
A constant velocity profile was assumed,
but a more appropriate logarithmic velocity
profile approximating the atmospheric
boundary layer [6] can be easily implemented.
By examining the velocity in the free
stream (axial) direction on the rotor disks,
the wake effect of the upstream turbines
could be illustrated. For the worst-case wind
direction with full overlap between the wake
and downstream wind turbine, the downstream
turbine’s power output is reduced by
almost 50%.
These results demonstrate that the VBM
is a first and important step towards simulating
the effects of wind conditions on the
potential power generated by wind farms,
forming the basis for their routine and
financially profitable operation in the electrical
grid by utility companies.
References:
- “Wind Power: Today and Tomorrow”, U.S.
Department of Energy, Energy Efficiency and
Renewable Energy, www.nrel.gov, March 2004.
- “Wind Energy, The facts. An Analysis of Wind
Energy in the EU-25”, European Wind Energy
Association, www.ewea.org, 2003.
- A.G.Brand, N.M. Komerath and H.M. McMahon,
“Windtunnel Data from a Rotor Wake/Airframe
Interaction Study”, Georgia Institute of
Technology, US Army research contract No.
DAAG 29-82-K-0094, 1986.
- D.A. Simms, M.M. Hand, L.J. Fingersh and D.W.
Jager, “Unsteady Aerodynamics Experiment
Phases II-IV. Test Configurations and Available
Data Campaigns”, NREL/TP-500-25950, July
1999.
- G. Xu, “Computational Studies of Horizontal Axis
Wind Turbines”, Ph.D. thesis, Georgia Institute of
Technology, May 2001.
- R.H. Stewart, “Introduction to Physical
Oceanography”, Department of Oceanography,
Texas A&M University, August 2003.
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