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American Institute of Aeronautics and Astronautics
1
Near-Wake Flow Simulations for a Mid-Sized Rim Driven
Wind Turbine
Bryan E. Kaiser1 and Svetlana V. Poroseva2
University of New Mexico, Albuquerque, New Mexico, 87131
Erick Johnson3
Montana State University, Bozeman, Montana, 87185
Rob O. Hovsapian4
Idaho National Laboratory, Idaho Falls, Idaho, 83415
A relatively high free stream wind velocity is required for conventional horizontal axis wind
turbines to generate power. This requirement significantly limits the area of land for viable
onshore wind farm locations. To expand a potential for wind power generation onshore, new
wind turbine designs capable of wind energy harvesting at low wind speeds are in
development. The aerodynamic characteristics of such wind turbines are notably different
from industrial standards. The optimal wind farm layout for such turbines is also unknown.
Accurate and reliable simulations of a flow around and behind new wind turbine designs are
required. The current paper investigates the performance of a mid-sized Rim Driven Wind
Turbine (U.S. Patent 7399162) developed by Keuka Energy LLC.
Nomenclature
σ = ratio of planform area to swept area (solidity)
= ideal torque
= induced torque
= ideal angular velocity of the turbine
= prescribed angular velocity of the turbine
a = axial induction factor
CT = thrust coefficient
CP = power coefficient
D = turbine diameter
f = aerodynamic loss factor
I = turbine mass moment of inertia
R = blade length
Re = Reynolds number
Tu = turbulence intensity
U = mean velocity in the axial direction
U∞ = free stream wind velocity in the axial direction
I. Introduction
requirement of a relatively high free-stream wind velocity limits areas suitable for wind energy harvesting by
conventional horizontal axis wind turbines (HAWTs). As a mean to overcome this limitation, small to mid-
1Graduate student, Mechanical Engineering, MSC01 1105, 1 UNM Albuquerque, NM 87131-0001, AIAA Student
Member.
2Assistant professor, Mechanical Engineering, MSC01 1105, 1 UNM Albuquerque, NM 87131-0001, AIAA Senior
Member.
3Assistant Professor, Mechanical Engineering, Montana State University, Bozeman, MT 87185, AIAA Member.
4Scientist, Idaho National Laboratory, Idaho Falls, ID 83415-3810.
A
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sized wind turbine designs capable of power generation at low wind speeds have started to receive a renewed
interest from industry and consumers. The Keuka rim-driven wind turbine (RDWT) (U.S. Patent 7399162)
developed by Keuka Energy LLC is one of such new designs currently in production and testing. The objective of
our study is to estimate its performance using computational simulations in a range of wind speeds characteristic of
states with a low wind speed (wind class three or below), such as, for example, Florida, New Mexico, and Texas.
The Keuka RDWT is a drag-driven wind turbine designed for wind energy extraction in locations of wind class
three or below. The design is passive-stall-controlled for simplicity and lower capital expense. It features high
solidity (16 blades) and is power-rated at 15kW1. The turbine diameter considered in the current study is
approximately 7.5 m. In the future, results of the current study will be used to investigate whether RDWT generates
wakes less destructive than those of the conventional three-bladed HAWTs and thus, can be implemented in larger
numbers in wind farms. They also will be used to optimize the number of blades to minimize the downstream wakes
and the flow disturbance, and to improve the RDWT efficiency.
In this study, fluid forces on the blades of RDWT and the flow structure in its near wake were examined
analytically and computationally. The analytical model (Gluart’s momentum theory2) is based on empirical data3
and provides estimates for the turbine thrust and power. It does not account for the flow turbulence though.
Computations are conducted using commercial computational fluid dynamic (CFD) software, STAR CCM+ by CD
Adapco4. Results of simulations are compared with the experimental data1 collected during six months from a
prototype RDWT installation at the test site at the Wind Science and Engineering center, Texas Tech University
located at the Reese Technology Center in Lubbock, Texas. Data for other turbines are used for comparison as well.
II. Analytical Model
Following the classical momentum theory, the wind turbine power
coefficient CP can be calculated analytically3 in terms of the axial induction
factor as follows:
= 4(1 ).
The axial induction factor a is the variable which corresponds to the
degree to which the turbine slows the mean velocity of the flow over the
turbine. Each root of the power coefficient equation represents a different
flow state and axial induction factor.
Similarly, two axial induction factors may be calculated for a given a
single thrust coefficient. The first corresponds to a windmill state and the
second one to a turbulent wake state. Both states are relevant to the
analysis of a flow around and behind RDWT as low angles of attack across
the blades, broad chord length, and high solidity (σ = 0.42) (Fig. 1)
promote separation in the wake behind RDWT.
Buhl4 derived an equation for calculating the turbulent wake state axial induction factor that fits the empirical data
curves and potentially accounts for the tip and hub losses:
= 4|1| 0.4
8
9+440
9+50
94 > 0.4
The RDWT blades are essentially twisted plates shown in Fig. 1. The shape allows for relatively easy analytical
derivation of fluid forces acting on the turbine. The RDWT thrust force and the thrust force coefficient are
calculated analytically by considering the momentum conservation in an incompressible flow and neglecting viscous
forces.
III. Computational Model
A complex structure of a flow around RDWT presents many challenges for conducting accurate and reliable
numerical simulations. The presence of dynamic stall, turbine operation over a broad range of Reynolds numbers,
and interaction with atmospheric turbulence are just a few of such challenges. Requirements for the appropriate
computational grid resolution render Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) to be
computationally unfeasible for industry. Reynolds-Averaged Navier-Stokes (RANS) turbulence models are a
Figure 1. The Keuka Wind Turbine.
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potential alternative without the computational cost of DNS
and LES. RANS models are typically used by industry for
simulating the flow of the far wake of wind turbines5 and
readily available in many CFD software packages. In this
study, the ability of RANS models to accurately simulate a
near-wake flow of RDWT and quantitatively make power
and thrust predictions was examined.
Our previous sensitivity studies of flow simulations over
a rotating disk6 and around a single RDWT blade7 informed
the choice of RANS models to be used for this study. It was
shown, that the standard k-ε turbulence model provides an
accurate description of the flow physics over the disk surface
if paired with a suitable grid free of highly skewed cells6. In
the current study, the realizable k-ε turbulence model8 was
chosen for computations. It generates solutions as accurate
as the standard k-ε model does, but maintains the solution
accuracy for lower quality grid cells4. Additionally, the realizable k-ε model in STAR CCM+ is accompanied by the
two-layer all y+ wall treatment option which uses the initial cell y+ value as a criteria whether to resolve explicitly
the viscous sublayer or to apply wall functions4,9.
Computations were also conducted with the shear stress transport (SST) turbulence model10 because of the
known model’s ability to accurately represent the structure of the adverse pressure-gradient flows including flows
with separation, and because the SST model is accompanied by a similar all y+ wall treatment as the realizable k-ε
model.
The STAR CCM+ second order upwind advection scheme was chosen for the computation of all derivatives4.
Hybrid computational grids were generated and utilized in our study as they offer a suitable compromise
between accuracy and ease of use11. A computational domain for the quarter-of-RDWT simulations is shown in Fig.
2. The grid is composed of cells of two different types (Fig. 3). The domain size is 4Rx4Rx10R, where R is the
RDWT radius. The thickness of 5 prism layers of the growth rate of 1.07 is 0.06 m. Polyhedral cells fill the
remaining volume and were varied in density. The grid parameters were adopted from our previous work7 where the
sensitivity analysis of simulations of a flow around a single blade was conducted. Polyhedral-only meshes for the
same domain were also created and varied by the growth rate from the turbine surface. The quarter-turbine grids
varied in size from 780,000 to 1,800,000 elements. Periodic boundary conditions were assigned to two planes that
cut across the turbine. Other planes that limit the computational domain were treated as pressure outlets.
The grid parameters used in simulations of a flow
around the whole RDWT were identical to the quarter-
turbine grids of the polyhedral cells only. The domain size
was 10Dx10Dx10D. The mesh sizes varied from 815,000 to
3,500,000 cells.
In simulations of the quarter of RDWT, the turbine was
located at x = 4R from the inlet plane. The whole turbine
was located at x = 5D. The uniform inlet velocity equal to
the free-stream wind speed was assigned as the inlet
condition in all simulations. Its value varied in the range of
inlet velocities from 1 m/s to 12 m/s corresponding to the
range of Reynolds numbers (based on the turbine diameter)
from 480,000 to 5,700,000. No symmetry planes or periodic
conditions were necessary in the whole turbine simulations.
Therefore, the remaining surfaces for this geometry were
specified as pressure outlets. Angular velocities of the
turbine were specified to correspond to the values obtained
from the RDWT prototype at the aforementioned free-
stream wind speeds. The turbine tower was not represented.
Figure 2. The quarter-turbine computational domain.
Figure 3. The quarter-turbine hybrid grid enlarged in
the area around the turbine rim
.
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IV. Results
In the previous study7, the mean axial induction factor was found
to be a = 0.0685 without including the tip and hub losses (f = 1)
for the flow around the quarter of RDWT. The mean thrust and
power coefficients corresponding to that mean axial induction
factor were calculated using the classical momentum theory and
the modifications2,3 for the turbulent wake states discussed above
in the Analytical Model section. They were found to be CT =
0.2552 and CP = 0.2377.
In the present study, grid-independent values of the torque
induced on the whole RDWT were computed for each set of the
inlet and angular velocities (as explained in the Computational
Model section) by using Richardson Extrapolation technique11. The
data for the quarter turbine were recalculated to include cases when
hybrid grids with prism layers were used. Computations were conducted
with both turbulence models. Grid convergence for the torque is shown in
Fig. 4 along with the extrapolated value and three computed torque values in the asymptotic range (Baker11) for the
complete turbine.
Figure 5 shows the distribution of the y+-values at the center of the wall cells in the quarter-turbine grid with and
without prism layers at the free stream wind velocity of 1 m/s and prescribed rotation. The complex geometry
causes a large variety of the wall cell y+-values. and justifies the implementation of the all y+ wall treatments for the
selected turbulence models.
Figure 5. Distribution of the y+-values at the center of the wall cells in the quarter-turbine grids at the free stream wind
velocity of 1 m/s.
The extrapolated torque , the turbine’s mass moment of inertia I, and the specified angular velocity from the
experimental data were used to calculate the ideal torque and ideal rotation rate , using the expressions below:
=,
= 0.
The product of the extrapolated torque (the torque induced by the flow) and the ideal rotation rate is the ideal
mechanical power of the turbine. The power coefficient values obtained with the two turbulence models for the
whole turbine at the free-stream wind velocity of 1, 3, 6, 9, and 12 m/s are shown in Fig. 6 along with the data for
the quarter turbine obtained using hybrid grids at the free-stream wind velocity of 1, 6, and 12 m/s. The computed
power coefficient curve suggests a peak power coefficient of 0.3 at the free-stream wind velocity of 4 to 5 m/s. The
calculated data appears to underpredict the turbine power performance to compare with the experimental data. The
experimental data also showed that the turbine cannot extract power at the wind speed less than 3 m/s.
Figure 4. Grid convergence study.
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The thrust coefficient was computed at the same free-stream
wind velocities. Its values were also compared with the data for
three industrial turbines12 (Fig. 7). The mean thrust coefficient
calculated from the experimental data in our previous study7 using
momentum theory (CT = 0.1954) disagrees with the computed
thrust coefficients in Fig. 7. Comparison of the computational
results and thrust coefficients from industrial turbines suggests that
the computed thrust coefficients may be underpredicted.
Experimental data for the flow structure in a wake of the RDWT
prototype is currently unavailable. Therefore, the simulation results
are qualitatively compared with the experimental data for other
turbines and with the other simulations data. Computations were
conducted on the finest polyhedral-only grids for the whole
turbine and its quarter using the two turbulence models.
Figure 8 shows that the mean axial velocity profiles at
the distances of one and three radius behind the turbine
obtained with the two turbulence models are in close
agreement with one another in a case of the whole turbine
simulations. Slight discrepancy of the results is observed
in simulations of the quarter turbine. In the figure, the LES
results for a conventional turbine from Sørenson et al13 are
also given for the comparison. The LES results were
obtained using a grid of 6,000,000 cells. The extent to
which the turbine geometry affects the near wake is
difficult to predict5. The RDWT design may be a reason
for the different maximum mean axial velocities obtained
in the current simulations and in LES13 at the distance of
one radius behind RDWT. However, underprediction of
the velocity deficits and turbulence intensity peaks as well
as overprediction of the turbulent kinetic energy
dissipation when RANS models14 are used in simulations of the
turbine wakes5,15 is well documented5,15 and appears to be the
primary cause of the difference between the RANS and LES solutions shown at the distance of three radius behind
RDWT.
Figure 9 shows the velocity contour plots for the whole turbine and its quarter obtained using polyhedral grids at
= 1 m/s.
Figure 7. Thrust coefficient.
Figure 6. Power coefficient.
Figure 8. Mean wake velocity.
American Institute of Aeronautics and Astronautics
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Figure 9. Mean wake velocity contours for U∞= 1m/s.
Figure 10 shows the simulation results for the turbulence intensity. Results obtained with the two turbulence
models are in agreement with one another for the whole turbine and its quarter. The reduced turbulence intensity
values obtained in the quarter-of-turbine simulations are suspected to be the result of using the symmetry plane
boundary conditions. Maeda et al.16 performed a wind tunnel test with the similar flow parameters and found the
turbulence intensity peaks to exist as far behind the turbine as five diameters. At x = 10D, Maeda et al. observed the
single broad, shallow peak. In the current simulations, a similar peak is observed at x = 1.5D. Therefore, the data of
Maeda et al.16 and that of Rados et al.15 may be an indication that the turbulence intensity is underpredicted in our
simulations.
Figure 10. Wake turbulence intensity profiles.
Conclusions
The realizable k-ε turbulence model with the two-layer all y+ wall treatment option produced remarkably similar
results to the SST turbulence model with the all y+ wall treatment option in all simulations. The realizable k-ε model
and SST model agreed better than the standard k-ε model and the SST model in our previous work.
The estimates of the power coefficient obtained using the mechanical torque and rotation method underpredicted
the turbine performance. The power coefficients obtained in the whole-turbine simulations were marginally more
accurate than those obtained in the quarter-turbine simulations. Similar results were observed for the thrust
coefficients, although validation was not performed for this coefficient.
Velocity and turbulence intensity profiles in the near-wake behind RDWT demonstrated that the selected RANS
models are capable of capturing the general shape of the flow structure. As no validation data exists for the RDWT
wake yet, comparison was made for other wind turbine designs. The results of such comparison suggest that the
velocity deficit, turbulence intensity, and turbulent kinetic energy in the RDWT wake may be underpredicted. This
conclusion has been well documented for the other turbine designs 15,17. Still, validation data specific for the RDWT
design are necessary to draw solid conclusions, because the turbine geometry may play a significant role.
American Institute of Aeronautics and Astronautics
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The results also indicate that the use of the symmetry plane boundary conditions with periodic inflow/outflow to
reduce the cost of simulations has a negative impact on the accuracy of computations of the velocity and turbulence
intensity profiles in the given flow geometry.
Acknowledgments
The research was supported in part by the Junior Faculty UNM-LANL Collaborative Research Grant and by the
Center for Advanced Power Systems (CAPS) at the Florida State University. The authors would also like to
acknowledge the Center of Advanced Research Computing of the University of New Mexico for providing the
access to high-performance computing facilities and consulting support for this research, and CD-Adapco for
providing STAR CCM+ to the University of New Mexico for academic purposes.
References
1 Rankin, A. J., Poroseva, S. V., and Hovsapian, R. O., “Power Curve Data Analysis for Rim Driven Wind Turbine,” ASME
Early Career Technical Journal, Vol. 10, 2011, pp. 27-32.
2 Spera, D. A., Wind Turbine Technology: Fundamental Concepts in Wind Turbine Engineeering, 2nd ed., ASME Press, 2009.
3 Buhl, M. L. Jr., “A New Empirical Relationship between Thrust Coefficient and Induction Factor for the Turbulent
Windmill State,” Technical Report, National Renewable Energy Laboratory, Golden, CO, 2005.
4 STAR-CCM+. Ver. 6.02.007, CD-Adapco.
5 Sanderse, B., van der Pijl, S. P., and Koren, B., “Review of Computational Fluid Dynamics for Wind Turbine Wake
Aerodynamics,” Wind Energy, Vol. 14, 2011, pp. 799-819.
6 Snider, M. A.,Poroseva, S. V., “Sensitivity Study of Turbulent Flow Simulations Over a Rotating Disk,” AIAA-2012-3146,
42nd AIAA Fluid Dynamics Conference and Exhibit Proceedings, 2012.
7 Kaiser, B. E., Poroseva, S. V., Snider, M. A., Hovsapian, R. O., Johnson, E., “ Flow Simulation Around a Rim-Driven Wind
Turbine And In Its Wake,” 58th ASME Turbo Exposition Proceeding, 2013.
8 Shih, T.-H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J. 1994. “A New k-epsilon Eddy Viscosity Model for High
Reynolds Number Turbulent Flows - Model Development and Validation”, NASA TM 106721.
9 Rodi, W., Mansour, N. N., "Low Reynolds Number k-epsilon Modelling with the Aid of Direct Simulation Data." J. Fluid
Mech, Vol. 250, 1993, pp. 509-529.
10 Menter, F. R., Rumsey, C. L., “Assesment of Two-Equation Turbulence Models for Transonic Flows,” AIAA-94-2343,
25th AIAA Fluid Dynamics Conference Proceedings, 1994.
11 Baker, T. J., “Mesh generation: Art or Science?”, Progress in Aerospace Sciences, Vol. 41, 2005, pp. 29-63.
12 Moskalenko, N., Krzysztof R., and Antje, O. "Study of wake effects for offshore wind farm planning." Modern Electric
Power Systems (MEPS), IEEE 2010 Proceedings of the International Symposium, 2010.
13 Sørensen, J. N., Mikkelsen, R., and Troldborg, N., "Simulation and modelling of turbulence in wind farms," Proceedings
EWEC 2007, 2007.
14 Wilcox, D. C., Turbulence Modeling for CFD. 3rd ed., D C W Industries, 2010, pp. 303-306.
15 Rados, K. G., Prospathopoulos, J. M., Stefanatos, N. C., Politis, E. S., Chaviaropoulos, P. K., and Zervos, A., “ CFD
Modeling Issues of Wind Turbine Wakes Under Stable Atmospheric Conditions,” EU UPWIND # SES6 019945.
16 Maeda, T., et al. "Wind tunnel study on wind and turbulence intensity profiles in wind turbine wake," Thermal Science,
Vol. 20, No. 2, 2011, pp. 127-132.
17 Tachos, N. S., Filios, A. E., and Margarls, D. P., “A Comparative Numerical Study of Four Turbulence Models for the
Prediction of Horizontal Axis Wind Turbine Flow,” Mechanical Engineering Science, Vol. 224, 2010, pp. 1973-1981.
