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A CFD based multibody dynamics approach in horizontal axis wind turbine.


The primary goal of wind energy technology is to minimize the cost of energy from wind power in order to make the cost of energy more competitive compared to other energy sources. How to reduce the cost of wind turbine per unit of energy is an important consideration in modern wind turbine researches. One prevailing trend in wind turbine technology throughout the past couple of decades has been growth in the size of the rotor to realize the advantages of scale and the generally higher winds available at greater heights. Advancement of the current state of the art has been achieved through efficient structural design and optimal material usage to produce the necessary structural efficiency for blades up to 60 meters in length. Geometrically consistent up scaling of blade length shows that the surface stresses at the blade surface due to aero dynamical, gravitational loads grow in proportion to the length of the blade, while the flap due to aerodynamic loads are independent of the size of the blade. Large wind turbine must operate under varying turbulent and predictable environmental conditions where efficiency and reliability are highly dependent upon well--designed material optimization strategies. The load along the blade varies quickly in time and space due to impact of gust that are significantly smaller in size than the length of the blades. Wind power is the fastest growing electric power industry in the world. Current global installed capacity exceeds 32000 MW with a projected growth rate of 10000 MW/year for the next five years. The phenomenal growth of this industry can be attributed, preliminary, to the rapid progress made in wind turbine technology. Over last couple of decades, technological progress has led to the development of turbines with high power captures efficiency. Today, many wind farms produce electrical power at a cost-of-energy (=4-6c/KWhr) which is comparable to that of coal and natural gas based power plants. Typical large wind turbines of today are massive structures with enormous blade spans (70-100m in diameter),tall towers (60-100m in height) with power rating in the 1-5 MW range. Amongst the technologies that enable realization of these machines, reduced weight plays a pivotal role. Modern large wind turbines are endowed with sophisticated composite materials which are organized to support several loads of operations such as start-up, shut-down, power production etc. Whenever wind turbine blades twist, there is a direct influence on the angle of attack, changing loads and affecting output power. This is directly exploited in classic pitch control used in not only wind turbines but in rotors of all types. When the pitch changes, they can affect not only average loads and power, but vibratory loads as well, influencing fatigue life throughout the system. This requires multi body dynamic analysis. Even quite small change in angle of twist can have significant impact. The relatively small size and short response time of multi body aerodynamic load calculation(MALC)analysis permits the development of an associated control system to achieve better design.

Problem description and computational method Physical model

The accurate evaluation of the impact of aerodynamic load reduces the cost of energy production. It will assist a complete new turbine design that fully integrates this new technology. The cost estimates for this new turbine design are subject to very large errors, so the cost of energy for the new turbine will be very hard to determine accurately. An alternative approach is to work with an existing turbine design and determine using MALC how much larger a rotor can be made without exceeding the fatigue loading experienced by the original rotor. The rotor with MALC can then be grown to where the blade-root flap fatigue damage accumulation approaches the original level for the baseline rotor. With appropriate control logic and MALC hardware, the fatigue damage accumulation on the tower and drive train with the larger rotor can be kept nearly the same as on the original rotor, so the original equipment can be retained.

From a design and manufacturing standpoint, wind turbine blades have many similarities to helicopter rotorcraft blades. The loading on a wind turbine blade and rotorcraft blade consist primarily of aerodynamic pressure loads. Of course, the speed of a wind turbine blade is much slower, so it experiences much lower aerodynamic pressures. Loading is also applied at the root of both wind turbine and rotorcraft blades. The overall pressure field on the blade causes a "bending moment" and torque at the root. A "bending moment" refers to the tendency of wind turbine blades to bend and twist during operation, which effectively alters their angle of attack and in turn has a negative effect on loads and energy production. For these reasons, blades are designed with a high level of bending stiffness.

The effect of wind turbine blade geometry is numerically analyzed using Computational Fluid Dynamics (CFD). Three different rotating blade tops are compared for attached flow conditions and the flow physics around the geometries are analyzed to this end, the pressure coefficient (Cp) is defined based on the stagnation pressure rather than the inflow dynamic pressure.

The primary airfoil is designated the S816. The tip airfoil, the S817, and the root airfoil, the S818, were derived from the S816 to increase the aerodynamic and geometric compatibilities of the three airfoils. The airfoil shapes shown in figure and the coordinates are contained in tables 11, III, and IV. The S816airfoil thickness is 21percent chord; the S817, 16-percent chord; and the S818, 24-percent chord.


S 816 Pressure Distributions Curves for Various Degree of Angle of Attacks

The in viscid (potential-flow) pressure distributions for the S816 airfoil for various angles of attack are shown in figure 2. Because the free-stream Mach number for all relevant operating conditions remains below 0.2, these and all subsequent results are incompressible.


S 817 Pressure Distributions

The in viscid(potential-flow)pressure distributions for the S817 airfoil for various angles of attack are shown in figure 3.


S 818 Pressure Distributions


Mesh system

Mesh Characteristics

* Tetrahedral mesh is used for meshing the blades (triangular in 2D)


-4 triangular faces

-3--edged corners

Subdivision Types of Tetrahedral


CFD simulation

The wind turbine tower and the ground are not included in the flow model and a uniform wind speed profile is assumed at the entrance of the domain. To generate the volume mesh for the three bladed rotors, the 120 degrees periodicity of the rotor is exploited by only meshing the volume around one blade. The remaining two blades are included in the computations through the use of periodic boundary conditions. Around the blade the grid is H-shaped and it is optimized by means of 2-D simulations, to correctly resolve the boundary layer. The computational domain used is tetrahedral shaped, extending in the axial direction roughly 5 diameters upstream and 10 diameters downstream of the rotor. In the plane of the rotor, the domain diameter is five times that of the rotor. The pressure distribution curves (fig: 4)shows the boundary conditions imposed: at the inlet face and at the lateral boundary undisturbed uniform wind velocity and turbulence are fixed; static pressure is set at the outlet; no-slip condition is selected for blade and nacelle surface.



Numerical studies using CFD method to simulate the wind turbine performance were adopted. The tunnel is of:

Diameter = 150m

Length = 465m

Windmill placement from the inlet of wind tunnel = 150m

Wind speed = 10m/s

Windmill speed = 15rpm

Angle of attack = 0 degree


It was found that the blade geometry, stagger angle, and number of blades have different duct blockage effects, and do affect the turbine performance (specifically the power coefficient and torque coefficient, etc). The fewer number of blades has higher through flow speed, while the larger number of blades provides larger torque. The best power coefficient lies in between the two extremes. The appropriate number of blades is important to match the generator performance curve for optimal overall performance efficiency.

In 1919, Betz, provided the theory of the wind turbine in which the maximum power coefficient is about 59% Most researches made efforts in achieving efficiency of the wind turbine (HAWT) and vertical axial wind turbines (VAWT) the efficiency seemed to barely reach about 42% Kogan and Nissim and Kogan and Seginer first referred to the wind turbine with convergent entrance and divergent exit that could reduce the cut-in speed. While in past years, most researches have placed emphasis on how the ducted wind turbine transforms energy effectively, literature on the issue of the effect of the number of blades on the overall performance is still lacking. Thus the major purpose of this present study is to investigate the energy transformation from wind energy to mechanical energy of the ducted wind turbine with varying the number of blades and provide the blade design process under the adopted duct geometry, blade chord distribution and number of blades. The research method comprises an analysis based on the use of computational fluid dynamics (CFD) technique.



Blade Aerodynamics

The aerodynamic torque responsible for power production and the structural loading of the wind turbine largely arise due to the forces and moments produced due to interaction of the blades with the wind.

Simulation Procedure

Turbine component pressure accumulation calculations require time-series load histories at the turbine locations of interest at a number of men wind speeds spanning the entire operating range of the turbine. For this work, these load histories were generated with structural dynamic stimulations of the turbine of interest performed with compute the aerodynamic forced on the blades. FAST utilities a model representation of the turbine to determine its response to applied forces.

The inner flow field mesh domain was rotating, and hence, the coordinate system of the numerical simulation was fixed on the rotor coordinate system. The solution of the velocity was relative velocity, Furthermore, the outer flow field domain was fixed on the absolute coordinate system and the solution of the velocity was absolute velocity. Thus the velocity and other a parameters between the interfaces of the two domains should be done coordinate transformation to conserver mass, momentum and energy.

Modeling of wind Turbine Dynamics

Over the last decade or so, several wind turbine simulators such as BLADED, Flex, Fast, SymDynetc have been developed for purpose of loads simulations. More recently, the dynamics captured by these simulators are used to extract control-oriented models. The typical inputs to wind turbine simulators are three-dimensional wind field data, turbine parameters and a generator model. The output consists time series of the variables of interest which often include mechanical loads, power produced etc.

Wind turbine simulators are designed to capture the structural dynamics of turbine components as well as the aerodynamic interaction of the blades with the wind (discussed earlier). For large wind turbines, the structural dynamics become especially significant because of the flexible nature of its components. To model the structural behavior of these components, one of the following three approaches are often used (a) the "Assumed Modes" method (as used, for example, in FAST and BLADED), (b) Multibody dynamics (as used in ADAMs-WT) and (C) Finite element analysis. Between these three approaches, finite element analysis is computationally the most expensive making it an unattractive option for quick loads calculations. On the other hand, the "Assumed Modes" method, also known as the model simulation, is computationally the least expensive. This method is based on the observation that responses of distributed parameter systems (such as a homogeneous towers, blades etc) can be approximated by a linear combination of a few dominant "modes" of the system. Utilization of such an approximation reduces the dynamics of a distributed parameter system to that of a finite degree of freedom (DOF) system--thus enabling rapid loads computations. The dynamics of large, horizontal-axis wind turbines can often be adequately captured using a five DOF model. The dominant modes include blade flap-out-of-rotor-plane deflection of the blade; is strongly coupled with blade edge and drive train torsion.

The analysis for pressure is normally carried out under static condition, but in this paper we are dealing with both static and dynamic pressure.

Analysis by using both the conditions helps in coming out with an even more efficient design. The figure below compares the blades at both the conditions. The figure shows that under static condition the pressure is constant throughout, but in the next figure we can see that the pressure shoots up to a higher value near the rotor and the areas surrounding it. From the analysis for total pressure, it indicates that the load acts maximum at the blade tip.







Pressure under static & dynamic conditions is analyzed. Analysis has also been carried out for total pressure. By using the results from the above conditions helps in coming out with an even more efficient design. The figure shows that under static condition the pressure is constant throughout, but during dynamic condition the pressure shoots up to a higher value near the rotor and the areas surrounding it. From the analysis for total pressure, it can be concluded that the load is maximum at the blade tip. The pressure is negative at the upper surface and positive at the lower surface as expected. As no disturbances are created in the flow we can say that the size of wind tunnel domain considered is optimum.


[1] T. Cebeci J.R. Shao, F. Kafyeke E. Laurendeau, Computational Fluid Dynamics for Engineers, Springer, Horizons Publishing Inc., Long Beach, California 2005.

[2] Eppler, Richard: Airfoil Design and Data. Springer-Verlag (Berlin), 1990.

[3] L.L. Freris, Wind Energy Conversion Systems, Prentice Hall International Ltd, 1990.

[4] FLUENT 6.3 User's Guide, Fluent Inc., Sep. 2006.

[5] Gary L. Johnson, Wind Energy Systems, Prentice Hall Inc, 1985.

[6] D.M. Somers, The S816, S817, S818 Airfoils, NREL, October 1991-July 1992.

[7] Sheng-Huan Wang and Shih-Hsiung Chen, Journal on Blade number effect for a ducted wind turbine, Springer, July 23, 2008.


C. Rajendran (1) and G. Madhu (2)

(1) Lecturer, Anna University, Coimbatore, Tamil Nadu, India E-mail:

(2) Head-Division of Fire and Safety Department, CUSAT, Kerala, India
Table 1: Geometry of the Blade.

 Non dim. Thickness
Radial Span wise to Chord
Station Span wise Station Chord Thickness Ratio
r mm Station Z mm z/L % c mm t mm t/c %

816 0 0.0 1310.0 1310.0 100.0

1150 334 1.4 1310.0 1310.0 100.0

2300 1484 6.4 1323.0 1294.0 97.8

3450 2634 11.4 1672.0 1141.0 68.2

4600 3784 16.3 2000.0 781.0 39.1

5750 4934 21.3 2263.9 545.9 24.1

6900 6084 26.2 2222.1 517.0 23.3

8050 7234 31.2 2165.5 490.4 22.6

9200 8384 36.2 2096.3 465.5 22.2

10350 9534 41.1 2016.5 442.3 21.9

11500 10684 46.1 1929.5 419.2 21.7

12650 11834 51.0 1832.6 394.1 21.5

13800 12984 56.0 1728.3 363.2 21.0

14950 14134 61.0 1616.3 323.0 20.0

16100 15284 65.9 1499.1 278.3 18.6

17250 16434 70.9 1376.1 234.9 17.1

18400 17584 75.8 1245.7 199.3 16.0

19550 18734 80.8 1111.1 177.8 16.0

20700 19884 85.8 969.0 155.0 16.0

21850 21034 90.7 824.9 132.0 16.0

23000 23184 95.7 682.6 109.2 16.0

25000 24184 100.0 436.0 69.8 16.0

Radial Twist
Station [theta]
r mm ([degrees]) Airfoil

816 0.0 Cylinder

1150 0.0 Cylinder

2300 0.0 97.1% cylinder &

3450 18.52 58.2% cylinder &
 41.8% S818

4600 16.34 19.8% cylinder &
 80.2% S818

5750 14.22 S818

6900 11.31 75.5% S818
 &24.5% S816

8050 9.10 54.9% S818 &
 45.1% S816

9200 7.38 40.2% S818 &
 59.8% S816

10350 5.99 31.1% S818 &
 68.9% S816

11500 4.84 24.8% S818 &
 75.8% S816

12650 3.90 16.2% S818 &
 83.2% S816

13800 3.12 S816

14950 2.42 79.7% S816 &
 20.3% S817

16100 1.87 51.3% S816 &
 48.7% S817

17250 1.35 21.3% S816 &
 78.7% S817

18400 0.91 S817

19550 0.51 S817

20700 0.16 S817

21850 -0.12 S817

23000 -0.41 S817

25000 -0.41 S817
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Author:Rajendran, C.; Madhu, G.
Publication:International Journal of Dynamics of Fluids
Date:Dec 1, 2010
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