Horizontal axis wind turbine dynamics were studied. The following findings are summarized: (1) review of the MOSTAS computer programs for dynamic analysis of horizontal axis wind turbines; (2) review of various analysis methods for rotating systems with periodic coefficients; (3) review of structural dynamics analysis tools for large wind turbine; (4) experiments for yaw characteristics of a rotating rotor; (5) development of a finite element model for rotors; (6) development of simple models for aeroelastics; and (7) development of simple models for stability and response of wind turbines on flexible towers

Dugundji, J.

English

NASA Technical Reports Server

~ 
(\C\.S~- ~~-1(P8) 1 \0 
DOE/NASA/3303-4 
NASA CR-16811 0 
M.I.T ASRL TR 197-5 
lC»(Enfe~CO[Q)merr~ Ob' Msihodology ior Horizontal 
A}tos \flJD~(Q] TMU-buUilS fD)YU1lsmic Analysis 
Summary Report 
John Dugundji 
Massachusetts Institute of Technology 
LIBRARY COpy 
September 1982 ! I '\Y 1 2 1983 
\.ANGLEY RESEARCH CENTER 
LIBRARY. NASA 
HAMJ:TOtlL VIRGINIA 
Prepared for 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
Lewis Research Center 
Under Grant NSG-3303 
for 
U.S. DEPARTMENT OF ENERGY 
Conser"ation and Renewable Energy 
Division of Phoio"oltaic Energy Technology 
I Inlllil lIn IIII nlll IIIII IIIIlllnl IIII lUI 
NF01915 
https://ntrs.nasa.gov/search.jsp?R=19830014476 2020-03-21T04:32:43+00:00Z
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DOE/NASAl3303-4 
NASA CR-16811 0 
M.I.T. ASRL TR 197-5 
Development of Methodology for Horizontal 
Axis Wind Turbine Dynamic Analysis 
Summary Report 
John Dugundji 
Aeroelastic and Structures Research Laboratory 
Massachusetts Institute of Technology 
Cambridge, Massachusetts 02139 
September 1982 
Prepared for 
National Aeronautics and Space Administration 
Lewis Research Center 
Cleveland, Ohio 44135 
Under Grant NSG-3303 
for 
U.S. DEPARTMENT OF ENERGY 
Conservation and Renewable Energy 
Division of Photovoltaic Energy Technology 
Washington, D.C. 20545 
Under Interagency Agreement DE-AI01-76ET20320 
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-1-
INTRODUCTION 
The present report briefly summarizes the work done at the Massachusetts 
Institute of Technology under NASA Grant NSG-3303, "Development of a Methodology 
for Horizontal Axis Wind Turbine Dynamic Analysis". The work took place over 
a perlod of three years. The NASA Technical Officer was David C. Janetzke, and 
the principal investigator was Professor John Dugundji of the Department of 
Aeronautics and Astronautics at M.I.T. Two graduate and one undergraduate 
student particlpated in this work. 
The stated purpose of this grant was, 
(a) To develop state-of-the-art design tools for horizontal axis wind 
turbine dynamics. 
(b) To review existing codings and analytical techniques to establish 
the state-of-the-art. 
(c) To develop simple auxilliary design models for structural dynamic 
loads and stability behavior of horizontal axis wind turbines. 
To accomplish some of the above purposes and ends, the work on this grant 
covered the below listed areas. 
1. Review of the ~DSTAS Computer Program 
A study and review was made of the MOSTAS computer code for horizontal 
axis wind turbines. The techniques and methods used in its analyses were 
examined in some detail. Some impressions of its strengths and weaknesses, 
and some recommendations for its application, modification and further 
-2-
development were made. Additionally, some basic techniques used in general 
wind turbine stability and response analyses for systems with constant and 
periodic coefficients were reviewed and summarized concisely. A report on 
this work was written by Dugundji and Wendell, Ref. 1. 
2. Analysis Methods for Rotating Systems with Periodic Coefficients 
A study and review was made of various analysis methods for determining 
the dynamic stability and forced response of rotating wind turbine systems with 
periodic coefficients. Floquet methods, multiblade coordinates and harmonic 
balance methods, rotating coordinates, and perturbation methods were all 
reviewed and described in a concise succinct fashion. This work resulted from 
the previous study of the MOSTAS Computer Program, and appeared in the 
Appendices of Ref. 1. A preliminary version of this work was given at the 
2nd DOE/NASA Wind Turbine Dynamics Workshop, Cleveland, Ohio, Feb. 24-26, 1981 
by Dugundji and Wendell and was published in the conference proceedings, Ref. 2. 
A revised and ammended version by Dugundji and Wendell has been submitted for 
publication in the AlAA Journal, Ref. 3. 
3. State-of-the-Art Review of Structural Dynamics Analysis Tools for 
Large Wind Turbines 
The principal investigator of this grant participated along with three 
others, namely, R.W. Thresher, K.H. Hohenemser, and W.C. Walton, Jr., in a 
state-of-the-art review on structural dynamics analysis tools for design of 
large wind turbines. This was based on personal impressions and information 
gathered at the 2nd DOE/NASA Wind Turbine Dynamics Workshop, Cleveland, Ohio, 
Feb. 24-26, 1981. The above dynamics workshop was attended, and a memorandum 
-3-
was written reviewing the meeting and attempting to describe the current 
state-of-the-art in wind turbine aerodynamics, structural dynamics, acoustics, 
and electrical and control systems. The author's contribution to this review, 
along with those of the three other reviewers is given in Ref. 4. 
4. Yaw Characteristics of a Rotating Rotor 
Some experiments were made on the fixed yaw moments and on the free yaw 
characteristics of a 2 foot (.6l0 m) diameter rotor with varying amounts of 
precone, spinning in a wind tunnel. Yaw moments were measured for both upwind 
and downwind configurations. Also, the rotor was set free and the free yaw 
behavior was examined. It was found that at high rotation speeds, the rotors 
were stable in yaw and lined up with the wind, while at low rotation speeds, 
the rotors were unstable and would yaw out of the wind. This prevented the 
turblne from spinning up, unless it was locked into the wind. A report on 
these experiments has been written by Bundas and Dugundji, Ref. 5. These 
simple experiments could provide useful data for checking out theoretical 
calculations for yaw characteristics of wind turbine rotors. 
5. Finite Element Models for Rotors 
A finite element program has been set up for obtaining the static 
qUlescent position, bending moments, vibration moments, aeroelastic stability, 
and dynamic response of a rotating blade on a fixed hub. The analysis allowed 
for flatwise bending, chordwise bending, and torsion of a twisted blade, and 
included aerodynamic forces, pitch link stiffness, and root attachment details. 
ThlS finite element analysis parallels in some details the analyses given by 
Friedmann and Straub, Reb. 6, and Sivaneri and Chopra, Ref. 7. Additionally, 
-4-
the finite element analysis has been extended to allow for small vibrations of 
a blade which is bent into an initially curved shape (i.e., large, swept back 
propeller blades). This finite element work formed an M.S. thesis by Kamoulakos, 
and appears as Ref. 8. 
6. Simple Models for Aeroelastic Stability of Wind Turbines with Fixed Hub 
This work presents a systematic derivation of an equivalent hinge model 
to study the flap-lag-torsion aeroelastic stability of an isolated blade. 
Equations of motion, aerodynamic forces, and an ordering scheme for higher 
order terms were derived, then a parametric study of the resulting equations 
was made to identify regions of possible aeroelastic stability. Comparisons 
of the equivalent hinge model with a generalized coordinate, modal model showed 
generally good agreement. This work formed part of a Ph.D. thesis by Wendell, 
and appears as the first part of Ref. 9. 
7. Simple Models for Stability and Response of Wind Turbines on Flexible 
Towers 
This work included formulation of a general 11 degree of freedom rotor-
tower system for a two-bladed rotor, and includes blade flapwise bending for 
each blade, blade chordwise bending for each blade, teetering motion of the 
rotor, three translations of the hub point, and three rotations of the hub 
point (pitch, yaw, and torsional motion of the shaft). Aerodynamic loads were 
obtained using quasi-steady strip theory and included wind shear and crossflow. 
Additionally, a systematic harmonic balance solution method was developed for 
the resulting system of second order equations with periodic coefficients. 
-5-
The method applies not only to steady state response calculations, but to 
stability and transient response analysis as well. 
The solution techniques above were applied to a simple 3 degree of 
freedom rotor-tower model which includes nacelle yawing, nacelle pitching, and 
rotor teetering. Transient response time histories were calculated and compared 
to a similar model by Janetzke and Kaza, Ref. 10. Agreement between the two 
was good, especially considering how few harmonics were used. Finally, a 
stabillty study was presented which examined the effects of support stlffness, 
support damping, inflow angle, and preconing. This rotor-tower work forms 
part of a Ph.D. thesis by Wendell, and appears as the second part of Ref. 9. 
CONCLUDING REMARKS 
It is hoped that the preceding investigations have contributed to better 
general knowledge and understanding of horizontal axis wind turbine analysis 
and behavior, needed for preliminary design of such turblnes. The principal 
investlgator wishes to acknowledge the helpful guidance and advice of Professor 
R.H. Miller of M.I.T. on this grant. Also Professor M. Martinez-Sanchez 
participated in various discussions. 
-6-
REFERENCES 
1. Dugundj i, J. and Wende 11, J. H., "General Revi ew of the MOSTAS Computer 
Code for Wind Turblnes", M.I.T. Aeroelastic and Structures Research 
Laboratory Report ASRL TR 197-1, also, DOE/NASA/3303-1, NASA CR-165385, 
June 1981. 
2. Dugundji, J. and Wendell, J.H., "Review of Analysis Methods for Rotating 
Systems with Periodic Coefficients", Proceedings of the 2nd DOE/NASA 
Wind Turbine Dynamics Workshop, Cleveland, OhlO, February 24-26, 1981, 
NASA CP-2185, 1981, pp. 165-172. 
3. Dugundji, J. and Wendell, J.H., "Review of Some Analysis Methods for 
Rotating Systems with Periodic Coefficients", paper submitted for 
publication in the AIAA Journal. 
4. Thresher, R.W., Dugundji, J., Hohenemser, K.H. and Walton, W.C., Jr .• 
"Structural Dynamics Analysis Tools for Design of Large Wind Turbines: 
State-of-the-Art Review", Report prepared for the Wind Energy Project 
Office, NASA Lewis Research Center, Cleveland, Ohio, September 1981. 
5. Bundas. D. and Dugundji, J., "Some Experiments on Yaw Stability of Wind 
Turbines with Various Coning Angles", M.I.T. Aeroelastic and Structures 
Research Laboratory Report ASRL TR 197-2, July 1981. 
6. Sivaneri, N.T. and Chopra, I., "Dynamic Stability of a Rotor Blade Using 
Finite Element Analysis", AlAA Journal, Vol. 20, No.5, May 1982 
7. Friedmann, P.P. and Straub, F., "Application of the Finite Element 
Method to RotarY-Wing Aeroelasticity", American Helicopter Society 
Journal, Vol. 25, No.1, January 1980, pp. 36-44. 
8. Kamoulakos, A., "Stability Analysis of Flexible Wind Turbine Blades 
Using Finite Element Method", M.I.T. Aeroelastic and Structures 
Laboratory Report ASRL TR 197-3, August 1982. Also, M.S. Thesls, M.I.T. 
Department of Aeronautics and Astronautics, August 1982. 
9. Wendell, J.H., "S1mplified Aeroelastic Modeling of Horizontal Axis Wind 
Turbines", M.I.T. Aeroelastic and Structures Research Laboratory Report 
ASRL TR 197-4, September 1982. Also, Ph.D. Thesls, M.I.T. Department of 
Aeronautics and Astronautics, September 1982. 
10. Janetzke, D. and Kaza, K.R.V., "Whirl Flutter Analysis of a Horizontal 
Axis Wind Turblne with a Two-Bladed Rotor", Proceedings of the 2nd 
DOE/NASA Wind Turbine Dynamics Workshop. Cleveland, OhlO, February 24-26, 
1981, NASA CP-2185, 1981, pp. 201-210. 
1 Report No I 2 Government AccesSIon No 3 RecIpient ~ Catalog No 
NASA CR-168110 
4 Title .nd Subtitle 5 Report Date 
Development of Methodology for Horizontal Axis Wind Turbine Dynamic September 1982 
Analysis 6 Performing Organization Code 
Summary Report 776-33-41 
7 Author(s) 8 Performing Organization Report No 
John Dugundji M. I. T. ARSL TR197-5 
10 Work Unit No 
9 "-rfOfmlng Orglnlutoon N.me .nd Address 
Massachusetts Institute of Technology 11 Contract or Grant No 
Cambridge, Massachusetts 02139 NSG-3303 
13 Type of Report and Perood Covered 
12 Sponsoring Agency Nlme and Addr~~ Contractor Report 
U. S. Department of Energy 
14 Sponsorong Agency eode Report No. Division of Photovoltaic Energy Technology 
WllBhlngton, D. C. 20545 DOE/NASA/3303-4 
15 Supplementary Notes 
Finul report. Prepared under Interagency Agreement DE-AIOl-76ET20320. Project Manager, David 
Jnnetzke, Energy Technology DiviSion, NASA Lewis Research Center, Cleveland, Ohio 44135. 
16 AbW.cl 
This report briefly summarizes the work done at the Massachusetts Institute of Technology under NASA Grant 
NSG-3303. The 3-year effort included: 
(1 ) Review of the MOSTAS computer programs for dynamic analysis of horizontal axis wind turbines 
(2) Review of various analysis methods for rotating systems with periodic coe~ficients 
(3) Review of structural dynamics analysis tools for large wind turbine 
(4 ) Experiments for yaw characteristics of a rotating rotor 
(5) Development of a finite element model for ro tors 
(6) Development of simple models for aeroelastlc 
(7) Development of simple models for stablllty and response of wind turbines on flexible towers 
17 K.y Words (SuQgeStotd by AuthOfhl) 18 Dostrobutlon Statement 
Wind turbine Unclassified - unllmited 
Dynamic analysis ST AR Category 44 
Rotor dynamics DOE Category UC-60 
111 s.curlly CI.ni! (of thOl r.port) 20 s.curoty CllSslf (of thIS page) 21 No of P.ge~ 22 Price-
Unclassified Unclassified 6 AOl 
• For sale by the National Technical Information Service Springfield Virginia 22161 


Development of methodology for horizontal axis wind turbine dynamic analysis

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