c I

’ A Comparison of Finite Element - Predictions and Experimental Data for the Forced Response of the DOE 100 kW Vertical Axis Wind Turbine

Donald W. Lobitz, William N. Sullivan

Prepared by Sandia National Laboratories Albuquerque, New Mexico 87 185 and Livermore, California 94550 for the United States Department of Energy under Contract DE-AC04-76DP00789

i

Issued hy Sandia National Laboratories, operated for the United States Department of Energy hy Sandia Corporation. NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Govern- ment nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, o r their employees, makes any warranty, ex- press or implied, or assumes any iegal liability o r responsibility for the accuracy, completeness, o r usefulness of any information, apparatus, prod- uct, or process disclosed, o r represents that its use would not infringe privately owned rights. Reterence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States (;overnment, any agency thereof or any of their contractors or suhcontractors, The views and opinions expressed here- in do not necessarily state o r reflect those of the United States Government, any agency thereof or any of their contractors o r suhcontractors.

Printed in the United States of America Available from National Technical Information Service U S . Department of Commerce 5285 Port Royal Road Springfield, VA 22161

NTIS price codes Printed copy: A02 Microfiche copy: A01

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.

TABLE OF CONTENTS

PAGE .

Abstrac t . . . . . . . . . . . . . . . . . . . . . . . 5

1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . 5

2 . Data A c q u i s i t i o n and Process ing . . . . . . . . . . . 6

3 . Ana lys is Method and F i n i t e Element Model . . . . . . . 7

4 . Resu l t s . . . . . . . . . . . . . . . . . . . . . . . 9

4.1 Rotor Natura l Frequencies . . . . . . . . . . . 9

4.2 C e n t r i f u g a l and G r a v i t y Load Response . . . . . 10

4.3 RMS V i b r a t o r y S t ress Response . . . . . . . . . 10

5 . Concluding Remarks . . . . . . . . . . . . . . . . . . 14

Acknowl edgements . . . . . . . . . . . . . . . . . . . 14

References . . . . . . . . . . . . . . . . . . . . . . 15

3 - 4

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A COMPARISON OF FINITE ELEMENT PREDICTIONS AND EXPERIMENTAL DATA FOR THE FORCED RESPONSE OF THE DOE lOOkW VERTICAL A X I S WIND TURBINE*

D. W. L o b i t z W . N. S u l l i v a n

Sandia Na t iona l Labora to r ies Albuquerque, New Mexico 87185

ABSTRACT

A s p e c i a l i z e d f i n i t e element c a p a b i l i t y has been developed t o p r e d i c t dynamic s t r u c t u r a l response o f t h e v e r t i c a l a x i s wind t u r b i n e (VAWT). cerned w i t h e v a l u a t i n g t h i s f i n i t e element a n a l y s i s techn ique. To achieve t h i s , several t ypes o f exper imenta l da ta taken from t h e DOE lOOkW r o t o r a re compared w i t h p r e d i c t i o n s . These da ta i n c l u d e parked r o t o r n a t u r a l f requenc ies , very low wind c e n t r i f u g a l and g r a v i t a t i o n q l 1 oad response , and v i b r a t o r y response f rom wind l oads cove r ing t h e r o t o r ope ra t i ona l spectrum. Genera l l y , t h e agreement between theo ry and exper iment i s very s a t i s f a c t o r y . I t i s concluded t h a t t h e a n a l y s i s package i s s u i t a b l e f o r eng inee r ing des ign. Shor t - comings observed i n model ing accuracy are b e l i e v e d t o be due p r i m a r i l y t o inadequacies i n b lade aerodynamic l q a d c a l c u l a t i o n s .

Th is r e p o r t i s con-

1. INTRODUCTION

A p a r t o f t h e c o n t i n u i n g DOE-sponsored research program on t h e v e r t i c a l a x i s wind t u r b i n e (VAWT) has been concerned w i t h t h e development o f r o t o r s t r u c t u r a l model ing techniques. A v a r i e t y o f f i n i t e element based t o o l s which have evo lved f rom t h e DOE e f f o r t and o t h e r s have been r e p o r t e d i n t h e l i t e r a t u r e . These t o o l s a re in tended t o analyse severa l s t r u c t u r a l des ign issues, such as t h e de te rm ina t ion o f r o t o r modes and f requenc ies E l l , i d e n t i f i c a t i o n o f aero- e l a s t i c i n s t a b i l i t i e s [2,31, and p r e d i c t i o n o f r o t o r response amp1 i t u d e s due t o aero- dynamica l l y a p p l i e d l oads [41. Regarding t h e f i r s t two issues , r e l a t i v e l y d e t a i l e d e f f o r t s a t exper imenta l c o n f i r m a t i o n

have been r e p o r t e d [1,21. The t h i r d i ssue , response ampl i tudes f o r wind l oad ing , i s cons ide rab ly more complex s ince i t i n v o l v e s bo th s t r u c t u r a l dynamic model ing and aerodynamic l o a d determi n a t i o n schemes. Because o f t h i s comp lex i t y and t h e l i m i t e d a v a i l a b i l i t y o f comprehensive s t r u c t u r a l data on o p e r a t i n g r o t o r s , t h e r e have been o n l y q u a l i t a t i v e a t tempts r e p o r t e d [41 t o compare ac tua l VAWT response data w i t h p r e d i c t i o n s . T h i s r e p o r t compares a p a r t i c u l a r r o t o r response a n a l y s i s technique r e f e r r e d t o as FFEVD C4l w i t h exper imenta l s t r a i n gage da ta c o l l e c t e d from t h e DOE lOOkW r o t o r [51. FFEVD i s a NASTRAN based f i n i t e element package which i s s t i l l i n a developmental stage. The v e r s i o n o f FFEVD eva lua ted here i n c l u d e s advanced steady s t a t e ( cons tan t wind speed) s t reamtube- type aerodynamic models and p r e v i o u s l y i d e n t i f i e d impor tan t r o t a t i n g system e f f e c t s E81. Not i n c l u d e d i n t h i s i n v e s t i g a t i o n a r e damping e f f e c t s ( s t r u c t u r a l and aerodynamic) and unsteady l oads due t o atmospheric tu rbu lence C9,lOI. These e f f e c t s may be i m p o r t a n t i n some a p p l i c a t i o n s , b u t t h e i r i n c l u s i o n i n FFEVD r e q u i r e s a d d i t i o n a l t h e o r e t i c a l work which i s c u r r e n t l y be ing developed.

Comparisons w i t h t h e exper imenta l data a re made f o r two 100 KW r o t o r c o n f i g u r a t i o n s . The t e s t e d c o n f i g u r a t i o n s correspond t o two guy cab le suppor t systems used which d i f f e r i n a x i a l cab le s t i f f n e s s by a f a c t o r o f t h ree . T h i s change was e f f e c t e d t o reduce r o t o r s t resses by s h i f t i n g a p a r t i c u l a r r o t o r mode f requency f a r t h e r f rom a known e x c i t a t i o n f requency [ill.

Two aerodynamic models a re used i n FFEVD t o e s t a b l i s h s e n s i t i v i t y t o 1 oad model s . These model s were CARDAA, a doubl e-mu1 t i p 1 e

5

streamtube model w i t h dynamic s t a l l and v a r i a b l e Reynolds number e f f e c t s C71, and FORCE, a s imp le r s i n g l e streamtube dev ice [6,121.

The lOOkW r o t o r was ins t rumented w i t h s t r a i n gages t o exper imen ta l l y eva lua te t h e s t r u c t u r a l i n t e g r i t y o f t h e r o t o r . Because o f s t r e s s concen t ra t i on e f f e c t s , t h e gages as p laced a re n o t op t ima l f o r p r o v i d i n g c o n f i r m a t i o n da ta f o r f i n i t e element models. Nonetheless, t h e i n s t r u m e n t a t i o n i s s u f f i c i e n t l y comprehensive t o p r o v i d e a useable da ta base. The s t r a i n gage da ta a re processed on-s i t e by min icomputer t o a v a r i e t y o f r e d u c t i o n formats. The major fo rmat used here i s t h e RMS v i b r a t o r y s t r a i n l e v e l expressed as a f u n c t i o n o f t h e wind speed. T h i s q u a n t i t y i s r e l a t i v e l y easy t o measure, i s p r e d i c t a b l e by t h e analyses, and i s i t s e l f an impor tan t f a c t o r f o r f a t i g u e l i f e e s t i m a t i o n C131. Other measures o f r o t o r response, such as f requency spec t ra and mean s t r e s s l e v e l s , a re a l s o used i n t h i s r e p o r t .

The f o l l o w i n g sec t i ons i n c l u d e a d e s c r i p t i o n o f t h e exper imenta l setup, d i scuss ion o f t h e FFEVD package and t h e r o t o r f i n i t e element model , p r e s e n t a t i o n o f se lec ted r e s u l t s , and concl ud ing remarks.

2. DATA ACQUISITION AND PROCESSING

There a re t h r e e n e a r l y i d e n t i c a l u n i t s o f t h e DOE lOOkW VAWT system i n ope ra t i on a t Rocky F l a t s , Colo. , Bush1 and, Tx. , and Mar tha ' s Vineyard, Mass. A l l t h e da ta r e p o r t e d here came f rom t h e Bushland r o t o r s ince i t i s t h e most comprehensively inst rumented.

S t r u c t u r a l i n s t r u m e n t a t i o n r e f e r r e d t o i n t h i s study c o n s i s t s o f 18 s t r a i n gages l o c a t e d as shown i n F i g u r e la,b. Blade gages a re concent ra ted a t t h e f o u r b lade l tower connect ion reg ions ( F i g . l b ) . The b lade/ tower connect ion i s e f f e c t e d w i t h a "s t rongback ' which i s an ex t ruded aluminum s e c t i o n welded t o t h e b lade t o p rov ide a f l a t su r face f o r bo1 t i n g t h e b lade t o t h e tower and s t r u t a t tachment p o i n t s . Gages t o measure tower bending s t r a i n s i n and o u t o f t he r o t o r p lane a re l o c a t e d j u s t below t h e m id - ro to r f l ange. Exper ience w i t h o t h e r VAWT r o t o r s and t h e des ign a n a l y s i s o f t h e lOOkW r o t o r E141 i n d i c a t e d t h a t these l o c a t i o n s exper ience t h e l a r g e s t s t r u c t u r a l loads .

A l l t h e gages a re s e t up f o r d i r e c t s t r a i n measurements and do n o t d i r e c t l y measure o v e r a l l s e c t i o n loads . T h i s i s because t h e system was designed t o assess component

- E L S 0 0 '

Lower Blade Root (4 Chan./Blade

B1 ade)

1

F i g u r e l a . Overa l l placement o f s t r a i n gage i n s t r u m e n t a t i o n on the DOE lOOkW r o t o r .

STRONGBACK

/ / LEADING E D G E LEADING W E L D

LING D

\ TRAILING EDGE

F i g u r e l b . Blade r o o t gage d e t a i l . A l l r o o t gages measure s t r a i n p a r a l l e l t o t h e l o n g dimension o f t h e blade.

i n t e g r i t y which i s determined by s t r a i n . For f i n i t e element comparisons w i t h data, o v e r a l l s e c t i o n 1 oads a re more d e s i r a b l e . U n f o r t u n a t e l y , l o a d de te rm ina t ion f rom d i r e c t s t r a i n read ings i s compromi sed somewhat by s t r e s s c o n c e n t r a t i o n f a c t o r u n c e r t a i n t i e s . f o r t h e l e a d i n g and t r a i l i n g weld gages which a re c l e a r l y i n t h e v i c i n i t y o f a s t r e s s r i s e r . Labora to ry measurements w i t h t e s t sec t i ons i n d i c a t e t h a t t h e s t r e s s c o n c e n t r a t i o n a t t h e weld gages ranges f rom 1.1 t o 1.5 f o r p u r e l y f l a t w i s e l oad ing . observed v a r i ab i 1 i ty i n s t r e s s c o n c e n t r a t i o n f a c t o r s i s e v i d e n t l y due t o h i g h s t r a i n g r a d i e n t s i n t h e gage v i c i n i t y . T h i s makes s t r a i n read ings very s e n s i t i v e t o gage l o c a t i o n and we ld smoothness. To a t 1 eas t approx imate ly account f o r t h e observed s t r e s s concen t ra t i ons , t h e a n a l y t i c a l

T h i s problem i s most acute

The

6

r e s u l t s f o r t h e weld ages are i nc reas a f a c t o r o f 1.3. Th is c o r r e c t i o n i s no f o r t h e o t h e r r o t o r gages.

j by used

Analog ou tpu ts from t h e s t r a i n gage b r idges a re d i g i t i z e d t o a t e n b i t b i n a r y word and s e r i a l l y m u l t i p l e x e d w i t h a PCM (Pulsed Code Modulator ) system a t tached t o t h e r o t o r . The h i g h l e v e l PCM o u t p u t s igna l i s passed t o t h e da ta a n a l y s i s so f tware through a s i n g l e p a i r o f r o t o r sl i p r i n g s . The sampl i ng r a t e o f t h e system corresponds t o 100 readings/sec f o r each gage channel. A l l analog i n p u t s t o t h e PCM a re low-pass f i l t e r e d t o 25hz t o e l i m i n a t e d i g i t a l a l i a s i n g .

The PCM da ta a re analysed o n - s i t e w i t h a HP 1000 s e r i e s min icomputer . Ana lys i s so f tware c a p a b i l i t i e s r e l e v a n t t o t h i s r e p o r t i n c l u d e t h e f o l l o w i n g :

( 1 ) Q U I K da ta a n a l y s i s - - A l l PCM channels a re mon i to red f o r a f i v e second p e r i o d and t h e maximum, minimum and average va lues computed. These va lues a re d i sp layed on t h e console f o r a l l channels i n a f r e q u e n t l y updated tabu1 a r format .

( 2 ) S t r a i n B I N S data--The "Method o f B ins" 1151 r e d u c t i o n scheme i s used t o determine t h e RMS s t r a i n vs. wind speed f u n c t i o n f o r each s t r a i n gage channel. PCM da ta a re mon i to red f o r one r o t o r r e v o l u t i o n and t h e RMS and mean s t r a i n l e v e l s a re computed a1 ong w i t h t h e cor respond ing mean wind speed. The RMS l e v e i s d e f i n e d as t h e root-mean- squared d i f f e r e n c e between s t r a i n read ings over a r e v o l u and t h e mean s t r a i n f o r t h a t r e v o l u t i o n . His towarns o f s t r

ion

i n RMS l e v e l s vs. w i i d speed " b i n s " may be c rea ted f rom thousands o f r o t o r r e v o l u t i o n s . By combining data taken on days w i t h d i f f e r e n t wind c o n d i t i o n s , t h e RMS s t r a i n l e v e l s can be determined f o r a wide range o f wind speeds.

! 3 ) Amp1 i t u d e Spectra- -Fast F o u r i e r t rans fo rm techniques a re used t o compute s t r a i n amp1 i tude f requency spec t ra f rom s t o r e d t ime s e r i e s data. The ampl i tude spec t ra a r e d e f i n e d as t h e square r o o t o f t he p roduc t o f t w i c e t h e s p e c t r a l d e n s i t y and t h e bandwidth. I n t h i s r e p o r t , t h e t y p i c a l t ime s e r i e s r e c o r d l e n g t h i s 30 seconds. Th is y i e l d s a f requency r e s o l u t i o n o f

.03 hz w i t h a maximum f requency o f 50hz.

Because of DC d r i f t i n s t r a i n gage b r i d g e ou tpu ts , a process o f ze ro ing t h e gages i s r e q u i r e d i f abso lu te s t r a i n measurements a re t o be used. A s t a t e o f zero s t r a i n i s de f i ned as a parked r o t o r i n n e g l i g i b l e winds. T h i s d e f i n i t i o n a l l o w s r e l a t i v e l y f requen t ze ro ing o f t h e gage system. The ze ro ing process does, however, e l i m i n a t e g r a v i t a t i o n a l l oads f rom t h e measurements. Th is i s inconsequent ia l f o r v i b r a t o r y s t r a i n measurements, b u t care must be used i n i n t e r p r e t i n g mean s t r a i n l e v e l s .

3. ANALYSIS METHOD AND FINITE ELEMENT MODEL

The method o f a n a l y s i s i s based on t h e f i n i t e element techn ique i n o rde r t o p r o v i d e model i ng v e r s a t i 1 i t y . The devel opment e f f o r t s have focused on t h e d e r i v a t i o n s o f mass, damping and s t i f f n e s s mat r ices , and f o r c e vec to rs app rop r ia te f o r t h e VAWT. Due t o t h e q u a s i - l i n e a r na tu re o f t h e f i n a l VAWT equat ions o f mot ion, e x i s t i n g s o l u t i o n procedures f o r s t a t i c , e igenva lue and f requency response a n a l y s i s can be used.

The equat ions o f mot ion a re developed r e l a t i v e t o a coo rd ina te system which r o t a t e s w i t h t h e t u r b i n e a t i t s angu lar v e l o c i t y . Normal ly t h e use o f a r o t a t i n g frame r e s u l t s i n t h e i n t r o d u c t i o n o f t ime-dependent c o e f f i c i e n t s because t h e suppor t system ( i n t h i s case the guy cab les) does n o t r o t a t e w i t h t h e t u r b i n e . However, i f t h e mass o f t h e suppor t system r e l a t i v e t o the r o t a t i n g components can be neglected, and i t s s t i f f - ness i n t h e p lane pe rpend icu la r t o t h e a x i s o f r o t a t i o n approximated as i s o t r o p i c , t h e suppor t system can be modeled as though i t were r o t a t i n g w i t h t h e t u r b i n e . For VAWTs these a re reasonable approx imat ions, and consequent ly , t h e t o t a l system can be modeled i n the r o t a t i n g frame w i t h o u t t ime-dependent c o e f f i c i e n t s . R o t a t i n g coo rd ina te system e f f e c t s , such as C o r i o l i s and c e n t r i f u g a l f o rces , must s t i l l be i nc luded .

For smal l mot ions, u, r e l a t i v e t o t h e r o t a t - i n g frame, t h e f i n i t e element equat ions o f mot ion a re represented by

[ M I { G } + C C I { i } - [ S I { u ) + [ K I { u }

Here M and K are t h e mass and s t i f f n e s s ma t r i ces . The q u a n t i t i e s , C and S, which d e r i v e f rom r o t a t i n g coo rd ina te system e f f e c t s , a re t h e C o r i o l i s and s o f t e n i n g ma t r i ces r e s p e c t i v e l y . The s o f t e n i n g m a t r i x

7

accounts f o r changes i n t h e c e n t r i f u a

deformations. These l a s t two ma t r i ces are developed i n d e t a i l i n C11.

f o r c e t h a t r e s u l t f rom t h e s t r u c t u r a 9

On t h e r i g h t hand s i d e o f Equat ion ( l ) , t h e t h r e e terms rep resen t t h e c e n t r i f u g a l , g r a v i - t a t i o n a l and aerodynamic f o r c e s r e s p e c t i v e l y . The f i r s t two a r e steady and do n o t change as t h e t u r b i n e r o t a t e s . The aerodynamic fo rce , however, g e n e r a l l y c o n s i s t s o f steady and o s c i l l a t o r y components. Fo r a steady wind, t h e o s c i l l a t o r y components a r e p e r i o d i c w i t h a p e r i o d cor respond ing t o one r o t o r r e v o l u t i o n .

S o l u t i o n s t o Equat ion ( 1 ) would be r o u t i n e except t h a t a s i g n i f i c a n t n o n l i n e a r i t y a r i s e s due t o s t r e t c h i n g o f t h e b lade i n i t s l o n g dimension. T h i s s t r e t c h i n g causes K t o be a f u n c t i o n o f t h e de format ion C161. I n c l u s i o n o f t h i s n o n l i n e a r i t y i n Equat ion ( 1 ) r e s u l t s

commensurate w i t h t h e q u a s i - s t a t i c d i sp lace - ment f i e l d assoc ia ted w i t h t h e steady aerodynamic, c e n t r i f u g a l and g r a v i t a t i o n a l l oads on ly , n e g l e c t i n g t h e o s c i l l a t o r y components o f t h e aerodynamic loads . T h i s i s accomplished th rough i t e r a t i v e s o l u t i o n o f t h e f o l l o w i n g equat ion :

computed b Equat ion (1) i n t he f requency domain:

s o l v i n g t h e f o l l o w i n g v a r i a n t o f

CMI{G}+CCI{~}-CSI{U}+[K~I{U} = { G } . ( 3 )

The v i b r a t o r y aerodynamic fo rces , F;, f o r steady wind c o n d i t i o n s a re computed u s i n g one o f two aerodynamic l o a d models. more s o p h i s t i c a t e d o f t h e two, CARDAA, i s a double mu1 t i p l e streamtube model w i t h wind shear , dynamic s t a l l and v a r i ab1 e Reynol ds number e f f e c t s 171. The s imp le r one, FORCE, employs a s i n g l e streamtube model [121. I n e i t h e r case, t h e aerodynamic f o r c e s a re computed f o r a re fe rence b lade as i t t u r n s th rough one complete r e v o l u t i o n , t a k i n g ca re t o rep resen t t h e fo rces i n the r o t a t i n g coo rd ina te system. These f o r c e s a re then F o u r i e r decomposed numer i ca l l y i n terms o f "pe r rev ' ' f requency components which rep resen t i n t e g r a l mu1 t i p l e s o f t h e r o t o r angu lar r o t a t i o n a l frequency, 5 2 , as shown be l ow :

The

i n complex sol u t i o n - procedures. t h i s , a r e v i s e d s t i f f n e s s m a t r i x i s developed

To avo id

1 Anxs in (nQt ) + Bnxcos(nQt)

1 Anys in (nn t ) + Bnycos(nnt)

1 Anzs in (nn t ) + Bnzcos(nnt)

[ K ( u ) I { u } = CSI{U}+{Fc}+{Fg}+{F, } , ( 2 )

where t h e aerodynamic loads . A r e v i s e d s t i f f n e s s m a t r i x , K ob ta ined a f t e r i t e r a t i o n o f Equat ion I;) i s used i n a l l subsequent c a l c u l a t i o n s . Resu l t s f rom computat ions us ing Kr rep resen t deformat ions about a s t a t e p res t ressed by g r a v i t a t i o n a l , c e n t r i f u g a l , and steady aerodynamic loads .

denotes t h e steady component o f

I n cases where t h e r o t o r i s operated i n very low winds, s o l u t i o n s o f Equat ion ( 2 ) w i t h { & } = I O } can be compared w i t h exper imenta l data. T h i s i s done i n t h e n e x t sec t i on under t h e s u b t i t l e o f " C e n t r i f u g a l and G r a v i t y Load Response . I '

To o b t a i n t h e modal c h a r a c t e r i s t i c s o f t h e r o t o r w h i l e r o t a t i n g a t a s p e c i f i e d angu lar v e l o c i t y , t h e r i g h t hand s i d e o f Equat ion (1) i s s e t t o zero. The s t i f f n e s s m a t r i x , however, corresponds t o t h e p res t ressed s t a t e d iscussed above. E igenvalue problem i s Hermetian due t o t h e skew-symmetry o f t h e C o r i o l i s m a t r i x . Thus, i n general t h e mode shapes w i l l be complex and the n a t u r a l f requenc ies a re r e a l . Complete development and Val i d a t i o n o f t h i s procedure can be found i n [ll.

The r e s u l ti ng

The frequency response o f t h e r o t o r , d r i v e n by t h e o s c i l l a t o r y aerodynamic loads , i s

where t h e An's and Bn 's a re F o u r i e r s ine and cos ine c o e f f i c i e n t s , r e s p e c t i v e l y . The aerodynamic l o a d s f rom e i t h e r CARDAA o r FORCE can be adequate ly represented w i t h s i x F o u r i e r harmonics.. Loads on o t h e r b lades l o c a t e d a z i m u t h a l l y away f rom t h i s re fe rence b lade by an angle, $ , a r e g i ven by,

1 Anzsin(nQt+n$)+BnZcos(nat+$)

I n t h i s manner t h e v a r i o u s pe r rev e x c i t a - t i o n s a re i s o l a t e d and cor respond ing r o t o r responses a r e ob ta ined w i t h s tandard f i n i t e element f requency response s o l u t i o n proced- u res .

The frequency response r e s u l t s a re i n t h e form o f s i n e and cos ine response c o e f f i c i e n t s , Cn and Dn r e s p e c t i v e l y , f o r each pe r r e v e x c i t a t i o n . v i b r a t o r y t e s t da ta w i t h p r e d i c t i o n s , t h e RMS o f t h e computed response i s requ i red .

To compare RMS

The RMS i s g iven i n terms o f t h e response c o e f f i c i e n t s by

RbIS = [I (Cn 2 + Dn)/2 2 11'2

a

Because o f i t s ex tens i ve l i b r a r y o f solu- t i o n procedures, t h e MacNeal-Schwendler ve rs ion o f NASTRAN 1171 was se lec ted f o r t h e implementat ion o f t h e above a n a l y s i s techniques. Procedures e x i s t i n NASTRAN f o r t h e i t e r a t i v e s o l u t i o n o f Equat ion ( 2 ) , complex e igenva lue a n a l y s i s and complex f requency response computation. A minor amount o f DMAP programming ( a NASTRAN f e a t u r e which a l l ows t h e user t o mod i fy t h e code w i t h o u t d e a l i n g w i t h t h e source code) i s r e q u i r e d t o t r a n s f e r t h e p res t ressed s t i f f n e s s m a t r i x t o subsequent s o l u t i o n procedures.

For t h e f requency response computations , two spec ia l p re-process ing tasks a re per- formed i n FFEVD. F i r s t , as the re i s no p r o v i s i o n i n NASTRAN f o r genera t i ng t h e Cor i ol i s and s o f t e n i n g ma t r i ces they are developed i n FFEVD and supp l i ed t o NASTRAN through i t s m a t r i x i n p u t op t i on . Secondly, aerodynamic l o a d s f o r t h e b lades a re c a l - cu la ted , F o u r i e r decomposed, and p u t i n a form acceptab le t o NASTRAN. these opera t i ons FFEVD reads t h e NASTRAN BULK DATA deck, e x t r a c t s necessary in fo rma- t i o n , per forms t h e r e q u i r e d computations, and adds t h e approp r ia te NASTRAN i n p u t cards t o t h e BULK DATA deck. I n t h i s manner , t h e speci a1 cons i d e r a t i ons f o r t h e f requency response a n a l y s i s o f VAWTs a re t ransparen t t o t h e user and the NASTRAN u t i l i z a t i o n appears r e l a t i v e l y r o u t i n e .

I n bo th o f

A spec ia l p o s t - p l o t t e r has a l s o been developed t o h e l p t h e user i n t e r p r e t t h e r e l a t i v e l y l a r g e amount o f NASTRAN o u t p u t data.

Due t o t h e s imp le s t r u c t u r a l na tu re o f t h e VAWT, f i n i t e element models c o n s i s t o f beam elements (CBEAM elements i n NASTRAN) , concent ra ted masses and 1 i n e a r sp r ings . The NASTRAN model o f t h e DOE lOOkW VAWT i s shown i n F i g u r e 2.

Each b lade i s represented by 42 CBEAM elements, t h e tower i s modeled by 12, and t h e b lade s t r u t s by two each. guy cab les a r e accounted f o r by two or thogonal h o r i z o n t a l sp r ings a t tached a t t h e t o p o f t h e r o t o r , and a v e r t i c a l l o a d a c t i n g down th rough t h e tower. The t o r - s iona l s t i f f n e s s o f t h e d r i v e t r a i n i s represented by a t o r s i o n a l sp r ing , and concent ra ted masses a re added a t b lade- to -b lade j o i n t s and t h e mid-tower f l a n g e connect ion. i s cons idered t o be i n f i n i t e l y s t i f f and i s modeled by p r o h i b i t i n g t rans1 a t i o n a l mot ion a t t h e t h r u s t bear ing .

The

The base o f t h e r o t o r

N e i t h e r s t r u c t u r a l nor aerodynamic damping a re i n c l u d e d i n t h i s model.

7

F ig . 2. NASTRAN f i n i t e element model o f t h e DOE lOOkW VAWT.

4. RESULTS

4.1 Rotor Na tu ra l Frequencies

A complete modal t e s t was n o t conducted on t h e lOOkW r o t o r . P a r t i a l measurements o f t h e parked r o t o r modes were completed t o a i d i n v e r i f y i n g t h e NASTRAN f i n i t e element model. Modal f requency da ta were ob ta ined by m o n i t o r i n g f r e e v i b r a t i o n response f o l l o w i n g hand e x c i t a t i o n o f t h e r o t o r u s i n g personnel suspended f rom a crane. By pushing t h e r o t o r by hand i n t h e a p p r o p r i a t e d i r e c t i o n and f requency a t a s o f t p o i n t o f t h e r o t o r , i t i s p o s s i b l e f o r an i n d i v i d u a l t o s e l e c t i v e l y e x c i t e t h e l o w e s t f requency modes t o amp1 i tudes measurable by t h e s t r a i n gages. T h i s techn ique was used t o determine t h e f requenc ies o f t h e f i r s t f i v e r o t o r modes.

Table 1 summarizes a comparison between t h e measured f ree v i b r a t i o n modes and those p r e d i c t e d by t h e NASTRAN f i n i t e element model. The agreement between measurements and NASTRAN i s e x c e l l e n t . T h i s con f i rms t h a t t h e f i n i t e element model i s a good dynamic r e p r e s e n t a t i o n o f t h e phys i ca l s t r u c t u r e .

9

Table 1. Parked Rotor Na tu ra l Frequencies

Mode if and Freq. (hz ) F req .( hz) D e s c r i p t i o n Meas. Theory

1. f i r s t f l a t w i s e , 1.7 1.6-1.6* b l a d e "drooping"

r o t o r ou t -o f -p lane

bending i n-p l ane

o u t - o f - p l ane

b lade

2. f i r s t " b u t t e r f l y " 2.2 2.1

3. f i r s t tower 2.7 2.7

4. 2nd " b u t t e r f l y " 3.4 3.5

5 . 2nd f l a t w i s e 3.6 3.6-3. *

* Double modes corresponding t o symmetric and a n t i symmetric r o t o r responses.

4.2 C e n t r i f uga l and G r a v i t y Load Response

P u r e l y c e n t r i f uga l and g r a v i t a t i o n a l l o a d s may be a p p l i e d t o t h e r o t o r s imp ly by mo to r ing t h e t u r b i n e i n n e g l i g i b l e winds. T h i s l o a d system i s w e l l d e f i n e d and t h e r e s u l t s a r e he1 p f u l i n l o c a t i n g e r r o r s i n t h e f i n i t e element model o r t h e i n s t r u m e n t a t i o n system.

F i n i t e element a n a l y s i s o f t h i s t e s t i s a s t a t i c s problem s i n c e a l l t h e a p p l i e d l o a d s a r e steady. The a n a l y s i s i s e f f e c t e d as desc r ibed i n Sec t i on 3. I n i t i a l l y , t h e response due t o b o t h c e n t r i f u g a l and g r a v i t y l oads i s c a l c u l a t e d . Response f rom another c a l c u l a t i o n f o r g r a v i t y l o a d i n g o n l y i s then sub t rac ted f rom t h e c e n t r i f u g a l and g r a v i t a t i o n a l l o a d r e s u l t s . T h i s i s done s ince t h e measured da ta has g r a v i t y l o a d i n g e f f e c t i v e l y s u b t r a c t e d due t o t h e gage z e r o i n g process. T h i s process i s n o t q u i t e e q u i v a l e n t t o a n a l y z i n g o r t e s t i n g w i t h o n l y c e n t r i f u g a l loads. T h i s i s because t h e r o t o r s t i f f n e s s g e n e r a l l y changes f o r t h e d i f f e r e n t l o a d cases and thus l i n e a r l o a d superposi ti on i s n o t appl i cab1 e.

Table 2 shows p r e d i c t e d and measured s t r e s s l e v e l s f o r a l l t h e b lade gage l o c a t i o n s o f F i g u r e 1. The agreement i s f a i r f o r t h e l e a d i n g and t r a i l i n g edge gages and poor f o r t h e weld gages. It i s b e l i e v e d t h a t t h e l a c k o f agreement f o r t h i s w e l l d e f i n e d t e s t i s p r i m a r i l y due t o complex s t r e s s c o n c e n t r a t i o n e f f e c t s near t h e b lade r o o t . T h i s t e s t i n v o l v e s b o t h b lade a x i a l and f l a t w i se bending 1 oads. T h i s p r e c l udes ass ign ing a s i n g l e s t r e s s c o n c e n t r a t i o n

~

Tab le 2. C e n t r i f u g a l and G r a v i t a t i o n a l Blade Stresses, 48.1 RPM Ro to r Speed

( F i g . l b ) Edge We1 d We1 d Edge

Theory, 1236 -1166 -84 1236 upper r o o t

i4eas. , 1375 210 423 n.a. upper r o o t

Theory, 1238 -6445 -4117 1238 lower r o o t

Meas. , 1756 -4057 -3857 1507 lower r o o t

Gage : Leadi ng Leadi ng T r a i 1 i ng T r a i 1 i ng

Notes: u n i t s f o r s t r e s s a r e p s i ; p o s i t i v e s t resses a r e t e n s i l e ; a l l r e s u l t s shown a r e 1 ess g r a v i t y - o n l y s t resses (see t e x t ) .

f a c t o r t o t h e a n a l y s i s . da ta were ob ta ined on f l a t w i se bending s t r e s s c o n c e n t r a t i o n s (see Data A c q u i s i t i o n sec t i on , above) , none a r e a v a i l a b l e f o r a x i a l l o a d i n g . S ince t h e a x i a l l o a d p a t h f rom t h e b lade t o t h e tower passes e x c l u s i v e l y th rough t h e strongback we1 ds , i t i s l i k e l y t h e r e a r e h i g h a x i a l l o a d s t r e s s c o n c e n t r a t i o n s near t h e weld t e r m i n a t i o n s . The f a c t t h a t t h e weld s t r a i n gage measurements i n Table 2 a r e more t e n s i l e than p r e d i c t i o n s i s c o n s i s t e n t w i t h t h i s hypothes is .

A l though l i m i t e d

A1 though t h e s t r e s s c o n c e n t r a t i o n i s s u e p reven ts t h i s t e s t f rom s o l i d l y v e r i f y i n g t h e f i n i t e element s t a t i c a n a l y s i s , i t i s apparent t h a t t h e model reasonably p r e d i c t s r o t o r response t o s t a t i c loads.

4.3 RMS V i b r a t o r y S t r e s s Response

RMS v i b r a t o r y s t r e s s da ta a re a v a i l a b l e f o r t h e DOE lOOkW VAWT i n two s t r u c t u r a l c o n f i g u r a t i o n s . The d i f f e r e n c e c o n s i s t s o f a t h r e e t o one r a t i o i n t h e guy c a b l e s t i f f n e s s , and h e r e a f t e r t h e two designs w i l l be i d e n t i f i e d as e i t h e r t h e s o f t o r s t i f f c a b l e c o n f i g u r a t i o n . As t h e s o f t cab le data was taken d u r i n g t h e h e a t o f t h e summer i n Bushland, Tx., t h e aerodynamic l oads f o r t h e f requency response analyses were computed w i t h an a i r d e n s i t y o f .066 l b m / f t 3 . On t h e o t h e r hand, t h e s t i f f c a b l e d a t a was taken d u r i n g t h e w i n t e r w i t h a corresponding d e n s i t y o f .072 1 bm/f t3 . I n a l l cases where t h e CARDAA aerodynamic model was used, t h e wind shear f a c t o r was s e t a t .17, a reasonable va lue f o r t h e s i t e . For t h e weld gage l o c a t i o n s , t h e p r e d i c t i o n s

10

were m u l t i p l i e d by a f a c t o r o f 1.3 t o account f o r t h e s t r e s s concen t ra t i on which e x i s t s i n t h e hardware b u t n o t i n t h e NASTRAN model. T h i s va lue was ob ta ined f rom l a b o r a t o r y measurements done on t h e s e c t i o n i n ques t ion .

Both aerodynamic model s were used i n t h e p r e d i c t i o n s , and, i n genera l , t h e FORCE model s u b s t a n t i a l l y underp red ic t s t h e data, whereas t h e CARDAA model demonstrates much b e t t e r agreement. Consequently, s ince CARDAA i s cons idered t o be t h e most accura te o f t h e two models, t h e m a j o r i t y o f t h e p r e d i c t i o n s a re made u s i n g it, and o n l y a few w i t h FORCE i n o rde r t o demonstrate t h e d i f f e r e n c e s .

The l e v e l o f agreement between da ta and p r e d i c t i o n s was s i m i l a r f o r t h e two t u r b i n e c o n f i g u r a t i o n s . Thus, t o a v o i d r e p e t i t i o n , o n l y a few comparisons f o r t h e s o f t cab le c o n f i g u r a t i o n a re i n c l uded here.

2000

- VI - a 1600

VI VI a

4.8 v)

? 1200 0 c) m

9

>

- - g 800 a

400

F i q . 3.

A FFEVO R e s u l t s , O u t - o f - P l a n e A 0 FFEVO R e s u l t s . I n - P l a n e

x O u t - o f - P l a n e D a t a

+ I n - P l a n e D a t a

0 "

x x x +

x + + A x x + + '

x 9 x +

+ +

+ x

x + .:+ 3 x +

* + f +

10 20 30 4 0

U i n d S p e e d f n p h l

RMS v i b r a t o r y r o t o r tower s t resses f o r t h e s t i f f cab le c o n f i g u r a t i o n , CARDAA aerodynamic model.

F i g u r e 3 shows RMS v i b r a t o r y s t r e s s comparisons between p r e d i c t i o n s and da ta f o r t h e r o t o r tower i n t h e s t i f f cab le c o n f i g u r a t i o n , u s i n g t h e CARDAA aerodynamic model. The theo ry tends t o underp red ic t i n low winds and o v e r p r e d i c t i n h i g h ones. The obse rva t i on t h a t t h e ou t -o f -p l ane response i s g r e a t e r than t h e i n -p lane i s c o r r e c t l y p r e d i c t e d .

C

Comparisons f o r t h e b lade edgewise response a re shown i n F i g u r e 4 . I n t h i s f i g u r e and subsequent ones, t h e x ' s rep resen t da ta f o r one o f t h e b lades, and t h e + I s , t h e o the r .

1200

1000

- 'Z A00 a - VI VI

w c)

YI 600 3 c)

L A .- > 400 YI

E r

200

( a )

120c

1000

- - VI a - VI Boo 0)

c) v)

,, L 2 600 I 9

5

YI

.-

r a 400

200

( b )

F ig . 4 .

FFLVD P i e d i c t f o n s

+ B l a d e 1 U a t a

x b l a d e 2 U a t a

+ +

0 + + +

+

+ x

t x

* +

+ +OX

t t

10 2 0 30 4 0

U l n d S p e e d l n p h l

0 FFEVD P r e d i c t i o n s

+ B l a d e 1 D a t a

x B l a d e 2 D a t a

X 0 +

x s O X +

x + X I

x + f + r

1 0 2 0 30 4 0

U l n d s p e e d ( m p h )

RMS v i b r a t o r y b l ade edaewi se s t resses f o r t h e s t i f ? cab le c o n f i g u r a t i o n , CARDAA aerodynamic model : ( a ) l ower t r a i l i n g edge, ( b ) upper l e a d i n g edge.

11

These two se ts p rov ide a measure o f t h e r e p e a t a b i l i t y o f t h e data. As w i t h t h e tower comparisons, t h e theo ry o v e r p r e d i c t s response i n h i g h winds. However, a t low w ind speeds t h e agreement i s q u i t e good.

: 1000.

v, u

1, L 0 ” z 750- 9

> VI

r E

-

5 0 0 -

The b lade weld gage comparisons a re shown i n F i g u r e 5 . t h e p r e d i c t i o n s and t h e da ta i s very s a t i s f a c t o r y . However, r e f e r r i n g t o p a r t s a and b o f F i g u r e 5, t h e i ncons is tency i n t h e corresponding da ta f rom each b lade produces some u n c e r t a i n t y i n assess ing t h e l e v e l o f agreement f o r t h i s case.

Genera l l y t h e agreement between

X B l a d e 2 D a t a

. +

0 FFEVO P r e d i c t i o n s . CI + B l a d e 1 D a t a VI

. I FFEVD P r e d i c t i o n s +

+ + + B l a d e 1 D a t a

x B l a d e 2 D a t a + + .+ x x

+ x x x +

+ + x

+ e x +

ZA VI

1200- .J VI

3

2 800-

+.3

>

x VI

LL

.-

400 -

+

X X

X +. + X

+ + +

x + + + .

X t + x +

x +. $ $ +

$

+ X X

* * x

f X

e + X

2 5 0 / x ; ; x x x : , + , ,

x + + + +

10 2 0 30 40

( a ) W i n d s p e e d [nph)

I 0 FFEVO P r e d i c t i o n s

+ B l a d e 1 D a t a

X B l a d e 2 D a t a CI

X

IO 20 30 4 0

( b ) W i n d s p e e d ( m p h )

RMS v i b r a t o r y s t r e s s comparisons f o r t h e s o f t cab le c o n f i g u r a t i o n a re shown i n F igu res 6 , 7 and 8. Using t h e CARDAA aerodynamic model , t h e agreement between da ta and p r e d i c t i o n s i s s i m i l a r t o t h a t ob ta ined f o r t h e s t i f f cab le c o n f i g u r a t i o n . curves severa l p o i n t s a re i n c l u d e d which correspond t o p r e d i c t i o n s us ing t h e FORCE aerodynamic model. These p o i n t s tend t o seve re l y underpredi c t t he da ta i n 1 ow w i nds , w i t h b e t t e r agreement f o r t h e h ighe r wind speeds. I n genera l , however, t h e FORCE r e s u l t s a re i n f e r i o r t o and l e s s conserva t i ve than those made w i t h CARDAA.

I On these

f : I 2 1600 m VI Y L ” VI

* v1

DL L 800

1000

- VI s - VI

750 ” Y)

2,

0 c)

z 500 I)

> VI

LL

.-

r

2 5 0

. 0 FFEVO P r e d i c t i o n s

+ B l a d e 1 D a t a *

2 x B l a d e 2 D a t a 2 $

f;

*

1 0 20 3 0 4 0

W l n d s p e e d ( m p h )

?i

t * t

IO 2 0 30 4 0

W i n d s p e e d ( rnph)

F i g . 5. CARDAA aerodynamic model; ( a ) upper t r a i l i n g weld, ( b ) l ower t r a i l i n g weld, ( c ) upper l e a d i n g weld, ( d ) l ower l e a d i n g weld.

1 2

RMS v i b r a t o r y b lade f l a t w i s e s t resses f o r t h e s t i f f c a b l e c o n f i g u r a t i o n ,

i c r n r r q t l y p r e d i c t e d b y - t h e * . .a-. - -

4a and 71, e s p e c i a l l y when a 16% inc rease i s a p p l i e d t o t h e s o f t cab le data t o normal ize i t t o t h e w i n t e r a i r dens i t y . App ly ing t h i s same f a c t o r t o t h e f l a t w i s e s o f t cab le data, t h e f l a t w i se response has a1 so decreased, a l though l e s s d r a m a t i c a l l y (F igu res 5d and 8). A1 t e r n a t i v e l y , t h e t h e tower response has inc reased (F igu res 3 and 6 ) and t h e

. . . . . -- - . - . . . - I I1 ...vubl. Both t h e t e s t data and t h e a n a l y s i s p r e d i c t i o n s c o n f i r m t h a t t h e s t r e s s reduc t i ons sought by t h e i n s t a l l a t i o n of s t i f f cab les were achieved.

1000 1

Y I O " " 7 2, I

1

yl c

CAPDAA M o d e l

>

FORCE M o d e l

I 0 I

A F F E V D R e s u l t s , O u t - o f - P l a n e

0 F F E V D R e s u l t s , I n - P l a t e

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I s t resses f o r t h e s o f t cab le c o n f i g u r a t i o n , IO 20 30 40 l ower l e a d i n g weld.

W i n d s p e e d ( m p h )

F i g . 6. f o r t h e s o f t cab le c o n f i g u r a t i o n .

RMS v i b r a t o r y r o t o r tower s t resses

e 1000

For bo th cab le c o n f i g u r a t i o n s , t h e a n a l y t i c a l r e s u l t s f o r t h e tower and edgewi se b lade response general l y o v e r p r e d i c t t h e da ta f o r h i g h winds. a re several p o s s i b l e exp lana t ions f o r t h i s

There

0 f *e

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RMS v i b r a t o r y b lade edgewise F i gu 1 ead

- ~

1 ower t r a i 1 i ng edge. i r e 9 ( a ) . Ampl i tude spectrum f o r upper l i ng edge gage, 30mph winds.

0 9

- FFEUD P R E D I C T I O W S

Anplltuder a r e I n M l c r o r t r a l n

33

F i g u r e 9( b) . Amp1 i tude spectrum f o r upper l e a d i n g weld gage, 30mph winds.

disagreement. a n a l y s i s i s seen f rom exami n i ng amp1 i tude spec t ra o f gage response. Two such spec t ra a re shown i n F i g u r e 9 f o r t h e l e a d i n g edge and 1 ead i ng we1 d gages , r e s p e c t i v e l y . Note t h a t t h e theo ry p r e d i c t s response on ly a t t h e i n t e g r a l pe r r e v s o f t h e r o t o r speed as d iscussed i n Sec t i on 3. F i g u r e 9 t h a t t h e r o t o r exper iences a more broad-banded response. T h i s i s b e l i e v e d t o be due t o atmospheric tu rbu lence. because o f t u r b u l ence o r b a s i c i naccu rac ies i n t h e aerodynamic l o a d model , t h e 1 per rev response component i s cons ide rab ly ove rp red ic ted f o r t h e l e a d i n g edge gage. Another f a c t o r i s t h a t t h e method o f b i n s da ta a n a l y s i s techn ique tends t o underest imate t h e response near t h e h i g h wind end where t h e da ta a re r e l a t i v e l y sparse C151. The e f f e c t s o f b o t h s t r u c t u r a l and aerodynamic damping, n e i t h e r o f which have been i n c l u d e d i n t h e a n a l y s i s , may a l s o reduce t h e p r e d i c t i o n s .

One major d i f f i c u l t y w i t h t h e

It i s apparent f rom

E i t h e r

5. CONCLUDING REMARKS

A l l t h e r e s u l t s p resented i n d i c a t e t h a t t h e FFEVD a n a l y s i s package i s a ve ry use fu l eng inee r ing des ign t o o l . The a n a l y s i s produced c r e d i b l e p r e d i c t i o n s o f a l l t h e s t r u c t u r a l da ta ob ta ined f o r two c o n f i g u r a t i o n s o f t h e lOOkW r o t o r opera ted over a wide range o f wind speeds.

While t h e l e v e l o f agreement i s encouraging, FFEVD c l e a r l y does n o t a b s o l u t e l y p r e d i c t

a l l response d e t a i l s w i t h h i g h accuracy. Th is i s undoubtedly due t o t h e s i m p l i f y i n g assumptions c u r r e n t l y imbedded i n t h e theo ry and t o exper imenta l d i f f i c u l t i e s . It i s wor thwh i l e t o cons ide r where t h e l i k e l y sources o f e r r o r a re i n t h i s s tudy and t o d iscuss ways t o e l i m i n a t e o r reduce them:

( 1) Aerodynamic Load Model i ng--Any 1 i n e a r f o r c e d v i b r a t i o n a n a l y s i s produces responses which a re p r o p o r t i o n a l t o t h e appl i e d 1 oads. produced by t h e CARDAA and FORCE l o a d models demonstrates t h i s . Whi le CARDAA rep resen ts t h e s t a t e - o f - t h e - a r t i n streamtube model ing approaches, i t has o n l y been p a r t i a l l y v e r i f i e d by comparing p r e d i c t e d and measured average r o t o r s h a f t to rque. Fur thermore, bo th the CARDAA and FORCE models a re based on steady winds w i t h t h e consequence t h a t f o rces a re produced e x c l u s i v e l y a t d i s c r e t e f requenc ies r e l a t e d t o t h e r o t o r speed. Examinat ion o f t h e response spec t ra c l e a r l y show t h a t atmospheric tu rbu lence s p o i l s such a s imp le r e p r e s e n t a t i o n o f l o a d spec t ra . E f f o r t s a re i n p rogress t o model unsteady l o a d e f f e c t s C91 and t o d i r e c t l y measure aerodynamic fo rces on VAWT blades C181. These e f f o r t s shou ld l e a d t o improved l o a d models f o r f u t u r e a p p l i c a t i o n i n FFEVD.

o f t h e lOOkW r o t o r was n o t ar ranged b e s t f o r o b t a i n i n g c o n f i r m a t i o n data. It i s recommended on f u t u r e t e s t s t h a t b lade gaging be arranged t o measure tens ion , f l a t w i s e moments, and edgewise moments r a t h e r than d i r e c t s t r a i n . T h i s can be done by l o c a t i n g a c t i v e b r i d g e elements f a r f rom s t r e s s concen t ra t i ons and by c a l i b r a t i ng t h e b r idges w i t h known loads p r i o r t o b lade i n s t a l l a t i o n

The d i f f e r e n c e s i n r e s u l t s

( 2 ) Exper imenta l Technique--The gaging

( 3 ) Rotor Damping-- The s t r u c t u r a l damping o f t y p i c a l VAWT r o t o r s i s very l o w ( t h e o r d e r o f 1% o f c r i t i c a l C191). I n c l u s i o n o f damping o f t h i s magnitude w i l l have a n e g l i g i b l e e f f e c t on FFEVD r e s u l t s f o r non- resonant ope ra t i ons . However, aerodynamic damping can, f o r c e r t a i n r o t o r modes, approach 5% o f c r i t i c a l C2,31. Th is may be 1 arge enough t o i n f l u e n c e non-resonant r e s u l t s . I n c l u s i o n o f aerodynamic damping i n t o FFEVD i s complex b u t can be done w i t h o u t a1 t e r i n g t h e bas i c s t r u c t u r e o f t h e package.

ACKNOWLEDGEMENTS

The i n f o r m a t i o n i n t h i s r e p o r t was ob ta ined w i t h t h e v a l u a b l e suppor t o f many i n d i v i d u a l s i n v o l v e d w i t h t h e DOE VAWT research program. The lOOkW r o t o r i n s t r u m e n t a t i o n system was designed and

14

imp emented by J . Burkhardt . and R. Davis o f USDA prov ided va luab le ass i s tance i n t h e day-to-day maintenance o f t h e i n s t r u m e n t a t i o n system and t h e r o t o r i t s e l f . The RMS s t r a i n b i n s data a n a l y s i s program was designed and implemented by P. S. Veers and J . McNerney. FFEVD pre- and post-processors were devel oped by T. M. Leonard w i t h c o n t r i b u t i o n s f rom R. A. Watson. D . J . Malcolm o f DAF I n d a l (Canada) made c o r r e c t i o n s which d i r e c t l y reso lved t e c h n i c a l d i f f i c u l t i e s w i t h t h e e a r l y ve rs ions o f FFEVD. F i n a l l y , D . E. Berg and T. M. Leonard prepared and debugged the CARDAA l o a d subrout ines used i n FFEVD.

R. N. C la rk

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1 5

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