Aerodynamic and structural modeling for vortex-excited vibrations in bundled conductors [Elektronische Ressource] / vorgelegt von Himanshu Verma

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• Publié par: technischen_universitat_darmstadt
• Publié le: 01 janvier 2008
• Nombre de lectures: 40
• Langue: English
• Poids de l'ouvrage: 7 Mo

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Aerodynamic and structural
modeling for vortex-excited
vibrations in bundled conductors
Himanshu VermaAerodynamic and structural modeling for
vortex-excited vibrations in bundled conductors
Dem Fachbereich Maschinenbau
an der Technischen Universit˜at Darmstadt
zur
Erlangung des Grades eines Doktor-Ingenieurs (Dr.-Ing.)
eingereichte
D i s s e r t a t i o n
vorgelegt von
Himanshu Verma, M.Tech.
aus Ambah (M.P.), Indien
Berichterstatter: Prof. Dr. Peter Hagedorn
Mitberichterstatter: Prof. Dr. rer. nat. Michael Sch˜afer
Tag der Einreichung: 29. Februar 2008
Tag der mundlic˜ hen Prufung:˜ 18. Juni 2008
Darmstadt, 2008
D 17This book is approved as a doctoral dissertation by:
Prof. Dr. Peter Hagedorn, Professor, Technische Universit˜at Darmstadt.
Ph.D. oral examination was held on June 18th 2008.
Members of the examination committee were:
Prof. Dr. Peter Hagedorn, Referent
Prof. Dr. rer. nat. Michael Sch˜afer, Korreferent
Prof. Dr.-Ing. Rainer Nordmann, Vorsitzer
Prof. Dr.-Ing. Wilfried Becker, 1. Beisitzer
Prof. Dr.-Ing. Samuel Schnabel, 2.
Verma, Himanshu
Aerodynamic and structural modeling for vortex-excited vibrations in bun-
dled conductors
Dynamics and Vibrations Group, Technische Universit˜at Darmstadt
Darmstadt, Germany
Zugl.: Darmstadt, Techn. Univ., Diss., 2008
Keywords: Vortex-excited vibrations, Transmission line, Bundled conductors, Stock-
bridge damper, Spacer damper, Energy balance principle, Computational Fluid Dy-
namics
ISBN 978-90-9023741-1
Copyright°c 2008 by Himanshu Verma
All rights reserved. No part of the material protected by this copyright notice may be
reproducedor utilizedin anyformor byanymeans, electronic or mechanical, including
photocopying, recording or by any information storage and retrieval system, without
the prior permission of the author.
Printed by PrintPartners Ipskamp in the Netherlands.
Frontandbackcoverofthis book, and thebookmarkillustratetwin-, triple-andquad-spacerdampers
produced by Ribe Electrical Fittings GmbH, Schwabach, Germany. AutoCAD picture on the front
coverrepresentstheschematicmodelofquad-bundletransmissionlineconductorwithN-spacerdampers,
taken from chapter 2 of this book.Acknowledgements
I would like to express my gratitude to all those who, directly or indirectly, have given
me their valuable support in the course of this work.
My utmost gratitude goes to my thesis supervisor Prof. Dr. Peter Hagedorn for
his continuous support, kindness, and his patience towards me. Since my flrst days in
GermanyasaDAADscholar,youhavebeenasourceofinspirationtome. Whetheritis
10 o’clock cofiee meeting or any technical discussion, you always managed to flnd time
for your people and inspire everyone in the group. I cannot but once again commend
yourwonderfulhospitalitytowardseachnewcomerinthegroup. Trulyit’syoursincere
efiorts which have kept the whole group as a family.
I would like to express my gratitude to my co-supervisor Prof. Dr. rer. nat.
Michael Sch˜afer, his former colleague Dr.-Ing. Sebastian Meynen and colleagues of
FNB for their support regarding Computational Fluid Dynamics part of my work.
I greatly appreciate the interest of Prof. Goutam Chakraborty, Prof. Satya
Chakravarthy, Prof. Anirvan DasGupta, Prof. Dr.-Ing. Richard Markert, Dr. Nandan
Kumar Sinha, Dr.-Ing. Nils Wagner and Prof. Utz von Wagner, and would
like to thank them for the technical discussions I had with them in difierent stages of
my work.
Thanks to DFG (Deutsche Forschungsgemeinschaft) and our industrial partner
Ribe Electrical Fittings GmbH for flnancially supporting this research work. Special
thanks to Hans-J˜org Krispin for our telephonic conversations and regular meetings,
which were a great opportunity for me to learn the industrial perspective of the trans-
mission line vibrations problem.
Now to the Mechanik group, where I spent flve memorable years of my life, and
met some of the most wonderful people. I would like to thank my colleagues: Kathrin
Baumann, AnkeB˜ottcher, AnaCostaConrado, AshishDighe, UliEhehalt, FlorianFis-
cher, Stefenie Gutschmidt, Daniel Hochlenert, Thira Jearsiripongkul, Martin Kreschel,
Alexander Lunensc˜ hlo…, Jhon Malta, Sandeep Kumar Parashar, Roland Platz, Daniel
Sauter, Martin Sch˜onecker, Nobert Skricka, Gottfried Spelsberg-Korspeter, Alireza To-
fangchiandTobiasVomstein. Thanksyouallforyoursupport andforprovidingsucha
fantasticworkenvironment. Iwouldalsoliketothankgorgeousladies-RenateSchreiber
andMariaRauck. Withoutyou, Iwouldn’thavehadmyappointmentsset, myhousing
problems sorted out and other administrative tasks neatly done. It were you who made
the group complete. Thank you all! I will always cherish the moments I spent with
you.
My stay in Germany would have never been so comfortable, homely and memo-
VVI Acknowledgements
rable without many of my friends. I would like to thank all my folks: Rajni Kumar
Akula,AtulAthavale,PoonamandDebasishBanerjee,ArijitandTanaliBhattacharya,
Abhay Davesthale, Masum Duman,˜ Ashwini and Rahul Harshe, Pragya and Chirag
Jain, Kamalpreet Kaur, Orio Kieboom, Monika Luca, Divya and Bhaskar Mehta, Ioan-
nis Michailidis, Sunil Kumar Omar, Kalpana and Sandeep Kumar Parashar, Ileana
Petroniu,AnitaSingh,KarelleandPrashantSoni,PallaviThiagarajanandManuAnna
Thomas. My life outside India wouldn’t have been as exciting and happening without
you people. In fact, you all are the reason that has made Germany my second home
over these years.
I would also like to thank all my teachers, who provided a good foundation for
my development. I owe a lot to the Department of Civil and Applied Mechanics at
S.G.S.I.T.S. Indore, where I did my Graduation, learned a lot, and spent some of the
best days of my life. A special thanks to my supervisor at IIT Bombay, Prof. Yogesh
M. Desai, who encouraged me to go for higher research.
A heart-fllled thanks to my love and life-partner Swati Gehlot, who has been an
inspirerandmotivatortomeforlastmanyyears. Withoutyou,Iwouldhaveneverbeen
abletoflnishthisresearchwork. Itwasyouwhohasalwaysprovidedherunconditional
support and encouragement in my tough days. You were the one knowing all my
weaknesses and still accepting me for what I am. Thank you Swati for always being
with me.
In India, the parents never say \I Love You" to their kids, as they breathe, think
and love for their kids: Mummy and Papa (Shashi Bala and Surendra Kumar Verma),
you have played a huge role in bringing me up to where I am today. It would be too
artiflcial if I have to thank you, but without your sacriflces and the opportunities you
provided me during my life’s journey, I wouldn’t have been able to achieve so much
and come this far. I consider myself fortunate for the freedom that you provided to
me taking some of life’s crucial decisions. Even if you were seldom physically near
me through these years in Europe, your thoughts and blessings have always been a
lighthouse for me, guiding me in the right direction. I cannot thank you enough but
just dedicate this book to you both. Please accept it!
And flnally but most importantly, I thank the Almighty for everything I have,
every opportunity I have been given, all right ideas and desired support given at the
right time. I thank You for your blessings for me. Without You, this journey would
have been an unlived dream...
Hamburg, 15. November 2008 Himanshu VermaContents
Acknowledgements V
Abstract XI
Kurzfassung XIII
1 Introduction 1
1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 State of the art: literature review . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Modeling of the aeolian vibrations in transmission line conductors 4
1.2.2 Power input from the wind . . . . . . . . . . . . . . . . . . . . . 6
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Mathematical model for a conductor bundle 11
2.1 Modeling the conductor bundle . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Equation of motion for the subconductors . . . . . . . . . . . . 11
2.1.2 Incorporating the spacer dampers . . . . . . . . . . . . . . . . . 14
2.1.3 Incorp the Stockbridge dampers . . . . . . . . . . . . 19
2.2 Difierent orientations of the spacer dampers . . . . . . . . . . . . . . . 22
2.3 Transcendental eigenvalue problem (TEVP) . . . . . . . . . . . . . . . 24
3 Solution of the transcendental eigenvalue problem (TEVP) 25
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.1 Standard EVP . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.2 Forms of standard EVP . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Nonlinear transcendental matrix . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Solution of the nonlinear TEVP . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Determinant search method . . . . . . . . . . . . . . . . . . . . 30
3.3.2 Alternate approach . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.3 Newton’s eigenvalue iteration method . . . . . . . . . . . . . . 31
3.3.4 Extension for the complex system matrix . . . . . . . . . . . . . 34
VIIVIII CONTENTS
3.3.5 Higher order approximation . . . . . . . . . . . . . . . . . . . . 37
3.4 Obtaining the eig