a theoretical model for the cross-flow induced fluid-elastic inst

8/2/2019 A Theoretical Model for the Cross-Flow Induced Fluid-Elastic Inst

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McMaster University

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6-1-1983

A Theoretical Model for the Cross-Flow InducedFluid-Elastic Instability in Heat Exchanger Tube

BundlesJames Howard Lever

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Recommended CitationLever, James Howard, "A Theoretical Model for the Cross-Flow Induced Fluid-Elastic Instability in Heat Exchanger Tube Bundles"(1983). Open Access Dissertations and Theses. Paper 1445.http://digitalcommons.mcmaster.ca/opendissertations/1445
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A THEORETICAL MODEL FORTHE CROSS-FLOW INDUCED

F L U I D ~ E L A S T I C ( I N S T A B I L ~ T YIN HEAT E X C 8 A N G E ~ TUBE BUNDLES

byJAMES HOIiARD LEVER, B.ENG., M.A.'Sc.

Submitted to theA Thesis . I-chool of Graduate Studies

in. Par t ia l Fulfi lment of the 'Requirements4 ~ g r the Degree. ~ : ' ~ ..,"'.~ ~ c t o r of Philosophy

,McMaster University

IJune 1983

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FLUID-ELASTIC INSTABILITY IN.HEAT EXc;HANGERS

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DOCTOR OF PHILOSOPHY (1983), (Mechanical Engineer ing) McMASTER UNIVERSITYHamil ton , Ontar io,TITLE: A Theoretica:l t Model fo r the Cros s- Fl ow InducedF lu id -E la s t i c I n s t a b i l i t y ' in Heat E x c h a ~ g e r TubeBundles .AUTHOR: James H"bward. Leve r , ' B.E!1g., (McMaster Univers i tyJ

M.A.Sc. (Univers i ty o f Toronto)SUPERVISOR: Dr. D.S. Weaver

,. NUMBER OF PAGES:

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xv, 235

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To my wi teKaren and daughter Al l i son ,and to my paren t s and s i s t e r s ; whoseaf fec t ihns are valued most of a l l .

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ABSTRACT

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A s i m p ~ e theore t ica l model has been developed fromf i r s t pr incples fo r the cross-f low induced f l u id -e l a s t i ci n s t ab i l i t y in hea t exchanger tube b u ~ d l e s . A se r ie s ofexper iments were conducted to veri fy t h e ~ a s i c assumptiont ha t only a s.ingle tube need be modelled in a flow channelwhich preserves the bas ic ge9metry of the array . The'mechanism of dynamic i n s t ab i l i t y i s found to be.one of flowt ed i s t r i bu t ion due to t ransverse tube motion and a phase lagresu l t ing from f l u i d ~ i n e r t i a . Sta t i c i n s t ab i l i t i e s in bothst reamwise and t ransverse d i rec t ions are" a lso pred ic ted , but

\a t h i ~ h e r ' reduced flow ve loc i t i e s ~ h a n the t ransversedynamic i n s t ab i l i t y . q ~ i t e good agreement i s found with'.ava i lab le exper imenta l data , p a r t i c u ~ a r l y for pa r a l l e l, .. ', t r i angu ia r and ~ q u a r e a r rays , without the need f or emp irica l.f lu id force coef f ic ien t s ; The model inc ludes the e f fec t s o f~ u b e array p a t t e ~ n and p i t ch .,

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ACKNOWLEDGEMENTS.The au thor would l ike to express h is s ince re g ra t i t ude

to Dr. D.S. Weaver, who fu l f i l l ed the ro les o f bothsuperv i so r and t eacher with enthusiasm and ded ica t ion .Many thanks Dave.

The author would a lso l i ke to thank Mr. WilliamD'Netto fo r ' h i s he lp fu l discuss ions during the modeldevelopment, pa r t i cu l a r th e t r an s i en t case s tudy , ' and Mr.Pete r Scot t and Mr. Ralph H arris fo r t h e i r considerab lee f f o r t s 'devoted to the computer generated s t ab i l i t y p lo t s .The care fu l and e f f i c i en t typ ing of th i s manuscr ipt by Mrs.,Mari lyn Warren i s a lso gra te fu l ly acknowledged, as i s th eFinanc ia l suppor t o f the Natura l Sciences and Engineering

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Research Counci l o f Canada.

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- rTABLE OF CONTENTS

ABSTRACTACKNOWLEDGEMENTSLIST OF FIGURESLIST OF TABLESNOMENCLATURE

. ~ H A P T E R 1 INTRODUCTIONCHAPTER 2 HISTORICAL BACKGROUNDCHAPTER 3 PRELIMINARY EXPERIMENTS

3.1 Experimental Equipment3.2 Experimental Resul ts

CHAPTER 4 FURTHER'SIMPLIFYING ASSUMPTIONS,CHAPTER,S THEORETICAL DEVELOPMENT

5.1 Transverse Dynamic In s t ab i l i t y5;1 . 1 Model Formulation5.1 .2 Solu t ion 'o f One-Dimensional 45Flow EquatJ.ons

(a) Upstream Region(b) Attached Flow Region

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5.1.3 Tube Dynamics5'.1.4 Stab i l i ty Analysis ,.

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, ' 5.,1.5 Pressure Force Coef f i c ien t 64and Phase Angle

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5.2 .1 Model Formula t ion

5 .3 Streamwise Vibra t ion5 .3 .1 Model Formula t ion

6.1 Geometric Parameters

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73737476

8182.8 85

85939596

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5 .3 .4 Streamwise Dynamic I n s t ab i l i t y

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' 5 .3 .2 S olu tio n o f the One-Dimensional Flow Equations

5.2 .3 Stab i l i t y Analys i s

5 .2 .2 Solu tion o f the One-Dimensional Flow Equations

.'5.3 .3 S t ab i l i t yAna l y s i s

7 .3 C,Jrr.pa.r i,;;on o ~ P r e d i c t e d ThresholdCurves with Experimental Stab i l i tyData fo r Indiv idual Arrays

7 .2 Numerical Th re sho ld Equa tio n sfo r Arrays o f I n t e r e s t

7.1 S tab i l i t y Threshold Curves inC;ompact Form

5.2 Transverse Sta t i c I n s t ab i l i t y

6 .2 Rela t ionship Between h and CD

5 .3 .5 Streamwise Sta t i c In s t ab i l i t yf "CHAPTER 6 TUBE-IN-CHANNEL MODEL PARAMETERS

CHAPTER 7 NUMERICAL RSSULTS

) 7 ' .3.1 Pa ra l l e l "Tr iangu la r Array, 104 "( P/d = 1 . 375

7.3 .2 Square Array, P/d = 1 . 33 1077.3 .3 Squars Array, P/d = 2 .0 110

7 .4 Pi t ch and Pat t e rn Ef fec t s 113

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,CHAPTER 8

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7.5 Pressure Force C o e f f i ~ i e n t andPhase Angle for TransverseDynamic In s tab i l i ty7.6 sens i t \v i ty A n a l y ~ f s

. " ~ DISCUSSION OF NUMERICAL RESULTS8.1 Predic ted Threshold Curves forIndiv idual Arrays L

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125129.129

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8.1 . 2

Relat ive Importance o fDynamic versus Sta t i c"I n s t ab i l i t i e s 'A g r ~ e m e n t B e t ~ e e n 'Theoret ica l TransverseDynamic Stab i l i ty Curvesand Experimental Data

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8.2 Discuss ion o f Pitch and Pat ternEffec t s".3 Pressure Force Coeff i c i en t andPhase ,Angle

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~ . 4 ' Considerat ion of the Sens i t iv i ty 143Analysis, , 8.,5 Behaviour of Transverse DynamicI r t s tab i l i ty Mechanism a t LowReduced Veloci ty

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CHAPTER 9 POSSIBLE MODEL EXTENSIONS AND EFFECTS 155OF NEIGHBOURING TUBE MOTION9.1 Inclusion of Viscos i ty Expl ic i t ly 155in I-D Flow Equations9.2 Development of a Two-Dimensional 157

M o d e ~ Formulation 9.2.1 ~ o d e l Formulation 158,9.2.2 ' Approach to tbe S olu tio n o f the 2-D Flow Equations 161

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9.3 Qual i ta t ive Effec t ofTube Motion

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Neighbouring,';-

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CHAPTER 10 SUMMARY AND CONCLUSIONSREFERENCESAPPENDIX A

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a theoretical model for the cross-flow induced fluid-elastic inst

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