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MECHANICAL DESIGN

O

HEAT

EXCHANGERS

AND

PRESSURE

VESSEL COMPONENTS

KRISHNA P

SINGH

Vice President of Engineering

Joseph

Oat

Corporation

Camden NJ

and

ALAN I SOLER

Professor of Mechanical

Engineering

Applied Mechanics

University of Pennsylvania

Philadelphia

P

Springer Verlag Berlin Heidelberg GmbH

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FIRST EDITION

Copyright

1984 by Springer-Verlag Berlin Heidelberg

Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 984

All rights reserved by the publisher. This

book or

parts thereof, may not be reproduced in any

form

without

the

written permission

of

the publisher.

Library

of

Congress Catalog No. 84-70460

Exclusive distribution rights outside

United States ofAmerica, Mexico and Canada

Springer-Verlag Berlin Heidelberg GmbH

ISBN 978-3-662-12443-7 ISBN 978-3-662-12441-3 eBook)

DOl 10.1007/978-3-662-12441-3

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This book is dedicated to:

ur wives, Martha Singh and Debby Soler

for their patience, understanding and support,

and

the late Dr. William G. Soler, an English teacher who spent countless hours

reading technical papers in order to comprehend his son s work.

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PREF CE

A tubular heat exchanger exemplifies many aspects

of

the challenge in

designing a pressure vessel. High or very low operating pressures and

temperatures, combined with sharp temperature gradients, and large

differences in the stiffnesses

of

adjoining parts, are amongst the legion of

conditions that behoove the attention of the heat exchanger designer.

Pitfalls in mechanical design may lead to a variety of operational problems,

such as tube-to-tubesheet joint failure, flanged joint leakage, weld cracks,

tube buckling, and flow induced vibration. Internal failures, such as pass

partition bowing or weld rip-out, pass partition gasket rib blow-out, and

impingement actuated tube end erosion are no less menacing. Designing to

avoid such operational perils requires a thorough grounding in several

disciplines

of

mechanics, and a broad understanding

of

the inter

relationship between the thermal and mechanical performance of heat

exchangers. Yet, while there are a number

of

excellent books on heat

ex-

changer thermal design, comparable effort in mechanical design has been

non-existent. This apparent void has been filled by an assortment of

national codes and industry standards, notably the

ASME

Boiler and

Pressure Vessel

Code

and the Standards

of

Tubular Exchanger

Manufacturers Association. These documents, in conjunction with

scattered publications, form the motley compendia of the heat exchanger

designer's reference source. The subject matter clearly beckons a

methodical and comprehensive treatment. This book

is

directed towards

meeting this need.

Many of

our readers have been witness to the profound changes that have

occurred in recent years in heat exchanger design practice. Only two short

decades ago, seismic analysis was an alien term to the heat exchanger trade.

Words like response spectrum , flow induced vibration , nozzle load

induced vessel stresses , etc., held little kinship to the heat exchanger design

technology. Today, these terms occupy a great deal of the designer's at

tention. A thorough grasp

of

the underlying concepts in flow induced

vibration and seismic analysis, along with pressure vessel mechanical design

and stress analysis techniques, is essential for developing cost effective and

reliable designs. Successful troubleshooting of problems in operating units

relies equally on an in-depth understanding of the fundamentals. Our object

in this book is to present the necessary body

of

knowledge for heat ex-

changer design and operating problems-resolution in a logical and

systematic manner.

The book begins with a comprehensive introduction to the physical

details

of

tubular heat exchangers in Chapter 1 followed by an introduction

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to the stress classification concept in Chapter

2

The following three

chapters are devoted

to

bolted flange design with particular emphasis on

devising means

to

improve joint reliability. Chapter 6 treats the so-called

boltless flanges. The subject

of

tube-to-tubesheet joints

is

taken up in

Chapter 7 wherein a method to predict the optimal tube expansion

is

presented.

The

subsequent four chapters deal with the tubesheets for

various exchanger styles, viz. V-tube, fixed

and

floating head, double

tubesheet, and rectangular tubesheets. Methods for complete stress analysis

of

tubesheets, with the aid of computer programs, are given. Additional

topics

of

mechanical design/stress analysis covered are: flat cover (Chapter

12);

heads (Chapter

13);

V-tubes (Chapter

14);

and expansion joints

(Chapter 15). Chapter 16 is devoted to fostering an understanding of flow

induced vibration in

tube

bundles; design methods

to

predict its incidence

and design remedies to obviate its occurrence are presented.

The group of chapters from 17 through

20

deal with heat ex

changer/pressure vessel support design and seismic analysis. Chapter 21 is

intended

to

introduce the application

of

the response

spectrum

analysis

technique

to

heat exchangers. Finally, Chapter 22 contains a brief resume of

operational

and

maintenance considerations in heat exchanger design.

Since

much of

the pressure vessel design theory requires some knowledge

of

plate and shell theory, a self contained treatment of this subject

is

given

in Appendix A at the end of the text. Additional material, pertinent to a

particular chapter, is presented in appendices at the end of each chapter.

Since many of the design/analysis techniques presented here require

lengthy computations, sometimes impossible by manual means, suitable

computer programs are provided in the text.

The

source listings

of

twenty

two (out of a total of twenty-seven computer codes), along with input in

structions, are provided in the text. In order

to

avoid manual transfer of

these codes, source codes (including the five codes

not

listed in the book) in

more computer amenable form (such as tape, mini-disc, cards, etc.), can be

obtained from the publisher separately.

This book

is

written with two audiences in mind. The practicing engineer,

too

harried

to

delve into the details of analysis, may principally use the

computer codes with the remainder of the

book

serving as a reference

source for design innovation ideas

or

for operational diagnostics work. A

university student or a researcher seeking

to obtain

an exoteric (as opposed

to

esoteric) knowledge

of

the state-of-the-art in heat exchanger technology

can concentrate on the theoretical developments. As such, this book can be

used for teaching a senior/first year graduate level course in heat ex

changers or pressure vessel design technology . We have made a con

certed

effort to

bridge the gap between analytical methods and practical

considerations.

Many men

and

women have contributed towards the successful con

clusion of this effort which sometimes appeared to us to be never ending.

From the Joseph Oat Corporation, M. J. Holtz, L Ng, R. Shah, F.

McAnany, deserve mention. The encouragement and support

of

Mr.

vi

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Maurice Holtz

of

the Joseph Oat Corporation Dr. William S. Woodward

of

the Westinghouse Corporation and Dr. Ramesh Shah

of

General

Motors Corporation are also acknowledged. Mr. Xu Hong

of

the Beijing

Institute

of

Chemical Technology contributed to the development

of

two

of

the computer codes during his term as a visiting researcher at the

University

of

Pennsylvania. Ms. Nancy Moreland

of

the Joseph Oat

Corporation pursued the task of word processing with unwavering zeal and

fervor and Mrs. Dolores Federico and Mr. John T. Sheridan both

of

Sheridan Printing Company brought forth tireless effort to bring out the

book in record time. We deeply appreciate their contributions.

Finally we acknowledge the contributions

of

our Ph D thesis advisors

Dr. Burton Paul of the University of Pennsylvania and Dr. Maurice A.

Brull

of

the Tel Aviv University. t was their original efforts which started

both of us on the paths leading to the creation of this book.

vii

K

P. SINGH

A 1 SOLER

Cherry Hill New Jersey

February 1984

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T BLE OF CONTENTS

1. HEAT

EXCHANGER CONSTRUCTION

1.1

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Heat Exchanger Styles. . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3

Heat

Exchanger Nomenclature. . . . . . . . . . . . . . . . . . . . 14

1.4 Heat Exchanger Internals . . . . . . . . . . . . . . . . . . . . . .

14

1.5 Tube Layout and Pitch . . . . . . . . . . . . . . . . . . . . . . . . 23

1.6 General Considerations in Pass Partition Arrangement.. 24

1.7 Impingement

Protection

. . . . . . . . . . . . . . . . . . . . . . . 25

1.8 Designing for Thermal Transients. . . . . . . . . . . . . . . . 34

1.9 Interdependence of Thermal

and

Mechanical Design

37

1.10 Feedwater Heater Design. . . . . . . . . . . . . . . . . . . . . . . 39

1.11 Codes and

Standards.

. . . . . . . . . . . . . . . . . . . . . . . . .

45

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Appendix

I.A Typical Shell and

Channel

Arrangements and

Parts

Identification. . . . . . . . . . . . . . . . . . . . 7

2. STRESS

CATEGORIES

2.1 I n t r o d u c t i o n 57

2.2 Beam Str ip Analogy . . . . . . . . . . . . . . . . . . . . . .

57

2.3 Primary and Secondary Stress. . . . . . . . . . . . . . . . . . . 60

2.4 Stress Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.5 General

Comments

68

2.6 Stress Intensity 68

2.7

An

Example of Gross Structural Discontinuity . . . . . .

69

2.8 Discontinuity Stresses at Head Shell and Skirt Junction.. 72

Nomenclature

, 79

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

3. BOLTED

FLANGE

DESIGN

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.2 Bolted Flange Types. . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.3 Flange Facings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

3.4 Flange Facing Finish. . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.5 Gaskets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.6 Bolt

Pre-Tensioning.

. . . . . . . . . . . . . . . . . . . . . . . . . 95

3.7 Flange Sizing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.8 Flange Moments. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101

3.9 Circular Rings under Distributed Couples. . . . . . . . . . 102

3.10 Deformation of a Flanged

Joint.

. . . . . . . . . . . . . . . . . 104

3.11

Waters

Rossheim, Wesstrom and Williams'

Method

for

Flange Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

3.11.1 Flange Ring (Element #

1

. . . . . . . . . . . . . . . . 109

3.11.2 Taper Hub (Element #2) 112

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3.11.3 Shell (Element 3) . . . . . . . . . . . . . . . . . . . . . 118

3.11.4 Compatibility Between Shell and Hub . . . . . . 118

3.11.5 Compatibility Between Hub and Ring

120

3.11.6 Longitudinal Stress in the Hub . . . . . . . . . 124

3.11. 7 Longitudinal Stress in the Shell. . . . . . . . . . . .

124

3.11. 8 Radial Stress in the Ring. . . . . . . . . . . . . . . . .

125

3:11.9 Tangential Stress in the Ring , 125

3.12 Computer Program FLANGE. . . . . . . . . . . . . . . . . . .

126

3.13 Stress Analysis of the Welding Neck Flange. . . . . . . . . 141

3.14 Controlled Compression Joint. . . . . . . . . . . . . . . . . . . 144

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

154

Appendix 3.A Derivation of Polynominal Expressions for

Hub Deflection (Eq. 3 11.20a) . . . . . . . . . . . . 156

Appendix 3.B Schleicher Functions 158

4. TUBESHEET SANDWICHED BETWEEN TWO FLANGES

4.1 I n t r oduc t i o n 161

4.2 The Structural

Model

. . . . . . . . . . . . . . . . . . . . . . . . 165

4.3 Tub e s h e e t 166

4.4

F l a n g e 170

4.5 Method

of

Solution. . . . . . . . . . . . . . . . . . . . . . . . . . .

170

4.6 Leakage Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

4.7 Two Example Problems. . . . . . . . . . . . . . . . . . . . . . . .

178

4.7.1 Classical Three Element Joint

178

4.7.2 Controlled Metal-to-Metal Contact

Joint

. . . . 180

4.7.3 Obse rv a t i o n s 187

4.8 Computer Program TRIEL 188

4.8.1 Input Data for Program TRIEL

188

4.8.2 Two Flanges Bolted Together. . . . . . . . . . . . . . 204

4.8.3 Other Applications. . . . . . . . . . . . . . . . . . . . . . 204

Nomenclature 204

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

5 BOLTED JOINTS WITH FULL FACE GASKETS

5.1 I n t r o d u c t i o n 209

5.2 General Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

5.3 Non-Linear Analytical Expressions Simulating

Gasket Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

5.4 Simulation of Bolt Effects. . . . . . . . . . . . . . . . . . . . . . 223

5.5 Calculation of Flange Stress 225

5.6 Application of the Method 226

5.6.1 Gasketed Joint Model

227

5.6.2 Analysis

of

a Full Face Gasket-Two Element Joint

233

5.6.3 Analysis of Ring Gasketed Joint. . . . . . . . . . . . 235

5.6.4 Ring Gasketed Joint with Compression Stop 236

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5.6.5 Analysis

of

Three Element Joint with Non-

Symmetric Load and Geometry . . . . . . . . . . . .

237

5.7 Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . .

237

Nomenclature

238

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Appendix

5.A

User Manual For Computer Code

GENFLANGE 239

6 JOINTS FOR HIGH PRESSURE CLOSURES

6 1

Introduction and Standard Industry Designs. . . . . . . .

289

6.2 Wedge Seal Ring Closure

297

6.2.1 Joint Description

297

6.2.2 Analysis

of

Sealing Action. . . . . . . . . . . . . . . . 300

6.2.3 Disassembly Analysis. . . . . . . . . . . . . . . . . .

301

6.2.4 Sizing the Retainer Shoe. . . . . . . . . . . . . . . . . .

301

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

304

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

305

7 TUBE-TO-TUBESHEET JOINTS

7

1

Joint

Types.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

307

7.2 Expanding

Method.

. . . . . . . . . . . . . . . . . . . . . . . . . .

307

7.3 Roller Expanding

308

7.4 Hydraulic Expansion. . . . . . . . . . . . . . . . . . . . . . . . . . 310

7.5 Impact Welding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

311

7.6 EdgeWelding 312

7.7 Butt Welding

315

7.8 Tube-to-Tubesheet Interface Pressure. . . . . . . . . . . . .

315

7.8.1 Initial Expansion of the Tube

317

7.8.2 Loading of Tube and Tubesheet. . . . . . . . . . . . 319

7.8.3 Displacement in the Tubesheet.

323

7.8.4 Unloading

of

the System . . . . . . . . . . . . . . . . .

324

7.8.5 Tube Pull-Out Load

325

7.8.6 Computation of Residual Pressure. . . . . . . . . .

328

7.8.7 Re-Analysis

of

the Tube Rolling Problem Using

the von Mises Yield Criteria. . . . . . . . . . . . . . .

329

7.9 Ligament Temperature , . . . . . . 329

7.9.1 Introduction 329

7.9.2 Analysis

330

7.9.3 Solution Procedure

335

7.9.4 Numerical Example-Computer Program

LIGTEM

336

7.10 Tube Removal and Tube Plugging. . . . . . . . . . . . . . . .

342

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

345

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

347

Appendix 7.A Coefficients of

[A]

Matrix and [F} Vector . . 349

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Appendix 7.B Computer Code for Evaluation

of

Residual

Roll Pressure Using Tresca Yield Condition 350

Appendix

7 C

Tube-Tubesheet Joint Loading Including

Thermal Effects . . . . . . . . . . . . . . . . . . . . . . 354

Appendix 7.D User Manual and Computer Code for Tube

Rolling Program GENROLL . . . . . . . . . . 368

8 TUBESHEETS FOR U-TUBE HEAT EXCHANGERS

8.1 I n t r o du c t i o n 387

8.2 Analysis of Perforated Region. . . . . . . . . . . . . . . . . . . 390

8.3 Analysis of Two Side Integral Construction

393

8.4 Analysis

of

One Side Integral One Side Gasketed

Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

8.5 Analysis

of

Two Side Gasketed Construction. . . . . . .

401

8.6 Tubesheet Stress Analysis. . . . . . . . . . . . . . . . . . . . . . 402

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

References

411

Appendix 8.A Computer Code UTUBE 412

9

TUBE SHEETS IN FIXED AND FLOATING HEAD HEAT

EXCHANGERS

9.1 Scope ofAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

415

9.2 Effective Pressure

on

Tubesheet Due to the Tube Bundle. 418

9.3 Analysis of a Perforated Circular Tubesheet . . . . . . . . 420

9.4 Analysis

of

an Unperforated Tubesheet

Rim.

. . . . . . . 424

9.5 Method of Solution and Computer Implementation 430

9.5.1 Differential Thermal Expansion Between the Shell

and the Tubes. . . . . . . . . . . . . . . . . . . . . . . . . .

431

9.5.2 Sample Application of Analysis

435

9.6 Modifications for Floating Head Exchangers. . . . . . . .

439

9.7 Simplified Analysis of Stationary Tubesheet in an

Integral or Floating Head Heat Exchanger. . . . . . . . . .

440

9.7.1 Evaluation ofIntegration Constants . . . . . . . . 444

9.7.2 Development of Expressions for Ring Rotation.. 447

9.7.3 Determination

of

Perforated Region Edge Force

Edge Moment and Shell Axial Force. . . . . . . . 450

9.7.4 Computer Analysis

453

9.8 Reduction ofAnalysis to Simplified Form. . . . . . . . . . 461

9.9 Range ofApplication of the TEMA Bending Equations

Given in Reference [9.1.1] . . . . . . . . . . . . . . . . . . . . . . 481

9.10 C l o s u r e 483

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

Appendix 9.A Solution of Coupled Plate Equations. . . . . . . 489

Appendix 9.B Computer Program FIXSHEET 490

9.B.l Scope 490

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9.B.2 Input Data for FIXSHEET . . . . . . . .

491

Appendix 9.C User Manual for Tubesheet Analysis

Program FIXFLOAT and Source Listing. . . . 500

Appendix 9.D Basic Computer Code for MICRO-FIXFLOAT

for Simplified Calculation

of

Tubesheet

Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

10.

SPECIAL TUBESHEET CONSTRUCTION

DOUBLE TUBESHEET

10.1 Introduction

517

10.2 Formulation

of

the Double Tubesheet Equations. . . . .

519

10.3 Theoretical Analysis

of

Double Tubesheet Construction

Using Plate

Theory.

. . . . . . . . . . . . . . . . . . . . . . . . . .

520

10.4 Solution

of

the Double Tubesheet Equations by Direct

Integration and Application to a Selected Unit. . . . . . .

528

10.5 The Finite Element Method in Tubesheet Analysis. . . . 534

10.6 Sample Results Using the Finite Element Method . . . . 536

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

539

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

540

Appendix 10.A User Manual for Double Tubesheet

Analysis Computer

Code DOUBLESHEET .

541

Appendix 1O.B Sample Input and Output Files for

Example Problem

of

Section 10.4

561

11. RECTANGULAR

TUBESHEETS APPLICATIONTO

SURFACE CONDENSERS

11.1

I n t r oduc t i on 565

11.2 The Condenser Tubesheet Design Problem . . . . . . . . .

565

11.3 Introductory Remarks on Analysis of a

Rectangular Tubesheet Using Beam Strips 570

11.4 Analysis

of

a Single Beam Strip. . . . . . . . . . . . . . . . . . 575

11.5 Development

of

Final Equations for Edge Displacements

581

11.6 A Specific Application

of

the Multiple Beam Strip

Method to Investigate the Effects

of

Tubesheet

Geometric and Material Parameters 586

11.7 Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . .

589

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

References

591

Appendix 11.A Coefficients

of

A-Matrix and

B

Vector

591

12. FLAT COVER

12.1

I n t r oduc t i on 593

12.2 Conventional Design Formulas. . . . . . . . . . . . . . . . . .

596

12.2.1 AS ME Code. . . . . . . . . . . . . . . . . . . . . . . . . .

596

12.2.2

TEMA

Standards. . . . . . . . . . . . . . . . . . . . . .

597

12.2.3 Heat Exchange Institute. . . . . . . . . . . . . . . . .

597

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12.3 Flange Cover Interaction. . . . . . . . . . . . . . . . . . . . . . .

598

12.3.1 Cover 598

12.3.2 Flange

Ring.

. . . . . . . . . . . . . . . . . . . . . . . . . . .

603

12.3.3 Interaction Relations. . . . . . . . . . . . . . . . . . . 604

12.4 Cover and Flange Ring Stresses. . . . . . . . . . . . . . . . . . 608

12.5 Loss

of

Heat Duty Due

to

Flow Bypass. . . . . . . . . . . .

. .

609

12.6 Thermal Performance

of

Two Tube Pass Heat

Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

610

12.7 Computer Program LAPCOV

612

12.7.1 Program Description. . . . . . . . . . . . . . . . . . . 612

12.7.2 Example

612

12.8 Flat Cover Bolted to a Welding Neck Flange 614

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624

13 PRESSURE VESSEL HEADS

13 1

I n t r o d u c t i o n 625

13.2 Geometry

of

Shells

of

Revolution . . . . . . . . . . . . . . . . 626

13.3 Membrane Theory for Shells of Revolution. . . . . . . . . . . 629

13.4 Stress Analysis of Membrane Shells under Internal

Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

634

13.5 Physical Interpretation of o 642

13.6 Derivation of ASME Code Formula for the Large End

ofaReducer

647

13.7 Membrane Displacement. . . . . . . . . . . . . . . . . . . . . . .

649

13.8 Evaluation

of

Discontinuity Effects. . . . . . . . . . . . . . . 656

Nomenclature 661

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662

14

THERMAL STRESSES IN U BENDS

14.1 I n t r o d u c t i o n 663

14.2 Ana l y s i s 666

14.3 Method of Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

672

14.4 An Example 674

14.5

Di s c u s s i o n

678

14.6 A Practial Design Formula 679

14.7 Computer Program UBAX 681

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

685

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686

Appendix

14

A Elements

of

B Matrix . . . . . . . . . . . . . . . . .

687

15 EXPANSION JOINTS

15.1 I n t r o d u c t i o n 689

15.2 Types of Expansion Joints 690

15.3 Stiffness of Formed

Head

Type Joints 694

15.4 Stresses in the Expansion Joint 700

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15.5 Finite Element Solution Computer Program

FLANFLUE 707

15.6 Bellows Expansion Joint for Cylindrical Vessels

709

15.7 Bellows Expansion Joints for Rectangular Vessels 710

15.8 Fatigue Life

713

Nomenclature 716

References 716

Appendix 15.A Computer Program EXJOINT

718

Appendix 15.B Computer Program EJMAREC _ 726

16

FLOW INDUCED VIBRATION

16 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

735

16.2 Vibration Damage Patterns 736

16.3 Regions

of

Tube Failure . . . . . . . . . . . . . . . . . . .

737

16.4 Vibration Mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . 738

16.4.1 Vortex Shedding 738

16.4.2 Fluid Elastic Excitation. . . . . . . . . . . . . . . . . 740

16.4.3 Jet Switching. . . . . . . . . . . . . . . . . . . . . . . . . 747

16.4.4 Acoustic Resonance. . . . . . . . . . . . . . . . . . . .

748

16.5 Fluid Inertia Model for Fluid Elastic Instability 749

16.5.1 Fluid Inertia

749

16.5.2 Stability Criterion . . . . . . . . . . . . . . . . . . . . . 755

16.6 Natural Frequency. . . . . . . . . . . . . . . . . . . . . . . . . . .

756

16.6.1 Basic Concepts. . . . . . . . . . . . . . . . . . . . . . . . 756

16.6.2 Single Span Tube. . . . . . . . . . . . . . . . . . . . . .

757

16.6.3 Multiple Span Tube 761

16.6.4 Tube under Axial Load 762

16.6.5 U Bend Region. . . . . . . . . . . . . . . . . . . . . . . . 764

16.7 Correlations for Vibration Prediction . . . . . . . . . . . . .

768

16.7.1 Fluid Elastic Correlations 768

16.7.2 Turbulent Buffeting Correlations 773

16.7.3 Periodic Wake Shedding 777

16.7.4 Acoustic Resonance Correlations. . . . . . . . . . 778

16.8 Effective Tube

Mass.

. . . . . . . . . . . . . . . . . . . . . . . . . 782

16.9 Damping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

788

16.9.1 Classification

788

16.9.2 Damping Coefficient. . . . . . . . . . . . . . . . . . . 788

16.9.3 Fluid Damping

792

16.9.4 Damping Data 792

16.10 Cross Flow Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . 795

16.10.1 Computer Models

795

16.10.2 Effective Velocity 796

16.10.3 Stream Analysis Method. . . . . . . . . . . . . . . .

798

16.10.4 Flow Distribution in the U Bend Region. . . .

800

16.11 Vibration Due to Parallel Flow. . . . . . . . . . . . . . . . . .

810

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16.12 Ideas for Preventing Flow Induced Vibration Problems..

813

16.12.1 Fluid Elastic Instabilities

813

16.12.2 Acoustic Resonance 820

16.13 Flow Induced Vibration Evaluation Procedure . . . . . .

823

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 830

References

833

Appendix 16.A Computer Program MULTSPAN

841

Appendix 16.B Natural Frequency

ofU Bends

Computer Program UVIB . . . . . . . . . . . . . .

851

Appendix 16.C Computer Program UFLOW 856

17 SUPPORT DESIGN AND EXTERNAL LOADS

17.1

I n t r o d u c t i o n 861

17.2 Types

of Supports Design

Data 861

17.3

Lo a d i n g s

866

17.4 Analysis for External Loads 869

17.5 Stresses in Annular Ring Supports Due to Vertical Loads 871

17.6 Lug Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879

17.7 Stresses in the Shell at Saddle Supports . . . . . . . . . . . . 881

17.8 Elementary Solution for Anchor Bolt

Loads.

. . . . . . . 886

17.8.1 Bolt Load Distribution in a Three Lug

Support System . . . . . . . . . . . . . . . . . . . . . . . 886

17.8.2 Foundation Response

of

Ring Type

Supports Mounted on Rigid Foundations. . . .

889

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

891

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

891

Appendix 17.A Computer Program RINGSUP 892

18

FOUR LEG SUPPORTS

FOR

PRESSURE VESSELS

18.1

I n t r o d u c t i o n

899

18.2 Problem Definition 902

18.3 Determination

of

the Most Vulnerable Direction

of

External Loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

903

18.4 Computation Procedure 909

18.5 An Example 909

18.6 Observations on the Optimization Method 910

18.7 Stress Limits 912

Nomenclature 914

References 914

Appendix 18.A Multiple Loadings on the Pressure Vessel

915

Appendix 18.B Computer Program FORLEG 916

19

SADDLE MOUNTED EQUIPMENT

19.1 Introduction 925

19.2 Determination of Support Reactions. . . . . . . . . . . . . .

928

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19.3 Foundation Stresses

93

9

An Example . . . . . . . . . . . . . . .

934

19.5 Bolt

Load-Rigid

Foundation

934

19.6 Computer Code HORSUP . . . . . . . . . . . . . . . . . . .

937

19.7 Stress Limits for the Concrete Pedestal and Anchor Bolts

938

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 939

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

20. EXTERNAL LOADS ON VERTICALLY MOUNTED

EQUIPMENT

20.1

I n t r oduc t i on 947

20.2 Maximization of Support Reactions . . . . . . . . . . . . . .

949

20.3 Foundation Response

955

2 4

Computer Program

VERSUP

96

20.4.1 Overview

of

the Code. . . . . . . . . . . . . . . . . . .

96

20.4.2 Input

Data

for Program VERSUP

961

Nomenclature

974

References

974

Appendix 20.A Partial

Compression-Thick

Ring

Base.

. . .

975

21. RESPONSE SPECTRUM

21.1

I n t r oduc t i on 979

21.2 Physical Meaning

of

Response Spectrum. . . . . . . . . . .

979

21.3 Response

of

a Simple Oscillator to Seismic

Motion.

. .

987

21.4 Application to Heat Exchanger Type Structures

991

21.5 An Example

996

21.6 System Response When the Natural Frequencies Are

Closely Spaced

1

21.7 System Response When Multi-Direction Seismic Loads

Are Imposed

1 1

21.8 Finite Element Method for Respone Spectrum Analysis

1 3

Nomenclature 1 4

References

1 5

22. PRACTICAL CONSIDERATIONS IN HEAT

EXCHANGER DESIGN AND USE

22.1 Introduction 1 7

22.2 Design for Maintenance

1 7

22.3 Selecting the Right Tube

1 13

22 4 Handling

1 13

22.5 Installation

1 16

22.6 Operation

1 16

22.7 Maintenance and Trouble Shooting 1 18

References

1 19

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PPENDIX

A Classical Plate and Shell Theory and its

Application to Pressure Vessels

A 1 Introduction

1 21

A 2 Basic Elasticity Equations

1 21

A 3 Specialization to the Bending and Extension ofThin

Walled Cylindrical Shells

1 24

A 4 Some Applications ofThin Shell Theory Results 1 29

A 5 Specialization to Bending and Extension ofCircular Plates

1 35

Nomenclature 1 39

References

1 4

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GLOSS RY OF COMPUTER PROGR MS

HE DSKIRT Chapter 2): Evaluation

of

discontinuity stresses at

ellipsoidal head-sheIl-skirt junction.

FL NGE Chapter 3) Flange analysis using Taylor Forge Method. 5 types

of

flange configurations: welding neck, slip on hub bed flange; lap joint;

hub bed lap joint;

nd

ring joint: Options: Given flange ring thickness

computer flange stresses - or given stress limits determine flange ring

thickness.

TRIEL Chapter 4 Stress analysis

of

a three element flanged joint

tubesheet sandwiched between two flanges) in

V tube

heat exchangers. The

concept

of

flange-tubesheet contact outside

of

the bolt circle

is

included in

the analysis controlled metal-to-metal contact). A two element joint, or a

bolted joint consisting

of

a flat cover and a welding neck flange, can also be

analyzed. Stresses in all elements are predicted.

GENFL NGE Chapter

5

Analysis

of

a two or three element bolted joint

having gaskets too wide to be modelled as line elements. Full faced gaskets

can be treated. Non-linear gasket stress strain curves are allowed. The

gasket compression and decompression history

is

followed using an in

cremental solution technique. Joint leakage pressure as

well

as bolt and

flange stress is computed. Effects

of

bolt overstress can be studied.

Compression stops at different locations can be accommodated.

LIGTEM Chapter

7

Prediction

of

temperature distribution in a tube

wall

nd

in a tubesheet ligament through the thickness

of

the tubesheet)

under specified thermal boundary conditions on the tubesheet surfaces, and

on the tube inside surface.

TBROLL Chapter

7

Fortran microcomputer code using CRT input and

output and also printer hard copy. Evaluates residual roll pressures using

Tresca Yield Condition.

GENROLL Chapter 7 Elastic-Plastic analysis

of

tube rolling process

and a single cycle

of

subsequent thermal loading. The von Mises Yield

Condition

is

assumed without strain hardening. Large deformation effects

are included. The code does an incremental analysis

of

loading, unloading,

and subsequent thermal cycling. The tube-tubesheet interface pressure

is

traced throughout the problem. Arbitrary

tube/tubesheet

material com

binations can be used.

UTVBE

Chapter

8

Interactive Microcomputer code written in BASIC

for analysis

of

a tubesheet in a

V tube

heat exchanger. The effect

of

un

perforated rim

is

included in the model. Support conditions permitted are:

integral construction both sides; one side integral, one side gasketed; and,

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two side gasketed. The effect

of

different gasket radii

on

each side

of

the

tubesheet

as

well

as

the effect

of

edge bolting

is

accommodated. Shell and

channel stresses are also computed.

FIX SHEET (Chapter 9 Performs a complete stress analysis

of

two side

integral tubesheets in fixed tubesheet heat exchangers. The two tubesheets

are identical, and vertical and horizontal orientations are permitted. The

effect of

elevation in vertically mounted units, the pressure loss due to fluid

flow,

nd

quasi-static seismic acceleration effects along the tubesheet axis

can be incorporated. Complete stress analysis

of

all portions of the unit are

obtained. The unperforated rim

of

the tubesheets is treated by plate theory,

so that there

is

no restriction on the width

of

the unperforated zone.

FIXFLOAT (Chapter 9

Program assumes heat exchanger symmetry so

only one tubesheet need be modelled. Analysis

of

the tubesheet

of

fixed

tubesheet exchangers,

or

the stationary tubesheet

of

a floating head unit can

be carried out. The program computes stresses in all relevant portions

of

the

exchanger for a given tubesheet thickness and unit geometry. Mechanical

and thermal loads are included, and a thickness based on the TEMA for

mulas can also be determined. The unperforated rim is treated by ring

theory and the tubesheet attachment to shell and channel can be two side

integral, one side integral and one side gasketed, or two side gasketed

co'nstruction. Bolt loading and different gasket radii on each side of the

tubesheet can be accommodated.

MICROFIXFLOAT (Chapter

9

Interactive microcoputer BASIC

code which uses the same basic theory as FIXFLOAT but utilizes additional

data, input by user, from graphs to predict the tubesheet stress, tube load,

and shell force.

PRESHEET* (Chapter

10

A pre-processor code to construct a finite

element model for analysis

of

single and double tubesheets for V-tube

construction or for fixed tubesheet exchangers. The pre-processor accepts a

minimum

of

user supplied geometry and material data and constructs the

necessary data file for a model with 310 node points and 27 elements. The

data file created is usable directly by the finite element code AXISTRESS.

AXISTRESS* (Chapter

10

A 2-D elastic finite elements code for plane or

axi-symmetric finite element analysis.

POSTSHEET* (Chapter

10

A post-processor for analysis

of

single

or

double tubesheets. The code processes the results

of

an AXISTRESS

analysis and presents the results in a form for easy checking

of

critical stress

areas.

DOUBLESHEET (Chapter

11

Solves field equations for closely spaced

double tubesheets under mechanical and thermal load. The tubesheets can

be either simply supported or clamped. The tubesheets are modelled as

thick

Listing not given in the text

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plates; the tubing between tubesheets is modelled by appropriate stiffness

elements which reflect the effects

of

both bending and shear in the tubes.

Stresses are computed for user specified radial locations in the tubesheet

and in the tubes.

LAPCOV Chapter

12

Responses

of

a Bolted Cover-Lap Joint Flange

Under Seating and Pressurized Conditions. Metal to metal contact at any

radius outside

of

the bolt circle is permitted.

UBAX Chapter 14 Computes the bending and direct stresses in the tube

overhang and U-bend regions due to a specified inter eg differential thermal

expansion, and an increase in U-bend radius due to a temperature rise. The

code incorporates the effect

of

baffle restraint on U-tube thermal growth.

EXJOINT Chapter 15 Stress and deformation analyses

of

expansion

joints using an improved theoretical analysis

of

the classical Kopp and

Sayre model.

EJM REC Chapter 15 Analysis of rectangular expansion joints using

EJM formulas.

FLANFLUE* Chapter 15 Pre- and Post-Processor for a finite element

analysis

of

a single convolution

of

an expansion joint. The codes are set up

to construct a data file for AXISTRESS, and to present the results

of

the

finite element analysis in a convenient form for checking stress in critical

locations. The spring rate of the joint

is

computed based on the finite

element results.

MULTSPAN Chapter 16 Computes natural frequencies and mode

shapes for a straight tube on multiple supports. The straight two ends are

assumed built-in and N-l intermediate supports can be located along the

tube.

UVIB* Chapter 16 Computes natural frequencies and mode shapes for

the out-of-plane vibrations of tubes in the U-bend region.

UFLOW Chapter 16 Computes the quantities needed

to

describe the

flow field in the U-bend region of a heat exchanger. t is assumed that

double-segmental baffles are present in the unit. The code computes the

flow velocity for different tube layers at various radial locations.

RINGSUP Chapter 17 Calculates the total membrane and bending stress

at the junction of an annular ring type support and the barrel of a pressure

vessel.

FORLEG Chapter 18 Determines the orientation of horizontal force and

overturning moment on a vertical unit with a four leg support structure that

maximizes the stress in one of the support legs. This stress

is

then computed

and all loads on the highly loaded leg are printed out for use in foundation

design and for use in local stress analysis of the vessel.

HORSUP Chapter 19 Analyzes a horizontal saddle mounted vessel

subject to discrete nozzle loads at arbitrary locations and to seismic inertia

Listing not given in the text

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loads. The program computes the overturning moment nd axial force at

both supports and determines the maximum concrete pressure and bolt

stress. The maximum support stress is also computed.

V RSUP Chapter 20) The code determines the support reactions in a

vertically mounted unit supported t

two locations. Both supports can resist

lateral loads and bending moments; only the bottom support resists torsion

or vertical force. The magnitudes

of

nozzle loads, but not their sense

of

action, is assumed given. The code determines the sense of action of all

components of nozzle loads so th t each one of the reaction components is

maximized in turn. These maximized reactions are combined with seismic -

loads to compute the maxi-max of each reaction component in turn. f the

sense of action of all loads is specified, then no maxima are found.

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Numbering Scheme for Equations Tables etc.; notes on

arrangement

o

the text

All equations are labelled as

chapter

number. section number.

equation number. For example, Eq. 3.10.4) means equation

number 4 in section 10 of Chapter 3 Tables and references are also

numbered in

an

identical manner. Appendices pertinent only to a

particular chapter are labeled with the chapter number followed by

an alphabetic appendix number A,

B,

C in sequence). Equations,

tables, etc. in appendices are labelled sequentially. For example,

equation 16.A.l

is

the first labelled equation in Appendix 16.A.

xxiii