Study of the tubesheet design of a multitubular reactor: report of a training 1 August - 15 October 1986 at the SIPM, Den Haag

Study of the tubesheet design of a multitubular reactor

Citation for published version (APA):

Jongerius, N. A. (1987). Study of the tubesheet design of a multitubular reactor: report of a training 1 August - 15 October 1986 at the SIPM, Den Haag. (DCT rapporten; Vol. 1987.034). Technische Universiteit Eindhoven.

Document status and date: Published: 01/01/1987

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Coco U ~ r - c e r L ~ s , , d - _ p L , ~ . ~ d 192260 WFW-rapport nr. WFW.87.034

STUDY

- -

OF THE TUBE SHEET DE5iGN

-

OF

fi

M U L T I T U B U L A R REACTOR

Report o f ä training 1 a u g u s t 1986

-

i5 o k t o b e r 1986

a t the C I P M , D e n Haag

CHftPTEFi SUMMARY & CONCLUSIONS

This study is performed within the framework of a training for a student of the Technical University in Eindhoven.

It

is based upon a n e.<isting design of a multitubular reöctor, which i5 found to be too e..pensive. Its price can be decreased b y reducing the dimensions of its components.

Since the shell, tubes, and spherics1 heads are simple parts, their dimensions can easily be optimally calculated.

It

is not eF~pected that a new evaluation of these parts will result in a cheaper reactor.

The tubesheet however is a more complicated component: the interpretation of the stresses due to the various loads can b e difficult.

If

this interpretation has not been carried out optimally, the tubesheets can become thinner.

Thereby also alternative constructions for the tubesheets a r e possible, which may reduce the required tubesheet material volume.

In this study possibilities to reduce the price o f the reactor by reducing the required tubesheet volume are evaluated.

First the e ~ i s t i n g design i 5 evaluated.

It

appeared, that within the stress limits based on the Codes (libe FISME 8 [ l l , British Standard 5500 [ 2 1 ) , the achieved tutesheet thicCne5ses were optinal. Secondly tuo alternative constructions are ez.amined: a thicl e n e s thin tutesheet, and dished tubesheets.

I n t h e c a ! r u f c t i o r , s fcr ? h e f i r E t e l t e r m t i v e u r , f c r t u n s t ~ ! v s z v ~

ri.-tair~ ha\*e t ~ z r fladt. f t e r f f c r t i 1 5 ~ 1 5 5 irri~c.ssitfe to arst.' o ~ , -elieb!e cunclu5icnc fr.r ? t . i s o ! ? ~ ~ n c + i k ~ . -

The second alternative, dished tubesheets cdn indeed give a ICL required tubesheet volume. However, t h i 5 goin in Lilo's is decreased because o f 2 required reinforcement ring.

The use of dished sheets has also large consequences on othe- fields: the price per L i l o w i l l increase because of the more difficult manufacturing of dished plates with very many holes, and the price o f the rest o f the construction may increase, e.g. because of changes o f the cätaiyst handling, and/or a higher reqirired shell.

Therefore it is not expected that i t is possible to achieve a price reduction that mal.es a further examination of this alternätive

interesting.

The calcuintions t h a t a r e p e r f o r m e t , ö r e tcaseo c n t h e stress iisl?r

alven by the Ccoes. These stress limits for shrk.e-dcun o f secoridary stresses to elastic behavicr are base3 o n ejestlc, ~ c i e a i l y p235tlc

meterial behavior. That m a n s that no wort.. hardening i s included.

It

appesred that i f worl. hardening is included, the sllosirabfe stresses f o r secondary stresses c ö n be higher. Since the tubesheet tbickners is determined by tata1 i = pririiary p l u s secondary? stresses, then a l e s s thicl. tubesheet can be used, which results in a cheaper reactor.

Contents

preface

CHAFTER

e :

S u R n a r y and conclusions CHhFTER 1 : Introduction

CHAFTER

2 : General 82.1: 8 2 . 2 : 8 2 . 5 : 5 2 . 4 :

Description o f the reactor vessel Stress classification

Description of the loads Determination o f worst cases

CHAPTER

3: Evaluation

of

the

present desion

10

i e

11 14 Introduction

Division of the stresses according to §2.? Checking the calculated thicknesses

Conclusion 53.1 :

83.2: §3.3:

53.4:

CHAPTER 4 : E i f f e r e n t si:ed tubesheets

In? t-c r i? i c ~ l ~ ~

ct:,

t 1 F,3 1 c tr, f 1 g u r i t 1 c r! 3

CHAPTER 5: Di-hed tubesheets

Introduction Assumptions

Required thickness of the tubesheet Required reinforcement ring

Volumes cf tubesheet and reinforcement ring Results

Evoluetion of the impact of the use of dished tubesheets Conclusion §S.l: §5.2: 95.3: g 5 . 4 : 95.5: 8 5 . 6 : Ei5.7: 85.8:

CHAPTER 6: Evaluation

of

the basis

of

&

stress limits

5 6 . 1 : §6.2:

§6.3:

Introduction

Elastic, ideally plastic material behavior Including work. hardening in the material behavior model Conclusion 34 34 36 37 6 6 . 4 : Literature

li5f

APFENDICEL

l i T e m p e r a t u r e differences between t u b e s ? / Caìcuìatlons arcfirding t o

er

55(3D 1985

3/ Calculötions a c c o r d i n g t o hCNE Nuclear C G d e A 8BO@ 5 / Temperature d i f f e r e n c e between tubebundle and shell 61 Determination o f equivalent precsure for dead w e i g h t

7 / Numerical v a l u e s

- 1 - CHFìF.1 E R

-

_{3 :}

The b a s i s o f this study is an existing dezign of a mGltitubular reactor, uhich 1 5 found tc. be too ehpensive. To achieve ä reduction o f

the price, the dimensions of the components, that are not prescribed b) the process that has to tale place in the reactor, can be reduced when allcwê!ble.

The global components are: shell, spherical heads, tubes, and

tubesheets (see figure 2 . 1 ). Since shell, heads and tubes are simple construction parts, i t can reasonably be assumed that they are

optimally calculated in the present design. The tubesheet's dimensions however are more complicated to determine.

The evaluation of the stresses in the sheet, that means which criteria must be satisfied by which stress because of which load, is difficult to perform.

If

this has not been done optimally, the

tubesheet 5 may become thinner , and thus cheaper.

&lso interesting i s a that alternative constructions for the tubesheets are possible.

The reactor càn be seen as a large, fi.b.ed tubesheet heat exchange-.

Therefore in this study the possibilities are evalueted to decrease the price o f the resctcr b y decressin2 the tots1 needed tubesttee?

volume.

Chapter 11 gives the global dimensions o f the reactor, the applied stress limits, and a description of the loads.

I n chapter 111, the evaluation o f the stresses that lead tu the present design are followed. I f thìs evcluation has not optimally bee? performed, a first reduction of the tubesheet volume possibly can be achieved.

N e x t to the present design, that consists in two nearly equally

thicl tubesheets, other constructions are possible. Chapter IU handle: the alternetive that a thicl. and a thin tubesheet are used. The

idea is that the power of à sheet to bear a moment increaser

quadratically with the thickness.

I f

more load can be t o r n b y onf tutesheet, this might give a tubesheet volume reduction.

given. This possibility is based on reduction of the bending stresses,

s o that the membrane stresses become determining. T h i s may give

thinner tubesheets.

pz-cih!~. E.g, E k 8 e l i o u in t h e attechmrnt o f tubcchect t c a h e i i , Q T E

three dinensìonai tutresheet con-tructzon.

It

1 5 very w a l l p@5Slb1€ that a tubesrleet volume reduction COT! b e ö z h ì e v e d kith t h e s e

alternatives. Houever, urithin the tine airellable for this stud, i the-c

could nr,t tie eveluated.

In chapter U an evaluötion of the use o f dished tubesheets is

T h e s e were only twc. c g n s t r U r t i o n o ! siternativef; nöng v:ore a r e

The stress limits used in the prevlous chapters are based o n an elastic, ideally plastic material behavior model.

In

chapter U I , the implementation o f work hardening in this model is evaluated.

Beside the evaluation o f the possibilities of tubesheet volume reduction, also is evaluated what the maximal allowable

temperature difference is between tubebundle and shell, based on occurring temperature differences between tubes. T h i s is done in Flppendix 3.

CHAPTER C.ENERAL

K.1

At the baci o f the r e p o r t , a f o l d out paper w i t h the u s e d v a r i a b l e names i s attached.

DESCRIFTION OF THE REFiCTOR VESSEL

The r e a c t o r can be seen a s a l a r g e heat e./changer (See f i g u r e 2 . 1 ) . I t c o n s i s t s in a c y l i n d r i c a l s h e l l , s p h e r i c a l heads, tubetundle and

two f i > . e d tubesheets.

The tubes a r e f i l l e d w i t h c a t a l y s t . i3 gasflow goes downward throuQh the tuhes from the upper t o the iower head. I n t h e t u b e s , the c a t a l y s t

and the ga- r e a c t . The heat t h a t r e s u l t s f r o n t h i s r e ä c t i o n i s

absorbed by the c o o l i n g f l u i d ( w a t e r o r oil) i n the s h e l l s i d e of the r e a c t o r .

L

. .

-

1

FEED

L

C O O W T OUT figure 2 . 1 - - .

- 3 -

The t o t e l tubesheet construction c a n be seer) a s consisting i n two

7

ports: the tubesheet and the ì-lammerheäd (see figure d . 2 ) .

figure 2 . 2

The tubesheet itself is a circular plate, perforeted for the tutez The hammerhead is the connection of tabesheet and she!l. The

I t : s suggested thst this construction 3 5 e . = p e n s i v e , and ancthrr within the Outer lube L i m i t Circle. The diamcter u i l 1 be called

De

.

groove i s implemented to reduce the stresses in the tubesheet. p ~ s s i b i l i t y , krhich would b e cheaper, i s proposed. In fipFendit. 4 is shown thot the origins1 constructicn i5 setisfactory,.

Dato Materiels

The materialr thst are used in the present design ere: She1 1 CA 533 6 r . E

Heads CA 533 6r.E

Tuteshert SF; iE2

FI

Tubes not spec i f i ed

These materiels are chosen by the designer. Evaluation Gf these choices does not fall within the scope of this study.

It

must be ncted f h p t the use of other materials will not influence the conclusions of this study, since i t only influences the stress ìimits that are valid f o r all considered aiternatives.

*

Parameter values f o r present design Parameter value Description

d* 30 mm di 26 mm dh 30 mm

D

6866 mm Do 6456 mm D, 6730 mm

D,

6730 mm

Outside diameter . o f tube Inside diameter o f shell Tube hole diameter

Outside diameter o f shell

Diameter o f outer tube l i m i t circle

Diameter to u h l c h shell fluid pressure 1 s exerted Diameter to which tube fluid pressure is exerted

- 4

-

e 2 3 5 / 2 4 5 m m es 66 mm

E

la5476 N:mm2

E s

194220 N:'mm2

Ed

1 8 4 1 13

N/FIFL

f Ze@ N/mmZ k 7 nm N 26220 37 mm P p, pz

T,

23s 'C e4 2 Firn

-

_{3 . 7 N/mmZ} 4 . 4 N/mn? A P 0.6 N/mm.Z Tt 235-260 'C Q s 1.379E-5 1/'C q t 1.265E-5 1 / ' C m u 0.189 3 e . 3 Thicknecs of l o w e r / u p p e r tubesheet

Shell thiclness including corrosion allowance Nominöl tube thiclnezs

Ela.tic m o d u i u s of tubesheet mötrriei Elastic r,odulus of shell msterial Elastic modulus o f tube material

Nomine1 design strength of tubesheet materiäl Ligament width

Nunber o f tube holes in tubesheet Tube pitch

Shell side design pressure

Tubeside (channel side) design pressure Pressure drop over the tubes due to catalyst Mean shell metal temperature less

l@*C

Mean tubewall metal temperature les

l@'C

Thermal expönsion coefficient of shell meteriöl Thermal e,-:pansion coefficient of tube material Ligament efficiency

Poisson ratio of tubesheet material

8 2 . 2 STRESS CLACSIFIChTION

92.3 DESCRIPTION OF THE LOADS

The loads that are exerted upon the tubesheets result f r o m several causes. The stresses these loads induce, w i l l be classified according t o 5 Z . ? , figure 2 . 3 .

-

Channel side pressure

The channel side pressure is not equal for the whole channel side. The gasflow through the tubes finds resistance from the catalyst. Therefore a p r e s s u r e difference tetween the upper and he lower heod

er. i s

t

s

.

We divide the pressure channel side in two parts:

.

Constant pressure channel side

.

Pressure drop

This is the pressure in the lower head

T h i s is the pressure difference between upper and lower head, which results from the resistance o f the catalyst.

-5-

BS

5500:

1985

luua 1.J.nuy 1986

? i

I

.

figure 2 . 3

-6-

The effect of the conEtant channel s i d e pnessure (pc) is

schematically given in figure 2.4.(a). Mök.imuF~ value is the tubecide design presrure.

Beceuse of the large amount of tubes, mcst of the load will te carried b y the tubes. The tubesheet will only deflect ne8r the edge o f the tuberheet, because of length difference between ttibebundle and shell. This gives discontinuity stresses, which t a n be

classified a+ secondary stresses ( s e e figure 2 . 3 ) .

-

--

Shell side pressure

T h r s l 0 3 d i E p c ä u E e ~ i v o ~ the 5 9 m e l ~ ö d CE the tkbe-heets I S the constent channel side pressure, except for the völue and the

direction. See figure 2.5(c!. Manrmum value is the shell s i d e design pressure.

occurring stresses due to this loading cause can be classified as secondary stresses.

Therefore the same discussicn is v a l i d , and thus the

-

-

Dead ueiaht

of

tubes. tutesheetr. cetalvst snd cc~oiinq f l u i d

Because all components, o f which t h e dead weight has t o be born by the tubesheets, are equally distributed over the reactor, the resuiting ioaci can be seen a5 o bistribüted !ûed cvsr t h e fotal tubesheet surface. F o r determination of the equivalent pressure, see appendix 6.

The tubes do not have ä staying action, but distribute the load over the two tubesheets..Therefore the loading can schematically be represented as figure 2 . 4 ( b ) . The resulting stresses can, like those due to pressure drop, be classifred as primary bending stresses.

-

Temoerature and expansion differences

The reaction of the gases in the tubes with the catalyst

produces heat. T h i s heat is absorbed by the cooling fluid. Therefore the shell has a lower temperature than the tubebundle. (See data

-7-

Secondly, t h e tube m a t e r i a l ha5 O thermal fapansion coefficier,t, different f r m that o f the she11 material.

Because o f this, ertpansion differences b e t w e é n t u b e b u n d l e end shell o c c u r . T h i s u i v e r distùntinuity stree5es i n the tubesheet: s e c o n d a r y .tresses.

by the tubes on the tutesheet ( s e e f i g u r e 2 . 4 ( d ) )

The load can be seen as a ncn u n i f o r m l y distributed l o a d , ep’erted

ia! ( b ) ( C )

figure 2 . 4

í d )

Conzideting these five loadings, it appears that they car, b e

divided in two c l ö s s e 5 : symmetrical m a ontirynmatricoì. Symmetrical

The loads in t h i s clsrs are:

-

channel side p r e s z u r e

-

shell r i d e pressure

-

temp. / e ~ p . differences See figure 2 . 4 ( o 1, ! c )

,

d ).

These loads g i v e only secondary stresses.

* hntisymmetrical

These loads are:

-

pressure drop i n tubes See figure 2.4(b).

These loads g i v e primary and secondary stresses.

-

decd weight

5 2 . 4

DETERMINATION OF

WORST CF1SES

The required thicknesses o f the tutesheets must be calculated s o that the stress limits w i l l not be exceeded f o r any load that can occur within the design values. The worst situation is the situation that gives the largest s t r e s s e s . f f the stress limits are satisfied

for this situation, they are satisfied f o r all occurring loads within t h e design values. Thus i f the required thickness 1 s to be determlned, first the worst loading situation must be found. This will be done in this paragraph.

direction. Since the combinations o f loading causes (see § 2 . 3 ) that

give this m a x i m u m load differ for the two tubesheets, the worst case has to be determined for each tubesheet separately.

-E-

Ir. p a r a ~ r a p h 2 . 3 the stre:seE resaltinp frcr., the different 1cad;nQ

c e ~ ~ 5 are divided in p r i m n r ) and serrndsry s t r e ~ s e r . h c c o - a i n ~ to figure 2 . 5 , different sire55 limits e . 1 ~ : : l i m i t - fc.r the priEöry s t r e s ~ e s o n l y , l i E ì f s fcr the primery plus secondcry s t r e s s e r , a ~ d

limits for primary, s e c c n d t r b plus peel s t r e s 5 e : .

T h e r e f o r e worst c a s e s must te fr;uvd fcr only primary stresses, a r @ for primary plus secondary s t r e z s e s . The last limits are not included in thit calculaticn, since no high c y c l e fotigue calculstions a r e

done.

-

U c u e r tubesheet

primary stresses

There are twc l o a d i n g c a u s e s , thöt g i v e primary stresses: desd weight end pressure drop. Since the resul?ingi lcad ic. pointed

d o i l n l c a r d f o r bcth caLices, the wctrst ìoöd:nQ C B E € 1 s : ma>imum pressure drop

d e e d weistit

p r r ~ s r y p l u s secondary

tresses

The downuard pointed ì o e i s are caused b y : cc.nstärit pressure chtnrtei side, dr3d weight ana p r e s s u r e drop. Shell side preccdre ar,c !er,sersture difference g i v e an upward 10312.

upword, and ma,’ 1 i - i ~ ~ l o e d downward:

Nok twc? p0551ble worst ì o a d i n p csses a r e p o s s i b i e : m b ~ ~ i m L i i r , ìoed

Upuerd: minimum pressure channel s i d e

m ä r . i m u m pressure shell side

no pressure drop dead w e i gh t

mar.imum temperature difference

Downward: m ä x i m u m pressure channel side minimum pressure shell side maximum pressure drop in i u ù e s dead weight

minimum temperature difference

Which load is worst can be found out when values f o r the pressures and temperature differences are substituted.

in megnitude neerly the sane load, s i r - 1 ~ ~ t h e therr.61 e,-.pan~i~irt

coeff:cients cf s h e l l and tgte ~ ‘ . ~ t e ~ i ë ì differ isie agpendir 5 ‘ .

The downward load contains a constant channel side pressure o f 4 . 4 N/mm2. The upward load only gives 3.? N / m d pressure

shell side. These pressures give the sans sort of stresses in the tubesheets, but f o r the sign and the value.

T h b s , s i n c e t h e c c n s t s n t p r e s s u r f chsnnel ~ i d e i s l a r g e r , t h e

i n d u c e d E t r e c s e - frcm t h e d c w n * ö r d load a r e h i p h e - t h e n frorr t h e u p w c r d l c c d . E e c a u s e t h e d o k n w a r d 1c.cci c o n t s i n c o l o a d from t h e p - e ~ r u r e d'op o v e r the t u b e - e x t r ö , t h e downwörd l o a d 1 - thE: w o r ~ t

I G e d .

-

Lower t u b e - h e e t p r i m a r y stresses L i k e f o r t h e u p p e r t u b e s h e e t , t h e worst l o a d i n g c a c e i s :

.

ma>.imum p r e s s u r e d r o p

.

d e a d w e i g h t

*

primary p l u s s e c o n d a r y s t r e s s e s The a w n u i a r d p c i n t e d l o a d s ö r e côuced t y : p r e s s u r e s h e l l s i d e , d e 5 d w e i B h t and pressure d r o p . C c r i s t a n t c h a n n e l s i d e pressure 2 n d t e V & p e r s t u r e d i f f e r e n L e g i v e a n QpLc'ard i c a d .

Now o g e i n twc p o s s i t l e wcrst I c e d i n g cases a r e p o s s i b l e :

f i ö b i m d n l o e d u p w a r d , a n d f i a i i n u m l e a d d o u r i w a r d :

Up uii 7 d : &a,& ìpIIur: pressure c h a n n e l s i d e

m i n i m c F pressUre s h e l l s i d e rip, pressure d r c p d e s d uelQ5t m i ~ i m ~ m t emrterature d i f f e r e n c e D o d n w a r d : p r i f i i m u m p r e s s u r e c h a n n e l s i d e fis-.:r4um p r e z s i l r e s h e l l s i d e marimurn p r e s s L i r e d r o p i n t u b e s d e c d w e i g h t ma?.imum t e m p e r a t u r e d:f f e r e n c e S i n c e a t e m p e r a t u r e d i f f e r e n c e o f 0'C g i v e r t h e same l o a d a s a d i f f e r e n e e of 5@'C, t h i s f o ä d i n g c a u s e d o e s n c t i n f l u e n c e uhich l o a d i n & c o m b i n a t i o n g i v e s t h e larcrest stresses.

T h e u p w a r d l o a d c c n t a i n s 4 . 4 N/mrct2 c o n s t a n t c h a n n e l s i d e

p r e s s u r e . i n e d o w n w a r d l o a d c û n t s i ï î s 3.7 !t/mm? ;he!! s i d e p r e z s u r e , a n d 0.6 N/mF.i,7 p r e s s u r e d r o p . S i n c e t h e p r e s s u r e d r o p m u s t b e c a r r i e d b y t h e t u b e s h e e t s , a n d t h e p r e s s u r e s s h e l l a n d c h a n n e l s i d e exert mostly on t h e t u b e s , t h e d o w n w a r d l o a d g i v e s t h e l a r g e s t stresses in t h e lower t u b e s h e e t , a n d is t h u s t h e worst l o a d i n g s i t u a t i o n . '

C H 6, P T

E

E

_{- -}

0; THE FRE SEN? DE 5 I 5.11

SZ. I N T R O D U C T I O N

The present design contö:ns :wc. neariy er,uäily thicl tutezhéots. Normally, tubesheet thiclnesser a r e determined using the Code rules. F o r large heat erchangers, a f u l l stress analysis is recommerided (Eritish Standard 55@@ 1 9 8 5 , page 3/83), since the code rules might lead to excessive thick tubesheets.

performed, Appendix 3 gives a calculation according t o A5ME Nucleer Code. Conparing theie results with the FEM-analysis, performed by the deaiyner of the present design, shows that the codes f o r this reactcr indeed l e a d tci excessive thicl. tubesheets.

In Appendir 2 a calculation öccording to b i t i s h Standard 55@@ is

In this chäpter, the FEN-anolysls is evaluated.

The perforclted tubesheet is modeled a s P plate with the s a n e dimersic.ns, but w i t h equivalent elastic ccnstaríts, according tc FiCME V I 1 1 C ’ i L . 2 f31.

r e c c hrd :

Firstly, i f the streszes are nct optimally interpreted, tco thicl tubesheets ~ i g h t result. Secondly, i t is possible thot , wher, t h e

deternining stress l i m i t is found, net the minimum p o s s i b l e tubesheet thicLne-s I S calcdlated. T h e r e two possibilities are cc.nridere? In the ne. t t wc~ paragraphs.

There are twa pcssibilities tho? not the optihiel thiclnrsz i s

U i i n g elastic FER-anoiyzis i t i r psrsible to ce!culate the distribution of the stresses in ä chosen cross section. F r o m this distributicn the stresses cërl be divided ir: ir;e~trorie, bending, and

peal. :tresses (Stoomwezen i53. j . T o be abir t o use the $tress

limits given by 5 2 . 2 , figure 2 . 2 , elss a division m d r t be made in primary and s e s m d a r y stressez.

(Division in global and local stresses is not appiicatle here, since the occurring primary membrane sireEses are e ~ p e c t e d to De v e r y

small, and thus not expected to have a l a r g e influence on the total prinary s t r e s s

o r not with elastic FEN-analysis, since then infinite elastic behavior is assumed. Therefore the loads have t o be divided in loads that do, and loads that do net give primary stresses.

It

is not possible t o determine whether a stress 1 5 self-relieving

This division of the loads has already‘been done in 5 2 . 3 :

-

antisymmetrlcal loads give primary stresses:

.

pressure drop

.

dead weight

-

symmetrical l o a d s give no primary stresses:

.

constant pressure channel side

.

pressure shell side

- 1 1 -

-

a calculation with l o á d e thet give primary'stressrs, tc find an

-

a calculation with a11 the Icads, to find the tctol cccurring upper value f o r the mä-.iriöl occurring primary stresses

-tresses.

I f

the primery stresses appesr to be limiting, a Letter

interpretation o f the stre5ses can ie3d to smaller primary stresses, thus t o thinner tubesheets, thus to a cheeper reactor. I f the tote! stresses are limiting, a better division of the tctal stresses in primary and secoridary stresses has no use.

According to the designer, the total stresses appeared to be

limiting, while the primery stresses remained far below their limitr. Since only data are given f o r the tctal stresses, this statenent con hot be controlled, and has t o be ässumed.

5 3 . 3 CHECKING O F THE CALCLtLATED THICKNESS

I t

is pcssible thet the thicknesses resulting from the tctal

s t r e s s e ~ are nct optimelly colculäted. Therefore ö contrsl caiculetioc

will be done.

The only dota available f o r t h i s evaluation (see fiiure 3.í j Mere for a similar reactor ves-el, with thici.er tubesheets and a smaller diameter. These data give the stresses in the tuberheet in the

(according to the designer1 heeviest loaded zone: the Outer Tube L;Kit Circle.

That this is indeed the heaviest loaded zone is probable: Firstly, the moment per length in t h e tubesheet (in negative

direction) increases with the radius r (Raark E41 page 362 case í 0 b ) : Pi = a ( ( 1

+

) * ( $ D ) ^ 2

-

( 3 i y )*rA2> (3.1 )

16

That means that the larger the radius r. the larger the moment and thus

the

lärger the stresses.

Cecondly, outside the

OTLC,

the tubesheet is not perforated anymore: the carrying surface increases, and the occurring stresses decrease. Therefore the

OTLC

can very well be the heaviest loaded zone.

Figure 3.1 gives the total radial, tangential, axial and shear stress in the s m a l l reactor through the thickness of the tubesheet, at

- 1 2 -

8

figure 3.1

T h e r e s t r e s s e s r r r i l l : f r o v the follcurng loads:

-

pressure channel side: 41 bar

-

p r e s s u r e shell side : 25 bar

-

p r e s s u r e drop tube.: : 6 bar

-

dead weight

-

t e m p e r a t u r e difference: 25'C ( t u b e t e m p e r a t u r e = Z70'C

shell tempersture= 245°C)

Comparing this l o a d i n g combination with the werst p o s s i b l e o n e , sie

9

~ . 4 , - l . i t mus: Ye n o t e d tha? this 1s

o?

ffre M o r s t situation.

From these s t r e s s e s the stresses in the t u b e s h e e t s o f t h e reactor

that is the subject of this study, will b e estimated.

E s t i m a t i o n o f t h e stresses in the "real" t u b e s h e e t s

T h e maximal s t r e s s e s that occur at the s u r f a c e o f the tubesheets of the small r e a c t o r a r e :

-

r a d i a i s t r e s s = 72 N/mmZ

-

tangential s t r e s s = 33 N / m m 2

Tct f i n d o n estimóte f o r the r e a l o c c u r r i n g s i r e s : i n the t u t e s h e e t s

o f the recictor c o r l s ì d e r e d ir! t h i s s t u d ) , t h r e e c o r r e c t i o n r m u s t b e

done :

1 i Accounting f o r the p e r f u r a t icn

2 / Accctunting f o r the larger diameter 3 / Ficcounting f o r the t h i n n e r tutesheets.

fìccounting for t h e p e r f o r a t i o n

T h i s can be done b y u s i n g the ligamefit e f f i c i e n c y m u . T h i s i s

t h e ligament length between two c l o s e s t h o l e s , d i v i d e d b y t h e p i t c h o f

the holes ( s e e f i g u r e 3 - 2 1

mu = F'

-

d o

f

The liyav,.,ent e f f i c i e r i c ) i s B m e a ~ u r e f o r tb,e decrecze i n s u r f a c e

T h e r e f o r e the r e s : crcurring s t r e s s e s a r e o f a c t o r i / f i d h i g h e r than,

W i t h P = 17 m n , and dj, = JOI m r , the ligament e f f i c i e n c y is L ^ . l E Ç

t h s t has t o c a r r y the l o a d . t h e c a l c u l a t e d s t r e ~ s e : .

*

ficcounting f o r t h e l a r g e r diameter

A l a r g e r diómeter r e s u l t s i n a g u a d r e t i c ä l i n c r e a s e o f the proment

per length i n the tubesheet:

The s t r e s s is l i n e a r l y r e l a t e d t o the moment (Roark i41 page 332):

= 6 * M ( 3 . 2 ) e * ? T h e r e f o r e the s t r e s s w i l l i n c r e a s e q u a d r a t i c a l l y w i t h t h e d i amet er. With:

De

o f small r e a c t o r = 6337 mm

Do

of considered r e a c t o r = 6456 mm,

the r e o l stresses become a f a c t o r (6456/6337)^2 = 1.038 larger

- 1 4 -

h t h i n n e r tubesheet g i ~ e : ö q u a d r p t i c n l i n c r e a s e c.f t h e stre::: s e e e q u a t i o n ( 3 . 2 ) .

Witk,: tubesheet t h i c l n e E 5 c.f s m 2 1 1 r e a c t c a r = 283 mpi

tubesheet thicl.nessec cf considere6 r e a c t o r = 235 ano 2 4 5 m m

The r e a l s t r e s s e s become ir f a c t o r i260,'235>"2 = 1 . 4 2 ( l o w e r

tubesheet ) and ( 2 8 P / 2 4 5 ) " 2 =

1

.31 (upper tubesheet ) l a r e e r becaueE of d i f f e r e n c e i n tubesheet t h i c l n e s s .

Then t h e t o t a l s t r e s 5 e s i n the t u b e r h e e t s become:

-

icwer tubesheet: 6- = E O / 0. i e 9 1.039 + i - 4 2 = 625 N / m m i

-

U p p e r tubesheet:

c

= 8P / E . 1 2 5 + 1 . E 2 5 1.31 = 57E N / m 2

i h e t c t a l s t r e s s must b e i i n i t e d t c 3 time-. t h e d e s i g n s t r e s s ! s e e

f i g z r e 2 . 5 ) .

E e z ~ ~ s e the estimäted s!resses r e e c h t t , e i r l i m i t s , w h i l e n c t e*,.ert

t f I é warsi lcoding caze i s ä p p l i r d , t h e t h r c l n e z s e r o f t h e c c n s i d e r ~ d r e a c t o r r a n t e t a l e n t o b e o p t i ~ a l l y c i l c u l o t e d .

C U ~ I C ~ U ~ ~ C ~ P : The tubesheet thick-neszes of the ccnzidered r e c c t o r 2-e oFtimàl!y c o l c d l a t e 3 c c n s i d e r i n g c r i , l ~ tc,tJ-1 ( ~ r i i ~ a r > * p l u s

seccrroary ) 5 t r e s - e s .

F r , r t h e d e - i - i n ~ i t h tGo n e a r l y equal t u t e s h t e t z , the tuberheet t h i c k n e s s e s a r e o p t i m e l l y c a l c u l a t e d w i t h i n t h e s t r e s s limits a s g i v e n in 5 2 . 2 , f i g u r e 2 . 3 .

-15-

5 \i ~ri i r e t r i c E 1 1 o s d I

T h e c e i c a d s are m c r t ! y borfi by t h e tube5 ( s e e figure ? . 4 ! a ) , i c S ,

( d ) , a n d f i g u r e 4 . 1 )

figure 4 . 1

The load is performed b y temperature/expsnsicn difference between tube bundle and shell, and pressures at channel- and shell side. tubesheets, which a r e as thin as allowable. I f we make one of the sheets thicl..er, the load on the other sheet will not change. That means that the thickening o f one tubesheet will not lead to

becoming thinner o f the other, and thus not lead t o reduction o f the total required tubesheet material volume.

Conclusion: The optimal configuration f o r symmetric loads consists in

c..--..- a u p p v a c

-

t h e i;rssen? cûÏif:gurat:on ccnsists i2 t w eyual!y thick

two equally thick tubesheets.

Antisvmmetricel loads

The tubes nor: do not hake a s t ä f i n p e f f e c t , but t h e y keep ö n t a r l ) conEtant d i r t e n - e b e t u e e n t h e t t i b e r h e e t E : the,, d l s t r i o ~ t e the l o e ~ over the twv sheets i s e t . figures 2.4:b) a n d 4 . 2 ) .

-16-

I

f i g u r e 4 . 2 f i g u r e I 4.3

Suppose again that the present c o n f i g u r a t i o n i 5 one w i t h two

e q u a l l y t h i c k tufjeEheets w i t h minimum t h i c ì n e s s . Under a load t h e t o t a l c o n s t r u c t i o n w i l l d e f l e c t . ( s e e f i g u r e 4 . 3 )

í T = E + M ( 4 . 1 , see ( 3 . 2 ) ) e 2

B tubezheet has t c grcu a f a c t c r '' V c ' 'I thic1.i.r t o b e a r o fector ' , E *

F i D r e load.

This means f o r the limit s i t u a t i a n , i n which one tuberheet c a r r i e s

a l l the l o a d , one sheet has tc. groLi' o fó:tor " E'" t h i c t e r , while

CHFiFTEF. & DI SHED TCIEESHEETS

J

f igure 5 . 1

TG

b e able to cälculate an eztimate f o r the required tutesheet thickness, SOFIE assumptions wil! be made. W i t h these, the required thickness is determined.

load in the plane cf the plate. This implies, that a reinforcement ring is necessary t o a v o i d b u c k l i n g o f the shell. The velumer cjf plate and ring are calculated, t o determine whether a reduction o f the

required tubesheet volume can be achieved with using dished

r u u e a h e e t S .

are evaluated.

Because the resulting tubesheets are very thin, they only con bear

L . . & - -

Finally the implications of this alternative on the existing design

8 5 . 2 FlSSUMPTIDNC

In the calculation, some assumptions are made:

I / The f o r m of the dished sheet 1s assumed spherical.

The form where the least bending stresses occur, will not be spherical, since that is the optimal form for ìoad perpendicular on the surface. Here the load is vertical.

stresses has not been performed yet. I f the alternative o f dished tubesheets is useful, i t can be done later.

-26-

T h i s assumption ha5 ne i n f i u e n c e e n the cs!cuJstion e f t h e tuéesheet t h i c l nes:, only on t h e determinatlcr. c f the \.elume. f r cri t he e w, 3 c t b e ri d i n g

1

e s s t u b e s he e t ' s L o 1 u me.

I i

i s however nct e,>.pected t h a t t h i - v c l u m e ~ w : l l d i f f e r v e r ) much

2,' The weciieriinc, of t h e sheet dde tG t h t h c l e c i s s a i d t c be

ä c c o u n t e d f o r w r t h the ìigamerrt e f f i c i e r i r y mu. 3s t h i s ä s s u f i p t i c n c o n s e r v a t i v e 7

The c r o s s s e c t i o n cf t h e p l ä t e chenye: uitt, t h e a n g l e Cr- ( s e e

f i g u r e 5.3) w i t h the h o r i z o n t a i o f the tubesheet: 5 e e f i g u r e E.:.

o c =

e'

f i g u r e 5 . 3

T h u s : the l a r g e r the angle O L , t h e l a r g e r t h f c a r r y i n g s u r f a c e . T h e r e f c r e , the weai.ening e f f e c t accounted f o r b y t h e ligament

e f f i c i e n c y , 1 1 tor, l a r g e fer an a n g l e tinequal t o

e.

T h e r e f o r e t h e assumption is c v n s e r v è t i v e .

-

-i; The p i i n i ~ u p i r e q u i r e û tutiesheet t h i c i nerlcer a r e deterr:inec] h ë 5 5 3 CF p r i n a r ) s t r e s s e s .

I t is v e r y we11 p o o s i b l e t h à t not the p r i n ä - y , b u t t h e seccridarj.

~ t r e 5 l c e i a r e l i m i t i n g . T h i s i d e a i d r d p p i r t e d b r the înDu;ledge,

t h a t , w h e n t h e e q d a l l y t h i c k , f i a t tubesheets Lilere c ö l c u i o t e d , ~ 1 the secondsry s t r e s s e s were determining. s ~

55.3 REQUIRE@ THICKNESS OF THE

DICHEE

PLATE

The loading o f the p l a t e i s shown i n f i g u r e 5.3

-.

-

- i I -

Eecause the tutesheet does í can ì no! bear bending-moments , the u n i f o r m distrituted boundóry force f d c t w o r i 5 under a n snGle o f K I .

The co!culeticn i s based upor' p'imz-y strecses. T h e r e f c r e the j o e j

1 5

-

Pressure drcp o v e r tube5 due to catêlyrt ( ~ p )

- Dead weight, accognted for b y equivalent pressure ípq)

the following steps: first, using the equilibrium of forces in vertical direction, an expression is derived for the vertical distributed b o i i c d a r y force f,.

Then with e'pressions for total tsundery force f&t a5 function c.f f, , ònd f o r the stress G o s a function o f the tubesheet thiclness 4 o n d

tuberheet is deternined.

tubesheet, and the l i m i t for the primor,' membrane stresses ä i c c j r d i n c i to 5 2 . 2 , figure 2 . 3 , an exprecsicn i s derived for the minimum required tubezhfrt t h i c t ness.

The determinotion of the required tubesheet thickness is done w i t h

t h e b ú u n d a r y force fct, an e x p r e s s i e n f o r the stress i n the Implemerting t h e ueekening effect o f t h e perforstion cf the

Equilibrium of fsrces in verticcl direction gives:

W:th f o r t c t i n d s r y force f ónd f o r m m b r a n e stress :

f. = fy/sinw. and G = f/e , t h e stress in t h e tubesheet is:

However, no account 1s taken for the weaLening effect of the holes. This can be done by using the ligament efficiency mu. (See assumption

3 and 63.3)

Implementing the wtaLening effect, the occurring stress increases with a factor I/mu. Thus:

T h e resulting thicknecres are \ e r ) low f see 5 5 . 5 , täkle 5 . 1 , rciw

2 ) . Therefore nc bending stresses c a n be corried b y the tuberheets: a reinforcement ring is rìecersary to avoid buckling of the shell.

5 5 . 4 REQUIRED REINFORCEMENT RING

I n the previous port, t h e v e r t i c a l equilibrium o f f o r c e - i s u r ~ i e d

out. The uniform dirtributed mer,,Srarie force alst has a horizoritöi ccv,ponent. In o r c e r tc attic! b u c i ì i n g o f t h e shell due i o this f o r c e ,

a reinforcement ring is necessary.

A r s u m p t i ~ n : The cr3cs sectien cf the ring i 5 T-formed. ?FILE : 5 E

rether c o m m c n chcice, s i n c e i t combined h i D h t stiffne.5

u l i t h loc f i ä t r r i a l volume. T c be a b l e to m r t e Z C F , ~

c a i c u l s t i o n s , t h e dimensions Gf the ring are taler, a i in figure 5 . 4 . Thot mean-. that only ene varieble reTain5 t o

t e deteri-cined. I t ma} b E p o s s i b l e to f i n d ö tetter configvreticn, but :his configura?lcn g i b e r ö good

e s t i m e t e fcr the r e q u i r e d d i m e n Z i o n s and t h e v o l u n e c f t b e r e t l d i r e d reinfcrcement ring.

..

c =

figure 5 . 4

There are f u o criteria o n which the minimal required cross sectional area of the ring is to b e determined.

-

Strength : The stresses in the ring may not exceed the maximal allowable membrane stress (see § 2 . 2 , f i g u r e 2 . 3 )

= f h

+ D

f i r k f l t h A, = c r o s s s e c t i o n a l s u r f a c e o f t h e r i n g and t h e r e l a t i o n : fc, = f v i t a n d w e f i n d : Z/ C t ä b i i i t y The l i m i t s then b e c o m e : I / Strength: 21 S t a b i l i t y : h ? ( f v + D

)*i

t a n d * C ) * L h > ( f r r 4 0.031 + t a n d

-?C.-

5 5 . 5 V'JLUMEC OF TLlEE5HEET F.NZ REiNFDHZEMENT RIt.1'3

T u b e s h e e t

T h e v c l u m e of ü p e r t o f a s p h e r e i s f e f i g u r e 5 . 5 ) i s í 7 3 :

figure 5.5

The k c l u r e o f a d i s b , e j t u b e r h e e t i s t h e difference tretwezTi t h e

voluntez of two sphere p a r t 5 : r e s p e z t i v é l y a p a r t w i t h h e i g h t j t e i r e ? e s p h e r e w i t h r a d i u s r t e , a n d 6 p a r t w i t h h e i g h t J fror, a sFhere ~ i t b r e d i L i 5 r. T h i s g i v e s for t h e \;Glume of t h e d i s h e d t u t r e s h e e t : Rei r!f o r c r m e n t The ring c a n b e s p l i t i n t w o p a r t s : a h o r i z o n t a l p a r t ( t h e " l ~ c , " of t h e T ) a n d a v e r t i c a l p a r t . Sea figure 5.4. T h e v o l u m e o f t h e h o r i z o n t a l p a r t is:

The volume o f t h e v e r t i c a l p a r t is: -

-31-

s:'

e m m m ' 3

ie

145 E . 4 9 20 7 4 2 . 8 8 30 50 1 . 9 8 59 1 . & i 50 3 3 1 . 4 4 4e EZ 2 9 1.35 7 0 27 1.43

ee

?E ? .56 8 9 . % 2 5 1.8@

--

55.6 RESULTS h mx

o*

n' 2 4 7 6 1

.se

2 9E D . 7 1 235 e . 4 4 156 B.31 1 E3 a . 2 1 1 JE

o .

14 1

es

G . 0 9 75 @ . P E 7 I (2. @E4

Celculaticn~ a r e performed with the fc1lcw:r:ç p e r s R e t e r v a l u e - , w h i c h repre5erlt e s 0032 a 5 pozsib!e the sltustìon ci the con-icicrec

reector:

-

Pressure d r @ p A p = O . E Ni'mm?

-

Diämeter tubesheet 2 = E73@ m m

-

Equivalent pressure f o r dead weight p = @ . Z E 5 N/mi.,2

-

hllowable Fiembrane stress

S

= 208 N / m m 2

- LiQament efficiency mu = 8.185

oa

The angle d i s varied between

le'

and E9.9'.

T h i s ~ i i e s for m i n i m ä l required tube-heet thicknes: e , vclurr

tubezheet

" 4 ,

h e i g h t cf reinforcement ring h , vc1ur.e reinforcer,fri

r i n s i + , and ?ctal v o l u m e Lk4 the values g i v e n in table 5 . 1

u

n ' 3 I t 7 . 5 5 3 . 5 8 2 . 4 2 1 . 9 1 1 .ES 1.54 1 . 5 2 1 .LE? 1.861

G r a p h i c a l representstion of the result 1 5 gi\'Erl in figure 5.6.

The total required tubesheet volume is Given cis a function of tne angle

.

fìs a reference, the volume o f the equcl tubesheet is represented bj.

the horizontal dotted l i n e in the graphic;

= p 1 + 6 . 7 5 “ * @ . 4 6 8

4 t Z

= 8 . 4 m”3

InterDretstion

According t o the results, a large tubesheet vc.lume reduction can b e

achieved f o r large angles o f attachment.

These r e s u l t s , houever, a r e determined ccnsidering only p r i m a r y stresses.

It

is very w e l l possible ( s e e Ftssumption 3 ) that t h e total í = p r i v l a r y p l u s s e c o n d a r y ) stre-ses are determinìng. T h i s would meön a l o r g e r reciuirecl tubesheet volume, but i t c ~ n still be a vc.lune redliction corpäred with the present required vclume.

Conclusion: I t i s possible that a tuibesheet vclume reduction csn b e a c h i e v e d b y u s i n g dished t u b e c h e e t s .

kthether this leacs tc a cheaper reñctor, will be discussed i n t h e ner. t paragraph.

55.7 E V A L U A T I D N O F THE IMFACT OF THE USE OF GICHED TUBESHEETS

The ure of dished tubesheets has impact on various a r e ä ’ s :

strength, manufacturing, ictal construction. These impocts are mentioned below.

Strength

-

T o avoid buckling of the shell, a reinforcement ring must be

implemented. This has already been accounted for.

Msnu f ac

t

uri nQ

-

Holes must be drilled in spherical plates, under angles less than

-

The äished sheets are more difficult t o manufacture than f l a t sheets

-

Machines are needed, than can handle objects, not o n l y with a These points result in an increase in the price per L i l o of the tubesheet material.

90

ConstructiGn

-

The t c t a l coristruction may hage t c become h i g t h r r , irl c r d e r t o male p l a c e f o r the e J t r a r o o & , needed f o r the d i s h e t s h e e t s

-

The c a t e l y i t handling murt be adzpted t c d i s h e d s h e e t s

-

Problem- can occur w i t h the ettachment o f the support g r i d s , when

the 5 h e e t s e r e v e r y dished. C o m e of t h e i r m u s t t h e r . b e s t t e c h e d t c t h e tubesheets

This g i v e s o higher p r i c e f o r t h e r e s t of the c o n - t r a c t i o n .

A l l these a s p e c t s are disadvantageous, when d i s h e d t u b e s h e e t s a r e used:

The s t r e n g t h ä s p e c t reducer tho, gain iri 1 . 1 1 0 ' s , manufacturing

a s p e c t s i n c r e a s e t h e p r i c e p e r L i l o , and the c o n z t r u t t i o n a l a s p e c t s

reduce the achieved f i n e n c i a l g a i n .

I t i s the-efore not e'pected, t h 3 t a p r i c e r t d u c t i u n csn be a c h i e v e o , bhich mab.es o f u r t h e r exäminaticn o f t h e a l t e r n o t i v e of

The s t r e s s l i n ì t r t h a t ä r e used u p t i 1 1 n G w , a r e b a - r d upcn

e l a s t i c , i d e a l l y F l e s t i c m a t e r i a l behavior. This means, t h e t rlcl worl hardening is encountered. T h i s chapter kil1 ei'aluate t h e r e s u l t c.f

i n c l u d ì n g w o r i . hardeninrj i n the m o t e r i a l behavior model on t h e c a l c u l a t i o n cf the tubesheet t h i c k n e s s e s .

56.2 ELASTIC,

IDEALLY

PLASTIC MATERIAL EEHAVIOR

This behcvior can be represented b y f i g u r e E . I . The material 2 1 l i n e a r l y e i a s t ì c , up t i l l the y i e l d s t r e c c C . When the y i e l d s t r e c c

i s r e a c h e d , the mate-ia1 w i l l keep y i e l d i n g . Y

S

-I

f i g u r e

E.l

These s t r e s s e s may never exceed t h e y i e l d s t r e s s , s i n c e then t h e materio! w o u l d keep y i e l d i n g , w h i c h would g i v e ufialiowskìe

. d i s t o r t i o n s . T o t a l s t r e s s e s

?he t o t ó l s t r e s s e s , t h ä t a r e the primary p l u s the ( s e l f r e l i e v i n g ) s e c o n d ó r y s t r e s s e s , moy not exceed twice the y i e l d s t ? e s s .

T h i s will be e x p l a i n e d , u n d e r t h e assumption t h a t t h e primary s t r e s s e s da n o t exceed t h e y i e l d stress.

See f i g u r e 6.2.

figure 6 . 2

L e t the calculated stress become higher then the yield s t r e c a

(point 1 ). I n r e o l i t y , stresses cannot er.;eed the yield stress 5 1 " ~ ~

y i c l d i n g will occur. Therefore, t h e material w i l l yield, w h i i e t h f

seccndary (self relievinB) stresses will decrease. T h i s t a k e s plece until the ictal streis ha5 reached the yield stress (pcint 2 ' . Then

t h e s 1 t u a t i c n : 5 ztäblc.

When now the load is released, pressure stresses ail1 occur ( p o i n t

3). As Icng a s this 1Gsd 1 5 lower then t h e yielo stress, applying c n d

relrac,ing G f the load results i n elastic deformótions between pcints 2 and 3.

S ~ i p p r s e n c u that t h e tztòi r t r e s s e i c e e d r t w o timer the yield strest (figare 6.2, p c l i n i 1

?.

-

figure 6.3

Again stress releasing will occur, untif the yield stress is reeched (point 2 ) . I f the load is released, pressure stresses will occur. But now they will exceed the yield stress (point 3), and the

material will yield agoiri (point 4 ) . Applying the load (point 5 ) means again yielding (point 2 ) : every load cycle

will

mean two times

S i n c e t h i s c a n cause l o u c y c l e f o ì i g u e , t h e t c t c l s t r e s s

muci r e f i e i n below twice the yield s t r e r z .

The s t r e s s - s t r a i n curve w i ì 3 l o o i n w a s figure 6 . 4 . When yiE!dinQ t a l e s p l a c e , the y i e l d s t r e s s increa5eç w i i h the s t r â i n .

figure 5 . 4

F r i pria $ 8 ç t re 5 E. e 5

I f n G w the primcry s t r f - s e + . c e ~ c k t h e y i e l d 8tre.s ( s e e f i g u r e C . 5 ,

p c i n t i ! , y ~ e l d i n ~ till! sts& w h e n the z t r o i n 1 - r e a c h e d , wt?f:e tbc-

y i e l d s t r e s s 1 5 equäi t o tne primary 5 t r e s s ( p c i n t 2 ) . T h i s m & d R + t h a t h i g h e r p r i m e r y s t r e s s e s c a f i be a l l o w e d , deperiding on t h e allowed s t r a i n .

- 3 7 -

T o t a l s t r e s s e s

_-

L e t OW t h e t c t a ! s t r e s s e...ceed t w i c e the y i e l d s t r e s s ( f i g u r e 6 . & , p c i n t

1

,).

figtlre 6.6

i n r e a l i t y , the Raterial will y i e l d u r i t r l the y i e l d s t r e s c for t h i s s t r a i n i s reached( point 2 ) . Note t h a t t h i s is a higher y i e l d s t r e s s . kihen t h s 1c.ad i s taheri away, the p r e s s u r e s t r e s s may i n c r e a s e ac Icng

a r I t i 5 l o w e r t h e n t h e neu y i e l d s t r e s s { p o i n t 3). Then the deformetion remäins e l ä s t i c .

~ ? 1 1 1 occur a g a i n , ~ i ; t a l s o the y i e l d s t r e s s w i l l i n c r e a s e . 50 i f the

t o t 3 1 s t r e s s i s nct t c c h i o h , a f t e r a few c y c l e : the loadino c y c l e ui!! G i v e c s ~ l y c l a z t i c , thus a l l o u l s h l e drfsrmetionc.

I f a f t e r u n l c < ä d i n Q t h e pressure b i e 1 0 s t r e s s is e > . c e e i e d , ) ' i e l d l r , g

-hl. 1 -

FiPFENDIYr 1: TEKFEFATVRE D I F F E F E K E : EETWEEN TULE1

_-

Introcf2ct ion

I t

i 5 pcssible, that one or more tubes Deccme !partly) blocl.ed, due

to fauliny, or faults.

In the tubes, o reaction takes place, by which heat is produced. Wher, now a tube gets (partly) blccl.ed, less gas can f l o k through, s c

less reaction will take place. Because less heat is produced, the tube will be colder than the other tubes.

Because the cold tube will expand less, an expansion difference occurs between the tubes. This causes discontinuity stresses in the tubesheet, since all the tubes are connected to i t . i4150 the cold tube is stretched, thus an axiäl stress will occur in the tube.

ets the sheil, what is the ma.<imum allcuable temperature difference

b e t w e e V tubebundle and she117

Assuming the cold tube will be totally blocked, and become as cold

t e r * p r i : 17% t r . t c ~ ~ ~ ~ ~ ~ :

-~

~. _ : :i T ,o - : u p * e j : : ttta? LL,:~ L ~ F I ; ~f t h e

? - L E 5 1 5 p : - f . E ' - , ? % Z E - . ; ' E cJ;;:,.'r & ' - - c S .

In Grder t o he s u r e , that the derived l i m i t s are coEservative, t w r ;

models will be used:

-

One f o r determining the mn.-.im~im a l l o u a b ì e temperature difference

for a.b.ia1 tension in the tube, and :hear-stress i n the tuleshett.

- A second to find the mar.inurn allcuable temperature difference for radial a n d tangential stresses in the tubesheet.

Mzdel 1

The worst situation for axial stress in the cold tube, and shear stress in the tubesheet, is, when only one tube remäins cold. I f mare tubes uere cold, the tubesheet would deflect more, s o that the

cold tube would be stretched less. Assumptions

-

No deflection o f the tubesheet. This is a conservative assumption, since the calculated stress values will be higher than in practice.

- -

The place where one cold tube will induce the largest stresses is

exactly in the center o f the plate.

This assumption is based upon the fact, that in the center of the tubesheet, the deflection due to temperature difference between tubebundle and shell is the largest.

-

The deflection at the center of the tubesheet due to

temperature difference between tubebundle and shell is equal to the expansion difference between these two.

Therefore: The elongation of the cold tube is equal to the expansion difference between tubebundle and shell

- F i l . : -

-

Turo t y t e i o f stresses are considrred: a.s.ie1 stress and sheor strer5. k x i a l stress in the tube.

The lengthening i 5 equöl t o the temperöture oiff.ererice between tubebündle and stress:

( A 1 . 1 ) ~l = 1 + $ * A T Hooke’s law: G = f * E * ( A l . 2 ) ( 6 1 . 1

1

and C f i l . 2 ) g i v e : ( A l . 3 )

G

=

% *

E d * A

The stress i n the tube i s thus linearly aependént tri the

temperöture difference.

With the parameter values:

-

Temperature e?:ponsion coefficient = 1 . 2 6 5 E-5 1/’C

-

Young5 moduius for tube neterial

E,

= 114113 N i m m 2

-

Ma,=.imulr, allowable ai.:al stress

5

= 60@ N/mm7 (3+design s t r s t z i :

the ma.%imum allowable temperature difference i s : T i m a r . 1 = 600

1.265E-5*184113 = 257 ‘ C

+ S h e a r stress ;c in tubesheet arounci the tube

T h e f o r c e t h a t must be born b y a cylindrical surface around the

.L. r u u ~ .L in the t ü b e s h s z t , is tho ssme s s the f o r c e t h a t strains t h e tube.

Thus :

G cross.sect.surf =

r *

carrying surf. tubesh. t A 1 . 4 )

cross sectional surface tube = p i 1 4 ( d , ^ 2

-

d ; ^ 2 )

carrying surface tubesheet = 6 k

*

e k = ligament length (see figure hl.1)

-61.3-

figure A l . l

Rewriting equation ( A 1 . 4 ) . and substituting e x p r e s s i o n s for the carrying surfaces, the e:-pression f o r t h e shear s t r e a s

7

brco-es:

W i t h parameter balbes a s g i v e n a b o v e , and

-

I n n e r diarteter tube d i = 26 mm

-

Guter dipmeter tube d c = 3@ m m

-

Tubesheet thickness e = 200 mm

-

Ligament length C. = 7 m m ,

the ma,k,imaE allouable teniperature difference is:

S i n c e we e l r e e d y have s n u p p e r l i m i t o f 257 ' C , the shear strers in t h e tubesheet 1s not determining.

Model

2

The maximum allowable temperature difference for radial and

tangential stress wlll now b e determined.

Assumptions:

-The staying action o f t h e t u b e s is neglected. T h i s is a conservative a s s u m p t i o n , since t h e tubesheet is now calculated to deflect more t h a n i n reality, so a l s o t h e calculated radial and tangential s t r e s s e s a r e t o o high.

-

T h e cold tube(s) i s t a r e ) p o s i t i o n e d in t h e middle o f the tubebundle. T h i s is the worst place, s i n c e t h e r e the deflection o f t h e tubesheet d u e to temperature d i f f e r e n c e b e t w e e n tubebundle a n d s h e l l , and thus t h e expansion difference, is maximal.

-

T h e l c a d , p e r f o r m e d tab t h e col^? t u b e s , 1 - t h o u g h t t c b e e q u s l ì y d i s t r i b u t e d o v e r the a r e s in w h i c h i t i s c o r # n e c t e c t o t h e t u b e s h e e t . T h i s g i v e r t h e ne7.t m z d e l ! s e e f i g u r e f i 1 . 2 ) : PI c i r c u l a r , mässive p l a t e , s i m p l y s u p p o r t e d a t t h e e d g e , l o a o e d w i t h a u n i f o r m l y d l s t r i t u t e d l c a l over E c i r c u l a r a r e a p c s i t i s n e d a t t h e c e n t e r of t h e p l a t e . f i g i i r e A l . 2 T h e l o a d o n t h e t u b e s h e e t d e p e n d : o n t h e e ì o n g ä t i o n o f t h e t u b e s : T h i s l e n ç t h e n i n g i A 1 I d e p e n d 5 on t h e e . . p a r , s i o n d i f f e r e n r e i ~ * l f Z * t h e mcrre t h e t u b e s a r e s t r e t c h e d , t h e h e a v i e r t h e l o a d . AT) a n d t h e d e f l e c t i o n af t h e t u b e s h e e t ( y ) : ( A l . 6 ì w i t h :

01

= e l o n g a t i o n of tabes ì = l e n g t h o f t u b e s d , = t h e r m . e , * . p . c o e f f . D T = temp. d i f f e r e n c e y = d e f l e c t i o n t u b e s b r e t T h e c e n t r a l d e f l e c t i o n ~f t h e t u b e s h e e t due t o o c i r c u l a r l o e d a ? t h e c e n t e r o f t h e p l a ? e is (Roar} I41, p a g e 366, cz5e 1 6 ) :

w i t h : q = d i s t r . l o a d E = s t i f f n e s s t u b e s h e e t e = t h i c k n e s s t u b e s h e e t

2,

= P o i s s o n r a t i o t u b e s h . a = r a d i u s t u b e s h e e t r = l o a d r a d i u s o T h e l o a d q i s t h e e q u i v a l e n t u n i f o r m d i s t r i b u t e d l o a d , w h i c h r e p r e s e n t s t h e f o r c e s f r o m t h e c c l d t u b e s . T h u s : Force on t h e t u b e = f o r c e on t h e t u b e s h e e t <=> N

+01/(1/?)

E

*

p i l 4 *(d,^2-djAZ) = q p i

*

r, ^ 2 ( A 1 . 8 ) ( = > 9 = N 2 /i1 E ( d r i 2

-

d c " 2 ) 4

1

r c " 2 w i t h :

E

= s t i f f n e s s t u b e m a t . d ; = i n n e r t u b e d i a m e t e r d , = outer t u b e d i ä m e t e r N = amount o f c o l d t u b e 5

These t h r e e e q u a t i o n 5 f o r m a r e t o f t h r e e e q u a t i o n s w l t h t h r e e u n l n o u n 5 .

I f we rewrite t h e e q u a t i o n s ! A 1 . 6 ! , (Al.’?) a n d (A1.8), w e f i n d :

íAl.Q! 6 1 C1 AT

-

y

(Al.10) y =

cz

* q

( A l . 1 1 ) q = c3

*Al

To c a l c u l a t e t h e o c c u r r i n g s t r e s s e s , t h e moments muet t e known. I n R o a r L 1 4 1 , p a g e 366, case 1 6 , we f i n d :

-

r a d i a l

- t a n g e n t i a l

--m

T h e stresses car; tis c e l c u l ö t e d f r o f i !Eoari i43, p a g r 2 3 ~ ) :

( A l . i 4 ) G = 6 + M

G ‘ 2

T n e mofiefits p r e l i n e a r l y d e p e n d e n t o n t h e disiribLted ìoed q , a n d

t h u s ( s e e e q u a t i o n (Fi1.5 tm 1 1 ) ) l i n e a r l y d e p e n d e n t on t h e t e w s t a t u r e d i f f e r e n c e .

on t h e m o m e n t s , t h e s t r e s s e s a r e a l s o l i n e a r l y d e p e n d e n t on t h e

t e m p e r a t u r e d i f f e r e n c e .

Because ( s e t e q t i e t i o n tHl.id)) t h e s t r e s s e s are l i n e a r l y d e p e n d e n t

R e w r i t i n g e q u a t i o n s ( A l . l 2 ) , ( A l . l 3 ) and ( A 1 . 1 4 ) g i v e s ( A i . 1 5 )

M

= C4 q

( A 1 . 1 6 ) M = C5 * ’ Q ( A 1 . 1 7 )

d

= C6 M