+ All Categories
Home > Documents > Andreou Ms

Andreou Ms

Date post: 04-Jun-2018
Category:
Upload: rudra-kumar-mishra
View: 226 times
Download: 0 times
Share this document with a friend
122
 SIMULATION OF A SOLAR HEATED HOUSE USING THE BOND GRAPH MODELING APPROACH AND THE DYMOLA MODELING SOFTWARE by Spyr os Andr eou A Thesis Submtted to the Faculty of the DEPARTMENT OF ELECTRI C A L AN D COMPUTER ENGI NEERI NG In Partial Ful f i l l ment of t he Requi r ement s For the Degree of MASTER OF SCI ENCE W TH A MAJ OR I N ELECTRI CAL ENGI NEERI NG I n t he Gr aduat e Col l ege THE UNI VERSI TY OF ARI ZONA  9 9
Transcript

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 1/122

 

SIMULATION OF A SOLAR HEATED HOUSE

USING THE BOND GRAPH MODELING APPROACH

AND THE DYMOLA MODELING SOFTWARE

by

Spyr os Andr eou

A Thesi s Subm t t ed t o t he Facul t y of t he

DEPARTMENT OF ELECTRI CAL AND COMPUTER ENGI NEERI NG

I n Par t i al Ful f i l l ment of t he Requi r ement sFor t he Degr ee of

MASTER OF SCI ENCEWTH A MAJ OR I N ELECTRI CAL ENGI NEERI NG

I n t he Gr aduat e Col l ege

THE UNI VERSI TY OF ARI ZONA

 99

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 2/122

2

STATEMENT BY AUTHOR

Thi s t hesi s has been subm t t ed i n par t i al f ul f i l l mentof r equi r ement s f or an advanced degr ee at The Uni ver si t y ofAr i zona and i s deposi t ed i n t he Uni ver si t y Li br ar y t o be madeavai l abl e t o bor rower s under r ul es of t he Li br ar y.

Br i ef quot at i ons f rom t hi s t hesi s ar e al l owabl ew t hout speci al per m ssi on, pr ovi ded t hat accur at e acknow -edgment of sour ce i s made. Request s f or perm ssi on f orext ended quot at i on f r om or r epr oduct i on of t hi s manuscr i pt i nwhol e or i n par t may be gr ant ed by t he head of t he maj or

depar tment or t he Dean of t he Gr aduat e Col l ege when i n hi s orher j udgment t he pr oposed use of t he mat er i al i s i n t hei nt er est s of schol ar shi p. I n al l ot her i nst ances, however ,perm ssi on must be obt ai ned f r om t he aut hor .

SI GNED:

APPROVAL BY THESI S DI RECTOR

Thi s t hesi s has been appr oved on t he dat e shown bel ow:

~~~rt ~Associ at e Prof essor

El ect r i cal and Comput er Engi neer i ng

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 3/122

3

ACKNOWLEDGEMENTS

I wi sh t o expr ess my gr at ef ul appr eci at i on t o my

parent s , Savvas and Andromachi , f or t hei r cont i nuous suppor t

t hr oughout my academ c car eer .

Fur ther mor e, I woul d l i ke t o ext end my deepest

appr eci at i on t o my academc advi sor Dr . Fr ancoi s Cel l i er f or

hi s val uabl e assi s t ance t o t hi s pr oj ect . He was al ways

wi l l i ng and avai l abl e f or hel p whenever I r equest ed i t . I

al so thank the other two members of t he exam ni ng comm tt ee,

Dr . Mal ur Sundareshan and Dr . Hal Tharp.

Speci al t hanks t o Qi ngsu Wang f or her assi st ance i n

t he DYMOLA sof t war e. Al so, t o Dr . Gr ani no Kor n f or maki ng

avai l abl e hi s comput er t o obt ai n t he DESI RE out put s. And,

f i nal l y t o al l my f r i ends who cont r i but ed t o t hi s pr oj ect t o

become r eal i t y.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 4/122

4

TABLE OF CONTENTS

LIST OF FIGURES •• • • • • •• ••••• • ••• • 7

ABS TRACT ••• •••••••••••••••••••••••••••••••••••••••••• 11

CHAPTER 1 INTRODUCTION •••••• •••••••••   • 12

CHAPTER 2 BOND GRAPHS ••••••••••••••••••••••••••••••• 16

2 1 Overview 16

2. 2 Basi c Def i ni t i ons . ••. . •••••. . . •. . •. . ••. ••. ••••. 17

2. 2. 1 Mul t i por t El ement s, Por t s, and Bonds •. . . 17

2. 2. 2 Bond Graphs •••. . •. •. . •••. •••••. •. ••. ••. • 19

2. 2. 3 Por t Var i abl es . . . . . . . •. . . . . ••. ••. . . •. . . . 19

2. 2. 4 Basi c Mul t i por t El ements •. . . . . . . ••. . . . . . 20

2 . 2. 5 Ext ended Def i ni t i ons •. •••••••••. •••. •. •• 21

2. 2. 6 General i zat i on t o Basi c Physi calTypes of Syst ems . . . •. . . . . . . . . •. •••. . . . . • 21

2. 3 The Concept of Causal i t y. . . . . . . . . . . . . . . . . . . . . . . 24

2. 4 Pseudo Bond Gr aphs and Thermal Syst ems . •. •. ••. . 27

CHAPTER 3 DYMOLA 30

3 1 Overview 3 

3. 2 Speci al Proper t i es of DYMOLA ModelDescriptions 31

3 . 2. 1 Some Pr oper t i es ••. . •. . ••••••. ••. ••. •. . •• 31

3. 2. 2 The  Cut Concept . . . . . . •. •••. ••. ••. ••. . . 34

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 5/122

5

TABLE OF CONTENTS ( cont i nued)

3. 2. 3 The Submodel Concept and  nodes i n DYMOl A ••••••••••••••••••••••. 38

3. 2. 4 Hi er ar chi cal Model st r uct ur e i n DYMOl A. . 41

3. 3 Gener at i on of DESI RE Model s .  44

3. 3. 1 Cr eat i on of a DESI RE Si mul at i onl ?~( ) ~~Cl I n•••••••••••••••••••••••••••••••• 47

3. 3. 1. 1 Descr i pt i on of t he Si mul at i onCont r ol Model . . . . . . . . . . . . . . . . . . 47

3. 3. 1. 2 Obtai ni ng Executabl e DESI REPrograms • • 48

3. 4 Some Unsol ved Probl ems •. . . . •••. ••. ••. •. . •. . •••. 49

CHAPTER 4 CONSTRUCTI ON OF BOND GRAPHS AND THEI RTRANSFORMATI ON I NTO DYMOl A ••••. • . . •. . . • . • . 52

4 1 Overview 52

4. 2 Some Basi c Rul es f or Const r uct i ng BondDi agr ams f or El ect r i cal Networ ks •. •. . •. . •••••. . 53

4. 3 Const ruct i on of a Bond Di agr am of a Si mpl eEl ect r i cal Network • . . •. . . . . . . • . . . •. ••. ••. . . . . . . 54

4. 3. 1 The St ep by St ep Pr ocedur e • . . • . . • . •. . . . . 54

4. 4 Tr ansf ormat i on of Bond Gr aphs i nt oDYMOLA Code ••••••••••••••••••••••••••••••••• •• 60

CHAPTER 5 CASE STUDY: MODELI NG- SI MUl ATI NGA SOLAR- HEATED HOUSE . •. •••. •••••••••••. •. • 71

5 1 Overview  71

5.2 Solar Heating.................................. 72

5. 3 Basi c Thermodynam c and General Concepts •. . . . . . 76

5. 4 Fl at Pl at e Sol ar - Col l ect or Model i ng . . . . . . •. . . . . 79

5. 5 Heat st or age Tank Model i ng 97

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 6/122

6

TABLE OF CONTENTS ( cont i nued)

5. 6 Water Loop Model i ng 100

5. 7 Habi tabl e Space Model i ng •••••••••••••••••••. ••• 104

5. 8 The Tot al Sol ar - Heat ed House ••••••••••••••••••• 113

5. 9 Choosi ng Appr opr i at e Par ameter s f or Anal yzi ngt he Ef f ect i veness of Our Syst em ••••••••••••. . •. 114

CHAPTER 6 CONCLUSION •• ••• •••••• •••••• •••••• • 118

APPENDI X RESULTS •••••••••••••••••••• ••••••••••••• 120

REFERENCES 121

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 7/122

Fi gur e 2. 1a

Fi gur e 2. 1b

Fi gur e 2. 1c

Fi gur e 2. 2a

Fi gur e 2. 2b

Fi gur e 2. 3

Fi gur e 2. 4

Fi gur e 2. 5

Fi gur e 2. 6

Fi gur e 2. 7

Fi gur e 2. 8a

Fi gur e 2. 8b

Fi gur e 3. 1

Fi gur e 3. 2

Fi gur e 3. 3

Fi gur e 3. 4

Fi gur e 3. 5

Fi gur e 3. 6

7

LIST OF FIGURES

Mul t i por t el ement s 18

The el ement s and t hei r por t s •••••••••••• 18

Format i on of a bond ••••••••••••••••••••• 18

Bond graph 18

A bond 18

The bond gr aph w t h power s di r ect edand bonds l abel ed . . . . . . . . . . . . . . . . •. . •. •. 19

Def i ni t i ons of t he basi c mul t i por tel ements 22

Pr esent at i on of a summar y of t hef our gener i c var i abl es bei ng usedi n some common physi cal syst ems . . . •••. •. 23

Meani ng of causal st rokes . •••••. . . . . . . . . 25

Desi r ed causal f orms and r el at i onsof t he basi c ni ne mul t i por t el ement s 26

Thermal r esi s t or and i - j unct i on •. •. . •. . . 28

Ther mal capaci t or and O- j unct i on . ••. •. •. 28

Model of a conduct ance usi ng i nputout put decl ar at i on •••••. •••. ••. •. •••. ••. 35

Model of a conduct ance usi ng cutdeclaration 35

Thr ee submodel s connect ed at por t A 37

Exampl es of at om c model s i n DYMOLA 39

Exampl es of a coupl ed model pr c 40

Coupl ed model s i n DYMOLA •••. . . . . . . . . . ••. 42

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 8/122

Fi gur e 3. 7

Fi gur e 3. 8

Fi gur e 3. 9

Fi gur e 4. 1

Fi gur e 4. 2

Fi gur e 4. 3

Fi gur e 4. 4

Fi gur e 4. 5

Fi gur e 4. 6

Fi gur e 4. 7

Fi gur e 4. 8

Fi gur e 4. 9

Fi gur e 4. 10

Fi gur e 4. 11

Fi gur e 4. 12

Fi gur e 4. 13

Fi gur e 4. 14

8

LIST OF FIGURES ( cont i nued)

A hi er ar chi cal l y st r uct ur ed syst em 43

Descr i pt i on of t he hi er ar chi calst r uct ur e of a syst em i n DYMOLA 45

Model speci f i cat i on f or pr c usi ngmodel type  ............... 46

An el ect r i cal net wor k w t h nodesl abel l ed ( r

 r ef er ence) ••••••. . •. •••••• 55

Layout of vol t age j unct i ons( a- j unct i ons) . ••••. . •••. . . . . . . . •. . . . . . . . 55

The assembl y of component s and sour ce 56

The cancel l at i on of r ef er ence nodeand associ at ed bonds •••••. . . . •. . •. . . . . . • 56

The condensat i on of bonds . . . . . . •. . . . . . •. 58

The r educed gr aph •. . •••••. •. . . . . •. . . . . . • 58

The bond graph 58

The compl et ed bond gr aph w t hi t s causal i t i es •••••••••. •••. . •••. . . ••. • 59

DYMOLA expanded bond graph w th eachnode i ndi cat ed . . ••. . •••. ••. . •. •••. •••. •. 61

DYMOLA code of the bond graph shownon Figure 4 9 63

The var i ous basi c DYMOLA model t ypes . . . . 64

Exper i ment used f or t he net wor k •. •. . •. . • 65

Gener at ed DESI RE pr ogr am •••••. ••. •. . •. . • 67

St at e- s pace r epr esent at i on of t henetwork 68

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 9/122

Fi gur e 4. 15

Fi gur e 5. 1

Fi gur e 5. 2

Fi gur e 5. 3a

Fi gur e 5. 3b

Fi gur e 5. 3c

Fi gur e 5. 3d

Fi gur e 5. 3e

Fi gur e 5. 3f

Fi gur e 5. 3g

Fi gur e 5. 3h

Fi gur e 5. 3i

Fi gur e 5. 3j

Fi gur e 5. 3k

Fi gur e 5. 31

Fi gur e 5. 3m

Fi gur e 5. 3n

Fi gur e 5. 30

Fi gur e 5. 3p

Fi gur e 5. 4a

Fi gur e 5. 4b

Fi gur e 5. 4c

LIST OF FIGURES ( cont i nued)

DESI RE out put

A sol ar heat ed house ••••••••••••••••••••

Model of a f l at - pl at e col l ect or •••••••••

Bond di agr am of a one- di mensi onal cel l

DYMOLA model t ype of a one- di mensi onal

9

69

74

8

83

cell 83

84odul ated conduct i ve sour ce ••. ••••. •. •. •

Bond di agr am of a heat exchanger .

DYMOLA model t ype of a heat exchanger . . .

Bond di agr am of a wat er spi r al •. . . •. ••••

DYMOLA model t ype of a wat er spi r al •. •. .

Bond di agr am of t her m c l oss

DYMOLA model t ype of therm c loss .

Bond gr aph of t he col l ect or . ••. •. ••. . . •.

DYMOLA model t ype of t he col l ect or . •. . •.

DYMOLA model t ype of mG •. ••. . . . •. ••. •. •.

DYMOLA model t ype of mGS

DYMOLA model t ype of mRS

DYMOLA model type of mC

DYMOLA model t ype of RS

85

85

87

88

89

89

91

91

95

95

96

96

96

The st or age t ank w t h t he col l ect orwat er l oop and heat er wat er l oop 99

Bond gr aph of t he st or age t ank . . •. . . . •. . 99

DYMOLA model t ype of t he st or age t ank . . . 1 1

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 10/122

Fi gur e 5. 5a

Fi gur e 5. 5b

Fi gur e 5. 6a

Fi gur e 5. 6b

Fi gur e 5. 6c

Fi gur e 5. 6d

Fi gur e 5. 7

Fi gur e 5. 8

LIST OF FIGURES ( cont i nued)

Bond di agr am f or wat er l oop

DYMOLA model t ype f or wat er l oop

Thr ee- di mensi onal di f f usi on cel l

DYMOLA model t ype of a t hree- di mens i onal

10

102

102

107

cell 108

The house r oom r epr esent ed as a10X10X10 cube •. ••••. . •••. ••••. . •. •. . •. . . 109

DYMOLA model t ype of t he SPACE ( house)

Aggr egat ed bond gr aph of t he over al l

110

Tabl e of some r esul t s

system • • • • 113

116

Si mul at i on r esul t s at var i ous nodes . . . . • 120

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 11/122

- ,

11

ABSTRACT

Thi s t hesi s di scusse~ t he appl i cat i on of t he bond

gr aph model i ng t echni que di r ect l y coded i nt o t he Dynam c

Model i ng Language ( DYMOLA) f or si mul at i ng a sol ar - heat ed

house. Sci ent i st s t hr oughout t he year s have i nvest i gat ed t he

expl oi t at i on of sol ar r adi at i on f or space heat i ng. I n t hi s

t hesi s , t he physi cal behavi or of such a syst em i s model ed

and si mul at ed i n a conveni ent , r obust and f ast manner . The

bond gr aph model i ng met hodol ogy has f ound w despr ead use i n

a w de r ange of syst ems. DYMOLA i s a model i ng l anguage wel l

sui t ed t o r epr esent bond gr aphs. DYMOLA i s a pr ogr am gener a-

t or t hat can map a t opol ogi cal syst em descr i pt i on, such as a

bond gr aph, i nt o a st at e- space descr i pt i on expr essed i n t he

f orm of a DESI RE si mul at i on pr ogr am

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 12/122

12

CHAPTER 1

INTRODUCTION

Engi neer s ar e t r ai ned i n i nvent i ng new means whi ch

w l l event ual l y l ead t o easi er sol ut i ons of t hei r pr obl ems.

One of t hem i s t o model and t hen t o si mul at e a cer t ai n number

of physi cal syst ems encount er ed i n t hei r ever yday l i f e w t h

t he mai n t ar get bei ng t o f i r st pr edi ct and secondl y t o st udy

t hei r physi cal behavi or .

The goal of t hi s t hesi s i s t o pr esent a moder n and

advanced model i ng- s i mul at i on t echni que appl i ed t o a sol ar -

heat ed house. The bond gr aph model i ng t echni que as wel l as

t he Dynamc Model i ng Language (DYMOLA) w l l be used.

Ther e exi st a number of bond gr aph model i ng t ool s on

t he . mar ket . The best est abl i shed t ool i s ENPORT- 7 (Rosencode

Associ at es I nc. , 1989) , a SPI CE- l i ke bond gr aph l anguage w t h

a gr aphi cal f r ont end. Ot her t ool s ar e TUTSI M ( van Di xhoor n,

1982) and CAMP (Granda, 1982) . However , none of these systems

i s abl e t o handl e t rul y hi er ar chi cal bond gr aphs as t hey w l l

be essent i al f or our endeavor . DYMOLA ( El mqvi st , 1978) i s t he

onl y model i ng l anguage avai l abl e whi ch can handl e t rul y

hi er ar chi cal nonl i near bond gr aphs i n a compl et el y gener al

f ashi on.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 13/122

13

I t i s at t r act i ve t o many engi neer s t o st udy t he

possi bi l i t y of expl oi t i ng t he f r eel y avai l abl e sol ar r adi a-

t i on f or heat i ng a house. For . a successf ul desi gn of such a

f aci l i t y, i t i s essent i al t hat t he syst em behavi or can be

si mul at ed so t hat var i ous al t er nat i ves can be t est ed pr i or t o

i mpl ement at i on. DYMOLA t oget her wi t h t he bond gr aph appr oach

t o physi cal syst em model i ng i s expect ed t o be t he qui ckest

and most accur at e method compar ed wi t h ot her s used i n t he

past t o descr i be such a syst em Bond gr aphs wer e i nvent ed i n

1960 by Henry Paynter , an M T prof essor ( Paynter , 1961) , and

DYMOLA was desi gned at t he Lund I nst i t ut e of Technol ogy i n

1979 by Hi l di ng El mqvi st i n hi s Ph. D. di sser t at i on (El mqvi st ,

1978) . However , t he appl i cat i on of DYMOLA to expr ess bond

graphs i s new and has never been done bef ore.

Bond gr aphs f i nd many appl i cat i ons i n var i ous

engi neer i ng di sci pl i nes because t hey make model i ng more

syst emat i c, because t hey make i t easi er t o deal wi t h

i nt er f aces bet ween subsyst ems of di f f er ent t ypes ( e. g. ,

el ect r o- mechani cal coupl er s ) , and because they si mpl i f y the

ver i f i cat i on of a cor r ect ener gy f l ow acr oss such i nt er f aces

and wi thi n the sUbsys tems. They are abl e to provi de a common

model i ng met hodol ogy not onl y f or el ect r i cal , mechani cal and

ot her f r equent l y si mul at ed syst ems, but al so f or l ess

commonl y si mul ated systems such as chem cal , ecol ogi cal or

bi omedi cal syst ems. They of f er a mor e gener al gr aphi cal

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 14/122

14

r epr esent at i on t han ei t her bl ock di agr ams or si gnal f l ow

gr aphs si nce t hey pr eser ve bot h t he comput at i onal and t he

topol ogi cal st r ucture of al l t he systems ment i oned above. As

t he wor d i ndi cat es, a bond gr aph i s a col l ect i on of el ement s

bonded t oget her . More i nf ormat i on about t hi s uni que model i ng

techni que i s provi ded i n the second chapter .

Af t er model i ng our sol ar - heat ed house i nt o bond

gr aphs, t he pr oduced di agr ams ar e di r ect l y coded i nt o DYMOLA,

a modul ar hi er ar chi cal cont i nuous- system model i ng l anguage.

I t s mai n advant age i s t hat i t can deal wi t h l ar ge- scal e

syst ems i n a modul ar and hi er ar chi cal manner . Mor eover , i t

i s ver y wel l sui t ed t o i mpl ement t he bond gr aph model i ng

methodol ogy, and i s abl e to map bond graphs i nto s tate- space

descr i pt i ons of t he t ype ~ = i ( ~, y, t ) . speci al f eat ur es of

DYMOLA are f ound i n the thi r d chapter .

The mai n subj ect of t he f our t h chapt er i s a

demonst rat i on of t he way i n whi ch DYMOLA can be used t o sol ve

t he pr esent ed pr obl em The t r ansi t i on f r om the bond di agr am

t o DYMOLA code i s a st r ai ght f or war d pr ocedur e r equi r i ng

sever al si mpl e r ul es bei ng pr esent ed i n a concr et e and

succi nct manner . DYMOLA i s so power f ul t hat i t can aut o-

mat i cal l y eval uat e t he causal i t y of t he bond gr aph, pr oduce

a st at e- space descr i pt i on f or t he syst em as wel l as gener at e

a si mul at i on program coded i n ei ther DESI RE (Korn, 1989b) or

SI MNON (El mqvi st , 1975) , two di r ect execut i ng cont i nuous-

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 15/122

15

system si mul at i on l anguages. Moreover , a si mpl e el ect r i cal

networ k i s i ncl uded, t r ansf ormed f i r st i nt o i t s bond di agr am

and then i nto DYMOLA code, wi th the hope that the reader wi l l

f ol l ow and comprehend al l t he present ed steps i n a conveni ent

manner .

As ment i oned bef ore, t he case study present ed i n thi s

t hesi s i s a sol ar - heat ed house, a r el at i vel y compl i cat ed

syst em i nvol vi ng var i ous subsyst ems and var i ous t ypes of

ener gy. The conf i gur at i on under st udy consi st s of a f l at -

pl at e sol ar col l ect or , one sol i d body st or age t ank, wat er

l oops, a heat exchanger , and t he habi t abl e space. Each par t

i s gover ned by a set of f i r st or der di f f er ent i al equat i ons

i l l ust r at i ng t he ener gy f l ow t hr ough t he subsyst em Each

subsyst em i s di r ect l y t r ansf ormed i nt o a bond gr aph

r epr esent at i on. The var i ous par amet er s used f or t he

si mul at i on wer e t aken f r oman ol der st udy of a si m l ar sol ar -

heat ed house per f ormed i n t he l at e 70 s ( Kass, 1978) , f r om

other sour ces i n t he l i t er at ur e (Def f i e and Bechman, 1980)

and f romusi ng our physi cal i nt ui t i on and common sense.

I t i s hoped t o have t he oppor t uni t y t o appl y bot h t he

bond gr aph model i ng t echni que and t he dynamc model i ng

l anguage i n i ndust r y obser vi ng t he physi cal pr oper t i es of

var i ous syst ems. Bei ng abl e t o t r ansl at e t hem i nt o bond

di agrams and then code t hemdi rect l y i nt o DYMOLA i s , i ndeed,

an exci t i ng exper i ence.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 16/122

16

CHAPTER 2

BOND GRAPHS

I n t hi s chapt er t he Bond Gr aph met hodol ogy i s

di scussed ext ensi vel y. I t st ar t s w t h an over vi ew of t hi s

uni que model i ng t echni que, t hen i t gi ves some basi c def i ni -

t i ons w t h i l l ust r at i ons and i t di scusses t he concept of

causal i t y. Fur t hermor e, a r ef er ence t o Pseudo Bond Gr aphs and

Thermal Systems i s gi ven.

2 1 ov er v i ew

Engi neer s needed t o f i nd a mor e gener al gr aphi cal

( symbol i c) r epr esent at i on whi ch at t empt s t o pr eser ve bot h t he

comput at i onal and t opol ogi cal st r uct ur e of any ki nd of

physi cal syst em They f ound out t hat bl ock di agr ams and

si gnal f l ow gr aphs onl y pr eser ve t he comput at i onal but not

t he t opol ogi cal st r uct ur e. Thus, a r el at i vel y new and

power f ul r epr esent at i on i s t hat of Bond Gr aphs whi ch has been

i nt roduced by Henr y Paynt er i n t he ear l y si xt i es ( Paynt er ,

1961) . Many t ypes of physi cal syst ems have been st udi ed

usi ng bond gr aphs i ncl udi ng el ect r i cal networ ks, mechani cal

r i gi d bodi es, hydr aul i c, t her mal and ener gy t ransduct i on

phenomena. Some r esear cher s r ef er t o Bond Gr aphs al so as Bond

Di agr ams. We shal l use bot h t ermnol ogi es i nt er changeabl y.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 17/122

17

I t i s t r ue, however , t hat f or t he begi nner t hi s

model i ng l anguage i s qui t e abst ract . Bl ock di agr ams and

si gnal f l ow di agr ams can be mor e easi l y compr ehended.

Never t hel ess, f or t he case of model i ng t he sol ar - house, a

r el at i vel y compl i cat ed syst em i nvol vi ng many di f f er ent t ypes

of ener gy f l ow bet ween i t s i nt er connect ed par t s, i t appear s

t hat t he bond gr aph pr ocedur e i s mor e appeal i ng due t o i t s

ease of appl i cat i on and gr eat er i nf ormat i on cont ent .

Model i ng a physi cal syst em i s a si mpl i f i ed abst ract

const ruct i on used t o pr edi ct i t s physi cal behavi or . That i s

exact l y what t he bond gr aph model i ng met hodol ogy i s

per f orm ng.

The pur pose of t hi s chapt er i s t o i nt r oduce t he

r eader t o t hi s abst r act model i ng met hodol ogy and t o pr ovi de

enough i nf ormat i on so t hat he/ she can easi l y compr ehend i t .

2. 2 Basi c Def i ni t i ons

2. 2. 1 Mu1t i por t El ement s, Por t s, and Bonds

The nodes of t he gr aph ar e cal l ed Mul t i por t El ement s

desi gnat ed by al pha- numer i c char act er s such as 1 and R, as

shown i n Fi gur e 2. 1( a) . The pl aces wher e a mul t i por t el ement

can i nt er act w t h i t s envi r onment ar e cal l ed Por t s desi gnat ed

by l i ne segment s i nci dent on t he el ement at one end. Fi gur e

2. 1 ( b) shows t he 1 el ement havi ng t hr ee por t s and t he R

el ement havi ng one por t . When pai r s of por t s ar e combi ned

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 18/122

18

1 R   R

I  C

R

 a b )

Fi gur e 2. 1 ( a) Mul t i por t el ement s( b) The el ement s and t hei r por t s

( c) For mat i on of a bond

R e

SE OTF  1 ~

I If

C I  a)   b )

Fi g~r e 2. 2 (a) Bond graph( b) A bond

134SE~O~TF~

2~

C

R

 

~6

I

Fi gur e 2. 3 The Bond Gr aph w t h power s di r ect edand bonds l abel ed

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 19/122

19

t oget her , bonds ar e f ormed. Thus, bonds ar e connect i ons

between pai r s of mul t i por t el ement s. For exampl e, Fi gur e

2. 1( c) shows a f ormat i on of t he bond between 1 and R.

2. 2. 2 Bond Graphs

A bond gr aph i s a col l ect i on of mul t i por t el ement s

bonded t oget her . I n a more gener al per spect i ve i t i s a l i near

gr aph wi t h nodes bei ng t he mul t i por t el ement s and wi t h

branches bei ng t he bonds. An exampl e of a bond graph i s shown

i n Fi gur e 2. 2( a) havi ng seven mul t i por t el ement s and si x

bonds.

Anot her def i ni t i on:

 A bond, r epr esent ed by a bol d hal f ar r ow, i s not hi ng

but a connector that si mul taneousl y connects two var i abl es,

one acr oss var i abl e, i n bond gr aph t er mnol ogy usual l y

r ef er red t o as t he ef f or t e, and one t hr ough var i abl e,

cal l ed t he f l ow f ( Cel l i er , 1990a) . Ref er t o Fi gur e 2. 2( b)

as wel l as t o t he next sUbsect i on f or mor e i nf ormat i on.

2. 2. 3 Por t var i abl es

Ther e ar e t hr ee di r ect and t hr ee i nt egr al quant i t i es

associ at ed wi t h a gi ven por t .

The f i r st t wo di r ect quant i t i es ar e cal l ed Ef f or t ,

e( t ) , one acr oss var i abl e and Fl ow, f ( t ) , one t hr ough

var i abl e, assumed t o be scal ar f unct i ons of an i ndependent

var i abl e ( t ) .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 20/122

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 21/122

21

J unct i ons . The t wo sources , t he t wo storages ( capaci t ance and

i ner tance) and t he di ssi pat i on ( resi st ance) ar e I - por t

el ement s wher eas t wo of t he j unct i ons ( t r ansf or mer and

gyr at or ) ar e 2- por t ones and t he ot her t wo ( 0 and 1) ar e at

l east 3- por t el ement s. The f ol l owi ng Fi gur e 2. 4 shows t he

symboI , def i ni t i on and name of t he ni ne basi c mul t i por t

el ement s. I n t he f i gur e, ~ st ands f or a gener al f unct i on

rel at i ng two var i abl es.

2. 2. 5 Extended Def i ni t i ons

Al though the f ol l owi ng f eatures are beyond the scope

of t hi s t hesi s t hey ar e wor t h ment i oni ng. The t erm Fi el d i s

al so used i n bond gr aph t erm nol ogy. Thus, t her e ar e

C- f i el ds, I - f i el ds and R- f i el ds whi ch ar e mul t i por t

gener al i zat i ons of - C, - I and - R r espect i vel y. Mor eover ,

t her e ar e t he Modul at ed Tr ansf ormer (MTF) and Modul at ed

Gyr at or ( MGY) .

Lat er i n t he f i f t h chapt er , when t he bond gr aph of a

t hr ee- di mensi onal cel l i s const r uct ed t he R- f i el d i s used

( t hr ee r esi st or s ar e connect ed i n x, y, z di r ect i ons, see

Fi gure 5. 6a) .

2. 2. 6 Gener al i zat i on t o Basi c Physi cal Types of Syst ems

We have al r eady seen f our gener i c var i abl es ef f or t ,

f l ow, momentum and di spl acement . The f ol l owi ng Fi gure 2. 5

demonstr at es a pr esent at i on summar i z i ng t he above f our

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 22/122

22

SYMBOL DEFINITION N ME

S Ee ,

e = e  t) s ou rc e o f e ffo rt

S Ff

f = f t) s o u rc e o f flo w

Ce e = < 1>q )

d

c a p a c i t a n c ef q  t) = q  to )   J fd t

e f = < 1 > p )d

i n e r t a n c ef p  t) = p to ) +J e d t

Re

<1>e ,f) = 0d

r e s i s t a n c ef

1 2 e 1= m e 2T F 

t r a n s f o r m e rf2 = m f 1m

1 2 e 1 = r f 2 

G Y  

g y r a t o re 2  rf 1r

1 3 e 1 = e 2 = e 3 c om m o n e ffo rt  0  

f 1 + f 2 -f3 = 0 j u n c tio n

t 21 3 f1 = f2 = f3 c o m m o n flo w 

e 1 e 2 - e 3 = 0 j u n c t i o n

t 2Fi gur e 2. 4 Def i ni t i ons of t he basi c mul t i por t el ement s

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 23/122

23

Efforte Flowf

Generalized Generalized

Momentum Displacementp q

E l e c t r i c a l v O l t ~ e c u r re n t flu x c h a r g eu [ ] i[ A ] c l > [ V s ] q [ A s ]

T r a n s l a t i o n a lf o r c e v e l o c i t y m o m e n t u m d i s p l a c e m e n t

F [ N ] . u [ m s ] I [N s ] x [m ]

t o r q u ea n g u l a r

t w i s t a n g l eR o t a t i o n a l v e l o c i t yT [ N m ]

Q[ ra d s · 1 ]  t[ N m s ] e [ra d ]

p r e s s u r e v o lu m e p re s s u r ev o l u m e

H y d r a u l i c P [ N m -2] f lo w m o m e n t u mv [m 3]c l> v[ m 3 s 1 ] IlN m -2s ]

c h e m i c a l m o la r flo w m o la r m a ssC h e m i c a l p o t e n t i a l Q N [ m o le s - 1 ] N [m o l]

u ] J e m o l - 1 ] d t

T h e r m o - t e m p e r a t u r e e n tro p y flo w e n t r o p y

d y n a m i c a l T [ O K ] ~ [W O K 1 ] S [ J e O K 1 ]d t

Fi gur e 2. 5 Pr esent at i on of a summar y of t he f our gener i cvar i abl es bei ng used i n some common physi cal syst ems

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 24/122

24

gener i c var i abl es bei ng used t o t he most common physi cal

system t ypes.

2. 3 The Concept of causal i t y

Bond gr aphs have t he pr oper t y of pr eser vi ng t he

t opol ogi cal as wel l as t he comput at i onal st ruct ur e of a

syst em When, f or exampl e, a gi ven el ect r i cal syst em i s

t r ansf ormed i nt o bond gr aphs i t s t opol ogi cal st r uct ur e i s

qui te evi dent to the reader . Never t hel ess, i t s computat i onal

st r uct ur e cannot be seen easi l y. Thus, t he i nt r oduct i on of

bond graph causal i t y comes i nt o account .

We say t hat i n bond gr aphs i nput s and out put s ar e

speci f i ed by means of t he causal st r oke. I t i s a shor t

per pendi cul ar l i ne made at one end of a bond or por t l i ne. I t

i ndi cat es t he di r ect i on i n whi ch t he ef f or t si gnal i s

di r ect ed, i mpl yi ng t hat t he ot her end whi ch does not have a

causal st r oke i s t he one t hat t he f l ow si gnal ar row poi nt s.

Fi gur es 2. 6( a) and 2. 6( b) i l l ust r at e succi nct l y t he meani ng

of causal i t y ( causal st r oke) .

The f ol l owi ng Fi gur e 2. 7 shows t he ni ne mul t i par t

el ement s wi t h t hei r desi r ed causal f orms and r el at i ons. I t

i s wor t hwhi l e sayi ng t hat f or r esi st ance bot h causal f orms

( as shown) ar e physi cal l y and comput at i onal l y possi bl e.

However , f or capaci t ances and i nert ances we woul d rat her pi ck

t he causal i t i es t hat numer i cal l y i nt egr at e over al l st at e

var i abl es.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 25/122

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 26/122

ELEMENT

E ff o rt S ou rc e

F lo w S ou rc e

R e s i s t a n c e

C a p a c it a n c e

In e r t a n c e

T r a n s f o r m e r

G y r a t o r

0 - J u n c tio n

1 - J un ctio n

  US LFORM

S E > I

S F I >

- - - - > • . . .1 R

R I >

->-C

> ~ I

I1 > T F I 2 >

1 > J T F 2 > I

I 1 > G Y 2 > I

1 > I G Y I 2 >

1~   I

3

26

  US LREL T I ON

e   t) = E t}

f   t) = F t}

f = C l> ~  e )

e = C l> R Q

e = C l > d   J f d t )

1 = C l >   ; U e d t }

e 1= m e 2 , f2 = m f1

f1 = f 2 /m e 2 = e 1 1 m

e 1= rf2 e 2 = rf111= e 2 / r   12 = e 1 / r

e 2 = e l , e 3 = e 1

1 1 = - f 2 + f 3 }

12 = 11 . 13 = 11

e l = - e 2 + e 3 )

Fi gur e 2. 7 Desi r ed causal f or ms and r el at i ons of t he basi cni ne mul t i por t el ement s

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 27/122

27

2 4 Pseudo Bond Graphs and Thermal Systems

Because of t he f act t hat t he sol ar - heat ed house i s a

t her mal syst em i t i s t i me t o i nt r oduce some bond- gr aph

representat i ons f or such a thermal system Thermal systems

have been pr esent ed as anal ogous t o el ect r i cal syst ems,

usual l y wi th temperature anal ogous to vol t age and heat f l ow

anal ogous t o cur rent . wi t h t hi s anal ogy i n m nd we have

sources anal ogous to vol t age and cur rent sour ces, thermal

resi stor s and capaci t or s, and a and 1 j unct i ons. However ,

there are no thermal i ner t i as ( i ner t ances) .

Ther e i s one maj or obst acl e. The pr oduct of

t emperat ure and heat f l ow i sn  t power . Heat f l ow i s by i t sel f

a power . Engi neer s, t hen, deci ded to name such a bond graph

i n whi ch t he pr oduct of ef f or t and f l ow i sn  t power a pseudo

bond gr aph. As l ong as the basi c el ement s i n t he pseudo bond

gr aph ar e cor r ect l y r el at ed t o t he e, f , p, and q var i abl es,

t he r ul es f or t he r egul ar bond gr aph t echni que can be

usef ul l y appl i ed. The t r ue bond gr aph r esul t s ( see Fi gur e

2. 8) , i f t emperatur e and ent r opy f l ow are used as ef f or t and

f l ow var i abl es r espect i vel y. I ndeed, t he pr oduct of

t emper at ure and ent ropy f l ow i s power .

The f ol l owi ng Fi gure 2. 8 shows a thermal resi stor and

I - j unct i on as wel l as a t her mal capaci t or and a- j unct i on

whi ch ar e goi ng t o be used i n t he f i f t h chapt er dur i ng t he

model i ng procedure of t he sol ar house.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 28/122

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 29/122

29

Despi t e t he f act t hat i n t he l i t er at ur e pseudo- bond gr aphs ar e

mor e popul ar t han t he t r ue- bond gr aphs i n model i ng t her mal

syst ems, i t may be ar gued t hat usi ng t he l at t er ones w l l be

mor e appr opr i at e f or model i ng t he sol ar house. Tr ue- bond gr aphs

ar e bet t er sui t ed t o r epr esent t he ener gy f l ow acr oss a

j unct i on t o and f r om ot her t ypes of ener gy, such as mechani cal ,

el ect r i cal , hydr aul i c, or pneumat i c. Thus, as shown i n t he

pr evi ous f i gur e, t emper at ur e ( T) woul d be t he ef f or t var i abl e

and ent ropy f l ow ( S ) woul d be t he f l ow var i abl e.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 30/122

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 31/122

31

Present l y, DYMOLA suppor t s DESI RE, SI MNON and FORTRAN and i t

woul d not be di f f i cul t t o enhance i t t o suppor t ot her

l anguages, such as ACSL, as w~ l .

DYMOLA uses t wo concept s: t he submodel concept as

wel l as t he cut concept . These w l l be cl ar i f i ed l at er i n

thi s chapter .

Ther e exi st cur r ent l y two di f f er ent i mpl ement at i ons

of DYMOLA, one coded i n PASCAL and t he ot her coded i n SI MULA.

The f i r st one r uns on VAX/ VMS and on PC compat i bl es, whi l e

t he l at t er r uns on UNI VAC comput er s.

3. 2 Speci al Pr oper t i es of DYMOLA Model Descr i pt i ons

3. 2. 1 Some Pr oper t i es

The f ol l ow ng ar e pr oper t i es of a DYMOLA model . Some

ar e quot ed di r ect l y f rom Cel l i er s book ( Cel l i er , 1990a) ,

others are paraphrased:

( 1) DYMOLA var i abl es can be of t wo t ypes: t he

t erm nal t ype and t he l ocal t ype. I f t hey ar e

connect ed t o somet hi ng out si de t he model , t hey

w l l be of t he t erm nal t ype; ot herw se, t hey

w l l be of t he l ocal t ype ( connect ed i nsi de t he

model ) .

( 2) Term nal s m ght be ei t her i nput s or out put s,

f r equent l y dependi ng on t he sur r oundi ngs t o

whi ch t hey ar e connect ed. The user has t he r i ght

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 32/122

32

t o decl ar e t hem t he way he want s t hem t o be by

expl i ci t l y speci f yi ng i nput or out put .

( 3) DYMOLA const ant s can be of t he par amet er t ype i f

t he user w shes t o do so. Par amet er val ues can

be assi gned f r om out si de t he model , but t hey can

al t er nat i vel y al so assume def aul t val ues.

( 4) Ter mnal s can have def aul t val ues. I n t hi s way,

t hey don t need t o be ext er nal l y connect ed

(Cel l i er , 1990a) .

( 5) The f i r st t i me der i vat i ve of st at e var i abl e x

can be expr essed i n t wo ways, ei t her t hr ough

der ( x) or t hr ough x . Second der i vat i ves can be

wr i t t en as ei t her der 2( x) or x .

( 6) The user cannot set i ni t i al condi t i ons f or t he

i nt egr at or s i nsi de a model , show ng cl ear l y a

f l aw of DYMOLA.

( 7) The synt ax expr essi on = expr essi on i s used i n

DYMOLA equat i ons, bei ng sol ved f or t he pr oper

var i abl e dur i ng t he pr ocess of a model

expansi on. DYMOLA accept s t he f act t hat t he l ef t

hand si de of an equat i on can have der

( t emperature) , whi l e t emperature appear s on the

l ef t hand si de of anot her .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 33/122

33

( 8) When mul t i pl yi ng t erms by a zer o par amet er , t hey

ar e aut omat i cal l y el i m nat ed dur i ng a model

expansi on. For exampl e, i f we have

La = 0. 0

and the model equat i on

La * der ( i a)   ua - ui - Ra * i a

t hen t he above i s r epl aced by

0. 0   ua - ui - Ra * i a

 3.1)

(3.2)

r esul t i ng i n t he f ol l ow ng t hr ee

s i mul at i on equat i ons:

( a) ua   ui   Ra * i a ( 3. 4)

( b) ui   ua - Ra * i a ( 3. 5)

( c) i a = ( uo - ui ) / Ra ( 3. 6)

dependi ng on t he envi r onment i n whi ch t he model

i s used.

 3.3)

possi bl e

I f La ~ 0. 0, t hen t he model equat i on i s al ways

t r ansf ormed i nto

der ( i a) = ( ua - ui - Ra * i a) / La ( 3. 7)

( 9) The above r ul e i ndi cat es t hat par amet er s w t h

val ue 0. 0 ar e t r eat ed i n a compl et el y di f f er ent

manner t han al l ot her par amet er s ( Cel l i er ,

1990a) . Par amet er s whi ch ar e not equal t o zer o

ar e mai nt ai ned i n t he gener at ed si mul at i on code,

wher eas t he ones w th 0. 0 val ue ar e not

r epr esent ed i n t he si mul at i on code.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 34/122

34

( 10) DYMOLA model s ar e modul ar because t he equat i ons

can aut omat i cal l y be sol ved dur i ng model

expansi on.

3 2 2 The Cut Concept

When advanci ng to hi gher l evel s of t he hi erarchy, t he

number of t he par amet er s wi l l be gr owi ng. Si m l ar t o r eal

syst ems wher e wi r es ar e gr ouped i nt o cabl es and cabl es ar e

grouped i nto t r unks, t he concept of cut has been i nt r oduced

i n DYMOLA t o gr oup var i abl es t oget her . Cut s cor r espond t o

compl ex connect i on mechani sms of physi cal syst ems l i ke

el ect r i cal wi r es, pi pes and shaf t s . A more pr eci se def i ni t i on

i s t he f ol l owi ng: Cut s ar e hi er ar chi cal dat a st r uct ur es t hat

enabl e t he user t o gr oup i ndi vi dual wi r es i nt o buses or

cabl es and cabl es i nt o t r unks. A cut i s l i ke a pl ug or a

socket . I t def i nes an i nt er f ace t o t he out si de wor l d

( Cel l i er , 1990b) .

The f ol l owi ng two f i gur es, 3. 1 and 3. 2, show a model

of a conduct ance ( i nver se of r esi st or ) i l l ust rat i ng t he

di f f er ent model descr i pt i ons bef or e and af t er usi ng t he

concept of cut . Thi s exampl e demonst r ates how a cont i nuous

model achi eves modul ar i t y.

wi t h cut decl ar at i ons the i nput and output var i abl es

do not change t he model descr i pt i on by swi t chi ng t hem

Never t hel ess, t he mai n advant age of cut i s t he two t ypes of

var i abl es, t he across and through var i abl es wi t h whi ch there

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 35/122

35

m o de l n am e : c on du cta nc einpu t: Iou tpu t: Vp ara m ete r: Ge qu atio ns : V   I /G

o r m ode l nam e: conduc tanceinpu t: Vou tpu t: Ip ara m ete r: G

e qua tio ns : I = V • G

Fi gur e 3. 1 Model of a conduct ance usi ng i nput out putdecl ar at i on

m o de l n am e : c on du cta ncecu t: A Va I I 8 V b I I

lo ca l: Vp ara m ete r: Ge qu atio ns : V = V a -V b

V = I I G

Fi gur e 3. 2 Model of a conduct ance usi ng cut decl ar at i on

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 36/122

36

i s associ at ed as i n t he r eal physi cal wor l d a connect i on

mechani sm The equat i ons whi ch descr i be t he phys i cal l aws at

t he connect i on mechani sm are aut omat i cal l y generat ed by t he

decl arat i on of cut and the connect i on statements .

Consi der t he f ol l owi ng exampl e: Thr ee submodel s

def i ned as  GH  Gz  and  G 3  have A and B as t hei r cut

var i abl es. V« and I ar e t he acr oss var i abl e and t he t hr ough

var i abl e associ at i ng wi th cut A, respect i vel y, bei ng decl ared

as ( see Fi gur e 3. 3)

cut A (V«/I)

Usi ng t he connect statement

connect G1:A at Gz:A at G3:A,

t he f ol l owi ng equat i ons are aut omat i cal l y generat ed:

GpV«   Gz.V« (3.8)

Gz•V«   G3• V« (3 • 9 )

Gp I + Gz• I + G3• I = 0 (3. 10)

The above equat i ons descr i be what exact l y happens at t he

boundar y of t he subsyst em wher e two or mor e el ement s ar e

connect ed. Ther eby, al l acr oss var i abl es ( t o t he l ef t of t he

sl ash separ at or ) ar e set equal , and al l t he t hr ough var i abl es

( t o t he r i ght of t he sl ash oper at or ) ar e summed up t o zer o

( Cel l i er , 1990b) .

When sever al cut s ar e gr ouped t oget her , a

hi er ar chi cal cut i s f or med i n t he same way as i ndi vi dual

wi r es ar e gr ouped t oget her i nt o a cabl e.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 37/122

37

V a G 1 V b  i t  B

B•

I

V a G 2 V b  i t  B

 I

V a G 3 V b  i t  B B B

•I

  a b

Fi gur e 3. 3 Thr ee submodel s connect ed at por t A

( a) Thr ee submodel s( b) Connect ed at A

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 38/122

38

Usi ng t he concept of cut , t he f ol l ow ng concl usi ons

can be der i ved:

( 1) When var yi ng t he I / O var i abl es, a model i n a

cont i nuous syst em can avoi d a change i n i t s

model descr i pt i on.

(2) I t separ at es t he physi cal l aws whi ch descr i be

t he st at i c and dynam c pr oper t i es of t he model

f r om t he physi cal l aws whi ch domnat e at sever al

subsyst ems at t hei r connect i ng poi nt s.

(3) Model s i n DYMOLA ar e sai d t o be i n pr oper

modul ar f or m so t hat t he user can bui l d t hem i n

a hi erarchi cal modul ar manner .

The above concept can be ext ended t o ot her syst ems

such as mechani cal , hydr aul i c and t her mal syst ems. Bei ng

i nt er est ed i n t he l ast ones, i t i s wor t hwhi l e ment i oni ng t hat

t emper at ur e and pr essur e ar e acr oss var i abl es, wher eas heat

f l ow i s a t hr ough var i abl e.

3. 2. 3 The Submode1 Concept and nodes i n DYMOLA

A submodel m ght be an at om c model , i . e. , a model

w t hout coupl i ng, or a coupl ed model .

Fi gur e 3. 4 i l l ust rat es at om c model s , wher eas t he

f ol l ow ng one ( Fi gur e 3. 5) i l l ust rat es a coupl ed model . I n

t he l at t er one, t he submodel s of a r esi s t or and a capaci t or

ar e depi ct ed whi ch ar e i n modul ar f orm The r esi st or s onl y

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 39/122

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 40/122

40

m o d e l p r c

s u b m o d e l r e s i s t o r 3 0

s u b m o d e l c a p a c i t o r 2 0c u t A V A i l

c u t B   V A / - Ic o n n e c t r e s i s t o r : B a t c a p a c i t o r : B a t B

c o n n e c t r e s i s t o r : A a t c a p a c i t o r : A a t A

e n d

Fi gur e 3. 5 Exampl e of a coupl ed model pr c

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 41/122

41

par amet er R i s 30 ( i ndi cat ed by t he ( 30) i n t he submodel

statement ) , whereas the capaci tor s onl y parameter C i s 20.

By coupl i ng t he t wo at om c model s t oget her , a coupl ed

model prc i s produced. prc stands f or paral l el connect ed

r esi st or and capaci t or . The coupl ed model i s i n pr oper

modul ar f orm and can be used t o const r uct l ar ger syst ems.

Thi s concept of coupl ed model s i n DYMOLA i s shown i n

Fi gure 3. 6.

The node st at ement wi l l be seen ver y of t en i n a

DYMOLA progr am Nodes are conveni ent ways t o make several

connect i ons act i ng l i ke t he power di st r i but or . We pl ug

several appl i ances i nto one di st r i butor . For exampl e, we can

have

node n

connect x: A at n

connect y: B at n

whi ch i s equi val ent to the si ngl e statement

connect x: A at y: B

3. 2. 4 Hi er ar chi cal Model st r uct ur e i n DYMOLA

Fi gur e 3. 7 depi cts a syst emnamed S decomposed i nt o

sever al sUbsystems:  Sl , S2 and  S3 . S2 i s decomposed

i nto  S21 and the l ast subsystem i s f ur t her decomposed i nto

 S31 and S32 showi ng an overal l hi erarchi cal st r ucture.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 42/122

42

RR  i I e B PRC

AT T

C  

A II • BC

 a

cut 1  •

cu t 1 cu t 2• .•  1Ll i J ·

u t 2

cu

Zc

t 1

 

ZA : cut-  ZB :

2

cu~ ZA I •• ~2

 b

Fi gur e 3. 6 Coupl ed model s i n DYMOLA

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 43/122

43

s

Fi gur e 3. 7 A hi er ar chi cal l y st r uct ur ed syst em

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 44/122

44

Fi gur e 3. 8 depi ct s one way t o descr i be t he

hi erarchi cal s t ruct ure of t he system ( S) i n DYMOLA. However ,

t hi s t echni que has a ser i ous f l aw. For exampl e, i f syst em

 S21 and  S32 are the same, the model speci f i cat i on must be

r epeat ed. I n or der t o avoi d dupl i cat i ng subsyst ems wi t h t he

same model s, DYMOLA i nt roduces a t erm cal l ed model t ype.

A model speci f i ed as model t ype r epr esent s a

gener i c model of a gener al cl ass of obj ect s. Thi s model

t ype can be used t o generat e several model s wi t h a submodel

stat ement so t hat dupl i cat i on wi l l be avoi ded ( Wang, 1989) .

For i nst ance, t he model r esi st or and t he model

capaci t or i n the model speci f i cat i on can now be def i ned as

 model t ype r esi st or and model t ype capaci t or .   The

f ol l owi ng Fi gur e 3. 9 demonst r at es t he same model

speci f i cat i on as bef ore but now usi ng model t ypes.

Af t er cr eat i ng model t ypes of any syst em i t

nat ur al l y comes t o t he user t o decl ar e l i br ar i es of model s.

Thi s l i br ar y i s set up f i r st when a syst em i s model ed and

then the hi er ar chy can be speci f i ed.

3. 3 Gener at i on of DESI RE Model s

As ment i oned bef ore, DYMOLA i s used to generate not

onl y SI MNON and FORTRAN model but al so DESI RE model s. The

f ol l owi ng command i s used f or thi s purpose:

out put desi r e model

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 45/122

45

M o d e l S

m o d e l S

en d

m o d e l S

m o d e l 8

en d

en d

m o d e l S3

m o d e l S3

en d .

m o d e l S

en d

e n d

en d

Fi gur e 3. 8 Descr i pt i on of t he hi er ar chi cal st ruct ur eof a syst em i n DYMOLA

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 46/122

m o d e l t y p e P R es u b m o d e l r e s i s t o r r t w o 3 0

s u b m o d e l c a p a c i t o r c o n e  2 0

c u t A V A / 1

c u t B V B / - I

c o n n e c t r t w o : A a t c o n e : A a t A

c o n n e c t r t w o : B a t c o n e : B a t B

e n d

Fi gur e 3. 9 Model speci f i cat i on f or pr eusi ng model t ype

46

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 47/122

47

However , bef or e pr oceedi ng, t he user has t o i ssue t he

command:

par t i t i on

whi ch mani pul at es al l t he equat i ons emanat ed by t he model

descr i pt i on and connect i on mechani sm Thi s wor ks i n t he

f ol l ow ng way: Fi r st , t he comput er w l l det erm ne i f a

var i abl e i s pr esent i n an equat i on or not . Secondl y, i t f i nds

out f or whi ch var i abl e each equat i on must be sol ved. Thi r dl y,

i t par t i t i ons t he equat i ons i nt o smal l er syst ems of equat i ons

whi ch must be sol ved at t he same t i me. At t he ver y end, i t

sor t s t he equat i ons i nt o t he cor r ect comput at i onal or der .

3. 3. 1 cr eat i on of a DESI RE Si mul at i on Pr ogr am

To cr eat e a DESI RE Si mul at i on Pr ogr am a cont rol

por t i on of t he DYMOLA pr ogr am i s added. I n or der t o r un t he

si mul at i on of a cont i nuous syst em t he basi c i nf or mat i on f or

si mul at i on cont r ol such as si mul at i on st ep, communi cat i on

poi nt s and si mul at i on t i me ar e r equi r ed.

3. 3. 1. 1 Descr i pt i on of t he Si mul at i on Cont r ol Model

I t s synt ax i s cmodel and i t must be st or ed i nt o a

f i l e w t h t he same f i l ename as t hat of t he cont rol l ed syst em

I t i s i ndi cat ed by t he f i l e ext ensi on ct l and i s compr i sed

of t hr ee par t s:

( 1) basi c par t

( 2) r un cont r ol bl ock

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 48/122

48

(3) out put bl ock

I n t he basi c par t t he f ol l owi ng i nf ormat i on i s st or ed:

  1 si mul at i on t i me

(2) s i mul at i on step si ze

(3) number of communi cat i on poi nt s

(4) i nput s ( opt i onal )

The r eader shoul d consul t Wang s t hesi s (Wang, 1989

concer ni ng t he f ormat of t he basi c par t .

The r un cont r ol bl ock i nvol ves t he r un cont r ol

st at ement s whi ch can appear i n t he r un- t i me cont r ol par t of

a DESI RE progr am

The output bl ock must contai n the si mul at i on output

r equi r ement s. Ther e ar e f our out put st at ement s whi ch ar e

 di spt , di spxy , t ype , and stash. Wang s thesi s gi ves

ext ens i ve det ai l s concerni ng t hei r synt act i c st ruct ures whi ch

ar e beyond t he scope of t hi s t hesi s . For t hi s t hesi s , we

requi r e si mul at i on graphs, so the di spt st atement i s goi ng

t o be used.

3. 3. 1. 2 Obt ai ni ng Execut abl e DESI RE Programs

The command

out put desi re program

wi l l cr eat e execut abl e DESI RE pr ogr ams. Fi r st , t he pr ogr am

ver i f i es i f t he si mul at i on cont r ol model associ at ed wi t h t he

syst em exi st s. Secondl y, i f t he above i s t r ue, t hen an

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 49/122

49

execut abl e DESI RE program i s generat ed; ot herwi se, an er r or

message i s di spl ayed.

The pr ocedur e of gener at i ng DESI RE model s wi l l be

shown wi t h exampl es i n t he next chapt er wher e a di r ect

pr ocedur e of t r ansf ormng bond gr aphs i nt o DYMOLA code i s

devel oped.

3 4 Some Unsolved Problems

Cur r ent l y, DYMOLA i s st i l l i n a devel opi ng st age. A

f ai r amount of r esear ch i s needed t o make DYMOLA a mor e

pr oducti onal code. Ther e ar e, i ndeed, some unsol ved pr obl ems

whi ch ar e l i st ed bel ow. They ar e good r esear ch t opi cs f or

DYMOLA s f ut ur e enhancement and advancement .

( 1) DYMOLA i s cur r ent l y abl e t o el i mnat e var i abl es

f r om equat i ons of t ype Q = f 3 . However , i t i s

unabl e to el i mnate var i abl es f r omequat i ons of

t ype   ± f 3   O.

( 2) DYMOLA must be abl e t o f i nd out dupl i cat e

equat i ons and t o get r i d of one of t hese

aut omat i cal l y. Thi s i s ver y i mpor t ant f or

hi er ar chi cal l y connected submodel s.

( 3) DYMOLA shoul d be abl e t o handl e super f l uous

connect i ons , i . e. , i f we speci f y t hat w2 = - w1,

i t i s obvi ousl y t r ue t hat al so b2 = - b1 

(Cel l i er , 1990a) . (w i s the angul ar vel oci t y and

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 50/122

50

b i s i t s cor r espondi ng angl e. ) Cur r ent l y,

DYMOLA cannot l et t he user speci f y t hi saddi t i onal connect i on and el i m nat e superf l uous

connect i ons dur i ng t he model expansi on.

( 4) DYMOLA must be capabl e of r ecogni zi ng t hat

connect i ons of out put s of i nt egrat ors can al ways

be t r ansf ormed i nt o connect i ons of i nput s of

such i ntegrator s . For exampl e, havi ng i a3   i a2,

i t i s obvi ousl y t r ue t hat i adot 3   i adot 2• Thi s

r ef ormul at i on can hel p el i m nat e st r uct ur al

s i ngul ar i t i es.

( 5) Gr oups of l i near al gebr ai c equat i ons ar e

cur r ent l y gr ouped t oget her and pr i nt ed out by

DYMOLA wi t hout bei ng sol ved. DYMOLA shoul d be

abl e t o r ewr i t e t he syst em of equat i ons i nt o a

mat r i x f or m si nce DESI RE can handl e mat r i x

expr essi ons ef f i ci ent l y and f ut ur e ver si ons of

DESI RE wi l l i ncl ude ef f i ci ent al gor i t hms f or

i nver t i ng mat r i ces (Wang, 1989) .

( 6) I f , f or exampl e, t he f ol l owi ng expr essi on i s

wr i t t en

x2 + z

2 + 2 * Y - 10   0

and i t i s desi r ed t o be sol ved f or x or z, t hen

pr obl ems wi l l ar i se. DYMOLA cannot sol ve f or

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 51/122

51

second or hi gher or der equat i ons. I t can sol ve

f or Y, however .

( 7) DYMOLA can handl e onl y cont i nuous- t i me systems.

I t st i l l cannot handl e di scr et e t i me syst ems

al t hough DESI RE can handl e t hem

The af or ement i oned unsol ved pr obl ems ar e t he most

not i ceabl e ones. For mor e i nf or mat i on, t he r eader can r ef er

t o Cel l i er s book ( Cel l i er , 1990a) and Wang s t hesi s ( Wang,

1989) .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 52/122

52

CHAPTER 4

CONSTRUCTI ON OF BOND GRAPHS

AND THEI R TRANSFORMATI ON I NTO DYMOLA

Af t er di scussi ng bot h t he bond gr aph met hodol ogy and

t he Dynamc Model i ng Language i n t he pr evi ous t wo chapt er s,

t hi s chapt er f ocuses on t he way t o combi ne t hese t wo t ool s

f or model i ng and si mul at i ng. A demonst r at i on f or const r uct i ng

a bond gr aph f or a si mpl e el ect r i cal net wor k i s gi ven and

t hen i t s gr aph i s t r ansf ormed i nt o DYMOLA code. I t i s a

si mpl e, di r ect pr ocedur e as w l l be seen.

4. 1 Over vi ew

A det ai l ed pr ocedur e f or const r uct i ng t he bond gr aph

i s pr ovi ded. The sampl e syst em i s goi ng t o be a si mpl e

el ect r i cal network. Several di agrams are drawn demonst rat i ng

t he st ep by st ep pr ocedur e so t hat t he r eader can f ol l ow i t

w t hout any di f f i cul t y.

Once t he bond gr aph f or t he gi ven syst em has been

const r uct ed, i t can be di r ect l y coded i nt o DYMOLA. Ther e ar e,

however , sever al r ul es f or t hi s pr ocedur e t hat shoul d be

obser ved. They ar e st ressed i n t he subsequent sect i ons of

t hi s chapt er . The basi c bond gr aph model i ng el ement s of R,

C, L, TF, GY and bond can be descr i bed once and f or al l and

st or ed away i n a DYMOLA model l i br ar y cal l ed bond. l i b.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 53/122

53

At t he ver y end, t he DYMOLA coded pr ogr am i s r un on

t hepc

I t i s goi ng t o be seen t hat DYMOLA i s so power f ul

t hat i t can aut omat i cal l y eval uat e t he causal i t y of a bond

gr aph, gener at e a st at e- space descr i pt i on f or t he syst em and

f i nal l y gener at e a si mul at i on pr ogr am i n cur r ent l y ei t her

DESI RE or SI MNON, t wo f l at di r ect execut i ng cont i nuous-

syst em si mul at i on l anguages. DESI RE i s goi ng t o be used f or

t hi s purpose.

4. 2 Some Basi c Rul es f or const r uct i ng Bond Di agr amsf or El ect r i cal Networ ks

Bef or e pr oceedi ng t o our const r uct i on of a bond

di agr am f or a si mpl e el ect r i cal net wor k, we need t o meet some

r egul at i ons gi ven i n t hi s sect i on.

( 1) I n t he a- j unct i on, al l ef f or t var i abl es ar e

equal , wher eas al l f l ow var i abl es add up t o

zero.

( 2) I n t he I - j unct i on, al l f l ow var i abl es ar e equal ,

wher eas al l ef f or t var i abl es add up t o zer o.

Ther ef or e, f or an el ect r i c ci r cui t di agr am t he a- j unct i on i s

equi val ent t o a node, or a node i n a DYMOLA pr ogr am

( El mqvi st , 1978). Moreover , t he a- j unct i on r epr esent s

Ki r chhof f s cur rent l aw, wher eas t he I - j unct i on r epr esent s

Ki r chhof f s vol t age l aw. I f t wo j unct i ons ar e connect ed w t h

a bond, one i s al ways of t he a- j unct i on t ype whi l e t he ot her

i s al ways of t he I - j unct i on t ype. I t can be sai d t hat

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 54/122

54

a- j unct i ons and 1- j unct i ons al ways t oggl e. Nei ghbor i ng

j unct i ons of the same type can be amal gamated i nt o one.

4 3 Cons t r uc t i on of a Bond Diagram

of a Simple Electrical Network

Because of my f am l i ar i t y t o el ect r i cal net wor ks, I

have chosen a si mpl e el ect r i cal networ k t o demonst r at e t he

st ep by st ep pr ocedur e f or const r uct i ng i t s bond gr aph.

The net wor k i s shown on Fi gur e 4. 1, wi t h i t s node

vol t ages l abel l ed a, b, c and r .

4 3 1 The Step by Step Procedure

The f ol l owi ng st eps must be f ol l owed f or const r uct i ng

i t s bond graph:

( 1) I t i s bet t er t o use vol t ages t han cur r ent s, so

Fi gur e 4. 2 shows t hr ee a- j unct i ons ( vol t age

j unct i ons) bei ng l ai d out wi t h subscr i pt s

cor r espondi ng to the nodes. The ref erence node

i s not r epr esent ed by a a- j unct i on.

( 2) Then, we r epr esent each br anch of t he ci r cui t

di agr am by a pai r of bonds r epr esent i ng t wo

a- j unct i ons wi t h a 1- j unct i on i n between t hem

( l - j unct i on = cur r ent - j unct i on) . Thi s i s

di spl ayed i n Fi gur e 4. 3

( 3) Set t i ng Vr t o zer o, we can r emove t he bonds

connect i ng t he r est of t he ci r cui t ( see

Fi gure 4. 4) .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 55/122

55

a Rb c

r

Fi gur e 4. 1 An el ect r i cal net wor k w t h nodes l abel l ed( r   r ef er ence)

V a R c V c

Fi gur e 4. 2 Layout of vol t age j unct i ons ( O- j unct i ons)

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 56/122

56

R

I 1

c

I  1

S E 1

Fi gur e 4. 3 The assembl y of component s and sour ce

R C

 0 1 0 1

I I I1 1 1

I  S E L 1 L 2

Fi gur e 4. 4 The cancel l at i on of r ef er ence nodeand associ at ed bonds

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 57/122

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 58/122

58

1

Fi gur e 4. 5 The condensat i on of bonds

R C SE 0   L 2

 L 1

Fi gur e 4. 6 The reduced graph

R C

 SE

> - 

> - 0 > -   > L 2

~

L 1

Fi gur e 4. 7 The bond gr aph

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 59/122

R : R 1

= 2 0 0 0

59

.v e  c

S E : u U o v 1 v 1 v L 2>   I : L 2

>   1 >   0 >   1= 2 0 V

 i e

.= 1 m H

1 0 1 0

i L VIe

I : L 1= 1 . 5 m H

Fi gur e 4. 8 The compl et ed bond gr aph w t h i t s causal i t i es

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 60/122

60

4. 4 Transformat i on of Bond Graphs i nt o DYMOLA Code

Af t er const r uct i ng t he bond gr aph f or t he sel ect ed

si mpl e el ect r i cal networ k, we ar e r eady t o t r ansf orm i t i nt o

DYMOLA code whi ch i s a st r ai ght f or war d pr ocedur e. The

f ol l owi ng rul es must be observed, however :

( 1) The O- j unct i ons ar e equi val ent t o DYMOLA s

 nodes.

( 2) Ther e i s no DYMOLA equi val ent f or 1- j unct i ons;

however , i f t he ef f or t and f l ow var i abl es ar e

i nt er changed, t hen t hey ar e t he same as

a- j uncti ons.

( 3) Havi ng t he above i n m nd, a model t ype bond

whi ch si mpl y exchanges t he ef f or t and f l ow

var i abl es can be cr eat ed and i nst al l ed i n

DYMOLA s l i brary. Bes i des , t he el ement s R, C, L,

TF and GY whi ch descr i be t he basi c bond gr aph

mul t i por t el ement s ar e i nst al l ed once and f or

al l i n DYMOLA s l i br ar y. They ar e i l l ust r at ed i n

Fi gur e 4. 11.

( 4) I n DYMOLA, al l el ement s shoul d be at t ached t o

O- j unct i ons onl y. I f we want t o at t ach an

el ement t o a 1- j unct i on, t hen we need t o pl ace

a bond i n bet ween ( Cel l i er , 1990a) . The

expanded bond graph i s shown on Fi gure 4. 9.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 61/122

R:R1 C :C 1

1 1  dR 1   dC 1

1 V1 1SE : U  

> 0 > 1),

0 > 1  , 0 >

v a.

dL2 I:L20

~

Ie

I:L 1

Fi gur e 4. 9 DYMOLA expanded bond graphw t h each node i ndi cat ed

61

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 62/122

62

(5) Nei ghbor i ng j unct i ons are al ways of t he opposi t e

sex, i . e. , O- j unct i ons and I - j unct i ons al ways

t oggl e.

( 6) For t unat el y, we do not need t o wor r y about

causal i t i es. DYMOLA i s per f ect l y capabl e of

handl i ng t he causal i t i es as i s seen dur i ng t he

execut i on of t he al gor i t hm assi gni ng t hem

However , as we saw ear l i er , we wer e per f ect l y

capabl e of assi gni ng causal i t i es. Thi s i s not

t rue ever y t i me. For exampl e, a non- causal

syst em r esul t s when we t r y t o connect t wo

sources of di f f erent val ues.

Now we are r eady t o t r ans l at e t he expanded bond graph

i nt o DYMOLA code as i ndi cat ed by Fi gur e 4. 10. The code i s

sel f - expl anat or y as we use t he st at ement s submodel ,

  connect , and node whi ch had been anal yzed i n t he pr evi ous

chapt er . Fur t hermor e, t he var i ous DYMOLA model t ypes as wel l

as t he Exper i ment used f or si mul at i ng the network are shown

i n the next two f i gures. Exper i ment i s t he si mul at i on cont r ol

model as descr i bed i n chapter t hree.

DYMOLA can f ur t hermor e be used f or obt ai ni ng var i ous

r esul t s such as causal i t y, el i m nat i on of r edundant

equat i ons, der i vat i on of a st at e- space represent at i on, and

generat i on of a si mul at i on program f or DESI RE. The ul t i mate

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 63/122

{bond gr aph model f or a s i mpl e RLC net wor k}

@r l c . r

@r l c . c

@r l c . i

@r l c . s e

@r l c . bnd

model RL C

s ubmodel ( SE) UO

s ubmodel ( R) RI ( R=200. 0)

s ubmodel ( 1 ) L l ( 1 =1. 5E- 3) , L 2( 1=I . OE- 3)s ubmodel ( C) CI ( C=O. l E- 6)

s ubmodel ( b ond) BI , B2, B3, B4, B5, B6

node vO, i O, v l , dRI , i c , d L2, dCl

out put y l

c onnec t UO at vOconnec t BI f r om vO t o i O

connec t B2 f r om i O t o dRI

connec t RI at dRI

c onnect B3 f r om i O t o v I

connec t L I at vl

connect B4 f r om vI t o i c

connect B5 f r om i c t o dCIconnec t CI at dCI

connec t B6 f r om i c t o dL 2

connec t L2 at dL2

UO. EO=20. 0

y l =L2. e

end

Fi gur e 4. 10 DYMOLA code of t he bond gr aphshown on Fi gur e 4. 9

63

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 64/122

64

model t y pe Rcut A ( e / f )par amet er R=l . OR* f = e

end

model t ype GY

cut A( el / f l ) B( e2/ - f 2)mai n cut C[ A B)

mai n pat h P<A - B>par amet e r r =l . Oel =r * f 2

e2=r * f 1end

model t y pe I

cut A  e / f

par amet er 1=1. 0I * der ( f ) = e

end

model t ype TF

cut A( el / f 1) B( e2/ - f 2)mai n cut C[ A B)

mai n pat h P<A - B>par ame te r m=l . O

e1=m* e2f 2=m* f 1

end

model t ype C

cut A  e / f)

pa r amet er C=l . 0

C* der ( e) = f

end

model t ype SFcut A( . / - f )

t er m nal FO

FO=f

end

model t ype SE

cut A  e / .)

t er m nal EOEO = e

end

model t ype bond

cut A  x / y) B ( y / - x)

mai n cut C [ A B)

mai n pat h P <A - B>

end

Fi gur e 4. 11 The var i ous basi c DYMOLA model t ypes

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 65/122

65

cmodel

s i mut i me 50. 0E- 6s t ep 50. 0E- 9

commupoi nt s  

c t b l oc k

s cal e = 1

XCCC = 1l abel TRY

drunr I i f XCCC<O t hen XCCC = - XCCC I s c al e = 2* s c al e I go t o TRYel s e pr oceed

c t end

out b l o ckOUT

yl =L2Se

di s pt y lout end

end

Fi gur e 4. 12 Exper i ment used f or t he net wor k

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 66/122

66

goal i s t he gener at i on of an execut abl e DESI RE pr ogr am usi ng

the f ol l ow ng commands:

  dymol a

> ent er model

- @r l c. dym

> ent er exper i ment

- @r l c. ct l

> out f i l e r l c. des

> par t i t i on el i m nat e

> out put desi r e pr ogr am

> stop

cl ar i f yi ng t he l ast por t i ons of t he l ast chapt er .

Then, we can r un DESI RE usi ng t he f ol l ow ng commands

  desi r e

> l oad ' r l c. des'

> r un

> bye

The gener at ed DESI RE pr ogr am as wel l as t he st at e- space

r epr esent at i on ar e shown i n t he f ol l ow ng two f i gur es

r espect i vel y ( see Fi gur e 4. 13 and Fi gur e 4. 14) . The

st at ement s above t he DYNAM C decl ar at i on of t he gener at ed

DESI RE program descr i be t he exper i ment t o be per f ormed on t he

model , and t he ot her st at ement s descr i be t he dynamc model .

The t i me of t he whol e compi l at i on i s l ess t han a t ent h of a

second. Fi nal l y, t he DESI RE out put of our net wor k i s shown i n

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 67/122

67

- - CONTI NUOUS SYSTEM RLC

STATE C1Se LI Sf L2 f

DER dC1Se dLl f dL2 f

OUTPUT yl

PARAMETERS and CONSTANTS:

R=200. 0

C=0. l E- 6

L1SI = . 5E- 3

L2SI = . OE- 3

- - I NI TI AL VALUES OF STATES:

CI Se=O

LI Sf =O

L2Sf =0

TMAX=50. 0E- 6   DT=50. 0E- 9   NN= OI

scal e = I

XCCC = 1

l abel TRY

drunr I i f XCCC<O then XCCC = - XCCC I scal e = 2*scal e I go t o TRY

el se proceed

DYNAM C

- - Submodel : RLC

B3Sx = L2Sf + LI Sf

- - Submodel : RI

RI Se = R*B3Sx

- - Submodel : CI

d/ dt CI Se = L2Sf / C

- - Submodel : RLC

BI Sx = 20. 0B4Sx = BI x - RI e

Fi gur e 4. 13 Gener at ed DESI RE Pr ogram(cont i nued on next page)

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 68/122

68

- - Submodel : L l

d/ dt L l f = B4 x / L l l- - Submodel : RLC

L2 e = B4 x - Cl e

- - Submodel : L2

d/ dt L2 f = L2 e/ L2 l

OUTyl =L2 edi s pt y l

 

/ P I C r l c . PRC

 

Fi gur e 4. 13 Generat ed DESI RE program ( cont i nued)

RLC B3 . x = L2. f   L l . fRl e = R*B3. xCl de re = L 2 . f / CRLC Bl . x = 20. 0

B4 . x = Bl . x - Rl . eL l de r f = B4. x/ lRLC L 2. e = B4. x Cl . eL2 der f = e/ l

Fi gur e 4. 14 St at e- space r epr esent at i on of t he net wor k

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 69/122

69

+

 

f

 I····················································· .

8

e B e e   B e

scale = 3 2 B e   B l

2 .58e-85

  y l u t

S.88e-85

Fi gur e 4. 15 DESI RE out put

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 70/122

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 71/122

71

CHAPTER 5

CASE STUDY

MODELING SIMULATING A SOLAR HEATED HOUSE

The mai n goal of t hi s t hesi s i s pr esent ed i n t hi s

chapt er . Havi ng st udi ed t he bond gr aph methodol ogy, DYMOLA,

and seen how t hese t wo t ool s can be combi ned t oget her , we ar e

r eady t o model and t hen t o si mul at e our sol ar - heat ed house.Bei ng a r el at i vel y compl i cat ed syst em i t i s appr opr i at e f or

model i ng pur poses t o di vi de i t i nt o sever al par t s, t hat i s ,

i nt o a hi er ar chi cal l y descr i bed st r uct ur e. Each par t i s

pr esent ed by i t s bond gr aph conver t ed i nt o i t s DYMOLA code as

wel l . Fi nal l y, al l t he par t s ar e combi ned t oget her r esul t i ng

i n t he whol e model of t he sol ar - heat ed house.

5 1 Overview

sci ent i st s t hr oughout t he year s have i nvest i gat ed t he

expl oi t at i on of sol ar r adi at i on f or space heat i ng. A sol ar

heat i ng syst em l i ke t he i nvest i gat ed one i s any col l ect i on of

equi pment desi gned pr i mar i l y t o use t he sun' s ener gy f or

heat i ng pur poses.

The above syst em i s a r el at i vel y compl i cat ed one

i nvol vi ng many di f f er ent t ypes of ener gy. Var i ous met hods

wer e used t hr oughout t he year s f or model i ng and si mul at i ng

such a syst em w t h m xed r esul t s. I t i s expect ed t hat usi ng

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 72/122

72

t he met hod descr i bed i n t hi s t hesi s, t hat i s, t he bond gr aph

model i ng met hodol ogy as wel l as DYMOLA f or gener at i ng a

si mul at i ng program f or DESI RE, the physi cal behavi or of such

syst ems can be model ed, si mul at ed and eval uat ed i n a

conveni ent , robust , and f ast manner .

The i nvest i gat ed conf i gur at i on consi st s of a f l at -

pl at e sol ar col l ect or , a sol i d body st or age t ank and t he

habi t abl e space. They ar e connect ed wi t h wat er l oops ci r cu-

l at i ng wat er t hr ough pi pes. Each par t i s t hor oughl y st udi ed

and anal yzed i l l ust r at i ng t he energy f l ow t hr ough each sub-

syst emand across t he bar r i er bet ween sUbsyst ems. Each one i s

t r ansf ormed i nt o a bond gr aph r epr esent at i on and i s t hen

di rect l y coded i nt o DYMOLA whi ch not onl y generates a DESI RE

pr ogr am but can al so pr ovi de us wi t h a set of f i r st or der

di f f er ent i al equat i ons ( a st at e- space represent at i on) . The

var i ous par amet er s used f or t he si mul at i on wer e t aken f r om

var i ous sources as ment i oned bef ore ( see l ast por t i on of t hi s

chapt er ) .

5. 2 Sol ar Heat i ng

A popul ar concept i on of sol ar heat i ng i s t o use t he

sol ar r adi at i on mor e or l ess di r ect l y wi t hout any nat ur al

i nt er medi at e st eps such as phot osynt hesi s. Thi s can be

pr i mar i l y accompl i shed by col l ect or s whi ch ar e devi ces

col l ect i ng sol ar r adi at i on ar r i vi ng f rom t he sun and

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 73/122

73

conver t i ng t hi s r adi ant ener gy t o a mor e desi r abl e one such

as heat . Thi s conver ted ener gy can be t ransf er red by a f l ui d

( usual l y hot wat er ) and ei t her ut i l i zed i mmedi at el y or st or ed

f or l at er use. Thi s heat can be used f or a si mpl e space

heat i ng. A gener al sol ar heat i ng syst em i s shown i n

Fi gur e 5. 1.

Let us descr i be i n gener al t erms t he col l ect or s and

t he st or age t ank as wel l as t he habi t abl e space.

Col l ect or s ar e t he hear t of any sol ar heat i ng syst em

col l ect i ng and t hen conver t i ng t he sol ar r adi at i on. The

si mpl est and cheapest one ( see Fi gur e 5. 2 i n sect i on 5. 4) i s

cal l ed t he f l at pl at e col l ect or . I t i s a f l at sheet of dar k

sur f aced met al possessi ng one or mor e l ayer s of gl ass above

and a l ayer of common i nsul at i on bel ow. The met al sheet i s

heat ed by sunl i ght whi ch comes t hr ough t he gl ass. The amount

of heat t hat can escape and di ssi pat e can be r educed by t he

gl ass and i nsul at i on; t her ef or e, t he met al sheet becomes ver y

hot . I n or der t o obt ai n t hi s heat f or ut i l i z i ng i t , t her e ar e

two ways t o do i t . Ei t her ai r can be passed above t he met al

or a f l ui d can be passed t hr ough t ubes bonded t o t he met al .

Ther ef or e, t he sunl i ght heat s ei t her ai r or wat er whi ch ar e

t r ansf er red t o ot her conveni ent l ocat i ons f or use.

When t he col l ect or suppl i es t he heat ed ai r or wat er ,

one of t wo t hi ngs must be done- - ei t her i t can be used at once

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 74/122

74

0- ~~:~ 

Col,.ctor :.

 0 . • • •  

E\tctric;ty

Fi gur e 5. 1 A sol ar heat ed house

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 75/122

75

or i t can be st or ed f or l at er use. Par t i cul ar l y, t he hot

wat er can be st or ed i n t ank syst ems desi gned i n such a way

t hat cool er wat er f r om t he bot tom can be sent t hr ough t he

col l ect or f or heat i ng and t hen r et ur ned t o t he upper par t of

t he t ank. I t i s not pr act i cal t o st or e hot ai r . The st or age

t anks ar e heavy and usual l y ar e set bel ow gr ound.

Havi ng heat ei t her f r om col l ect or s or t he st or age

t ank, we have t o use i t ; f or exampl e, f or space heat i ng

( habi t abl e space) . Hot wat er passes t hr ough a heat pump

( mght be cool i ng or heat i ng devi ce) and a heat exchanger i n

whi ch t he ai r bl ows ar ound t he hot wat er coi l s f r om t he heat

st or age t ank. Ther eby, t he habi t abl e space i s heat ed\

Above, t he pr ocedur e has been descr i bed i n whi ch

sol ar r adi at i on i s conver ted t o a f or m of ener gy f or heat i ng

a house. We ar e r eady now t o model t he basi c par t s, t hat i s

t he col l ect or , t he st or age t ank, t he wat er l oops ( col l ect or

and heat er wat er l oop) and t he habi t abl e space. The col l ect or

wat er l oop ( CWL) i s connect ed bet ween t he col l ect or and t he

st or age t ank; wher eas, t he ot her one ( heat er wat er l oop:

HWL) i s connect ed bet ween t he st or age t ank and t he heat er

( heat exchanger ) . I n model i ng our sol ar house, we have been

car ef ul t o make our syst em causal , t hat i s, t o sat i sf y al l

causal i t y condi t i ons. To st ar t w t h, we have t o know some

basi c t hermodynamc concept s whi ch ar e pr esent ed i n t he next

secti on.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 76/122

76

5. 3 Basi c Thermodynam c  n Gener al Concept s

The f i r st t hi ng needed i s t o def i ne ent r opy and t he

f i r st l aw of t hermodynam cs. So, ent ropy ( S) i s def i ned as

S - Q- T  5.1

wher e Q i s heat ( i n J oul es) and T i s t emper at ur e ( i n Kel vi n) .

The f i r st l aw of t hermodynam cs st at es t hat t he t ot al

energy Et, bei ng a const ant , equal s t o t he sum of f r ee ener gy

E  and t he t hermal ener gy Q.

( 5. 2)

Al so ent ropy f l ow can be def i ned as

dS _ .1 QQ

dt - T dt ( 5. 3)

and when mul t i pl i ed by t he t emper at ur e T gi ves heat f l ow

whi ch i s power needed t o const r uct t he bond di agr ams.

Moreover , t he heat equat i on

 5.4)

descr i bes bot h t he t hermal conduct i ve and convect i ve f l ow of

heat .

I n t hermodynam cs, we need t o f am l i ar i ze our sel ves

w th three separate physi cal phenomena provi di ng mechani sms

f or heat t r ansf er or heat f l ow. They ar e conduct i on, convec-

t i on, and r adi at i on.

I n heat conduct i on, t hermal ener gy i s t r anspor t ed by

t he i nt er act i ons of i t s mol ecul es i n spi t e of t he f act t hat

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 77/122

77

mol ecul es do not move t hemsel ves . For i nst ance, when one end

of a r od i s heat ed, t he l at t i ce at oms i n t he heat ed end

vi br at e wi t h gr eat er ener gy t han t hose at t he cool er end so

t hat t hi s ener gy i s t ransf er red al ong t he r od. I n t he case

of a met al r od, t he t r anspor t of t hermal ener gy i s ai ded by

f ree el ect rons whi ch are movi ng t hroughout the met al and they

col l i de wi t h t he l at t i ce at oms.

I n convect i on, heat i s t r anspor t ed by a di r ect mass

t r ansf er . For i nst ance, warm ai r near t he f l oor expands and

r i ses because i t possesses l ower densi t y. Thermal energy i n

t hi s war m ai r i s t ransf er red f r om t he f l oor t o t he cei l i ng

al ong wi t h t he mass of warm ai r .

The l ast mechani sm of heat t r ansf er i s t hr ough

thermal radi at i on i n whi ch energy i s emt ted and absorbed by

al l bodi es i n t he f or m of el ect romagnet i c r adi at i on. I f a

body i s i n t hermal equi l i br i umwi t h t he envi r onment , i t em t s

and absor bs ener gy at t he same r at e. However , when i t i s

warmed t o a hi gher t emper at ur e t han i t s envi r onment , i t

r adi at es away mor e ener gy t han i t absor bs so t hat i t cool s

down as t he sur r oundi ngs get warmer . As a r esul t , i n Ar i zona

peopl e avoi d havi ng dar k pai nt ed car s because t hey

emt / absorb l i ght much more st r ongl y than l i ght ones.

As we saw i n t he t hi r d chapt er , DYMOLA pr ovi des a

modul ar i zed hi er ar chi cal l y st r uct ur ed model descr i pt i on.

Thus, t he ent i r e sol ar house has been di vi ded i nt o f i ve maj or

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 78/122

78

hi erar chi cal st r uctures bei ng the ones as ment i oned bef ore.

Each of t hese consi st s of smal l er hi er ar chi cal st r uct ur es( submodel s) . For i nst ance, t he sol ar col l ect or consi st s of

t he l oss and t he spi r al submodel s. Fur t hermor e, t he spi r al

compr i ses of t wo ot her smal l er submodel s bei ng t he heat

exchanger and t he one- di mensi onal cel l . Thi s hi er ar chy

cont i nues even f ur ther wi t h t he one- di mensi onal cel l

consi st i ng of two other submodel s, the modul ated conduct i ve

source (mGS) and the modul at ed capaci t ance (mC) . Al l t hese

ar e descr i bed i n det ai l l at er i n t hi s chapt er .

Al l t hese hi er ar chi cal st r uct ur es pr ovi de t he

researcher a conveni ent way to study the physi cal behavi or of

each par t i cul ar par t of t he sol ar house i n gr eat er det ai l .

I n t he l ast por t i ons of t he pr evi ous sect i on,

t he t ermcausal was ment i oned, i . e. , t o sat i sf y al l causal i t y

condi t i ons. To achi eve t hi s, we have t o avoi d t he so- cal l ed

al gebr ai c l oops and t he st r uct ur al si ngul ar i t i es. Thi s has

been done by choosi ng t he pr oper el ement s i n assi gni ng

causal i t i es and not t o have any f r ee choi ce as depi ct ed i n

Fi gur e 2. 7 and by not over speci f yi ng i n t he descr i pt i on of

each par t i cul ar model . Thus, our sol ar - heat ed house wi l l be

a causal syst em and wi l l possess a uni quel y det er mned

causal i t y.

Now we ar e r eady t o pr oceed wi t h t he model i ng

procedure st ar t i ng i n the next chapter .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 79/122

79

5 4 Flat Plate Solar Collector Modeling

We shal l st ar t model i ng t he ent i r e sol ar house by

model i ng i t s f l at pl at e col l ect or . A si mpl er descr i pt i on t han

t he pr evi ous gi ven one f or t he sol ar col l ect or i s t o i magi ne

i t as a bl ack body accumul at i ng sol ar heat t hr ough r adi at i on

so t hat t he t emper at ur e r ai ses i nsi de. The col l ect or s ( may be

one or sever al ones) ar e usual l y f i l l ed by ai r possessi ng a

l ar ge heat capaci t y. I nsi de t hem a w ndi ng wat er pi pe goes

back and f or th bet ween t he t wo ends i n or der t o maxi m ze t he

pi pe sur f ace. Let ' s cal l t hi s a wat er spi r al . The heat i ng of

t he wat er i n t he pi pe occur s when a most l y conduct i ve heat

exchange t akes pl ace bet ween t he col l ect or chamber and t he

wat er pi pe. We shal l descr i be t he col l ect or wat er l oop as a

pump whi ch ci r cul at es t he wat er f r om t he col l ect or s t o t he

st or age t ank. As a r esul t , t he heat t r ansf er occur s i n a

most l y convect i ve manner . The wat er spi r al s can be connect ed

ei t her i n par al l el or i n ser i es and t he pump i s dr i ven by a

sol ar panel . The sol ar l i ght i s conver t ed i nt o el ect r i ci t y

i nsi de t he panel . As a r esul t , t he pump ci r cul at es t he wat er

onl y on a sunny day, whi ch i s meani ngf ul . Fur ther mor e, t he

wat er pi pe i s pr ot ect ed by a f r eeze pr ot ect i on devi ce whi ch

al so sw t ches t he pump on when t he t emper at ur e f al l s bel ow

5°C out s i de.

A model depi ct i ng such a f l at pl at e sol ar col l ect or

i s shown i n Fi gur e 5. 2. The ef f i c i ency of t he sol ar col l ect or

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 80/122

80

 Sol¥ ~

R.o~hon \, :. . 

Fi gur e 5. 2 Model of a f l at - pl at e col l ect or

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 81/122

81

depends upon sever al f act or s such as cl i mat i c condi t i ons

( ambi ent t emper at ur e, wi nd) , number of cover s and t hei r

r adi at i ve pr oper t i es, i nci dent sol ar angl e, r adi at i ve

proper t i es of absorber pl ate, spaci ng of covers and absorber ,

f l ui d t ype and i nsul at i on of col l ect or encl osur e. The

f ol l owi ng assumpt i ons wer e made bef or e model i ng t he

col l ect or :

( a) The heat f l ow i nt o t he col l ect or i s basi cal l y a

r adi at i ve heat f l ow, model ed by a f l ow sour ce

whi ch i s dependent on t hr ee f act or s, day of t he

year , t i me of t he day and weat her .

( b) Ther e i s l oss f r om t he col l ect or t o t he

surr oundi ngs whi ch has conduct i ve, convect i ve

and r adi at i ve el ement s wi t h t he f i r st t wo mor e

domnant . I t i s basi cal l y model ed as a t empera-

t ur e sour ce and as a modul at ed conduct ance

char act er i zed by t he absor ber and envi r onment .

( c) There exi st s conduct i ve heat exchange between

t he col l ect or space and t he hydr aul i c spi r al .

And f i nal l y,

( d) Ther e i s convect i ve heat t r anspor t i n t he

spi ral .

The wat er spi r al i nt roduced pr evi ousl y wi l l be

r epr esent ed as a ser i es of one- di mensi onal cel l s. The bond

di agram and the DYMOLA model type of such a cel l are depi cted

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 82/122

82

i n Fi gur es S. 3a and S. 3b, r espect i vel y, w t h t he causal i t i es

cor r ect l y mar ked. The mGS el ement i s a modul at ed conduct i ve

sour ce modul at ed w t h t emper at ur e and, f ur ther mor e, i t i s

modul at ed w t h t he wat er vel oci t y i n t he pi pe as shown i n

Fi gur e S. 3c. Thi s el ement ( one- di mensi onal cel l ) has been

model ed t hr ough i t s conduct ance r at her t han t hr ough i t s

r esi st ance because t he conduct ance changes l i near l y w t h t he

water vel oci t y.

The bond gr aph of t he one- di mensi onal cel l f avor s

heat f l ow f r om t he l ef t t o t he r i ght ; t her ef or e, i t i s not

symmet r i cal . Our deci si on t o r epr esent t he heat ( ent ropy)

f l ow i n such a way i s j ust an appr oxi mat i on. I f , f or exampl e,

t he mGS el ement i s spl i t i nt o t wo equal par t s, one t ur ni ng

l ef t and t he ot her r i ght , t hi s choi ce i s not desi rabl e

because of t he i nt roduct i on of al gebr ai c l oops i dent i f i ed

w t h t he choi ces of causal i t i es ( Cel l i er , 1990a) .

The next st ep i s t o devel op t he heat exchanger model

bei ng used t o descr i be t he exchange of heat acr oss t he bor der

of t wo medi a. I n t hi s par t i cul ar case, t he heat exchanger i s

used t o model t he heat t r anspor t f r om t he col l ect or chamber

t o t he wat er spi r al . I t s bond di agr am as wel l as i t s DYMOLA

model t ype ar e shown i n t he f ol l ow ng t wo f i gur es ( S. 3d and

S. 3e) .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 83/122

83

  ~ 11D  1

Fi gur e 5. 3a Bond di agr am of a one- di mensi onal cel l

{bond gr aph f or one di mens i o nal c el l }

model t ype oneD

submode l ( MGS) Gc el l ( a=1. 5, b=O. 72)submode l ( MC) Cce l l ( gamma=72. 0 )

s ubmodel ( b ond) Bl , B2, B3

node nl , n2

t er m nal vwat er

cut Cx( ex/ f x) , Ci ( ei / - f i )

mai n pat h P<Cx - Ci >

connec t B1 f r om Cx t o n1

connec t B2 f r om n1 t o n2

connec t Gcel l f r om n2 t o Ci

connec t B3 f r om n1 t o Ci

connec t Ccel l at Ci

Gce l l . vel =vwat er

end

Fi gur e 5. 3b DYMOLA model t ype of a one- di mensi onal cel l

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 84/122

84

G

eonwetiw.-::~ --. ;a;;;. . . .  ._ ht t t r 6n sport

  eondvct t-t..t trlf lsportv

Fi gur e 5. 3c Modul at ed conduct i ve source

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 85/122

rmRS~

o  

-tmRS ./

Fi gur e 5. 3d Bond di agr am of a heat exchanger

{bond gr aph f o r Heat er ( heat exchanger ) }

model t ype HE

submode l ( MRS) RI H( t het a=8 . 0E+2) , R2H( t het a=8 . 0E+2)cut A( el / f l ) , B( e2/ - f 2)mai n cut C[ A B]mai n pat h P<A - B>

connec t RI H f r om A t o Bconnec t R2H f r om B t o Aend

Fi gur e 5. 3e DYMOLA model t ype of a heat exchanger

85

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 86/122

86

Af t er model i ng t he one- di mensi onal cel l model and t he

heat er model , we ar e r eady t o pr oceed wi t h t he model i ng of

t he wat er spi r al whi ch i s a di st r i but ed paramet er syst em We

have deci ded t o r epr esent t he wat er spi r al wi t h t hr ee one-

di mensi onal cel l s connect ed i n ser i es and heat exchanger s

at t ached i n between. Obvi ousl y, our deci si on i s an approxi -

mat i on of a pr ocess wi t h di st r i but ed par amet er s. The bond

gr aph of a wat er spi r al whi ch i s a 3- por t el ement i s depi ct ed

next ( see Fi gur e 5. 3f ) . Fur t hermore, i t s cor r espondi ng DYMOLA

model t ype i s shown i n Fi gur e 5. 3g.

The f i nal el ement t o be devel oped f or t he compl et e

col l ect or model i s t he l oss el ement f r om t he col l ect or

chamber t o t he sur r oundi ngs. Thi s l oss i s par t l y conduct i ve

and par t l y convect i ve and i t s bond di agr am i s shown i n

Fi gur e S. 3h. I t i s a I - por t el ement . I t s DYMOLA model t ype

i s al so shown ( Fi gur e 5. 3i ) . The ef f or t sour ce denot es t he

out si de envi r onment , wher eas t he mG el ement denot es t he heat

di ssi pat i on t o t he envi r onment . The di ssi pat ed heat i s

pr opor t i onal t o t he di f f er ence i n t emperat ur es between t he

i nsi de and t he out si de. The mG el ement i s a modul at ed

conduct ance whi ch i s ver y si m l ar t o t he mGS el ement f ound

ear l i er . I t i s model ed wi t h t he t emper at ur e as wel l , but t hi s

t i me, t he modul at i on i s wi t h r espect t o t he wi nd vel oci t y

i nst ead of t he wat er vel oci t y.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 87/122

000 0

111 1 

O~lD~O~lD~O~lD~O

 o

1O~Sp1~O

Fi gur e 5. 3f Bond di agr am of a wat er spi r al

87

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 88/122

88

{bond gr aph Spi r al }

model t ype Spi

5ubmodel ( HE) HEI , HE2, HE3, HE45ubmode l ( oneD) oneDl , oneD2 , oneD3

node nl , n2

t er m nal vwat er

cut i nwat er l ( el / f l ) , o ut wat er l ( e2/ - f 2 ) , C( e3/ f 3)

mai n cut D[ i nwat er l out wat er l ]

mai n pat h P<i nwat er l - out wat er l >

connect HEI f r om C t o i nwat er l

connect oneDl f r om i nwat er l t o nl

connect HE2 f r om C t o nlconnect oneD2 f r om nl t o n2

connec t HE3 f r om C t o n2

connec t oneD3 f r om n2 t o out wat er lconnec t HE4 f r om C t o out wat er l

oneDI . vwat er =vwat er

oneD2. vwat er =vwat er

oneD3. vwat er =vwat er

end

Fi gur e 5. 3g DYMOLA model t ype of a wat er spi r al

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 89/122

89

mG

f ....O ~ l D S BO~Ik-SE

Fi gur e 5. 3h Bond di agr am of t her mc l oss

{bond gr aph f or LOs s }

model t ype Los s

s ubmodel ( SE) out t emp

s ubmodel ( MG) Gl os s( a=1. 5, b=O. 72)

s ubmodel ( bond) Bl , B2, B3

node n, nG, nS

mai n cut A( e/ f )

t er m nal Tout , vwi nd

connec t Bl f r om A t o n

connec t B2 f r om n t o nG

connec t Gl o s s at nG

connec t B3 f r om n t o nS

connec t out t emp at nS

out t emp. EO = Tout

Gl os s . vel = vwi nd

Gl os s . Tout = Tout

end

Fi gur e 5. 3i DYMOLA model t ype of t her mc l oss

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 90/122

90

For t he one- di mensi onal cel l , t he mGS el ement i s used

because t he ener gy i s not l ost . The ener gy i s si mpl y t rans-

por t ed r i ght away t o t he next node. Thi s i s t he r eason t hat

a new bond gr aph el ement cal l ed a r esi st i ve sour ce ( RS) has

been i nt r oduced ( Thoma, 1975) . Obvi ousl y t he GS el ement i s

l / RS. On t he ot her hand, t he mG el ement i s used i n t he l oss

because t he behavi or i s l i ke t he el ect r i cal case wher e t he

r esi st ances ( conduct ances) di ssi pat e heat and l ose ener gy.

Not i ce t hat i n t her modynam cs, t he RS ( R) and C el ement s ar e

nonl i near . I n DYMOLA, t hey ar e model ed by t wo new bond gr aph

el ements , mRS and mC, respect i vel y.

The over al l bond di agr am f or t he col l ect or can now be

dr awn as shown i n t he Fi gur e 5. 3j . The mC el ement whi ch i s

modul at ed w t h t emper at ur e i s t he heat capaci t ance of t he

col l ect or chamber . The SF el ement i s t he heat i nput f rom

sol ar r adi at i on whi ch must be model ed separ at el y.

We can use t he hi er ar chi cal cut concept of DYMOLA t o

combi ne t he two cut s i nt o an aggr egat ed bond gr aph r epr esen-

t at i on pi ct or i al l y r epr esent ed by a doubl e bond. The t wo cut s

can be named as i nwat er and outwat er and t he hi er ar chi cal cut

can be named as wat er . The di sadvant age of t he doubl e bond

r epr esent at i on i s t hat causal i t i es cannot be shown any

l onger .

Fi nal l y, t he DYMOLA model t ype of t he col l ect or can

be devel oped as depi ct ed i n t he next f i gur e ( Fi gur e 5. 3k) .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 91/122

- O~COl1~O

COll~O

Fi gur e 5. 3j Bond gr aph of t he col l ect or

{bond gr aph f o r Col l ec t or }

model t y pe COL L

s ubmodel ( MC) Cc ol l

s ubmodel ( SF ) SDOT

s ubmodel ( S pi ) Col l Spi r a l

s ubmodel ( L os s ) Col l L os s

t erm nal SO, Tout , v wi nd, v wat er

cut i nwat er ( el / f l ) , out wat er ( e2/ - f 2)

mai n cut wat er [ i nwat er out wat e r l

connec t SDOT at Col l Spi r al : C

connec t Ccol l at Col l Spi r al : C

connec t Col l Los s at Col l Spi r al : C

SDOT. FO=SO

Col l L os s . Tout = Tout

Col l L os s . vwi nd = vwi nd

Col l Spi r a l . vwat e r = vwat er

end

Fi gur e 5. 3k DYMOLA model t ype of t he col l ect or

91

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 92/122

92

I n usi ng t he f our el ement s, i . e. , mC, mG, mGS and

mRS, t her e ar e some physi cal concept s whi ch must be men-

t i oned. Cel l i er pr ovi des a ver y compr ehensi ve anal ysi s f or

t hese physi cal concept s and, t her ef or e, i t i s used i n t hi s

t hesi s ( Cel l i er , 1990a) .

We can wr i t e t he capaci t y of a body t r anspor t i ng heat

i n a di ssi pat i ve manner as

llT=

8

QQ=dt ( 8 . T) dSdt ( 5. 5)

wher e

~T = t emper at ure di f f er ence

8 = t hermal res i s tance

S = ent r opy

Q = heat

The above equat i on l ooks l i ke Ohm s l aw and i t can be

wr i t t en al so as

dS~T = R dt R = 8 . T ( 5. 6)

The t hermal r esi st ance can now be wr i t t en

8 = ~) . ~) ( 5. 7)

wher e

  = speci f i c t hermal conduct ance of t he mat er i al

A = ar ea of cr oss sect i on

  = l engt h

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 93/122

93

The three el ements mG, mGS and mRS, are model ed based

on t he above concept s and t hei r DYMOLA model t ypes ar e

i l l ust r at ed at t he end of t hi s sect i on al ong w t h t he me

el ement .

NOw, t he capaci t y of t he body t o st or e heat can be

wr i t t en as

dT~ =  y

dt( 5. 8)

wher e  y = t hermal capaci t ance.

The pr evi ous equat i on can al so be wr i t t en as:

~S = C dTdt

( 5. 9)

wher e C   t

T

The t erms t hermal r esi st ance and   t hermal

capaci t ance ar e i nt r oduced because of t he t r adi t i onalrel at i onshi p between t emperature and heat al though t hroughout

t hi s t hesi s ent r opy i s used ext ensi vel y.

Cont i nui ng, t he t hermal capaci t ance of a body can be

descr i bed as

-y = c . m   5. 10

wher e

m = mass of t he body

c = speci f i c t hermal capaci t ance of t he mat er i al

Mass can f ur ther be wr i t t en as

m =   V   5. 11

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 94/122

94

wher e

  = densi t y

v = vol ume

and

v = A . dx

Now f r om ( 5. 10) we have

c = ~ = ~c~ ~e~~A~_ ~n=xT T

( 5. 12)

The t i me const ant can now be det ermned:

T = R • C = 8 • Y =c .  

( 5. 13)

The l ast equat i on pr ovi des us w t h t he capabi l i t y of det er -

m ni ng t he di mensi ons of bot h t he r esi s t i ve and capaci t i ve

el ement s i n our bond gr aph.

Let us i l l ust r at e t he model i ng by means of t he i - t h

comput at i onal cel l . The equat i ons descr i bi ng such a cel l wer e

devel oped t o be:

dTi 1nSf ( 5. 14)

dt C

nTi = Ti-1 - Ti ( 5. 15)

Sf -1=

nTi ( 5. 16)R

S~x = Sf -1nTi ( 5. 17)Ti

nSf = S f-1   S~x - S~ ( 5. 18)

where Ti  i s t he t emper at ur e of t he comput at i onal cel l t o t he

l ef t and Sf i s t he ent ropy f l ow t o t he comput at i onal cel l t o

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 95/122

{bond gr a ph modul at e d c onduc t anc e}

model t ype MG

mai n cut A e/ f )

t er m nal vel , T out

par amet er a=l . O, b=l . O

l oc al G, Gl

GI = a* vel   b

G = Gl / Tout

G* e = f

end

Fi gur e 5. 31 DYMOLA model t ype of mG

(modul at ed w t h T and Vw nd)

{bond gr aph conduc t ance s our ce f o r one di mens i onal cel l }

model t ype MGS

cut A el / f l ) , B e2/ - f 2 )

mai n cut e[ A B)mai n pat h P<A - B>

t er m nal vel

par amet e r a=l . O, b=l . Ol ocal G, GI

GI =a*vel +b

G=f 2* GI

G* e l =f l

f l * el =f 2* e2

end

Fi gur e 5. 3m DYMOLA model t ype of mGS

(modul at ed w th T and Vwat er )

95

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 96/122

96

{ Bond Gr aph of a heat modul a t ed r es i s t i ve s our c e )

model t ype MRS

cut A el / f l ) , B e2/ - f 2)

mai n cut C[ A B]mai n pat h P<A - B>

par amet e r t het a =l . O

l oc al R

R = e2* t het a

R* f l = el

el * f l = · e 2* f 2

end

Fi gur e 5. 3n DYMOLA model t ype of mRS

(modul at ed w t h T and 8)

{ Bond Gr aph modul at e d c apac i t o r / c ompl i anc e}

model t ype MC

cut A e / f

pa r ame t e r gamma=I . O

l oc al C

C=gamma/ e

C* der e) = f

end

Fi gur e 5. 30 DYMOLA model t ype of mC(modul at ed w t h T and 7)

{bond gr aph f or a r es i s t i v e s our ce}

model t ype RS

cut A el / f l ) B e2/ - f 2)

mai n cut C[ A B]

mai n pat h P<A - B>

par amet e r R=l . 0

R* f l = el

el * f l = e2* f 2

end

Fi gur e 5. 3p DYMOLA model t ype of RS( el ect r i cal pr i mar y si de)

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 97/122

97

t he r i ght ( pl ease see t he bond di agr am on Fi gur e 5. 3a t o

f ol l ow t he above equat i ons) .

One cl ar i f i cat i on shoul d be made whi ch i s t he

f ol l owi ng: The RS el ement s may have both si des, pr i mary and

secondary, as thermal ones and they are model ed as shown i n

Fi gur e 5. 3n. On t he ot her hand, i f t hei r pr i mar y si de i s

el ect r i cal t hen t hei r DYMOLA model t ype i s di f f er ent and i s

shown i n Fi gur e 5. 3p. We ar e goi ng t o meet t hi s case when

desi gni ng t he el ect r i cal backup devi ce f or t he st or age t ank

( see next sect i on) .

5 5 Heat storage Tank Modeling

Af t er t he col l ect or model was made avai l abl e, t he

i mmedi at e next st ep i s t o model t he heat st or age t ank.

Fr equent l y, t he st or age t ank i s r eal i zed as a l ar geand wel l i nsul at ed wat er heat er . However , i n order t o model

a wat er heat er cor r ect l y, we must t ake t he mxi ng t hermo-

dynamcs i nt o account . Thi s makes t he model i ng pr ocedur e

di f f i cul t . Ther ef or e, a sol i d body st or age t ank was used

t oget her wi t h anot her wat er spi r al so t hat t he wat er f r omthe

col l ect or l oop and f r omthe heat er l oop never mx. One wat er

spi r al deposi t s heat i n t he st or age t ank, whi l e t he ot her

pi cks i t up agai n.

I nsi de t he st or age t ank t her e i s a second wat er

spi r al whi ch r epresent s t he heat er wat er l oop pi cki ng up t he

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 98/122

98

heat f r om t he st or age t ank. Whenever t he st or age t ank

t emper at ur e f al l s bel ow a cr i t i cal val ue, an i nst al l ed

el ect r i cal heat er heat s t he st or age t ank el ect r i cal l y up t o

t he m ni mum mai nt enance t emper at ur e.

Anot her pump dr i ves t he heat er wat er l oop and t hi s

pump i s swi t ched on whenever t he r oomt emper at ur e f al l s bel ow

20°C dur i ng t he day or 18°C dur i ng t he ni ght . I t i s swi t ched

of f whenever t he room t emperat ure rai ses beyond 22°C dur i ng

t he day or 20°C dur i ng t he ni ght .

Summar i zi ng, t he st or age t ank cont ai ns two wat er

spi r al s, one bel ongi ng t o t he col l ect or wat er l oop and t he

ot her one bel ongi ng t o t he heat er wat er l oop. Thi s i s

depi ct ed i n Fi gur e 5. 4a. Mor eover , an el ect r i cal backup

devi ce i s i nst al l ed and i t i s t ur ned on onl y i f t he t emper a-

t ur e i n t he st or age t ank f al l s bel ow i t s cr i t i cal val ue. I t

i s used onl y dur i ng eveni ng hour s when t he pr i ce of el ec-

t r i ci t y i s l ower . The over al l bond di agr am f or t he st or age

t ank i s shown i n Fi gur e 5. 4b. The mC el ement r epr esent s t he

heat capaci t y of t he st or age t ank, wher eas t he f l ow sour ce

t oget her wi t h t he RS el ement denot e t he backup devi ce. The

pr i mar y si de of t hi s r esi st i ve sour ce i s el ect r i cal whi l e t he

secondar y si de i s t herm c.

As we not i ce, t he st or age t ank i s a 4- por t el ement .

When wr i t i ng i t s DYMOLA model t ype, we combi ne t he cut

i nwat er l wi t h t he cut outwat er l t o t he hi er ar chi cal cut

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 99/122

99

S p i r a l s

  e a t e ro l l e c t o r

Fi gur e 5. 4a The st or age t ank w t h t he col l ect or wat er l oopand heat er wat er l oop

o 0

1  Sp1k-O~Spl

1  o 0

SF~ RS~O

Fi gur e 5. 4b Bond gr aph of t he st or age t ank

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 100/122

- .

100

i nwat er , wher eas we combi ne t he cut out wat er 2 w t h t he cut

i nwat er 2 t o t he hi er ar chi cal cut out wat er . By decl ar i ng a

mai n pat h wat er , a l ogi cal br i dge has been cr eat ed f r om t he

hi er ar chi cal cut i nwat er t o t he hi er ar chi cal cut out wat er .

Thi s i s depi ct ed i n t he f ol l ow ng f i gur e ( Fi gur e 5. 4c) .

5 6 water Loop Modeling

An exampl e of a convect i ve mechani sm i n our sol ar

house i s t he t ranspor t of t he heat f r om t he sol ar col l ect or

t o t he wat er heat er connect ed by a pi pe cont ai ni ng wat er . The

wat er i s ci r cul at ed f r om t he wat er heat er ( st or age t ank) t o

t he col l ect or and back by a pump.

We have al r eady seen t wo wat er l oops, t he col l ect or

wat er l oop and t he heat er wat er l oop, and bot h ar e model ed

exact l y i n t he same way.

Each of t he pi pes i s model ed by t hr ee one-di mensi onal

cel l s connect ed i n ser i es as i l l ust rat ed i n t he bond di agr am

( see Fi gur e 5. 5a) . The one- di mensi onal cel l has been

devel oped pr evi ousl y. We shal l assume t hat t he pi pes ar e

t herm cal l y wel l i nsul at ed, t hat i s, t her e i s not any l ost

heat t o t he sur roundi ngs on t he way. As shown, i t i s anot her

4- por t el ement . I n devel opi ng i t s DYMOLA model t ype, we shal l

combi ne t he cut i nwat er 1 w t h t he cut out wat er 2 t o t he

hi er ar chi cal cut i nwat er . I n addi t i on, we shal l combi ne t he

cut out wat er l w t h t he cut i nwat er 2 t o t he hi er ar chi cal cut

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 101/122

{bond gr aph s t or age t ank}

model t ype ST

s ubmodel SF ) SOOTs ubmodel RS) Rl R=l O. O)

submodel MC) Ct ank gamma=9. 0E+4)

s ubmodel Spi ) Spi t a nk l , Spi t a nk2

t e r m nal SO, vwat e r

cut i nwat er l e l / f l ) , out wat er l e2/ - f 2)

cut i nwat er 2 e3/ f 3) , out wat er 2 e4/ - f 4 )

mai n cut i nwat er [ i nwat er l out wat er l ]mai n cut out wat er [ o ut wat e r 2 i nwat e r 2]

mai n pat h wat er <i nwat er - out wat er >

connec t Spi t ank l : C at Spi t ank2: C

connec t Ct ank at Spi t ank l : C

connec t Rl f r om SOOT t o Spi t ank l : C

SDOT. FO=SO

Spi t ankl . vwat er = vwat e r

Spi t a nk2. vwat e r = vwat e r

end

Fi gur e 5. 4c DYMOLA model t ype of t he st or age t ank

101

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 102/122

Ok 1Dk Ok 1Dk Ok 1DJ c O

I I I

Fi gur e 5. 5a Bond di agr am f or wat er l oop

{bond gr aph w t r l oop heat e r +col l ec t or ) }

model t ype WL

5ubmodel oneD) oneDl , oneD2, oneD3 , oneD4 , oneDS, oneD6

node nl , n2, n3, n4

t er m nal vwat er

cut i nwat er l el / f l ) , out wat er l e2/ - f 2)

cut i nwat er 2 e3/ f 3 ) , out wat er 2 e4/ - f 4)

mai n cut i nwat er [ i nwat er l out wat er 2]

mai n cut out wat er [ i nwat e r 2 out wat er l ]

mai n pat h wat er <i nwat er - out wat er >

connec t oneDl f r om i nwat er l t o nlc onnect oneD2 f r om nl t o n2

connect oneD3 f r om n2 t o out wat e r l

connec t oneD4 f r om i nwat e r 2 t o n3connec t oneD5 f r om n3 t o n4

connect oneD6 f r om n4 t o out wat er 2

oneDl . vwat er =vwat er

oneD2. vwat er =vwat er

oneD3. vwat er =vwat er

oneD4. vwat er =vwat er

oneDS. vwat er =vwat er

oneD6. vwat er =vwat er

end

Fi gure 5. 5b DYMOLA model t ype f or water l oop

102

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 103/122

103

outwater . Moreover , we decl are a mai n path water creat i ng a

l ogi cal br i dge f r om t he hi er ar chi cal cut i nwat er t o t he

hi erar chi cal cut outwater ( see Fi gure 5. 5b) .

Assum ng t hat t her e i s no ai r i n t he pi pe and t he

wat er i n i t i s t ot al l y i ncompr essi bl e, sever al i mpl i ci t

physi cal si mpl i f i cat i ons can be t aken i nt o consi der at i on.

Thi s l eads t o t he concl usi on t hat t he wat er f l ow vi a t he

whol e pi pe has a const ant vel oci t y Vw•

The hydr aul i c f l ow i sexpressed i n ms- 1 denot ed by ~v and t he vol ume of wat er i n a

one- di mensi onal cel l i s V = A . fiX. Thus, t he amount of

ent ropy l eavi ng t he i - t h cel l per t i me uni t t o t he r i ght i s

gi ven by

  ~v8 i out = fl8i V   5. 19

whi ch can al so be wr i t t en as

8 f out =   c   ~v  Ti   5.20)

Dur i ng the same t i me, a si m l ar amount of heat i s t r anspor t ed

i nt o t he cel l f r om i t s l ef t nei ghbor bei ng

8 f i n =  C . ~ v ) T i 1   5. 21

Combi ng t he pr evi ous t wo equat i ons, we concl ude t hat

8 f conv = G conv flTi

and

G conv= C ~v

V 5.22)

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 104/122

104

Consequent l y, convect i on i s si mpl y a second convect i ve

r esi st ance bei ng connect ed i n par al l el w t h t he conduct i ve

r esi s t ance. Ther ef or e, convect i on augment s t he t her mal

conducti vi t y.

As ment i oned bef or e, sever al si mpl i f i cat i ons wer e

made. I n r eal i t y, t her e i s f r i ct i on bet ween t he l i qui d and

t he wal l , and f r i ct i on w t hi n t he l i qui d. We woul d not i ce

t hat i n t hi s case t he l i qui d f l ows f ast er at t he cent er of

t he pi pe and sl ower near t he wal l . The hydr aul i c f r i ct i on i s

a di ssi pat i ve pr ocess pr oduci ng mor e heat and t her eby mor e

ent r opy sour ces shoul d be appl i ed t o t he t hermal uni t .

Fur t hermor e, i f t he assumpt i on of i ncompr essi bi l i t y

wer e not made, t hen t he whol e si t uat i on woul d be much mor e

compl i cat ed. I n t hi s case, we woul d need t o t ake i nt o con-

si der at i on t he pneumat i c pr ocess besi des t he t hermal pr ocess.

The pneumat i c process generates a t i me- and space- dependent

f l ow r at e ~v( t , x} whi ch can be used t o modul at e t he convect i ve

r esi st ance of t he t her mal uni t . Over al l , t he whol e si t uat i on

becomes ver y i nvol ved.

5. 7 Habi t abl e Space Model i ng

I t was deci ded t hat t he habi t abl e space ( house) woul d

be a cube w t h di mensi ons 10m x 10m x 10m ( see Fi gur e 5. 6c) ,

mai nl y f or r easons of si mpl i ci t y.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 105/122

10S

However , bef or e st ar t i ng t o model t he house, a t hr ee-

di mensi onal cel l as wel l as a t wo- di mensi onal cel l have been

devel oped. The concept of a one- di mensi onal cel l whi ch has

been devel oped pr evi ousl y can be ext ended t o t he t wo- and

t hr ee- di mensi onal case. So, l et us assume t hat each t hr ee-

di mensi onal cel l consi st s of one capaci t or and t hr ee

r esi st or s, one t o i t s l ef t , one t o i t s f ront and one bel ow as

depi ct ed i n Fi gur e S. 6a t oget her w t h i t s bond di agr am I t

can al so be seen f r om t he f i gur e t hat t he necessi t y t o at tach

ever y el ement t o a- j unct i ons f or DYMOLA model i ng has been

t aken i nt o consi der at i on. The DYMOLA model t ype CEL

descr i bi ng t he t hr ee- di mensi onal cel l has been devel oped as

wel l and i t i s depi ct ed i n Fi gur e S. 6b. The t wo- di mensi onal

case consi st s of t wo r esi st or s ( xy, yz, xz di r ect i ons) and a

capaci t or .

We shal l assume t hat t he ent i r e house consi st s of one

r oom onl y and t hat a si ngl e l ar ge r adi at or i s used f or

heat i ng pur poses. The r adi at or exchanges heat w t h t he r oom

i n a par t l y conduct i ve and par t l y convect i ve manner . I t i s

at t ached t o t he l ef t wal l of t he house somewher e cl ose t o t he

f l oor so t hat t he heat i nput t akes pl ace at t he l ef t l ow

out s i de center t hree- di mensi onal cel l . Because the di mensi ons

of t he r adi at or ar e much smal l er t han t hose of t he house, a

deci si on was made not t o model t he r adi at or . Ther ef or e, t he

out wat er l of t he heat er wat er l oop has been si mpl y connect ed

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 106/122

106

w t h t he i nwat er 2 of t he heat er wat er l oop. Mor eover , anot her

heat exchanger has been at t ached at t hi s node w t h t he

r esponsi bi l i t y of exchangi ng t he heat bet ween t he heat er

wat er l oop and t he house.

Fr om Fi gur e S. 6c, i t can be seen t hat t he house has

27 nodes. At t hese nodes one- , t wo- and t hr ee- di mensi onal

cel l s ar e pl aced w t h t he except i on of t he f i r st node. So,

nodes 2 and 3 ar e one- di mensi onal i n x di r ect i on, 4 and 7 ar e

one-di mensi onal i n y di r ect i on, 10 and 19 are one-di mensi onal

i n z di r ect i on. The t wo- di mensi onal cel l s ar e l ocat ed at

nodes 5, 6, 8, 9 ( xy di rect i on) , 11, 12, 20, 21 ( xz di r ec-

t i on) and 13, 16, 22, 25 ( yz di r ect i on) . Fi nal l y t hr ee-

di mensi onal cel l s ar e pl aced at t he r emai ni ng nodes, i . e. ,

14, 15, 17, 18, 23, 24, 26, 27. These nodes ar e connect ed

t hr ough t hei r pat hs accor di ngl y as depi ct ed i n Fi gur e 5. 6d.

We need al so t o pl ace our heat sour ce and one addi t i onal

capaci t or at t he f i r st node whi ch i s act ual l y t he ex poi nt of

t he second node. The house l oses heat t hr ough t he f our wal l s

and t hr ough t he r oof , but not t hr ough t he f l oor so t hat at

nodes 5 and 14 t her e ar e no l osses. The pr evi ousl y devel oped

l oss el ement s ar e at t ached t o each of t he a- j unct i ons as

appr opr i at e. I n t he case of a cel l adj acent t o t wo or t hr ee

out si de wal l s, we at tach one combi ned l oss el ement t o t he

cor respondi ng node onl y because of t he emergence of al gebrai c

l oops. Ther ef or e, nodes 2, 4, 6, 8, 11, 13, 15, 17, 23 have

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 107/122

107

Fi gur e 5. 6a Thr ee- di mensi onal di f f usi on cel l(RS el ements are actual l y mRS el ements )

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 108/122

108

 bond gr aph f or a t hr ee di mens i o nal c el l )

model t ype CEL

s ubmo del MRS) Rx t he t a =O. 5) , Ry t he t a =O. 5) , - >

Rz t heta=O. 5 )

s ubmode l MC) C gamr na=l 5 2310. 0 )s ubmodel bond) Bx l , Bx 2, Bxa, By l , By 2, Bya, Bz l , Bz 2, Bz anode Nx , Nx a, Ny , Ny a, Nz , Nz a

cut Cx ex/ f x) , Cy ey/ f y) , Cz ez / f z ) , Ci e i / - f i )pat h Px<Cx - Ci >, Py<Cy - Ci >, Pz<Cz - Ci >

connec t Bxl f r om Cx t o Nx

connect By l f r o m Cy t o Ny

connect Bz l f r o m Cz t o Nzconnec t Bx2 f r om Nx t o Ci

connec t By2 f r om Ny t o Ci

connect Bz 2 f r o m Nz t o Ci

c onnec t Bxa f r o m Nx t o Nxaconnec t Bya f r om Ny t o Nya

connec t Bz a f r om Nz t o Nz a

connec t Rx f r om Nxa t o Ci

connec t Ry f r om Nya t o Ci

connec t Rz f r om Nz a t o Ciconnec t C at Ci

end

Fi gur e 5. 6b DYMOLA model t ype of a t hr ee- di mensi onal cel l

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 109/122

109

 

19

1810

1

 ---_ 5 > < :. • .. • . . • .. • . . • .. • .. • . . • .

- -  9

3

Fi gur e 5. 6c The house r oom repr esent ed as a 10x10x10 cube

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 110/122

110

model SPACE

submodel S F) Ts p

submodel MC) C gamma=152310. 0 )

submode 1 L S1) 12, 14, 16, 18, 111, 113, 115 , 117, 123

submode 1 L S2) 11, 13, 17, 19, 110, 112, 116 , 118, 120, 122, 124, 126

s ubmodel L S3) 119 , 121 , 125 , 127

s ubmodel CXD) d2, d3s ubmode1 CYD) d4, d7

s ubmode1 CZD) dl 0, d19submode1 XYC) d5, d6, d8, d9

s ubmode 1 XZC) d11, d12, d20, d21

submode 1 YZC) d13, d16 , d22, d25

s ubmode1 CE L) d14, d15 , d17, d18, d23, d24, d26, d27

i nput Tout , vwi nd, SO

out put yl

c onnec t Px) d2- d3, d5- d6, d8- d 9, - >

dl l - d12, dI 4- d15, d17- d18, - >d20- d21 , d23- d24 , d26- d27

connec t Py) d4- d7, d5- d8, d6- d9, - >dI 3- dI 6, d14- dI 7, dI 5- dI 8, - >

d22- d25, d23 - d26, d24 - d27

connec t pz ) dl 0- dI 9, d11- d20, dI 2- d21, - >

d13- d 22, d14 - d 23 , dI 5 - d 24, - >d I 6 - d25 , d17 - d26 , d18 - d27

connect 11 at d2: Cx

c onnec t 12 at d2: Ci

connec t 13 at d3: Ci

c onnec t 14 at d4: Ci

c onnec t 16 at d6: Ci

connec t 17 at d7: Ci

c onnec t 18 at d8: Ci

c onnec t 19 at d9: Ci

c onnec t 110 at dl O: Ci

connec t 111 at dl l : Ci

c onnec t 112 at d12: Ciconnec t 113 at dl 3: Ci

connect 115 at dl 5: Ci

connect 116 at d16: Ci

connect 117 at d17: Ci

conne c t 118 at d18: Ci

Fi gur e 5. 6d DYMOLA model t ype of t he SPACE ( house)

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 111/122

 connec t 119 at d19: Ci

c onnec t 120 at d20: Ci

c onnec t 121 at d21: Ci

c onnec t 122 at d22: Ci

c onnec t 123 at d23: Ci

c onnec t 124 at d24: Ci

c onnec t 125 at d25: Ci

c onnec t 126 at d26: Ci

c onnec t 127 at d27: Ci

c onnec t Ts p at d2: Cx

connec t C at d2: Cx

connec t d5: Cx at d4: Ci

c onnec t dB: Cx at d7: Ci

c onnec t dl l : Cx at dl 0 : Cic onnec t dl 4: Cx at d13: Ci

c onnec t d17: Cx at dl 6 : Cic onnec t d20: Cx at dl 9: Ci

c onnec t d23: Cx at d22: Ci

c onnec t d26: Cx at d25: Ci

c onnec t d4: Cy at d2: Cx

connec t d5: Cy at d2: Ci

connec t d6: Cy at d3: Ci

c onnec t dl 3: Cy at dI O: Ci

c onnec t dl 4 : Cy at dl l : Ci

c onnec t dl 5 : Cy at dl 2 : Ci

c onnec t d22: Cy at dl 9: Ci

c onnec t d23: Cy at d20: Cic onnec t d24: Cy at d21: Ci

c onnec t dI O: Cz at d2: Cx

connec t dl 1 : Cz at d2: Ci

c onnec t dl 2 : Cz at d3: Ci

c onnec t dl 3 : Cz at d4: Ci

c onnec t dl 4: Cz at d5: Ci

c onnec t dl 5: Cz at d6: Cic onnec t d16: Cz at d7: Ci

connec t d17: Cz at dB: Ci

c onnec t dl B: Cz at d9: Ci

I I . Tout = Tout

I 2. T out = ToutI 3. T out = Tout

14. Tout = Tout

16. Tout = Tout

17. Tout = Tout

I B. T out = Tout

Fi gur e 5. 6d ( Cont i nued)

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 112/122

112

19. Tout = Tout110. Tout = Tout

I 1I . Tout = Tout

112 . Tout = Tout

113 . Tout = Tout115. Tout = Tout

116. Tout = Tout

117. Tout = Tout

118. Tout = Tout

119. Tout = Tout

120. Tout = Tout

121. To ut = Tout

122 . Tout = Tout

123. Tout = Tout

124 . Tout = Tout

12S. Tout = Tout

126. Tout = Tout

127. T out = Tout

11 . vwi nd = vwi nd 117. vwi nd = vwi nd12 . vwi nd = vwi nd 118. vwi nd = vwi nd13. vwi nd = vwi nd 119 . vwi nd = vwi nd14. vwi nd = vwi nd 120 . vwi nd = vwi nd16. vwi nd = vwi nd 121. vwi nd = vwi nd17. vwi nd = vwi nd 122 . vwi nd = vwi nd18 . vwi nd = vwi nd 123 . vwi nd = vwi nd19. vwi nd = vwi nd 124 . vwi nd = vwi nd110. vwi nd = vwi nd 125. vwi nd = vwi nd111. vwi nd = vwi nd 126. vwi nd = vwi nd112 . vwi nd = vwi nd 127 . vwi nd = vwi nd

113 . vwi nd = vwi nd115. vwi nd = vwi nd Tsp. FO = SO

116. vwi nd = vwi nd yl = d ei

end

Fi gur e 5. 6d ( Cont i nued)

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 113/122

 

113

a l *MG l oss el ement , nodes 1, 3, 7, 9, 10, 12, 16, 18, 20,

22, 24, 26 have a 2*MG l oss el ement and nodes 19, 21, 25, 27

have a 3*MG l oss el ement . ( The r eader m ght go back t o Fi gur e

5. 3h and see t he l oss el ement . ) The cor respondi ng DYMOLA

model t ype f or t he house has been named SPACE and i t i s

depi ct ed i n Fi gur e 5. 6d.

Thi s concl udes t he model i ng of al l t he par t s of t he

sol ar house.

5 8 The Total Solar Heated House

The over al l syst em i s a ser i es connect i on of t he

previ ousl y pr esent ed aggregat ed bond graph el ement s , t hat i s,

t he col l ect or , t he col l ect or wat er l oop, t he st or age t ank,

t he heat er wat er l oop, t he heat exchanger and t he house. Thi s

i s depi ct ed i n Fi gur e 5. 7.

 COll..: ::aWL~ST~ WL~HE   l.House

Fi gur e 5. 7 Aggr egat ed bond gr aph of t he over al l syst em

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 114/122

114

5. 9 Choosi ng Appr opr i at e Par amet er s f or Anal yzi ngt he Ef f ect i veness of Our Syst em

unt i l now, t he model i ng of t he t ot al sol ar house has

been di scussed. Now we ar e r eady t o t est t he ver sat i l i t y of

DYMOLA to descr i be such a compl ex physi cal syst em af t er i t

has been model ed by t he bond gr aph met hodol ogy.

The best appr oach t o si mul at e i s t o st ar t f r om t he

habi t abl e space ( house i t sel f ) as i ndi cat ed i n t he t ot al

aggr egat ed f i gur e. We shal l i magi ne t hat t her e i s an

ar bi t r ar y heat sour ce heat i ng t he house, assumng t hat t he

i ni t i al t emper at ur e i nsi de t he house i s l SDC ( 2SSDK) . Our

goal i s t o det ermne t he t i me t hat i t t akes f or t he t emper a-

t ur e t o r each i t s st eady- st at e val ue i n var i ous l ocat i ons

i ns i de t he house.

The DYMOLA model t ype SPACE (model SPACE i n t hi s case

because t he house i s our mai n syst em now) has been used t o

gener at e t he DESI RE pr ogr am The same pr ocedur e as descr i bed

i n Chapt er 4 has been used. However , t he PC was unabl e t o

gener at e t he DESI RE pr ogr am because i t was exceedi ng i t s

memor y ( heap) capabi l i t y.

Theref ore, a deci si on was made to use the VAX. Usi ng

t he VAX, we wer e abl e t o gener at e a SI MNON pr ogr am ( cur -

r ent 1y, t he VAX ver si on does not pr ovi de a DESI RE pr ogr am

generat i on capabi l i t y yet ) . However , t he conver si on of t he

SI MNON pr ogr am i nt o a DESI RE pr ogr am i s not a di f f i cul t

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 115/122

115

pr ocedur e. Af t er doi ng t hat , we ar e r eady t o si mul at e t he

house ( habi t abl e space) .

The f ol l owi ng el ement s must be cal cul at ed bef or e

pr oceedi ng: t he modul at ed r esi st i ve sour ce ( t het a) , t he

modul at ed capaci t ance ( gamma) bei ng i nsi de t he one- , t wo- and

t hr ee- di mensi onal cel l s. These val ues wi l l be t he same

ever ywher e i n t he house. Mor eover , t he modul at ed conduct ance

i n t he l oss el ement s ( a and b) must be eval uat ed. Pl ease

r ef er t o Fi gur es 5. 3n, 5. 30 and 5. 31 wher e t he par amet er

val ues f or t hese el ement s are speci f i ed i n parentheses.

A l ogi cal and econom cal heat source ( ent ropy source)

i s f ound t o be 20 J / K. Our i nt ui t i on was based on an aver age

mont hl y ut i l i t y bi l l t hat peopl e spend f or heat i ng t hei r

house dur i ng wi nt er t i me.

I t i s f ound t hat t he a, b and t het a par amet er val ues

af f ect t he over al l heat i ng of t he house. Fi gur e 5. 3c hel ps

us t o f i nd a, b. The angl e must be kept smal l ar ound 25° and

b i s appr oxi mat el y one- hal f of t he t angent of t hat angl e.

These a and b val ues det erm ne how wel l t he house i s i nsu-

l at ed. Moreover , t he val ue of t het a depends on t he ai r i nsi de

t he house. Formul a 5. 7 det ermnes t he val ue of t het a but t he

physi cal constant   f or ai r i s not r el i abl e. We have used

some f l exi bi l i t y i n deci di ng t he val ue of t het a whi ch i s

about 0. 5 sec. K/ J .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 116/122

 .

116

Fi nal l y, t he val ue of gamma can be f ound usi ngf ormul a 5. 12 and i t i s f ound t o be 152310 J j K ( not t o be

conf used wi t h ent r opy) .

Havi ng f ound al l t he necessar y par amet er s, t he

s i mul at i on can now be per f ormed. We s i mul ated t he house, and

di spl ayed the temperature i n the vi ci ni t y of t he heat source,

and al so at f ar t her away nodes. The f ar t hest one, node 27,

caused t he most pr obl ems and di d not gi ve sat i s f act or y

r esul t s.

Var i ous r esul t s ar e i n t he f ol l owi ng t abl e: ( see

Appendi x A f or gr aphs wi t h y1, y2, y3, y4 and y5 cor r espond-

i ng t o nodes 16, 20, 22, 9 and 26 r espect i vel y. Not i ce t hat

y2 i s t he same as y3 because of symmet r y of t he nodes,

t her ef or e onl y one of t hei r gr aphs i s shown) .

Node   Tsteady state  0C) Ti me ( see)

3 77 1. 40E+59 24 2. 00E+5

14 63 1. 50E+516 3S 1. 50E+517 29 1. SOE+520 32 1. 50E+5

22 321. 50E+5

26 15 1. SOE+527 10 1. 70E+5

Fi gur e 5. S Tabl e of some r esul t s

The out s i de t emper at ure was assumed t o be O· C.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 117/122

 

117

From the above resul t s , we can observe that the temperature

i n most of t he nodes of t he house i s not consi st ent . I n t he

vi ci ni t y of t he heat sour ce, t he t emperat ur es ar e ver y hi gh,

whereas i n the f ar t hes t nodes of the house, the temperatures

ar e l ow. Thi s makes us bel i eve t hat t he heat di ssi pat i on

t hr ough t he house ( e.g. by means of convect i on) i s not

model ed cor r ect l y.

The t emper at ur e at ever y node r eaches i t s st eady-st at e val ue i n a l i t t l e over a day. Thi s makes sense. I t

t akes a l ong t i me t o heat t he house t o i t s st eady- st at e

t emper at ur e wi t h an economcal heat er such as t he one we

used.

The next st ep was t o add t he heat er wat er l oop and

constant temperature sour ce at the storage tank to produce

t he 20 J / K ent ropy ( heat ) source. Never t hel ess, combi ni ng al l

t he DYMOLA model t ypes t oget her , t he whol e pr ogr am wi l l

become ver y l ar ge so we deci ded t o st op t he si mul at i on

anal ysi s. I t i s t r ue, however , t hat by havi ng a computer wi t h

enough heap (memor y) t hat can handl e such l ar ge pr ogr ams, t he

whol e s i mul at i on anal ys i s can be per f ormed unt i l we reach t he

col l ect or . At t he end, we wi l l have a ver y l ar ge DYMOLApr ogr am wi t h al l t he hi er ar chi cal st r uct ur es of t he sol ar

house connect ed t oget her .

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 118/122

 .

118

CHAPTER 6

CONCLUSION

Thi s t hesi s t ouches on a moder n and advanced

model i ng- s i mul at i on t echni que appl i ed t o a l arge and compl ex

physi cal system - the sol ar heated house.

The bond gr aph model i ng met hodol ogy has been st udi ed

extensi vel y as wel l as a sof tware tool cal l ed DYMOLA desi gned

t o i mpl ement bond graphs. How wel l t hey wor k t oget her was

demonstr at ed i n Chapt er 4.

Bond gr aphs wer e successf ul i n pr ovi di ng us wi t h a

compl et e and easi l y comprehens i bl e model of the sol ar house,

a rel at i vel y compl i cat ed syst em Furt hermore, DYMOLA proved

t o be a sui t abl e sof twar e t ool f or i mpl ement i ng t he

hi er ar chi cal bond gr aphs encount er ed i n t he syst em Bot h

t ool s, l i ke SPI CE, can be combi ned t oget her f or st udyi ng t he

behavi or of several l ess compl ex syst ems such as el ect r i cal

and mechani cal ones.

On t he negat i ve aspect , bond gr aphs as t hey ar e

devel oped t oday, ar e not sui t abl e f or model i ng di st r i but ed

parameter syst ems i n several space di mensi ons. As al l ot her

gr aphi cal t echni ques, bond gr aphs become cl umsy when appl i ed

t o di st r i but ed par amet er pr obl ems i n mor e t han one space

di mensi on.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 119/122

119

Ther e ar e many oppor t uni t i es f or r esear ch. Bot h bond

gr aphs and DYMOLA can be f ur t her devel oped so t hat t he st udy

of compl ex syst ems can become mor e f easi bl e and at t r act i ve t o

t he r esear cher.

Thi s t hesi s has pr ovi ded new i nsi ght i nt o t he pr ocess

of model i ng compl ex physi cal syst ems. For t he f i r st t i me, t he

bond gr aph model i ng t echni que was expanded t o hi er ar chi cal

model descr i pt i ons. I t has been shown t hat t he gener al

pur pose cont i nuous- s yst em model i ng l anguage DYMOLA can be

ef f ect i vel y used t o descr i be hi er ar chi cal nonl i near bond

graphs.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 120/122

 

120

APPENDIX

GRAPHS

+ ~ :  : .

~ : :: . .~   :

· .· . y1

~ ~ ~   j ~

· .

  . .e : : 8 8 ~ · ~ B e · · · · · · · · · · · · · · · · · · · · ·. · : · · ·. . · · · · · . . · i : 5 · ~ B 5 ·. . · . . · · . . · · · · i~ · ~B5 

scale = 3 . 2 8 e B l 111II111 ~ 1   ~ ~ 3 ~ ~ us. t

Si mul at i on r esul t s at var i ous nodes

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 121/122

121

REFERENCES

Bl undel l , Al an ( 1982) , Bond Graphs f or Model i ng Engi neer i ngSystems, El l i s Horwood Publ i shers , Chi chester , uni tedKi ngdom and Hal s ted Press, New York.

Cel l i er , Francoi s E. ( 1990a) , Cont i nuous SystemModel i ng andSi mul at i on, Vol ume 1: cont i nuous Syst em Model i ng,Spr i nger Ver l ag, New York.

Cel l i er , Fr ancoi s E. ( 1990b) , Hi erar chi cal Non- Li near Bond

Gr aphs: A uni f i ed met hodol ogy f or model i ng compl exphysi cal syst ems, Pr oc. Eur opean Si mul at i on Mul t i -conf er ence, SCS Publ i shi ng.

Coppas, C. H. ( 1975) , Si mul at i on of Resi dent i al Sol arHeat i ng Syst ems, MS Thesi s, Dept . of El ect r i calEngi neer i ng, Uni vers i t y of Tol edo, August 1975.

Def f i e, J ohn A. and Bechman, W l l i am A. ( 1980) , Sol arEngi neer i ng of Thermal Processes , J ohn W l ey, New York.

El mqvi s t , Hi l di ng ( 1975) , SI MNON - An I nt eract i ve Si mul at i onPr ogr am f or Non- Li near Syst ems User s Manual , MS

Thesi s, Repor t CODEN: LUTFD2/ ( TFRT- 7502) , Dept . of Aut o-mat i c Cont rol , Lund I nst i t ut e of Technol ogy, Lund, Sweden.

El mqvi st , Hi l di ng (1978) , A St r uctured Model Language f orLarge cont i nuous Systems, PhD Di sser t at i on, Repor tCODEN: LUTFD2/ ( TRFT- 1015) , Dept . of Aut omat i c Cont r ol , LundI nst i t ut e of Technol ogy, Lund, Sweden.

Gr anda, J . J ose ( 1982) , Comput er Ai ded Model i ng Pr ogr am(CAMP) : A Bond Gr aph Pr epr ocessor f or Comput er Ai dedDesi gn and Si mul at i on of Physi cal Systems Usi ng Di gi t alSi mul at i on Languages, PhD Di sser t at i on, Dept . of Mechani -cal Engi neer i ng, Uni ver si t y of Cal i f or ni a, Davi s.

Howel l , J ohn R. , Banner ot , Ri char d B. , and Vl i et , Gar y C.( 1985) , Sol ar - Thermal Ener gy Syst ems, McGr aw- Hi l l BookCompany, New Yor k.

Karnopp, Dean C. and Rosenberg, Ronal d C. (1975) , SystemsDynam cs , A Uni f i ed Approach, J ohn W l ey, New York.

8/13/2019 Andreou Ms

http://slidepdf.com/reader/full/andreou-ms 122/122

122

Kar nopp, Dean C. and Rosenber g, Ronal d C. ( 1972) , A

Def i ni t i on of t he Bond Graph Language, Tr ans. ASME,J our nal of Dynamc Syst ems, Measur ement , and Cont r ol ,Sept ember 1972, pp. 179- 182.

Kass, Pi er re ( 1978) , Si mul at i on of a Sol ar House, MSThesi s , Dept . of Aut omat i c Cont rol , Swi ss Feder alI nst i t ut e of Technol ogy Zur i ch, December 1978.

Kor n, Gr ani no A. ( 1989a) , NEUNET/ DESI RE User s Manual , 6801E. opata Rd. , Tucson, AZ 85715.

Kor n, Gr ani no A. ( 1989b) , I nt er act i ve Dynam c- Syst emSi mul at i on, McGr aw- Hi l l , New Yor k.

Paynt er , Henry M ( 1961) , Anal ys i s and Des i gn of Engi neer i ngSystems, M I . T. Pr ess, Cambr i dge, MA.

RosenCode Associ ates, I nc. ( 1989) , The ENPORT Ref erenceManual , 200 Nor t h Capi t ol Bui l di ng, Lansi ng, M chi gan48933.

Ti pl er , Paul A. (1982) , Physi cs, Vol ume 1, Wor t h Publ i shersI nc. , New York.

Thoma, J ean U. ( 1975) , Ent r opy and Mass Fl ow f or Ener gyConver s i on, J . Fr ankl i n I nst i t ute, 299(2) , pp. 89- 96.

van Di xhoor n, J . J an ( 1982) , Bond Graphs and the Chal l engeof a Uni f i ed Model l i ng Theor y of Physi cal Syst ems, i n:


Recommended