The automatic optimal control process for the operation changeover of heat exchangers

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Te aua pal rl pre fr e pera agever f ea exager K. L. Lu B. eeyer 4 & M. L very f e Feeral Are Fre Haburg Geray very f Saga fr See & Telgy P. R. Ca Tg J very P. R. Ca 4 GKSS Reear Cere Geray Abra Crl prble ex wely e appla f ea exager. A ew eay pera ae f a ea exager a be aeve by ajug e le paraeer f e exager a gve eay pera ae w a ya pre. Te ajug pre uually exeue e ba f a aua rl prple. I e paper e aua pal rl el apple aeve e arge eay pera ae f e exager w e rl ajue are eere arg e ae paraeer f e exager ye; a raal aua rl el e rl ajue are eere arg e upu paraeer f e exager. Cpare w e raal aua rl el e rl pre f e aua pal rl el beer. A exaple ue. Keywr: Te aua pal rl el e pera agever ea exager ae paraeer pal feeba. Iru Te raal aua rl e a -alle frequey-a e urg e rl pre e ajue f pu paraeer are eere arg e real-e upu paraeer f e ya ye []. Hwever a lle fful fr e be apple e ulpu ul-upu ye a e-vara ye a rl pre afary. é Hea Trafer III B. Su C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

4 Hea Trafer III Te er aua pal rl e a ae-pae e w e ajue are eere arg e ae paraeer f e ya ye. Te ae paraeer lue ly e upu paraeer bu al e er paraeer fr exaple e vara rae f e upu paraeer f e ya ye. Te pa arge f e rl pre ay be u e u e. Dya ye a ave e ae rafer fu r rafer fu arx ay ave ffere er ae ru erefre a g rl e ul er e er araer f e ya ye. Te aua pal rl e ae era e relap ag e pu paraeer e er ae paraeer a e upu paraeer. I e e e feeba f e ae paraeer ly e feeba f e upu paraeer a eere e rl pre. I paper e aua pal rl pre fr e pera agever f ea exager ue. Te a a are w eere e ae paraeer a e ae equa f e exager ye w eere e pal rl bje a w eere e feeba fr rl ajue. Te ya beavur f ea exager Te ya beavur f a ea exager u be eere e up aua pal rl el. Aug a e a flw rae f e l rea a uer flw w-rea ea exager age e ya beavur f ule eperaure a be eue fr e fllwg expre Q C p[ ] M C p C p[ ] Q M C p [ ] [ ] Q F K l[ ] a 4 K [ ] b Here e lg ea eperaure fferee apple w re aurae a e are ea eperaure fferee ue leraure [4]. Eq. a a be raferre a fllw by rug eq. a 4 a rug learza Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

] [ 5 ] [ 4 6 g e Laplae rafr e e rafer fu a be bae a H F p p a ξ 7 H F p p a ξ 8 were 4 H 4 H 4 H a H a / ] [ p / ] [ ξ Slarly e ya beavur aue by er le paraeer a al be bae ey are al e fr f eq. 7 a 8. Te ae equa f e ya exager ye. Oe-pu u a e-upu y lear ye Te ya exager ye a a e rafer fu f eq. 7 r 8 a be erbe by e fllwg ffereal equa e e a: u b u b u b u b y a y a y a y a 9 w al : y j j u j é Hea Trafer III B. Su C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75- Hea Trafer III 5

6 Hea Trafer III were u efe a e pu paraeer ajue paraeer f e ya exager ye a y e upu paraeer arge paraeer. Te ree expre f e ffereal equa a be gve a: y a y a y bu bu bu Le x y µ u x x µ u x x µ u Te ae equa f e ya exager ye e ree expre wll be wre a: A Bu y C Du were e ver f ae paraeer f ya ye a e effe are are expree repevely a µ µ A B µ a a a a µ C [ ] D µ rally e effe D equal zer; erwe e pu paraeer wll be rely raferre e upu paraeer.. Mul-pu a e-upu y lear ye Te ree expre f e ffereal equa fr a ul-pu a eupu lear ye a be wre a: y a y a y a B B B Le x y M x x M x x M Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

Hea Trafer III 7 Tu e ae equa f e ya exager ye wll be gve a: A B a y C D a Slarly e ae equa f a ul-pu a ul-upu lear ye a be bae a: A B b Y C D b were Y e ver f upu paraeer f ya ye. 4 Te aua pal rl el Te e f ya prgrag rally ue lve e ul-per e pre. I e e e wle pre ve ay per a e pal e fr ea per ee be eere beaue ere ay ex re a e pble e u a ere f pal e fr ul-per wll eure a e wle pre pal. I e paper e e f ya prgrag apple ba e aua pal rl el fr e pera agever f ea exager. 4. Te aeaal erp Aue a e wle rl pre ve per. Te ree expre f e ae equa f a lear e-vara ye wre a: Φ Γ Y H 4 were Φ Γ a H are effe are. Fr a ya exager ye ubje e abve ree expre a w al value f ae * paraeer a e f pal rl ajue ee be eere w e rl aeble Ω w ae e fal ae paraeer f e exager ye be w er ae aeble.e. S a e bjeve fu be u. * * * J J 5 u Ω * T e f pal rl ajue alle e pal rl aeble. Fr u eva f e upu paraeer fr er ew arge eay value a u ajue eergy up f e pu paraeer f e exager e egrae bjeve fu wll be elee a: J Σ W 6 Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

were a W are wegg are repevely v v v r w w w W 4. Te eera f pal rl ajue Te pal rl ajue fr ea per wll be eere repevely. Geerally fr a per f e pre w al ae paraeer e pal rl ajue f pu paraeer * ee be eere w ae e fllwg bje fu be a u: W R Cerg e rafer prple f ae paraeer Γ Φ Le R Te pal rl ajue * a be eere a Φ Λ * 7 were Γ Γ Γ Λ W a e bje fu wll be f Φ Φ ~ 8 were ~ Λ Γ ~ Φ Φ Tu e pal l f ae paraeer a upu paraeer y Y a be bae uquely. Fr a a ye a e ya exager ye aalye paper e are Φ Γ Λ a H are all a effe are e aua pal rl el bee ple. é Hea Trafer III B. Su C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75- 8 Hea Trafer III

Hea Trafer III 9 5 Cae uy Here a w-rea ea exager ye ue. Waer ae a wrg flu a e aa f e exager a eg p are le Table. I ay be e a f e ajue f e le paraeer f e exager are le a % f er al value a e eg p repevely e ya exager ye a be ae a a lear ye [5]. Table : Te aa f e w-rea ea exager a eg p. u u KF K Kw/ C C C C C Kw/ C Kw/ C Kw/ C. 46.99 6. 5.4. 5.. 8. Fgure : Te alula agra f e aua pal rl el. 5. Oe-pu u a e-upu y lear ya pre Suppe e exager perae ealy a eg p. If e ule eperaure f e rea u ee be age up a ew eay arge value 7.4 C w we wa w w eere e pal rl ajue f e a flw rae f e l rea fulfl e a w bee a prble f aua pal rl. Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

Hea Trafer III Te a flw rae f e l rea ere be e pu paraeer u f e ya exager ye a e ule eperaure f e rea ere be e upu paraeer y. Te ae belg e e-pu a e-upu ye. Te ya exager ye ere be a a ye e ae equa f ya pre are e fr f eq.. Te alula agra f e aua pal rl el w Fg. w e pal feeba effe arx Λ a a effe arx a be ffle-alulae a elee are le Table. Te pal rl ajue f e pu paraeer e a flw rae f e l rea urg e rl pre are w Fg. w are w e lear reg f e exager. Table : Te elee f pal feeba effe arx Λ ]. [ Ierave uber 4 8 6 4 8.5.49.6.48.55.56.56 -.98 -.4499 -.5859 -.695 -.6 -.64 -.64.5. Ma flwrae f l rea Kg/.4....9.8 6 9 5 8 Te S Oupu eva C -. -.4 -.6 -.8 - -. -.4 -.6 -.8 4.5 8.5.8 7. Te S Fgure : Te pal rl ajue. Fgure : Te pal eva. Te pal eva f e upu paraeer e ule eperaure f rea are w Fg.. Te wegg are W are eere expereally e ae ere ay ex e pee f ver- Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

Hea Trafer III ajue.e. e ule eperaure f e rea Fg. ay exee ew arge eay value fr e e befre reae eay value. 5. Mul-pu a e-upu y lear ya pre Suppe e ule eperaure f e rea ee be age up a ew eay arge value 4. C w we wa w w eere e pal rl ajue f b e a flw rae f e l rea a e a flw rae f e rea fulfl e a. Here e a flw rae f e l rea a rea are ere be e pu paraeer f e ya exager ye a e ule eperaure f e rea ere be e upu paraeer. Te ae belg e w-pu a e-upu lear ye. Table : Te elee f pal feeba effe arx Λ. Ierave uber 4 8 6 4 8.44.5.845.97.9..4.5 -.98 -.99 -.47 -.645 -.7 -.76 -.7 -.7.5 -.8 -.6 -.7 -.7 -.79 -.7 -.7.5.97.749.858.889.898.9.9 Ma flwrae f l rea Kg/.5.4....9.8 4 8 6 Te S Ma flwrae f rea Kg/ 4. 4. 4.9.8.7.6.5.4..75 7.5. 5 8.8 Te S Fgure 4: Te pal rl ajue. Fgure 5: Te pal rl ajue. Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

Hea Trafer III Te elee f e pal feeba effe arx are bae by ffle erave alula a w Table. Te pal rl ajue f e pu paraeer urg e rl pre are w Fg.4 a Fg.5 wle e pal eva f e ule eperaure f e rea fr arge value are w Fg.6. -.5.8 4.75 7. 9.5.9 4. 6.6 9.4 - Oupu eva C -.5 - -.5 - -.5-4 -4.5-5 Te S Fgure 6: Te pal eva fr e arge eperaure. Te reul w a e pal rl ajue f b e a flwrae f l rea a rea are w e lear reg f ya exager ye a ere ex ver-ajue 6 Clu Te pera agever f ea exager a be aeve by e aua pal rl eque. Cpare w e raal aua rl el rl pre beer a prple re reaable e e e e rl ajue are eere arg e ae paraeer f exager w lue ly e upu paraeer bu al e er paraeer fr exaple e vara rae f e upu paraeer f exager ye. Te ue exaple w e eque praable. Awlegee Te pree reear wr belg e prje Opal eg flexbly aaly a ya ula f ulrea ea exager ewr Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

Hea Trafer III.RO94/9 uppre by e Deue Fruggeeaf DFG a e prje Fel yerge a rl f ea rafer pree w ulple rea.g6 uppre by e aal Develpe Prgra f Ca fr Key Fuaeal Reeare. Referee [] L. e Gexag Huag Mel algr a aae rl fr furrea plae-f ea exager J. very f Saga fr See a Telgy l.. pp.57-6. [] Te Maea Depare Teaer-rag very f Ea Ca Iru e Mer Crl Tere Te Pre f Saga See a Telgy pp.57-66 984. [] F.E. Re Trae repe f e uerflw Hea Exager J. f Hea Trafer l.6. pp.6-66 984. [4] F.E. Re Trae repe f e parallel-flw Hea Exager J. f Hea Trafer l.7. pp.77-7 985. [5] Y.-F. u Z.-H.Ca M.-L. L a A.-J. L Lup paraeer el fr ya perfrae f w-rea plae-f ea exager J. f Ceal Iury a Egeerg Ca l.48.6 pp.7-78 997. Hea Trafer III B. Sué C. A. Brebba & A. Mee Er 4 WIT Pre www.wpre. ISB -85-75-

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