Optimization by Using Bat Algorithm on Shell and Tube Heat Exchangers

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1 Avalabl onln a Indan Journal of Advanc n Chmcal Scnc Indan Journal of Advanc n Chmcal Scnc S (06) 37-4 Opmzaon by Ung Ba Algorhm on Shll and Tub Ha Exchangr T. K. Tharakhwar *, K. N. Sharamu, B. Durga Praad 3, Bharah Kumar Dparmn of Mchancal Engnrng, Sddaganga Inu of Tchnology, Tumkur , Karnaaka, Inda. Dparmn of Mchancal Engnrng, PES Inu of Tchnology, Bngaluru , Karnaaka, Inda. 3 Dparmn of Mchancal Engnrng, Jawaharlal Nhru Tchnologcal Unvry, Ananapur , Andhra Pradh, Inda. Rcvd 4 h Fbruary 06; Rvd 3 March 06; Accpd nd May 06 ABSTRACT In h udy, h ky objcv opmzaon on hll and ub ha xchangr bad on h oal co whch nclud oprang co and nvmn co. Th opmzaon carrd ou ung ba algorhm for h hr ca ud gvn n h opn lraur. Ba ar h only mammal wh wng and hr bhavor bad on h cholocaon, whch hlpful for hm o dc pry, avod obacl, and loca hr roong crvc n h dark. Th varou dgn paramr ar ub lngh, ub damr, pch z, baffl pacng, and numbr of ub. Th rul ar rpord and compard wh prvou lraur. I found ha h co oband from ba algorhm qu machng wh ohr algorhm. Th objcv o opmz varou dmnon of h hll and ub ha xchangr o a o g maxmum ha ranfr coffcn and mnmum dgn co. Th mhod ud Krn for fndng prur drop and ha ranfr coffcn. Th numbr of raon akn for fndng h opmal oluon for a ngl objcv funcon <0 raon and h nur l compuaonal m. Ky word: Ha xchangr, Ba algorhm, Pumpng powr.. INTRODUCTION A ha xchangr a dvc ha ud o ranfr hrmal nrgy bwn wo or mor flud, bwn a old urfac and a flud or bwn old parcula and a flud a a dffrn mpraur and n hrmal conac hll and ub. An xpanon jon an mporan componn n h ca of fxd ubh xchangr for cran dgn condon. Th lcon crra for a propr combnaon of h componn dpnd on h opraon prur, mpraur, hrmal r, corroon characrc of flud, foulng, clanably, and co. Bcau of h drd ha ranfr n h ha xchangr ak plac acro h ub urfac, h lcon of ub gomrcal varabl mporan from a hrmal prformanc pon of vw. Tub z pcfd by oud damr and wall hckn. Smallr damr ub yld hghr ha ranfr coffcn and o rul n a compac ha xchangr. Howvr, largr damr ub ar ar o clan, mor ruggd, and hy ar ncary whn h allowabl ub d prur mall. Fora gvn urfac ara, h mo conomcal xchang pobl wh a mall hll damr and long ub, conn wh h pac and h avalably of handlng facl [,]. *Corrpondng Auhor: E-mal: khara@yahoo.com. BAT ALGORITHM Th cholocaon characrc of mcroba can dvlop varou ba nprd algorhm. In h bac ba algorhm dvlopd by Yang (008) [3], h followng approxma or dalzd rul wr ud.. All ba u cholocaon o n danc, and hy alo know h dffrnc bwn food pry and background barrr n om magcal way.. Ba fly randomly wh vlocy v a poon x wh a frquncy f mn, varyng wavlngh λ and loudn A 0 o arch for pry. Thy can auomacally adju h wavlngh of hr md pul and adju h ra of pul mon r ϵ [0, ] dpndng on h proxmy of hr arg. 3. Alhough h loudn can vary n many way, can b aumd ha h loudn var from a larg (pov) A 0 o a mnmum conan valu A mn. 3. MATHEMATICAL MODELS Th ha xchangr urfac ara gvn by Krn [4], Snno al. [5]: A U o Q T lm F () 37

2 Indan Journal of Advanc n Chmcal Scnc S (06) 37-4 Whr Q h ha load, U h ovrall ha ranfr coffcn, T LM h logarhmc man mpraur dffrnc, F h corrcon facor. Th ha ranfr ra gvn by: Qm c p (T T o )m c p (T o T ) () Uo d + Rf + 0 ( Rf + ) h d h 3.. Tub Sd h k d R 08. Pr 3 w 04. (3) (4) Whr f h Darcy frcon facor gvn a follow [6]: C Pr k p ρ R vd (5) (6) Whr Pr and R r ub d Prandl and Rynold numbr. v m N. π d N 4 p (7) Whr Np h numbr of pa and N h numbr of ub [5,7]: N k n D d 0 (8) Whr k and n ar coffcn ha ar akn valu accordng o flow arrangmn and numbr of pa. 3.. Shll Sd h D 36 k R Pr ( ) D ( ) 4( p πd0 / 4 ) πd 0 (for quar pch) w (9) (0) Whr D h hll hydraulc damr and compud a gvn by Krn [4], Snno al. [5]: C pr k p ρ vd R v m A ρ () () (3) Whr v h flow vlocy for h hll d and can b oband [4,5]: ad.b- d o P Whr A h cro con ara normal o flow Logarhmc Man Tmpraur Dffrnc ( T To ) To T Tlm ln T T / T T ( ) ( ) ( ) ( o o ) (4) (5) 3.4. Prur Drop and Objcv Funcon In all h ha xchangr, hr clo phycal and conomcal affny bwn ha ranfr and prur drop. For a conan ha capacy ha xchangr, ncrang h flow vlocy wll cau a r of ha ranfr coffcn. Howvr, an ncra of flow vlocy wll cau mor prur drop whch rul n addonal runnng co. P P ublngh + P ublbow ρ P v L p. d f+p. N (6) Dffrn valu of conan p ar condrd by dffrn auhor. Krn [4] aumd p4 and Snno al. [5] aumd p.5. ρv Pf L. B. D D P m m P+ P n ρ ρ a33 C a +aa (7) (8) (9) 38

3 Indan Journal of Advanc n Chmcal Scnc S (06) 37-4 Whr C h capal nvmn a 8000, a 59. and a for xchangr mad wh anl l for boh hll and ub [8]. C oo P.C.H (0) C odd ny k C00 ( + ) k () C C +C odd () Whr C oal co akn a h objcv funcon, whch nclud capal nvmn (C ), nrgy co (C ), annual oprang co (C oo ) and oal dcound oprang co (C odd ) [4]. 4. RESULTS AND DISCUSSION 4.. Ca A ha xchangr for dlld war and raw war wh ha load 0.45 MW. Th ha xchangr ha wo ub d paag wh rangl pch parn and on hll d paag. Th followng uppr and lowr bound for h opmzaon varabl wr mpod, hll nrnal damr D rangng bwn 0. m and. m, ub oud damr d o rangng from 0.05 o 0.05 m, baffl pacng B rangng from 0.05 o 0.5 m and ub lngh L rangng from o 5 m. All valu of dcound oprang co wr compud wh n y 0 yar, annual dcoun ra 0%, nrgy co C 0. / kw h and an annual amoun of work hour H 7000 h/ yar mlar o ohr rarch. Th oprang and phycal paramr of h ha xchangr ar hown n Tabl. Dgn paramr ar aumd o olv h problm wh BA wh rangular pch parn. A can b n n Tabl, h rul oband from BA ar br han rul of ohr algorhm. Ha xchangr ara Tabl : Th oprang and phycal paramr of h hll and ub ha xchangr. Varabl Shll d (dlld war) Ca udy Tub d (raw war) m (kg/) T ( C) 95 5 T o ( C) Ρ (kg/m 3 ) C p (kj/kgk) Μ (Pa ) k (W/mK) R f (m k/w) n BA mhod ha bn rducd comparon wh ohr mhod of ha xchangr dgn. Rducon of ha xchang ara ruld n l numbr of ub and rducon of h ub lngh, h numbr of ub dcrad a compard o rfrnc GA, ABC, BBO and ncrad a a rfrnc. Th capal nvmn dcrad corrpondngly 5.84, 6.69,.7 and.67% n comparon wh h orgnal dgn, GA, ABC and BBO, rpcvly. Th combnd rducon of capal nvmn and oprang co ld o a rducon of h oal co of abou.68% n comparon wh orgnal dgn and 8.3, 5.3, 0.57 and 0.6% n comparon wh GA, ABC, and BBO, rpcvly. Co comparon of prn approach and ohr mhod hown n Fgur for h ca udy. Th numbr of raon akn for convrgnc hown n Fgur l han fv raon. 5. CONCLUSION In h udy, a oluon mhod of h hll and ub ha xchangr dgn opmzaon problm wa Tabl : Ca. Varabl Orgnal dgn GA ABC BBO Prn work BA D (m) L (m) B (m) d o (m) P (m) C l (m) N v (m/) R 4,95 0, Pr h (W/m K) f ΔP (Pa) D (m) v (m/) R 8,38, Pr h (W/m K) F ΔP (Pa) U o (W/m K) A (m ) C ( ) 5,507 49,59 44,559 44, C oo ( /yar) C odd ( ) C ( )

4 Indan Journal of Advanc n Chmcal Scnc S (06) 37-4 Fgur : Ovrall co comparon for ca udy. Fgur : Convrgnc of BA for ca udy. Nomnclaur a Numrcal conan K Numrcal conan Q Ha duy (W) a Numrcal conan Pr Tub d Prandl numbr a 33 Numrcal conan Pr Shll d Prandl numbr A Ha xchangr urfac ara (m ) R Shll d Rynold numbr B Baffl pacng (m) R Tub d Rynold numbr C l Claranc R f Shll d foulng ranc (m K/W) C Enrgy co ( /kwh) R f Tub d foulng ranc (m K/W) C Capal nvmn ( ) P Tub pch (m) C oo Annual oprang co ( /yar) T Shll d nl flud mpraur (K) C odd Toal dcound oprang co ( ) T o Shll d oul flud mpraur (K) C p Spcfc ha (kj/kg K) T Tub d nl flud mpraur (K) C Toal annual co ( ) T o Tubd oul flud mpraur (K) D Hydraulc hll damr (m) U o Ovrall ha ranfr coffcn (W/m K) d Tub nd damr (m) v Shll d flud vlocy (m/) d o Tub oud damr (m) v Tub d flud vlocy (m/) D F Shll nd damr (m) Tmpraur dffrnc corrcon facor f Shll d frcon coffcn Grk lr f Tub d frcon coffcn P Prur drop (Pa) H Annual oprang m (h/yar) ΔT lm Logarhmc man mpraur dffrnc (K) h Shll d convcv coffcn (W/m K) Π Numrcal conan h Tub d convcv coffcn (W/m K) P Dny (kg/m 3 ) I Annual dcoun ra (%) Dynamc vcoy (Pa ) K Thrmal conducvy (W/mK) η Ovrall pumpng ffcncy L Tub lngh (m) Subcrp m Shll d ma flow ra (kg/) c Cold ram m Tub d ma flow ra (kg/) Hydraulc N p Numbr of ub pa h Ho ram n Numrcal conan Inl o Oul n y Equpmn lf (yar) Shll d N Numbr of ub T Tub d P Pumpng powr (W) W Wall 40

5 Indan Journal of Advanc n Chmcal Scnc S (06) 37-4 propod bad on h ulzaon of a ba algorhm. Bad on propod mhod, a compur cod wa dvlopd and hr ca wr olvd by. Rfrrng o h lraur, h oal co mnmum compard o orgnal dgn and qu machng wh ohr algorhm. Furhrmor, h BA algorhm allow for a rapd oluon for h dgn problm. Bcau h numbr of raon ook for convrgnc l han 0 and av h compuaonal m. I nabl o xamn a numbr of alrnav oluon of good qualy, gvng h dgnr mor dgr of frdom n h fnal choc wh rpc o radonal mhod. Hnc, h prn algorhm can b ud for any opmzaon applcaon mor confdnly. 6. REFERENCES. Y. A. Kara, O. Gurara, (004) A compur program for dgnng of hll and ub ha xchangr, Appld Thrmal Engnrng, 4: A. L. H. Coa, E. M. Quroz, (008) Dgn opmzaon of hll-and-ub ha xchangr, Appld Thrmal Engnrng, 8: X. S. Yang, (008) Naur Inprd Mahurc Algorhm, nd d. UK: Lunvr Pr. 4. D. Q. Krn, (950) Proc Ha Tranfr, Nw York: McGraw-Hll. 5. R. K. Snno, J. M. Coulon, J. F. Rchardon, (005) Chmcal ngnrng. In: Chmcal Engnrng Dgn, Vol. 6. Oxford: Burworh- Hnmann. 6. G. F. Hw, (998) Ha Exchangr Dgn Handbook, Nw York: Bgll Hou. 7. R. K. Shah, K. J. Bll, (000) Handbook of Thrmal Engnrng, Florda: CRC Pr. 8. M. Taal, I. Bulaov, J. Klm, P. Shlk, (003) Co maon and nrgy prc forca for conomc valuaon of rrof projc, Appld Thrmal Engnrng, 3: 89. *Bblographcal Skch I am Tharakhwar T.K. Purung Ph.D. n Sddaganga Inu of Tchnology, Tumkur. I hav 9 yar of Tachng work xprnc n Mchancal Engnrng Dparmn, S.I.T, Tumkur. Currnly h poon occupd Aan Profor. Th work carrd ou by m a rarch work. Bcau u a novl compuaonal chnqu calld Ba algorhm. Th algorhm ubanad by h concluon and rul. Fnally, h Ba algorhm compard wh ohr algorhm o fnd ou br opmal rul. Th arcl nowhr publhd anywhr. 4