OptimumDesignofCompoundPressureVessel. Optimum Design of Compound Pressure Vessel

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1 Global Jounal of Reseaches in Engineeing Mechanical andmechanicsengineeing Volume 13 Issue 11 Vesion 1.0 Yea 013 Type: Double Blind Pee Reviewed Inenaional Reseach Jounal Publishe: Global Jounals Inc. (USA) Online ISSN: Pin ISSN: Opimum Design of Compound Pessue Vessel By Md. Tanjin Amin, Aminu Rahman & D. Abu Rayhan Md. Ali Univesiy of Engineeing & Technology (BUET), Bangladesh Absac- Effec of compounding invesigaed heoeically by finie elemen modeling. The vaiables ae inefeence adius & shinkage oleance. Equivalen von Mises sess is used as yield cieion o evaluae he opimum inefeence adius. Fo wo diffeen woking pessue he effec of he aio of oue & inne adius (b/a=k) value on he opimum inefeence adius is also noiced. The opimum inefeence adius solely depends on shinkage oleance. Fuhemoe, pecenage educion of von Mises oleance is compaed fo diffeen woking pessues & diffeen k values as well as fo diffeen maeials. Keywods: auofeage, esidual sess, von mises sess, woking pessue, pessue vessel, elaso-plasic juncion. GJRE-A Classificaion : FOR Code: p OpimumDesignofCompoundPessueVessel Sicly as pe he compliance and egulaions of: 013. Md. Tanjin Amin, Aminu Rahman & D. Abu Rayhan Md. Ali. This is a eseach/eview pape, disibued unde he ems of he Ceaive Commons Aibuion-Noncommecial 3.0 Unpoed License hp://ceaivecommons.og/licenses/by-nc/3.0/), pemiing all non commecial use, disibuion, and epoducion inany medium, povided he oiginal wok is popely cied.

2 Md. Tanjin Amin α, Aminu Rahman σ & D. Abu Rayhan Md. Ali ρ Absac- Effec of compounding invesigaed heoeically by finie elemen modeling. The vaiables ae inefeence adius & shinkage oleance. Equivalen von Mises sess is used as yield cieion o evaluae he opimum inefeence adius. Fo wo diffeen woking pessue he effec of he aio of oue & inne adius (b/a=k) value on he opimum inefeence adius is also noiced. The opimum inefeence adius solely depends on shinkage oleance. Fuhemoe, pecenage educion of von Mises oleance is compaed fo diffeen woking pessues & diffeen k values as well as fo diffeen maeials. Keywods: auofeage, esidual sess, von mises sess, woking pessue, pessue vessel, elaso-plasic juncion. I. Inoducion Compound cylindes ae widely used in he field of high pessue echnology such as hydaulic pesses, foging pesses, powe plans, gas soages, chemical and nuclea plans, miliay applicaions ec. To enhance load beaing capaciy and life of mulilaye pessue vessels, diffeen pocesses such as shink fi and auofeage ae usually employed. Shink fi inceases load capaciy. Many eseaches have focused on mehods o exend lifeimes of vessels. Majzoobi e al. have poposed he opimizaion of bimeal compound cylindes and minimized he weigh of compound cylinde fo a specific pessue [1]. The vaiables wee shinkage adius and shinkage oleance. Pail S. A. has inoduced opimum design of wo laye compound cylinde and opimized inemediae, oue diamee and shinkage oleance o ge minimum volume of wo laye compound cylindes []-[3]. Hamid Jahed e al. have invesigaed he opimum design of a hee-layeed vessel fo maximum faigue life expecancy unde he combined effecs of auofeage and shink fi [4]. Miaje Ayub A. & Pail Sunil A. have found minimum volume of hee-laye open ype compound cylinde consideing plane sess hypohesis [5]. Yang Qiu-Ming e al. have pesened a simple and visual ool o calculae he esidual sess and descibe he disibuion of esidual sess fo boh he elasic-pefecly plasic model and he sainhadening mode [6]. Auho α: Depamen of Mechanical Engineeing, Bangladesh Univesiy of Engineeing & Technology (BUET), Dhaka-1000, Bangladesh. moshia.ni@gmail.com Auho σ: Depamen of Mechanical Engineeing, Bangladesh Univesiy of Engineeing & Technology (BUET), Dhaka-1000, Bangladesh. aminu.bue07@gmail.com Auho ρ: Pofesso, Depamen of Mechanical Engineeing, Bangladesh Univesiy of Engineeing & Technology (BUET), Dhaka- 1000, Bangladesh. amali@me.bue.ac.bd II. Analyical Appoach As saed ealie, an elaso-plasic behavio has been designaed in his wok. Figue 1 : Bi-linea Sess Sain Cuve The model, shown in fig. 1 is descibed as follows: E y In which, σ is he effecive sess, σ y is he iniial yield sess, E p is he slope of he sain hadening segmen of sess sain cuve, and ε is he effecive sain. a) Tangenial & Radial Sess Paen To obseve he sess paen in a compound cylinde, a sample cylinde wih inenal diamee a = 0.1m, inefeence adius c = 0.15m, and exenal adius b = 0.0m has been consideed. Maeial Popeies of his cylinde summaized in able I Table 1 : Maeial Popeies Maeial σ y E(GPa) υ Seel An oue cylinde wih he inenal diamee slighly smalle han he oue diamee of he main cylinde is heaed and fied ono he main cylinde. When he assembly cools down o oom empeaue a compound cylinde isobained. In his pocess he main cylinde is subjeced o an exenal pessue leading o a compessive adial sess a he ineface. The oue cylinde o he jacke is subjeced o an inenal pessue leading o a ensile cicumfeenial sess a he inne wall. Unde his condiion as he inenal pessue inceases he compession in he inne cylinde is fis eleased and hen only he cylinde begins o ac in ension. P (1) Yea ume XIII Issue XI Vesion I Vol Global Jounal of Reseaches in Engineeing ( A ) 013 Global Jounals Inc. (US)

3 c) Compaison of Oveall von Mises Sesses Accoding o he hid sengh heoy, he uivalen sess is as follows [1]-[13]: III () Global Jounal of Reseaches in Engineeing ( A ) Vol ume XIII Issue XI Vesion I Yea Figue : Radial & Tangenial Sess Disibuion hough he Walls of a Compound Cylinde Though oue cylinde is fied on he op of he inne cylinde, a compessive sess is developed in he nea boe egion. Hee in he fig., compessive sess is developed in he inne diamee while ensile sess occus a he oue poion. Hee he iniial sess is compessive so if inenal pessue is applied, hen a ensile sess will be developed & his ensile sess even quie high, bu he esulan sess no ha high because of his compessive sess. b) Compaison of Sess beween Single cylinde & Compound Cylinde By using Lame s uaion fo hick-walled cylinde, he sess paen is obained fo boh single cylinde & compound cylinde. If hese wo cylindes undegoes same inenal pessue hen he oveall sess paen will change, which is shown in Fig. 3, hee he inenal pessue is 50 MPa. Figue 3 : Compaison of Sesses beween Single & Compound Cylinde Because of he compessive angenial sess a inne boe, he esulan angenial sess becomes lowe in he compound cylinde han he oiginal angenial sess developed a he single cylinde. Radial sess doesn vay significanly afe compounding. Radial sess doesn vay significanly afe compounding. Maximum sess occus a he juncion poin of inne & oue cylinde ahe han inne boe. Figue 4 : Compaison of von Mises sesses beween Single & Compound cylinde accoding o he hid sengh heoy The uivalen sess based on he fouh sengh heoy is as follows [1[-[13]: IV 1 Subsiuing Eq.(), we obain: Figue 5 : Compaison of von Mises sesses beween Single & Compound cylinde accoding o he hid sengh heoy IV z z ( 3 ( ) z (3) )/ (Lame fomula) 3 III (4) 013 Global Jounals Inc. (US)

4 Eq. (3) s he elaion beween he hid & he fouh sengh heoy fo a cylinde and also he elaion beween he Tesca s & Mises yield fom. As he fig. 4 & 5 sugges, maximum von Mises sess sas o deceases fom inne boe o juncion of wo cylindes. Sess suddenly inceases because of he conac pessue beween wo maing suface. I again deceases fom juncion poin o oue poion. i. Sample calculaion In his case sudy, a=0.1m, b=0.m, c=.15m, woking pessue, Pwoking = 50MPa. Fom hid sengh heoy, MVS = 666 MPa Fom fouh sengh heoy, MVS =577 MPa Fom hese wo heoies, i is obseved ha MVS fo boh is vey simila. Indeed hee is no significan vaiaion beween hese wo mehods. Fouh sengh heoy is consideed fo all compaison. III. Numeical Resul The compounding pocess may be simulaed by Finie Elemen Mehod, making use of elasic-plasic analysis. I is possible o model he compound cylinde by applying pessue o he inne suface of he model, and hen analyzing i fo diffeen inefeence adius & diffeen shinkage oleance. Using a 3D axisymmeic elemen available in ANSYS V11 SP1, a finie elemen mesh of a cylinde wih an inside adius 100 mm and ouside adius of 00 mm was geneaed. An inenal pessue of 50 MPa was applied. The sess disibuions wee evaluaed in he compound cylinde. The von Mises uivalen sess was used in he subsuen analysis. Sucual Seel of flexible siffness behavio has been used. Compound cylinde wih he dimension; a = 0.1 m, b = 0. m, an elasic plasic maeial s model wih σ = 800 MPa; Modulus of elasiciy E = 07 GPa; ν = 0.9; wee used fo numeical modeling. Hee, he effecs of following facos ae consideed in he compounding pocess. The consideed facos ae: Inefeence adius;. Value of k (b/a); 3. Diffeen maeial a inne cylinde. a) Change of Inefeence Radius The cylindes wee subjeced o diffeen inenal pessues of 100, 00 and 300 MPa. Fom he numeical simulaion wih ANSYS sofwae, he cuve of he von Mises sess disibuion was obained fo each woking pessue. Fom he cuve, he values of maximum von Mises sesses (MVS) wee exaced. This sesses wee hen ploed agains inefeence adius fo each woking pessue. The esuls ae shown in fig. 6. Figue 6 : Vaiaion of MVS veses inefeence adius a diffeen woking pessue I is obseved ha wih he incease of inefeence adius, he MVS deceases slighly. Because a small inefeence adius, lowe conac pessue is developed a he juncion of he wo cylindes. When he adius inceases hen he conac pessue inceases and hee is much compessive sess a he inne boe egion esuling lowe MVS. Wih he incease of inefeence adius much sess is developed a he oue cylinde; esuling a highe oveall sess disibuion. The value of MVS is calculaed fo diffeen inefeence adius fo diffeen woking pessues. Table : Von Mises Sesses a Diffeen Inefeence Radius fo Diffeen Woking Pessue Inefeence Radius (mm) Pessue 100 Pessue 00 Pessue Fom he able II, i is obseved ha he minimum values of MVS ae a 80 mm & 300 mm. This means in hose adius angenial sesses a inne wall of inne cylinde and inne wall of oue cylinde almos same. Fo a consan value of inefeence adius (80 mm) he pecen educion of MVS is calculaed fo diffeen woking pessue. Table 3 : Effec of Woking Pessue a Maximum Von Mises Sess Woking Pessue single cylinde compound cylinde % educion of MVS Yea ume XIII Issue XI Vesion I Vol Global Jounal of Reseaches in Engineeing ( A ) 013 Global Jounals Inc. (US)

5 Fom he able III, i is obseved ha he pecen educion of MVS is highe a modeae & highe woking pessues. Global Jounal of Reseaches in Engineeing ( A ) Vol ume XIII Issue XI Vesion I Yea b) Change of Shinkage Toleance In he peceding case minimum MVS was found in beween 80 mm & 300 mm of inefeence adius. Now he cylinde is subjeced o a woking pessue 00 MPa and inefeence adius is consideed as 80 mm. Fom he cuve, he values of maximum von Mises sess (MVS) ae exaced. This sesses ae hen ploed agains he shinkage oleance. The esuls ae shown in fig. 8. Figue 8 : Vaiaion of MVS vesus diffeen shinkage oleance I is obseved ha he developed MVS sas o decease wih he incease of he shinkage adius. Wih he incease of he shinkage adius, he compessive sess in he inne boe egion inceases & so ha MVS deceases. Bu afe a ceain poin wih he incease of he shinkage adius, MVS inceases because hen he sess of he inne boe of he oue cylinde inceases. And also hee is a close elaion beween he numeical esul & heoeical esul shown in he fig. 8. c) Values of k Consan inne diamee Fo consan inne adius (a = 0.1m) of he inne cylinde & consan inefeence adius, c = 80 mm cylinde wih diffeen k values (k=,.5, 3) ae subjeced o same woking pessue. Hee he woking pessue emains consan a Pwoking = 00 MPa Fom numeical simulaion, he value & he posiion of MVS ae exaced. This MVS is hen ploed agains he diameal inefeence fo each k value. The esuls ae shown in fig. 9 Figue 9 : Effec of k (b/a) on he diameal inefeence (consan inne adius = 0.1m) As in fig. 9, suggess fo diffeen values of k, he minimum MVS obains a highe value of hicke cylinde a lowe diameal inefeence. Fo a consan woking pessue (Pwoking = 00 MPa), pecen educion of MVS is calculaed fo diffeen k values. Table 4 : Effec Of K = (B/A) On Mvs A Consan Inne Radius k single cylinde compound cylinde % educion of MVS Fom able IV, i is obseved ha, pecen educion of MVS is highe fo highe value of k. So, he pocess is moe beneficial wih he incease of he hickness of he cylinde. Consan oue diamee In he peceding case he inne adius of he inne cylinde was kep consan. Now by assuming he oue adius (b= 0.m) consan, cylinde wih hee k values of.0,.5, 3.0m ae consideed. Fom he numeical simulaion, he cuve of MVS disibuion is obained fo each value. The developed MVS ae hen ploed agains diameeal inefeence a fig. 10. Figue 10 : Effec of k (b/a) on he diameal inefeence (consan oue adius = 0.m) 013 Global Jounals Inc. (US)

6 As in fig. 10, sugges fo diffeen values of k, he minimum MVS obains a highe value of hicke cylinde a highe diameal inefeence. Fo a consan woking pessue (Pwoking = 00 MPa), pecen educion of MVS is calculaed fo diffeen k values. Table 5 : Effec Of K = (B/A) On Mvs a Consan Oue Radius k single cylinde compound cylinde % educion of MVS Fom he able V, i is noiced ha fo same k value, developed MVS is almos same hough he value of inne & oue adius have been changed. So he opimum diameal inefeence depends on k value only. If he inne & oue adius ae changed keeping he k value consan, hen hee will be no such change in diameal inefeence. Fom above wo gaphs i can be said ha, consan inne adius of inne cylinde is moe effecive han ohe one. Because in inne adius consan pocess he minimum von Mises sess found in lowe diameal inefeence. d) Diffeen Maeial as inne cylinde Now inne cylinde of he compound cylinde is eplaced by cas ion cylinde and coppe cylinde especively. Hee he woking pessue emains consan a Pwoking = 00 MPa Fom he numeical simulaions, he cuve of von Mises sess disibuion is obained fo diffeen maeial model. Fom he gaph, he value & he posiion of he maximum von Mises sess ae exaced and ploed agains diameal inefeence. Figue 11 : Effec of diffeen maeial on diameal inefeence Fom he fig. 11, i is obseved ha cas ion & coppe alloy shows minimum von mises sess a small diameal inefeence. This means if maeial of low ensile sess is compounded by a high ensile sess maeial, hen a lowe diameal inefeence hey show he desied effec. Hee cas ion & coppe alloy ae sepaaely shown in fig. 1. Figue 1 : Effec of diffeen maeial on diameal inefeence (Cas ion & Coppe alloy) Fom fig. 1, i is noiced ha, hese wo meals jackeed by seel wok bee a small diameal inefeence. IV. Conclusion The following decisions can be aken fom he invesigaions menioned in his pape: 1. In compound cylinde, maximum von Mises sess does no occu a smalle inefeence adius insead of ha, i occus a midway secion.. Maximum sess depends on he inefeence adius as well as diameal inefeence. 3. The opimum diameal inefeence depends on k value only ahe han inne & oue adius. 4. The hicke he cylinde he moe will be he educion in MVS. 5. Two elemen cylinde of diffeen maeial educes diameal inefeence moe han wo elemen cylinde of same maeial. Yea ume XIII Issue XI Vesion I Vol Global Jounal of Reseaches in Engineeing ( A ) 013 Global Jounals Inc. (US)

7 Global Jounal of Reseaches in Engineeing ( A ) Vol ume XIII Issue XI Vesion I Yea The size of a compound cylinde could be educed by significan amoun wih espec o is uivalen single cylinde fo he same woking pessue. 7. The diffeence beween a compound cylinde and is uivalen single cylinde becomes moe significan a highe woking pessues. Appendix Table : Nomenclaue Symbol Meaning uni a Inne adius (m) b Oue adius (m) c Inefeence adius (m) σ y Yield sess σ θ Tangenial sess σ Radial sess σ z Longiudinal sess V. Acknowledgmen The auhos deeply acknowledge he financial & echnical suppo of he Depamen of Mechanical Engineeing, Bangladesh Univesiy of Engineeing & Technology, Dhaka, Bangladesh. Refeences Réféences Refeencias 1. Majzoobi G.H. & Ghomi A., (006) Opimizaion of compound pessue cylindes, Jounal of Achievemens in Maeials and Manufacuing Engineeing, Vol. 15, Issue 1- Mach-Apil.. Pail Sunil A., (005) Opimum Design of compound cylinde used fo soing pessuized fluid, ASME Inenaional Mechanical Engineeing Congess and Exposiion (Poceeding of IMECE05), Nov 5-11,005,Olando, Floida USA. 3. Pail Sunil A., (011) Finie Elemen Analysis of opimized compound cylinde, Jounal of Mechanical Engineeing Reseach, Vol. 3(1), Issue Mach. 4. Jahed Hamid, Fashi Behooz & Kaimi Movaid, (006) Opimum Auofeage & Shink-Fi Combinaion in Muli-Laye Cylindes, Jounal of Pessue Vessel Technology, Tansacions of he ASME, pp , Vol. 18, MAY Miaje Ayub A., Pail Sunil A.,(011) Minimizaion of maeial volume of hee laye compound cylinde having same maeials subjeced o inenal pessue, Inenaional Jounal of Engineeing, Science and Technology, Vol. 3, No. 8, 011, pp Yang Qiu-Ming, Lee Young-Shin, Lee Eun-Yup, Kim Jae-Hoon, Cha Ki-Up and Hong Suk-Kyun, (009) A esidual sess analysis pogam using a Malab GUI on an auofeaged compound cylinde, Jounal of Mechanical Science and Technology, Vol. 3, pp A. Ghomi, Opimum Design of hick-walled pessue cylindes (in Pesian), MS.c final pojec, Bu-Ali SIna Univesiy, Hammadan, Ian, A. R. Ragab, S. E. Bayomi, Engineeing Solid Mechanics, Fundamenals and Applicaions. Boca Raon CRC pess, Gae N. Vandeplaas, Numeical Opimizaion Techniques fo Engineeing Design wih Applicaions, McGaw-Hill, New Yok, Edgad Himmelblan, Opimizaion of Chemical Pocesses, McGaw-Hill, G. H. Majzoobi, G. H. Faahi, M. K. Pipelzadeh and A. Akbai, Expeimenal and Finie Elemen Pedicion of Busing Pessue in Compound Cylindes, Inenaional Jounal of Pessue Vessels and piping, vol. 81, pp , G.J. Fanklin, JLM. Moison, Auofeage of cylindes: pedicion of pessue, exenal expansion cuves and calculaion of esidual sesses Poceeding of insiue of Mechanical Enginees, vol. 174, pp , J.F. Havey, Theoy and design of pessue vessels, New Yok: Van Nosand Reinhold Company Ld., Global Jounals Inc. (US)