Indin Journl of Science nd Technology, Vol 8(33), DOI: 10.17485/ijst/2015/v8i33/79043, December 2015 ISSN rint) : 0974-6846 ISSN (Online) : 0974-5645 Design nd Modelling of Hemisphericl nd Flt Dish End Pressure Vessel Akshy T. Poojry 1, Rhul S. Shrm 2, Meet H. Ptel 3, Dhrmik U. Sheth 4, Chndrknt R. Kini 1 nd Rjesh Nyk 1* 1 Mechnicl nd Mnufcturing Deprtment, Mnipl Institute of Technology, Mnipl University, Mnipl - 576104, Krntk, Indi; kshy_poojry@yhoo.co.in, chndrkini@gmil.com, rjesnyk@gmil.com 2 Mechnicl Engineering, All Indi Shri Shivji Memoril Society's (AISSMS) COE, Pune - 411001, Mhrshtr, Indi; rhulshrm.ol@gmil.com 3 Mechnicl Engineering, Ydvro Tsgonkr Institute of Engineering nd Technology (YTIET), Mumbi - 410201, Mhrshtr, Indi; meetptelmumbi@gmil.com 4 Mechnicl Engineering, Vidyvrdhini College of Engineering nd Technology, Mumbi - 401202, Mhrshtr, Indi; dhrmiksheth49@yhoo.in Abstrct Pressure vessels re widely used in industries for processing nd storing fluids which re t different temperture nd pressure in nlogous to mbient. The design of these pressure vessels become the most prmount fctor s ny discrepncy would cuse the vessel to explode, leding to injure mny humns nd filure of the setup. This pper designs the pressure vessel ccording to the pressure vessel hndbook for both hemisphericl nd flt dish end pressure vessel so s to determine the most economic nd efficient design. The vrious stresses engendered within the vessel were clculted nd were lerned to be within the permissible limits. The outer nd inner dimeter of the vessel ws found to be 607mm nd 480mm nd the thickness of the vessel ws determined to be 63.5mm. This design could withstnd n internl pressure nd temperture of 150psi nd 500 F. The dimensions obtined from the design were further used to model both hemisphericl nd flt dish end pressure vessel with help of CAD in Cti V5R19. Keywords: Design nd Three Dimensionl Modelling, Flt Dish End Pressure Vessel, Hemisphericl Dish End Pressure Vessel 1. Introduction Pressure vessels re designed for industril use such s in nucler rectors nd in mining. But side from this, they re lso used in people s everydy ctivities like in heting wter nd in distilltion. They re cpble of storing liquefied gses with ll sfety. They re useful in storing nd disseminting unstble chemicls such s propne, mmoni, nd LPG. Most people perceive tht the cylindricl tnks describe the ppernce of pressure vessel. While this shpe is n ccepted form, this is not the only possible shpe for pressure vessels. In ddition to cylinders, mny mnufcturers hve mde pressure vessels likened to sphere nd cone shpes. Of ll the other shpes tht cn be creted, experts sy tht sphere is the most protective one. Sdly, mny mnufcturers nd designers tell tht sphere is difficult nd costly. Consequently, most of businesses nd people hve used the cylinders insted. A pressure vessel is closed continer tht is designed to hold the contents t certin pressure. Gs or liquids cn be kept t pressures nd tempertures different from the mbient. Exmples include hot wter storge tnks nd diving cylinders. Submrines nd spce ships re bsiclly gint pressure vessels. Pressure vessels re most commonly mde of steel becuse steel is strong nd cn resist impcts. The cylinder cn lso be mde of other metls, crbon fibres, or polymers. They re often lined * Author for correspondence
Design nd Modelling of Hemisphericl nd Flt Dish End Pressure Vessel with metl, cermics, or other polymers. Lining protects the structurl integrity of the pressure vessel nd gives dded protection ginst leking. The most stble design for pressure vessel is sphere-shped tnk. The pressure in pressure vessel nturlly bows the wlls of the vessel out. A sphereshped vessel tkes dvntge of tht nturl tendency. Despite this, most pressure vessels re not sphere-shped becuse sphere is difficult nd expensive to mke. As result, most pressure vessels re cylinder-shped with rounded cps on ech end. Common forms of pressure vessels include thin-wlled vessels, storge tnks, nd trnsportble continers. Thin-wlled vessels re those with dimeter tht is 10 times or more the thickness of the wll. Storge tnks re kind of super thin-wlled vessel. Trnsporttion vessels re mss produced thinwlled vessels. The lest common type is the thick-wlled vessel. This is vessel with dimeter tht is less thn 10 times the thickness of the wll. Frhd Nbhni et l. 1 conducted this experiment to study the cuse of stress development in pressure vessel nd the mesures tht should be tken to void them. Increse in thickness cused decrese in the stress. While nozzle is pressure relief device but it comes with disdvntge of stress concentrtion which ws strengthened using reinforcement pd hving chemicl composition of 0.4%-1.20% titnium. A skirt length of dditionl 254mm ws provided t the end of enclosure heds which cuses the trnsfer of stresses to the wll of the heds regions thus mking the pressure vessel more resistnt to lodings. Sulimn Hssn et l. 2 performed this work to show optimiztion of design of pressure vessel using Ant Colony Optimiztion lgorithm (ACO). The work intended to reduce the cost nd optimize the design by providing dequte stiffness nd strength nd reducing the weight. The thickness of the shell nd dish end, length nd rdius of the pressure vessel were four prmeters used for optimiztion. The use of ACO proved better results. Siv Krishn Rprl nd T. Seshih 3 designed nd nlysed the multi-lyered high pressure vessels nd discussed its dvntges over monoblock vessel. 26.02% sving of the mteril is seen in multi-lyered compred to monoblock. A reduction of 4.85% in stress vrition from inside to outside is seen in multi-lyered compred to monoblock vessel. The experiment lso concluded tht multi-lyered pressure vessels re better for high temperture nd high pressure operting conditions. Bndruplli Prneeth nd T. B. S. Ro 4 hd min objective to nlyse the pressure vessel nd piping design using finite element method in ANSYS. The theoreticl vlues obtined for multi-lyered pressure vessel using different formuls were very close to those vlues obtined in ANSYS. The use multi-lyered pressure vessel proved beneficil compred to monoblock vessel. Sumit V. Dubl et l. 5 proposed to use ASME codes in prctice for design of pressure vessel s it is relible stndrd for design. In ddition to this the design with ASME codes hve n dvntge of low overll cost, universl pproch, less time consuming nd esy replcement. Aniket A. Kulkrni nd Keshv H. Jtkr 6 performed n experiment nd concluded the structurl nlysis of pressure vessel nd they lso determined the optiml solution on the bsis of compring the stress, strin nd deformtion. Zid Khn et l. 7 designed nd nlysed the lrge openings nd structurl stbility of pressure vessel. It ws concluded tht ASME hs estblished universlly ccepted rules for design nd fbriction of lrge openings nd it incorportes chnges to prevent filure. Kirtikumr Tmboli 8 nlysed the ftigue, stress concentrtion fctor, ftigue curve of pressure vessel using FEA technique. It concludes tht the mximum ftigue dmge frction ws less thn unity s prescribed in the codes. Yshrj Jywnt Slunke nd K. S. Mngrulkr 9 concluded tht weight of Liquid Petroleum Gs (LPG) cylinder is reduced by replcing the conventionl mteril by low density GFRP mteril, for which ANSYS hve been used. A weight svings of 10.20kg is observed using FRP composite. FRP composite LPG cylinders offer Lek before fil pproch of design which my be design dvntge in terms of sfety nd relibility. But FRP proved expensive thn steel. 2. Results nd Discussions All the empiricl formuls nd design procedure for the design of pressure vessels were dopted from the pressure vessel hndbook by Eugene F. Megyesy 10. Cylindricl pressure vessels cn be clssified s either thin-wlled or thick-wlled. If the wll thickness-to-rdius rtio of 2 Vol 8 (33) December 2015 www.indjst.org Indin Journl of Science nd Technology
Akshy T. Poojry, Rhul S. Shrm, Meet H. Ptel, Dhrmik U. Sheth, Chndrknt R. Kini nd Rjesh Nyk cylinder is 1/10 or less, it is considered to be thin-wlled. The thickness of the wll over here is considered 5mm nd the rdius of the pressure vessel is 240mm. 5/240 = 1/48 1/48<1/10 Therefore the considered pressure vessel is thin wlled pressure vessel nd the proceeding clcultions will be further bsed on the thin wlled pressure vessel. For thin-wlled cylinders the tngentil or circumferentil or hoop stress due to n internl pressure cn be ssumed to be uniformly distributed cross the wll thickness. Hoop stress (S 1 ) = PD 2t Where, P = Internl pressure in psi. D = Men dimeter in inches. t = Wll thickness in inches. For closed cylinder, Axil or Longitudinl stress (S 2 ) = PD 4t Where, P = Internl pressure in psi. D = Men dimeter in inches. t = Wll thickness in inches. It will lso be induced becuse of the pressure cting on the ends of the cylinder s the end of the vessel re closed. This will be generlly less thn the hoop stress. 2.1 Design According to Internl Pressure When the internl pressure is known t = P*R S*E-0.6P Where, R = Inside rdius in inches = 240mm. S = Mximum llowble stress of SA-283 is 13800psi. E = Joint efficiency. = 0.85 for spot exmined = 1 for rdiogrphy 150 * 9.44 t = = 0.121649 inches or 3.08988mm ( 13800 * 0.85) -( 0.6 *150) When thickness of the shell is known P = S*E*t = 13800*0.85*0.1969 R+0.6t 9.44 + (0.6*0.1969) P = 241.64psi or 16.66br. 2.2 Design According to Externl Pressure Set 1 = =3.94 = = 23.89 Do 607 t 1 (thickness t is found from Figure 1). A = 0.035 t 500 F E = 27*10 6 B = 13000 (From Figure 2.) 4*B 4*13000 ) = = 725.55psi or 50.0249 br. 3 (Do/t) 3*23.89 = Set 2 = =3.94 = = 47.78 Do 607 t 0.5 found from Figure 1). (thickness t is A = 0.01 t 500 F E = 27*10 6 B = 11000 4*B 4*11000 ) = = 306.96 psi or 21.1641 br. 3 (Do/t) 3*47.78 = Set 3 = =3.94 = = 196.38(thickness Do 607 t 0.121649 is found from Figure 1). A = 1*10-3 t 500 F E = 27*10 6 B = 930.69 4*B 4*930.69 ) = = 91.65 psi or 6.3190 br. 3 (Do/t) 3*19638 = Since the mximum llowble pressure is less thn the design pressure. Therefore the design is reworked by chnging the thickness of the shell. Set 4 = =3.94 = = 7.96 (thickness t is found from Do 607 t 3 Figure 1). A = 0.2 t 500 F E = 27*10 6 B = 16000 4*B 4*16000 ) = = 2680.07 psi or 184.78 br. 3 (Do/t) 3*7.96 = t Vol 8 (33) December 2015 www.indjst.org Indin Journl of Science nd Technology 3
Design nd Modelling of Hemisphericl nd Flt Dish End Pressure Vessel Set 5 = =3.94 = = 79.63 Do 607 t 3 (thickness t is found Figure 1). A = 4.5 t 500 F E = 27*10 6 B = 6000 4*B 4*6000 ) = = 100.64 psi or 6.9264 br. 3 (Do/t) 3*79.63 = Set 6 = =3.94 = = 59.63(thickness t is Do 607 t 3 Figure 1. Chrt to determine the thickness (t) of the vessel 10. 4 Figure 2. Chrt for determining the vlue of fctor B 10. Vol 8 (33) December 2015 www.indjst.org Indin Journl of Science nd Technology
Akshy T. Poojry, Rhul S. Shrm, Meet H. Ptel, Dhrmik U. Sheth, Chndrknt R. Kini nd Rjesh Nyk found from Figure 1). A = 6.5*10-3 t 500 F E = 27*10 6 B = 8500 4*B 4*8500 ) = = 189.76 psi or 13.08 br. 3 (Do/t) 3*59.63 = The ) is 13.08 br. The mximum llowble pressure vlues cn be vried incorporting stiffening rings or by vrying the thickness. These design vlues re considered since Design Pressure ) must be 30psi or 10% more thn mximum llowble working pressure. Note: If the vlue of A lies on to the left region of the chrt, there is different formul to clculte the vlue of P. P = 0.0625*E = 0.0625*(27*106) = 0.105468psi (Ro/t)2 (240/0.06)2 3. Internl Pressure 3.1 Circumferentil Stress in Thin Wlled Pressure Vessel (S 1 ) = psi D = Men Dimeter = 543.5mm = 21.40inches. P = 150Psi = 10.34br. t = 5mm = 0.1969inches. S 1 = 150*21.40 psi = 8151.34psi or 56201510.91N/m 2 2*0.1969 3.2 Longitudinl Stress in Thin Wlled Pressure Vessel (S 2 ) = PD psi 4t D = Men Dimeter = 543.5mm = 21.40inches. P = 150Psi = 10.34br. t = 5mm = 0.1969inches. S 2 = 150*21.40 psi = 4075.67psi or 28100755.4570N/m 2 4*0.1969 The temperture tken into considertion is 500 F nd the mteril used for mnufcturing of pressure vessel is SA-238 Grde C steel. The mximum llowble stress vlue for SA-283 C grde steel is 13800 psi or 89631844.8111888 N/m 2 (Figure 3). Hence the design is sfe. 4. Design of Circulr Flt Heds Thickness of the hed plte (t) = d. The bove formul is used only if the inner dimeter (d) does not exceeds 24inch. d = 18.89inch. = 18.89 0.13*(150)/(13800*0.85). t = 0.712641inches or 18.10mm. 5. Sphere nd Hemisphere Hed (Internl Pressure) P = Internl pressure; R = Inner rdius PR 150*9.44 t = = = 0.060435 inch. 2SE-0.2P 2*13800*0.85-(0.2*150) 2*S*E*t P = = 149.99 psi. R+0.2*t 180*9.44 t = = 0.07254 inch or 1.8425 mm. 2*13800*0.85-(0.2*180) Figure 3. Mximum llowble stress vlues 10. Vol 8 (33) December 2015 www.indjst.org Indin Journl of Science nd Technology 5
Design nd Modelling of Hemisphericl nd Flt Dish End Pressure Vessel 6. Sphere nd Hemisphere Hed (Externl Pressure) P = B/(R o /t). A = 0.125/(11.94/0.07254). A = 7.59*10-4 The vlue of A lies on to the left region of the chrt, there is different formul to clculte the vlue of P. Tble 1. Dimensions of the pressure vessel Prmeter Dimensions in mm Dimensions in inches Outer Dimeter (D o ) 607 23.89 Inner Dimeter (D i ) 480 18.89 Thickness of the Shell (t) 63.5 2.5 Men Dimeter (D m ) 543.5 21.40 P = 0.0625*E = 0.0625*(27*106) = 62.28psi. (Ro/t)2 (11.94/0.07254) 2 )<Design Pressure ) t = 4mm or 0.1575inch. A = 0.125/(11.94/0.1575) = 1.64*10-3 The vlue of A lies on to the left region of the chrt, there is different formul to clculte the vlue of P. P = 0.0625*E = 0.0625*(27*106) (Ro/t)2 (11.94/0.07254) 2 P = 293.63psi. Therefore P >P t = 4mm or 0.1575inch. 7. Criticl Height bove which Compressive Stress Governs (Internl Pressure + Wind Lod) H = PDM = 150*21.40 = 509.4591feet or 155283.13368mm. 32t 32*0.1969 8. Modelling of Hemisphericl Dish End Pressure Vessel nd Flt Circulr Dish End Pressure Vessel The pressure vessels were modelled in universlly ccepted softwre clled CtiVersion 5 (V5) Relese 19 (R19). This softwre gives wide ccess to tools for modifiction of the model nd is very user friendly. Tble 1 shows the dimensions of both the modelled pressure vessel. Figure 4. Hemisphericl dish end pressure vessel. Figure 4 nd Figure 5 shows the CAD model of hemisphericl dish end pressure vessel nd flt circulr dish end pressure vessel respectively modelled in Cti V5R19 13. The inlet port from where the fluid enters the pressure vessel hve been provided t perpendiculr direction to the dish end in both types of vessel (left side of the vessel when viewed from the Isometric view). The outlet port is provided t the top which hs the smllest bore dimeter nd flnge with provision for fstening (the port t the rer of the vessel when viewed from Isometric view). The fluid needs to be trnsported by mens of externl pressure source. The lrgest hole provided t the top is the mnhole for repir nd mintennce purpose nd the hole djcent to it is provided for inspection purpose, both these holes hve been fstened with blind plte. Two drin ports re provided t the bottom of the vessel for drining out the fluid from the vessel. Three supports re provided which re fstened with the help of foundtion bolts to the ground which re rectngulr in shpe. 6 Vol 8 (33) December 2015 www.indjst.org Indin Journl of Science nd Technology
Akshy T. Poojry, Rhul S. Shrm, Meet H. Ptel, Dhrmik U. Sheth, Chndrknt R. Kini nd Rjesh Nyk Figure 5. Flt circulr dish end pressure vessel. 9. Conclusions Circumferentil Stress in Thin Wlled Pressure Vessel (S 1 ) = 56201510.91 N/m 2. Longitudinl Stress in Thin Wlled Pressure Vessel (S 2 ) = 28100755.4570N/m 2. Pressure Vessel Specifictions. Temperture = 500 F or 260 c. Operting pressure ) = 150psi or 10.3421br. Mteril used for mnufcturing = SA-238 Grde C. Outer Dimeter (D o ) = 607mm or 23.89inches. Inner Dimeter (D i ) = 480mm or 18.89inches. Men Dimeter (D m ) = 543.5mm or 21.40inches. Thickness of the shell (t) = 63.5mm or 2.5inches. Mximum llowble stress = 13800psi or 95147650.6457N/ m 2. Criticl Height bove which compressive stress governs (Internl Pressure + Wind Lod) H = 155.2831m. Design of Circulr Flt Heds thickness (t) = 18.10mm. 10. References 1. Nbhni F, Ldokun T, Askri V. Reduction of stresses in cylindricl pressure vessels using finite element nlysis. Finite Element Anlysis From Biomedicl Applictions to Industril Developments; p. 379 90. 2. Hssn S, Kvi K, Rj D, Sridhr K. Design nd optimistion of pressure vessel using metheuristic pproch. Applied Mechnics nd Mterils. 2014; 465-466:401 6. 3. Rprl SK, Seshih T. Design nd nlysis of multilyer high pressure vessels. IJERA. 2012 Jn-Feb; 2(1):355 61. ISSN: 2248-9622. 4. Prneeth B. Ro TBS. Finite element nlysis of pressure vessel nd piping design. Interntionl Journl of Engineering Trends nd Technology. 2012; 3(5):567 70. 5. Dubl SV, Gjjl SY, Ptil VG. Review on stresses in cylindricl pressure vessel nd its design s per ASME code. IJETT. 2014 My; 11(6):300 5. 6. Kulkrni AA, Jtkr KH. A review on optimiztion of finite element modelling for structurl nlysis of pressure vessel. IJETT. 2014 Jun; 12(1):20 2. 7. Khn Z, Kdm GA, Ptil VG. Review on effect on lrge opening structure stbility of vessel nd its design s per ASME code. IJETT. 2014 Jun; 12(8):382 7. 8. Tmboli K. Ftigue nlysis of pressure vessel by FEA techniques. IJETT. 2014 Jul; 13(1):25 8. 9. Slunke YJ, Mngrulkr KS. Stress nlysis of composite cylinder for the storge of liquefied gses. IJETT. 2014 Jul; 13(8):394 5. 10. Megyesy EF. Pressure vessel hndbook. 12th ed; 2001. 11. Kozk D, Smrdzic I, Stoic A, Ivndic Z, Dmjnovic D. Stress nlyses of cylindricl vessel with chngeble hed geometry. Scientific Bulletin, Series C: Fscicle: Mechnics, Tribology, Mchine Mnufcturing Technology. 2009; 23(100). ISSN: 1224-3264. 12. Brnic J, Turklj G. Nuk o cvrstoci II. Rijek: Zigo; 2006. 13. Poojry AT, Jgnnth S, Nyk R, Kini CR. Modelling nd equivlent stress nlysis of flt dish end pressure vessel. Interntionl Journl of Current Engineering nd Technology. 2015 Oct; 5(5):3110 4. 14. Hjmohmmd MH, Frji J, Mokhtri A, Khosrojerdi R, Shrfi T. Studying effect of geometricl prmeters on the buckling of cylindricl shells under hydrosttic pressure. Indin Journl of Science nd Technology. 2013 Nov; 6(11):5527 32. Nomenclture P = Internl pressure in psi. D o = Outer dimeter in inches. D i = Inner dimeter in inches. D m = Men dimeter in inches. t = Wll thickness nd thickness of the hed plte in inches. R = Inside rdius in inches. S = Mximum llowble stress of SA-283 in psi. E = Joint efficiency. P = in psi. P = Design pressure in psi. S 1 or h = Circumferentil stress in thin wlled pressure vessel in psi. S 2 or 1 = Longitudinl stress in thin wlled pressure vessel in psi. H = Criticl height in m. Vol 8 (33) December 2015 www.indjst.org Indin Journl of Science nd Technology 7