Design and Optimisation of Pressure Vessel Using ...

$SSOLHG0HFKDQLFVDQG0DWHULDOV9ROV SS ‹ 7UDQV7HFK3XEOLFDWLRQV6ZLW]HUODQG GRLZZZVFLHQWLILFQHW$00

Design  and  Optimisation  of  Pressure  Vessel  Using  Metaheuristic   Approach   1 1

Sulaiman  Hassan,  2Kavi  Kumar,  3Ch  Deva  Raj,  4Kota  Sridhar  

Mechanical  &  Manufacturing  Department,  University  Tun  Hussein  Onn  Malaysia,Malaysia   2

Faculty  of  Science  Technology  and  Human  Development,  University  Tun  Hussein  Onn   Malaysia,Malaysia   3

4

Mechanical  Engineering  Department,  RVR  &JC,Guntur,India  

Mechanical  &  Manufacturing  Department,  University  Tun  Hussein  Onn  Malaysia,Malaysia   1

[email protected],  [email protected],  [email protected],     4 [email protected]  

Keywords:  -­  Design  optimization,  Ant  colony  optimization  Algorithm,  Pressure  Vessels  

Abstract:   The   objective   of   design   optimization   of   pressure   vessels   is   cost   reduction   by   reducing   weight   with   adequate   strength   and   stiffness.   Optimization   is   the   act   of   obtaining   the   best   result   under  given  circumstances.  Conventional  design  aims  at  finding  acceptability  design  which  merely   satisfies  the  functional  and  other  requirements  of  the  problem.  In  general,  there  will  be  more  than   one  acceptable  designs  and  the  purpose  of  design  optimization  is  to  choose  the  best.  In  the  present   work   parameters   such   as   thickness   of   the   shell,   and   dish   end,   length   and   radius   of   the   pressure   vessel   are   optimized   by   making   use   of   ACO   has   been   shown   for   a   Pressure   vessel   problem   with   four  variables  and  four  design  constraints.  It  is  found  that  the  results  obtained  from  ACO  are  better   as  its  search  is  for  global  optimum  as  against  the  local  optimum  in  traditional  search  methods.  The   results  of  the  ACO  have  been  checked  using  ANSYS,  and  it  is  found  to  perform  satisfactorily.       Introduction   The  pressure  vessels  are  to  store  fluids  under  pressure.  The  fluid  being  stored  may  undergo  a   change  of  state  inside  the  pressure  vessel  as  in  case  of  steam  boilers  or  it  may  combine  with  other   reagents  as  in  a  chemical  plant.  The  pressure  vessels  are  designed  with  great  care  because  rupture  of   a   pressure   vessel   means   an   explosion   which  may   cause   loss   of   life   and   property.   The   material   of   pressure  vessels  may  be  brittle  such  as  cast  iron,  or  ductile  such  as  mild  steel.     Literature  survey   This   paper[1]   presents   a   hybrid   swarm   intelligence   approach   (HSIA)   for   solving   nonlinear   optimization   problems   which   contain   integer,   discrete,   zero-­one   and   continuous   variables.   This   paper[2]   presents   the   design   process   of   the   pressure   vessels   and   experimental   results   acquired   by   high-­pressure  tests.  This  paper[3]  presents  a  practical  review  of  the  use  of  PC-­based  Finite  Element   software  in   the   analysis   of  typical   pressure  vessel   components.  This  paper[4]  presents   a  modified   particle   swarm   optimization   (PSO)   algorithm   for   engineering   optimization   problem   with   constraints.   This   paper[5]   a   generic   algorithm   based   on   Ant   Colony   Optimization   to   solve   ulti-­ objective   optimization   problems.   The   proposed   algorithm   is   parameterized   by   the   number   of   ant   colonies  and  the  number  of  pheromone   trails.  This  paper  [6]  proposes  the  Omicron  ACO  (OA),  a   novel   population-­based   ACO   alternative   originally   designed   as   an   analytical   tool.   This   paper[7]   makes  a  comparison  of  the  effectiveness  of  the  three  methods  on  a  particular  optimization  problem,   namely  the  tuning  of  the  parameters  for  a  PID  controller.     Ant  Colony  Algorithm   Ant   behavior   was   the   inspiration   for   the   metaheuristic   optimization   technique   the   ant   colony   optimization   algorithm   (ACO),   is   a   probabilistic   technique   for   solving   computational   problems   which  can  be  reduced  to  finding  good  paths  through  graphs.    

$OOULJKWVUHVHUYHG1RSDUWRIFRQWHQWVRIWKLVSDSHUPD\EHUHSURGXFHGRUWUDQVPLWWHGLQDQ\IRUPRUE\DQ\PHDQVZLWKRXWWKHZULWWHQSHUPLVVLRQRI773 ZZZWWSQHW,'



WK0HFKDQLFDODQG0DQXIDFWXULQJ(QJLQHHULQJ

This  algorithm  is  a  member  of  ant  colony  algorithms  family,  in  swarm  intelligence  methods,  and  it   constitutes   some   metaheuristic   optimizations.   Initially   proposed   by   Marco   Dorigo   in   1992   in   his   PhD  thesis,   the  first   algorithm   was  aiming  to   search  for  an  optimal  path  in   a  graph;;   based  on  the   behavior   of   ants   seeking   a   path   between   their   colony   and   a   source   of   food.   The   original   idea   has   since   diversified   to   solve   a   wider   class   of   Numerical   problems,   and   as   a   result,   several   problems   have  emerged,  drawing  on  various  aspects  of  the  behavior  of  ants.          

Problem  Formulation     The  Problem  is  to  design  a  compressed  air  storage  tank  with  a  working  pressure  of  1000  psi  and  a   minimum  volume  of  750  ft3.  The  schematic  of  a  pressure  vessel  is  shown  in  Fig.6.1.  The  cylindrical   pressure  vessel  is  capped  at  both  ends  by  hemispherical  heads.  Using  rolled  steel  plate  (SAEJ  2340   TYPE   830   R),  the   shell  is   to   be  made   in   two   halves   that   are   joined   by   two   longitudinal   welds   to   form   a   cylinder.   Each   head   is   forged   and   then   welded   to   the   shell.   Let   the   design   variables   be   denoted   by   the   vector   X=[x1,   x2,   x3,   x4]T,   x1   is   the   spherical   head   thickness,   x2   is   the   shell   thickness,  x3  and  x4  are  the  radius  and  length  of  the  shell,  respectively.       The   objective   in   this   Project   is   to   minimize   the   manufacturing   cost   of   the   pressure   vessel.   The   manufacturing   cost   of   the   pressure   vessel   is   a   combination   of   material   cost,   welding   cost   and   forming  cost.  That  can  be  refer  in  Sandgren  (1990)  for  more  details  on  how  cost  is  determined.     The  constraints  are  set  in  accordance  with  respective  ASME  codes.  The  mathematical  model  of  the   problem  is:      

Objective  function     Here   our   main   objective   is   to   reduce   the   cost   by   reducing   weight   of   Pressure   Vessel.   So   the   objective  function     2

       

2

0.6224 x1 x 2 x3  1.7781x1 x3  3.1661x 2 x 4  19.84 x 4 x1

f ( x)        

x1 x2

x3 x4

 

 Radius  of  the  shell   L  Length  of  the  shell   Ts  Thickness  of  the  shell   Tb  Thickness  of  the  dish  end   R

Design  variables   x   x   x   x  

Radius  (  R)   Length  (L)   Thickness  of  the  shell     Thickness  of  the  dish  end  

 

Design  parameters   1.   Circumferential  or  Hoop  Stress   2.   Longitudinal  Stress     3.   Volume  

x3 Ts

x4 Th

x1

x2  

2

L

R

 

$SSOLHG0HFKDQLFVDQG0DWHULDOV9ROV



Design  constraints   The  four  important  constraints  under  consideration  are     1.  Hoop  stress  ”Allowable  stress   g1 x 0.0193x1  x4 d 0       2.  Longitudinal  stress  ”  Allowable  stress   g2 x 0.00954 x1  x3 d 0      

3.  Volume  ”  î  inch3     4 3 2 g 3 x 750 u 1728  Sx1  Sx1 x2 d 0 4.  Length   3 g 4 x x2  240 d 0  

  Variable  bounds   The  upper  and  lower  bounds  on  two  design  variables  are   1.   25 d x1 d 150  

25 d x2 d 240   3.   0.0625 d x3 d 1.25   2.  

4.   0.0625 d x4 d 1.25 Note:  All  are  in  inch     Problem  Description     A  typical  input  data  required  to  develop  a  mathematical  model  for  pressure  vessel  design  is   Pressure  vessel    material    =  SAE  J2340  ±  830R   Where  R=High  Strength  Recovery  Annealed   1.   Modulus   of   elasticity   (E)   =   200x109   4.   Allowable  Yield  Strength  =  540  MPA   2 N/mm   5.   Applied   Pressure   =   6.80272   N/mm2       2.   Yield  Strength  =  960  MPA   (1000  PSi)     3.   Factor  of  safety  =  1.78      Input  ACO  parameters:   ĮLVD7ULDOSDUDPHWHU    ȕLVD7ULDOSDUDPHWHU    7KHUDWHRISKHURPRQHHYDSRUDWLRQȡ   

=0.2   Number  of  iterations  =  5000   Number  of  ants  =  150   Number  of  Divisions  for  x1  =  150   Number  of  Divisions  for  x2  =  250  

   

Number  of  Divisions  for  x3  =  10   Number  of  Divisions  for  x4  =  10  



WK0HFKDQLFDODQG0DQXIDFWXULQJ(QJLQHHULQJ

Fixing  up  the  above  parameters  is  a  very  crucial  in  an  optimization  problem  because  there  are  no   guide   lines   for   these.   One   has   to   fix   the   ACO   parameters   for   a   particular   depending   on   the   convergence  of  the  problem  as  well  as  on  solution  time.  After  executing  various  run  with  different   ACO  parameters  depending  on  convergence  of  the  value.       Results  and  Discussions     The  values  of  best  design  variables  and  the  constraints  for  the  5000  iteration  obtained  after  running   the  program  for  Ant  colony  algorithm  written  in  the  C-­language  is  given  below.             Graphical  Results  

    The  optimum  values  are  obtained  at  2829  th  iteration  and  it  remain  as  constant  from  the  point  on   word  that  indicates  that  the  optimal  value  is  global  minima.     x1  =  Radius  of  the  shell  =  40  inch     x2  =  Length  of  the  shell  =  232.26  inch     x3  =  Thickness  of  the  shell  =  0.537  inch       x4  =Thickness  of  the  shell  =0.775  inch      g1  =Constraints  of  Hoop  Stress  =  -­0.003    g2  =  Constraints  of  Longitudinal  Stress=  -­0.156       g3  =  Constraints  of  volumes  =  -­138821    g4  =  Constraints  of  Length  =  -­7.74     Finally  function  value  f(x)  =      4856.205  $     These  results  are  compared  with  the  results  of  the  pervious  works  using  various  other  optimization   methods  and  are  in  a  table  given  below  

   

$SSOLHG0HFKDQLFVDQG0DWHULDOV9ROV



ANSYS  Analysis:                                                        Design  of  pressure  vessel     1

ELEMENTS /EXPANDED TYPE  NUM

Y Z

X

 

                                                                                                                                                               

Structure  of  pressure  Vessel       1 NODAL  SOLUTION STEP=1 SUB  =1 TIME=1 /EXPANDED SEQV          (AVG) DMX  =.313E-­05 SMN  =127.635 SMX  =456.355

Z

Y X

MN

MX

127.635 200.684 273.733 346.782 419.83                                                                                                                                                                 164.16 237.208 310.257 383.306 456.355

von  misses  Stress  of  pressure  vessel    

 

 

Conclusion                        In  the  present  work  parameters  such  as  thickness  of  the  shell,  and  dish  end,  length  and  radius   of   the   pressure   vessel   are   optimized   by   making   use   of   Ant   colony   metaphor;;   powerful   non-­ traditional  optimization  method  and  these  results  are  compared  with  other  Optimization  Methods.                      It  is  found  that  the  results  obtained  from  ACO  are  better  as  its  search  is  for  global  optimum  as   against  the  local  optimum  in  traditional  search  methods.  The  results  of  the  ACO  have  been  checked   using  ANSYS,  and  it  is  found  to  perform  satisfactorily.                      It  can  be  concluded  that  by  applying  Ant  colony  algorithm,  the  optimal  design  parameters  for   the   pressure   vessel   are   obtained   and   the   objective   minimization   of   cost   by   reducing   weight   of   Pressure  vessel  is  achieved.                      In   the   present   study   the   application   of   ACO   has   been   shown   for   a   Pressure   vessel   problem   with  four  variables  and  four  design  constraints.    



WK0HFKDQLFDODQG0DQXIDFWXULQJ(QJLQHHULQJ

References   [1]   GUO   Chuang-­xin,   HU   Jia-­sheng   ,   YE   Bin   ,   CAO   Yi-­MLD ³Swarm   Intelligence   For   Mixed-­ 9DULDEOH'HVLJQ2SWLPL]DWLRQ´  Journal  of  Zhejiang  University  SCIENCE  ISSN  1009-­3095   [2]   Tae-­Hwan   Joung,   In-­Sik   Nho,   Chong-­Moo   Lee,   Pan-­Mook   Lee,   Seung-­Il   Yang,   Seok-­Won   Hong  ³A  Study  on  the  Pressure  Vessel  Design,  Structural  Analysis  and  Pressure  Test  of  a  6,000   m  Depth-­UDWHG8QPDQQHG8QGHUZDWHU9HKLFOH´WKH,QWHUQDWLRQDOVRFLHW\RI2IIVKRUHDQG3RODU Engineers  ISBN  1-­880653-­64-­8   [3]   0LFKDHO $3RUWHU'HQQLV +0DUWHQV3HGUR0DUFDO ³2Q8VLQJ )LQLWH (OHPHQW $QDO\VLVIRU Pressure  Vessel  'HVLJQ´  PVP  Vol.  368,  ASME,  New  York,  NY,  pp.  139-­146.     [4]   ;LDRKXL +X 5XVVHOO &(EUWKDUW