Design and Analysis of Filament Wound Toroidal Pressure Vessel

Design and Analysis of Filament Wound Toroidal Pressure Vessel

1J. Mohammed Iliyas,

1 M. Tech student,

Department of Mechanical Engineering, Princeton College of Engineering & Technology,

Hyderabad, India,

2Prof. Vvrls. Gangadhar,

2Professor,

Department of Mechanical Engineering, Princeton College of Engineering & Technology, Hyderabad, India,

Abstract – The main objective of this investigation is to study and compare experimentally the deformations, stresses, buckling load multipliers, frequency values for Conventional Toroidal Pressure vessel and Filament wound Pressure Vessel used to store CNG. The Toroidal Pressure vessel and Filament wound Pressure Vessel are modeled in 3D modeling software Creo 2.0. Theoretical calculations and analysis is also carried to determine stress and displacement values for toroidal pressure vessel. Static, Buckling and Modal analyses are performed on Toroidal Pressure vessel and Filament wound Pressure Vessel and the results were compared . The analysis is done in Ansys.

Key words Pressure Vessel, Toroid, Filament and Buckling

1. INTRODUCTION TO PRESSURE VESSEL Pressure vessel is defined as a container with a pressure differential between inside and outside. Pressure vessels often have a combination of high pressures together with high temperatures and in some cases flammable fluids or highly radioactive materials. The design is such that the pressure vessels should withstand design pressure without any leak. Pressure vessels are used in a number of industries like, power generation industry for fossil and nuclear power, the petrochemical industry for storing, in hydraulic units for aircraft and Solid Rocket motor cases, liquid pressure vessels as storage tanks for launch vehicles in space industry, and processing crude petroleum oil in tank farms as well as storing gasoline in service stations. Toroidal vessels are commonly used for the storage of pressurized fluids in automotive and aerospace applications due to their optimal use of space. Here, the aim is to provide insight into the effect of openings on toroidal pressure vessels.

   Pressure vessels have been manufactured by filament winding for a long time. Although they appear to be simple structures, pressure vessels are difficult to design. Filament-wound composite pressure vessels have found widespread use not only for military but also for civilian applications. This technology originally developed for military use has been adapted to civilian purposes and was, in a later stage, extended to the commercial market. A potential widespread application for composite pressure vessels is the automotive industry. Emphasis on reducing emissions promotes the conversion to CNG or hydrogen fuelled tanks worldwide. Filament-wound composite pressure vessels utilizing high strength/modulus to density ratio offer significant weight savings over conventional all-

   metal pressure vessels for the containment of high pressure gases and fluids. Composite pressure vessels are expected to withstand a maximum burst pressure at a maximum internal volume and a minimum weight.

2. OBJECTIVE

   The main of this thesis is to compare the analytical results for Conventional Toroidal Pressure vessel and Filament wound Pressure Vessel used to store CNG. The Toroidal Pressure vessel and Filament wound Pressure Vessel are modeled in 3D modeling software Creo 2.0.Theoretical calculations are done to determine stress and displacement values for toroidal pressure vessel. Static, Buckling and Modal analyses are performed on Toroidal Pressure vessel and Filament wound Pressure Vessel and compared for the deformations, stresses, buckling load multipliers, frequency values. The analysis is done in Ansys

3. LITERATURE SURVEY

   The following works are done by some authors on toroidal pressure vessels: The work done by J Bachut[1], presents results of a numerical study into the buckling resistance of geometrically perfect and imperfect steel toroidal shells with closed cross-sections. Elastic and elastic-plastic buckling analyses of shells subjected to uniform external pressure were carried out for a range of geometries, boundary conditions and material properties. Toroids with circular and elliptical cross-sections were investigated. In the work done by Rakendu R[2], an attempt is made to study of the effect of openings of 10 mm to 150 mm on toroidal pressure vessels. Also find out the variation of stress concentration factor for different diameter of hole.

   To find the effect of position of hole, the holes of different diameters are placed at two different locations of the shell. In the paper by Lei ZU[3], presented an overview and comprehensive treatment for toroidal and domed pressure vessels. Since the geodesic winding has severe boundary conditions that confine the layup optimization, the non-geodesic trajectories are here extensively applied to enlarge the design space. The mathematical description of the geodesics and non-geodesics on a generic shell of revolution is briefly presented.

4. PRESSURE VESSELS MODELS

   3d Model Of Toroidal Pressure Vessel

   Fig – Final model

   3D MODEL OF FILAMENT WOUND TOROIDAL PRESSURE VESSEL

   Fig Final Model of Filament wound pressure vessel

5. THEORITICAL CALCULATIONS FOR STRESS AND DISPLACEMENT FOR TOROIDAL

   PRESSURE VESSEL

   Introducing the aforementioned values the following expression for the shell point transversal displacements in the radial direction is obtained

   r0 = * (r0 (r0+ b))

   2

   MATERIAL – STEEL

   Fig Total Deformation for Steel

   Fig Equivalent Stress for Steel

   The Meridoinal Stress

   = * r0+b

   r0

   where Normal Stress = 2

6. ANALYSIS OF TOROIDAL AND FILAMENT WOUND TOROIDAL PRESSURE VESSEL

1. STRUCTURAL ANALYSIS OF FILAMENT WOUND TOROIDAL PRESSURE VESSEL

   Fig Equivalent Elastic Strain for Steel

2. BUCKLING ANALYSIS OF FILAMENT WOUND TOROIDAL PRESSURE VESSEL

   MATERIAL- KEVLAR

   Fig Total Deformation 1 for Kevlar

   Fig Total Deformation 2 for Kevlar

   Fig Total Deformation 3 for Kevlar

3. MODAL ANALYSIS OF WITH FILAMENT WOUND TOROIDAL PRESSURE VESSEL

   MATERIAL – CARBON FIBER

   Fig Total Deformation at Mode1 for Carbon Fiber

   Fig Total Deformation at Mode2 for Carbon Fiber

   Fig Total Deformation at Mode3 for Carbon Fiber

   Fig Total Deformation at Mode4 for Carbon Fiber

   Fig Total Deformation at Mode5 for Carbon Fiber

   VII. RESULT & DISCUSSIONS

   STATIC ANALYSIS

   MATERIALS	DEFORMATION (mm)	STRESS (MPa)	STRAIN
   STEEL	0.55313	739.46	0.0040025
   KEVLAR	0.61059	707.49	0.004253
   CARBON FIBER	0.29737	833.73	0.0023469

   MATERIALS	DEFORMATION (mm)	STRESS (MPa)	STRAIN
   STEEL	0.55313	739.46	0.0040025
   KEVLAR	0.61059	707.49	0.004253
   CARBON FIBER	0.29737	833.73	0.0023469

   Table Static analysis results of Filament wound toridal pressure vessel

   Graph Comparison of Deformation values for two models and different materials

   COMPARISON OF DEFORMATION VALUES FOR TWO MODELS AND MATERIALS

   COMPARISON OF DEFORMATION VALUES FOR TWO MODELS AND MATERIALS

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0.1

   0

   WITH FWPV

   WITHOUT FWPV

   0.7

   0.6

   0.5

   0.4

   0.3

   0.2

   0.1

   0

   WITH FWPV

   WITHOUT FWPV

   MATERIALS

   MATERIALS

   DEOFRMATION (mm)

   DEOFRMATION (mm)

   From the above graph it is observed that the total deformation is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Carbon Fiber material.

   COMPARISON OF STRESS VALUES FOR TWO MODELS AND MATERIALS

   1000

   800

   600

   400

   COMPARISON OF STRESS VALUES FOR TWO MODELS AND MATERIALS

   1000

   800

   600

   400

   200

   0

   200

   0

   WITH FWPV

   WITHOUT FWPV

   WITH FWPV

   WITHOUT FWPV

   STRESS (N/mm2)

   STRESS (N/mm2)

   Graph: Comparison of Stress values

   MATERIALS

   MATERIALS

   The stress value is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Kevlar material.

   Table Static analysis results of Toroidal pressure vessel

   Graph: Comparison of Strain values

   COMPARISON OF STRAIN VALUES FOR TWO MODELS AND MATERIALS

   0.005

   0.004

   STRAIN

   STRAIN

   MATERIALS	DEFORMATION (mm)	STRESS (MPa)	STRAIN
   STEEL	0.47742	250.38	0.0013985
   KEVLAR	0.52034	240.4	0.0014948
   CARBON FIBER	0.26662	280.29	0.00082847

   MATERIALS	DEFORMATION (mm)	STRESS (MPa)	STRAIN
   STEEL	0.47742	250.38	0.0013985
   KEVLAR	0.52034	240.4	0.0014948
   CARBON FIBER	0.26662	280.29	0.00082847

   0.003

   0.002

   0.001

   0

   MATERIALS

   WITH FWPV

   WITHOUT FWPV

   From the above graph it is observed that the strain is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Carbon Fiber material.

   1. BUCKLING ANALYSIS

      Table Buckling results of Filament wound toroidal pressure vessel

      MATERIALS	VARIABLES	MODE1	MODE2	MODE3
      STEEL	Deformation (mm)	1.0771	1.0808	1.0766
      	Load multiplier	279.27	279.4	279.43
      KEVLAR	Deformation (mm)	1.0996	1.0938	1.0923
      	Load multiplier	249.12	249.15	249.29
      CARBON FIBER	Deformation (mm)	1.07	1.0709	1.0729
      	Load multiplier	589.58	589.98	590.5

      Table Buckling results of Toroidal pressure vessel

      MATERIALS	VARIABLES	MODE1	MODE2	MODE3
      STEEL	Deformation (mm)	1.1389	1.034	1.0316
      	Load multiplier	455.77	522.7	541.89
      KEVLAR	Deformation (mm)	1.1263	1.0295	1.0248
      	Load multiplier	417.13	476.18	495.03
      CARBON FIBER	Deformation (mm)	1.1783	1.054	1.0522
      	Load multiplier	845.5	985.68	1014.2

      COMPARISON OF LOAD MULTIPLIER VALUES FOR TWO MODELS AND MATERIALS AT MODE 3

      1200

      1000

      800

      600

      COMPARISON OF LOAD MULTIPLIER VALUES FOR TWO MODELS AND MATERIALS AT MODE 3

      1200

      1000

      800

      600

      400

      200

      0

      400

      200

      0

      LOAD MULTIPLIER

      LOAD MULTIPLIER

      Graph: Comparison of Load multipliers values

      The load factor is the factor that multiplies all loads, such that at that load buckling will occur. By observing the graph, it can be observed that the load multiplier value is more for Carbon Fiber, so the pressure vessel buckles faster for Kevlar than Steel and Carbon Fiber. Carbon Fiber buckles at more loads. The toroidal pressure vessel has more load multiplier values than Filament wound toroidal pressure vessel.

      From the below graph it is observed that the deformation is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Kevlar

      1.1

      1.08

      1.06

      1.04

      1.02

      1

      0.98

      1.1

      1.08

      1.06

      1.04

      1.02

      1

      0.98

      WITH FWPV

      WITH FWPV

      DEOFRMATION (mm)

      DEOFRMATION (mm)

      Graph: Comparison of Deformation values

      COMPARISON OF DEFORMATION VALUES FOR TWO MODELS AND MATERIALS AT MODE 3

      COMPARISON OF DEFORMATION VALUES FOR TWO MODELS AND MATERIALS AT MODE 3

      WITHOUT FWPV

      WITHOUT FWPV

      MATERIALS

      MATERIALS

   2. MODAL ANALYSIS

Modal analysis is the study of the dynamic properties of structures under vibrational excitation.

Modal analysis is the field of measuring and analysing the dynamic response of structures and or fluids during excitationThe modal analysis results of results of pressure vessels with different materials are as follows

WITH FWPV

WITHOUT FWPV

WITH FWPV

WITHOUT FWPV

Table Modal analysis results for Filament wound Toroidal pressure vessel

MATERIALS

MATERIALS

The above table clearly represents the analysis results for different materials like steel, Kevlar and carbon fiber and comparison can be done for respective results.

Table Modal analysis results for Toroidal pressure vessel

DEOFRMATION (mm)

DEOFRMATION (mm)

Graph: comparison of deformation values at mode5

COMPARISON OF DEFORMATION VALUES FOR TWO MODELS AND MATERIALS AT MODE 5

COMPARISON OF DEFORMATION VALUES FOR TWO MODELS AND MATERIALS AT MODE 5

3

2

1

0

WITH FWPV

WITHOUT FWPV

3

2

1

0

WITH FWPV

WITHOUT FWPV

MATERIALS

MATERIALS

From the above graph it is observed that the deformation is less for toroidal pressure vessel than Fialment wound pressure vessel and it is less for Steel.

From the below graph it is observed that the frequency values are less for filament wound toroidal pressure vessel than toroidal pressure vessel, so vibrations are less for filament wound pressure vessel and it is less for Steel.

COMPARISON OF FREQUENCY VALUES FOR TWO MODELS AND MATERIALS AT MODE 5

2500

2000

1500

1000

COMPARISON OF FREQUENCY VALUES FOR TWO MODELS AND MATERIALS AT MODE 5

2500

2000

1500

1000

FREQIENCY (Hz)

FREQIENCY (Hz)

Graph: comparison of frequencies values

1. CONCLUSION

   Theoretical calculations are done to determine stress and displacement values for toroidal pressure vessel. By observing the calculations, the displacement is less for Carbon Fiber than Kevlar and Steel. The values are similar with that of analytical results.

   By observing the static analysis results, the total deformation is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Carbon Fiber material. From the stress results it is observed that by using steel for filament wound pressure vessel fails because the stress values are more than its allowable strength but for Kevlar and Carbon Fiber the stress values are less than their respective allowable strength values. The stress value is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Kevlar material. The strain is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Carbon Fiber material.

   Based on the buckling analysis results, the load factor is the factor that multiplies all loads, such that at that patcular load buckling will takes place. From the results, it can be observed that the load multiplier value is more for Carbon Fiber, so the pressure vessel buckles faster for Kevlar than Steel and Carbon Fiber. Carbon Fiber buckles at more loads. The toroidal pressure vessel has more load multiplier values than Filament wound toroidal pressure vessel. It was found that the deformation is lower for toroidal pressure vessel than Filament wound pressure vessel and it is less for Kevlar.

   By observing the modal analysis results, the deformation is less for toroidal pressure vessel than Filament wound pressure vessel and it is less for Steel. The frequency values are less for filament wound toroidal pressure vessel than toroidal pressure vessel, so vibrations are less for filament wound pressure vessel and it is less for Steel.

2. FUTURE SCOPE

   500

   0

   500

   0

   WITH FWPV

   WITH FWPV

   WITHOUT FWPV

   WITHOUT FWPV

   In the present work, comparative analysis is carried between the toroidal pressure vessel and filament wound pressure vessel, by which it is found that filament wound pressure vessel did not yield better for stresses but withstands vibrations. So more experiments has to be done on filament wound pressure vessel so as that the stresses will be reduced. Analytically use of composites is validated for pressure vessel, but practical experimentations has to be done for further investigation.

   MATERIALS

   MATERIALS

3. REFERENCES

1. J Blachut and OR Jaiswal, On Buckling of Toroidal Shells under External Pressure, Computers and Structures, 2000, 77, 233-251.

2. Rakendu R, MK Sundaresan and Pinky Merin Philip, Finite Element Analysis of Toroidal Pressure Vessels Using FEASTSMT/PreWin, European Journal of Advances in Engineering and Technology, 2015, 2(11): 62-68, ISSN: 2394 – 658X

3. Lei ZU, Design and optimization of filament wound composite pressure vessels, ISBN: 978-90-8891-382-2, Printed in the Netherlands by Uitgeverij BOXPress,

   Oisterwijk

4. Calum Fowler – Rmit University Melbourne, Australia Review of Composite Toroidal Pressure Vessel Research, Design And Development For OnBoard Cng And Hydrogen Storage

5. Vladan Velikovi, Stress and Strain States in the Material of the Stressed Toroidal Container for Liquefied Petroleum Gas, Scientific Technical Review, 2007, LVII, No.3-

6. H.J. Zhan, Static and dynamic analysis of toroidal LPG tanks, UNIVERSITY OF OTTAWA, Canada, 2008

7. Avinash Kharat and V V Kulkarni, Stress Concentration at Openings in Pressure Vessels- A Review, International Journal of Innovative Research in Science, Engineering and Technology,2013,2(3), 670-677.

8. SUTCLIFFE,W.J,: Stress analysis of toroidal shells of elliptic cross ssection, Int. J. Mech. Sci., 1971, 13, pp. 951- 958.

9. YAMADA,G., KOBAYASHI,Y., OHTA,Y., YOKOTA,S.: Free vibration of a toroidal shell with elliptical cross-section, J. Sound. Vibr., 1989, 135, 411-425.

10. Pravin Narale and PS Kachare, Structural Analysis of Nozzle Attachment on Presure vessel Design, International Journal of Engineering Research and Applications, 2012, 2(4), 1353- 1358.

11. Vikas Sharma, Aniket Kumar, Anshika Yadav, CNG: Always been in pursuit of energy to meet his ever increasing demand, International Journal of Science, Technology & Management