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Procedía Engineering

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Procedía Engineering 64 (2013) 1040 - 1047

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International Conference on DESIGN AND MANUFACTURING, IConDM 2013

Design and analysis of pressure vessel assembly for testing of missile canister sections under differential pressures

S. Ravinder3', S. Prakash3, S.V. Vijay Kumar Raju3, S. Rajua, P. Janaki Ramulu3'*, S. Narendarb

In this work, a pressure vessel is designed to simulate differential pressure conditions on components of missiles and canisters. This design mainly concerned with two pressure chamber mounted concentrically, out of which outer chamber experiences internal pressure and the other experiences external pressure. The operating pressure conditions are 45><105 Pa external and lOxlO5 Pa internal. The chamber is designed for lOOxlO5 Pa external and 50xl05 Pa internal pressure with consideration of safety issues involved in the operation. Primarily, the design is based on IS 2825 unfired pressure vessel code and materials are chosen as per the standard ASTM A516 Gr. 70 pressure vessel steels. The other mounting fixtures, supporting channels and beams are as per the standard and all the other materials are of IS 2062 structural steel. The design is iterated many times to satisfy the desired requirements. The equivalent stresses and strain energy stored in the critical location of both pressure vessels are calculated. The fatigue life of the entire system are also estimated based on the stress and strain based designs with consideration of the fully reversed and zero based loading conditions.

© 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of the organizing and review committee of IConDM 2013 Keywords: Pressure vessel, Fatigue, Von Mises Stress, factor of safety, Equivalent stress

Nomenclature/Abbreviation

Pint Design internal pressure (MPa)

Pext Design external pressure (MPa)

Dj Inside diameter of shell (mm)

D2 External diameter of shell (mm)

J Weld j oint efficiency factor

t Thickness (mm)

E Young's modulus (MPa)

f Allowable stress value (MPa)

L Effective length (mm)

k Ratio of elastic modulus E of the material at the design temperature to the room temperature

ASTM American Society for Testing and Materials t'r$RWPVFlat Steel Ribbon Wound Pressure Vessel

IS Indian Standard

Gwek symbols

g 0.2% of proof stress (MPa)_

* Corresponding author. Tel.: +91 9494581470 E-mail address: srirama309@gmail.com

IjG students in the Department of Mechanical Engineering, Vardhaman College of Engineering, Shamshabad, Hyderabad-501 218 Professorin the Department of Mechanical Engineering, Vardhaman College of Engineering, Shamshabad, Hyderabad-501 218 Defence Research and Development Laboratory, Kanchanbagh, Hyderabad-500 058

Abstract

1877-7058 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of the organizing and review committee of IConDM 2013 doi:10.1016/j.proeng.2013.09.181

1. Introduction

Pressure vessels are used to store and transmit liquids, vapours, and gases under pressure in general. The pressure of these finds will exert pressure equally in all direction on the walls and ends of the pressure vessels. Because of the internal loading, stresses are including on certain sections of the cylinder (pressure vessel) wall. Pressure vessels are used in a variety of applications in both industry and the private sector. They appear in these sectors as industrial compressed air receivers and domestic hot water storage tanks. Other examples of pressure vessels are: diving cylinder, recompression chamber, distillation towers, autoclaves and many other vessels in mining or oil refineries and petrochemical plants, nuclear reactor vessel, habitat of a space ship, habitat of a submarine, pneumatic reservoir, hydraulic reservoir under pressure, rail vehicle airbrake reservoir, road vehicle airbrake reservoir and storage vessels for liquefied gases such as ammonia, chlorine, propane, butane and LPG [1-3].

Chuanxiang (2000) [4] studied the analysis of controllable stress distribution and suggested the optimal design of flat steel ribbon wound pressure vessel. The analysis showed that stresses were distributed on FSRWPV wall by controlling pre-stress and winding angle of its flat steel ribbon in the similar manner. Dong and welding (2000) [5] developed a stress modeling for evaluating the residual stresses in weld of pressure vessel and piping applications. Mayer et al. (2000) [6] reviewed the fatigue design procedure for pressure vessel. They discussed mainly fatigue design stress parameters, being: (a) the stress intensity range and (b) the principal stress range, and evaluated these parameters. It is concluded that a practical and conservative approach for a given weld details is to calculate geometric stress parameters at the critical location. A stress analysis of a cylindrical pressure vessel loaded by axial and transverse forces on the end of a nozzle was done by Petrovic (2001) [7]. The finite element method was applied to determine the state of stress in the cylindrical shell.

In the similar manner there were few other studied related to the cylindrical pressure vessel design, bending stress calculation from finite element analysis for pressure vessels applications in structural design, functionally graded material layers used to reduce normal and shear stress gradients due to internal pressure and thermal loadings at the interface of a two-layered wall pressure vessel, optimised the design procedure for anisotropic pressure vessel, resk analysis of CNG composite pressure vessel, An exploratory study on pressure vessel design procedures based on load and resistance factor design method for subsea blowout preventers subjected to external hydrostatic pressure was presented recently [8-14].

The present problem of designing a pressure vessel to operate in differential loading environment is analysed by considering all the factors involved during the design. The standards applicable for the pressure vessel design and material selection, welding, testing methodologies etc., are considered strictly. The outer shell should support an operating internal pressure of 45><105 Pa and the inner shell should support an operating external pressure of lOxlO5 Pa. The chamber is designed for 100x10s Pa external and 50*105 Pa internal pressure with consideration of safety issues involved in the operation. Along with the both cylindrical shells, separate spherical shells are designed to operate in the above mentioned operating conditions. A bottom square plate is designed to support both the loading of the pressure vessels and a supporting fixture for housing all the above said components is also designed in this work.

2. Working of pressure vessel

The present pressure vessel is used for pressure qualification of canister and missile components to justify whether the given component may withstand the applied pressure or not. The canister is in cylindrical shape with top dome which is a major part in underwater missile launching system. This canister isolates the missile from water during launch and it allows moving the missile after ignition. Fig. 1 shows working of pressure vessel. The pressure vessel bottom dome consists of 12

Fig.l Working of pressure vessel

auxiliary communicating chambers, out of these 6 are located in lower PCD and remaining in higher PCD. For internal pressurization of canister the pressure is admitted through some of lower PCD chambers remaining chamber of same PCD are for depressurization for setting the required pressure. For external pressurization of canister pressure is admitted through some of higher PCD communicating chambers. Nitrogen cylinders are incorporated for required pressurization. The canister is placed on base plate by means of bolted joints.

2. Preliminary Calculations

The minimum thickness required for circular cylindrical pressure vessel of inside diameter Dl and internal pressure .P^ is calculated according to the standard IS 2825 is

t= PmlDl- (1)

200 f J - Pinl

Here P = 101.97 kPa, D! = 2000 mm, /= 24.46 kg/mm2 and J = 1 (Double welded butt joints with full penetration -excluding butt joints with metal backing strips which remain in place). The units of all these parameters are according to the standard. The minimum thickness required for the cylindrical shell obtained from these calculations is 42.58 mm.

The minimum thickness required for spherical shell of inside diameter D1 and internal pressure P-ml is calculated according to the standard IS 2825 is

t =-И-*--(2)

Here P = 101.97 kPa, Di = 2000 mm,/= 24.46 kg/mm2 and J = 1. The units of all these parameters are according to the standard. The minimum thickness required for the spherical shell obtained from these calculations is 21.06 mm.

The minimum thickness required for circular cylindrical pressure vessel of outer diameter DQ and external pressure Pext is calculated according to the standard IS 2825 is

**+0.053

Here = 5 MPa, D0 = 2000 mm, i = 1800 mm, ¡r = 562.7 MPa and к = 1 (Ratio of elastic modulus £ of the material at the design temperature to the room temperature). The liiiits of all these parameters are according to the standard. The minimum thickness required for the cylindrical shell obtained from these calculations is 22.735 mm.

The minimum thickness required for spherical shell of outside diameter D0 and external pressure Pext is calculated according to the standard IS 2825 is

t = E-& (4)

Here Ре« = 5 MPa, D0= 1000 mm and a = 562.7 MPa. The units of all these parameters are according to the standard. The minimum thickness required for the spherical shell obtained from these calculations is 11.11 mm.

The minimum values predicted were not sufficient for the present design. The values chosen for all the components are based on the analysis performed. The complete details are given the following section.

3. Components of the Pressure Vessel Assembly

The design of pressure vessel which we dealt consists of following parts,

1. Two concentric (internal and external) main cylinders.

2. External cylinder top and bottom dome

3. Internal cylinder top dome

4. Communicating chambers

5. Baseplate

6. Rig

• Main cylinder is the major integral part of pressure vessel. This cylinder allows external linkages such as power cables, thermocouples and sensors through communicating chambers which are welded to it. Two flanges are joined to main cylinder and this flange's allows main cylinder to connect with top and bottom dome by means of bolted joints. The number of bolts required depends on vertical force created by pressure applied in the cylinders.

• External main cylinder experiences internal pressurisation and internal cylinder with outside pressurisation.

• Internal main cylinder covered with internal top by means of bolted joints.

• Main cylinders are covered with top and bottom domes to form a pressure vessel. In this pressure vessel, we used hemispherical type domes to minimise the force created by pressurisation by increasing the contact area.

• Top dome is equipped with four hooks for lifting purpose. Bottom dome is moved upward and downward (connecting and dis connecting with main cylinder through base plate) with the help of screw jack.

• Bottom dome has 12 communicating chambers in which 6 are located 20° from the origin (Used to introduce pressure in to main cylinder to maintain maximum of 100*105Pa) and remaining with 50° from origin (Used to introduce pressure in to internal cylinder through hose pipes with flanges to maintain maximum of 50xl05 Pa). These 12 communicating chambers purpose is to introduce the pressure (N2 gas) in to pressure vessel.

• The complete internal and external cylinders are mounted on base plate. This base plate withstands force created by internal pressurisation and self-weight of complete internal and external cylinders. Base plate is connected to rig structure.

• Rig is a supporting structure which withstands complete pressure vessel and assembly and it also takes force created by pressurisation and self-weight of complete pressure vessel assembly. This total rig structure is modelled with I, C and L- section beams which are joined in such a way that to optimise the whole assembly.

Fig. 2. Front view of external main cylinder Fig. 3. Top view of external main cylinder

The Figure 2 and 3 are shows the front and top view of external main cylinder for better understanding of location of communicating chambers.

The boundary conditions and problem settings are indicated in the Table 1.

Table 1. The boundary conditions for problem setting

Assembly_Fixed support_Pressure

External main cylinder Top and bottom flange Internal surfaces of main cylinder, 6

communicating chambers and their flanges

External bottom domes Flange Internal surface of dome, 13

communicating chambers and their flanges

Internal main cylinder Top and bottom flange Internal surface of cylinder

Internal and external top domes Flange Internal surface of dome

Rig structure Bottom L- section beams Base plate

4. Structural Analysis on Pressure Vessel Components

The outer circular cylindrical shell has an outer diameter of 2140 mm, thickness of 70 mm and length of 3000 mm. The inner circular cylindrical shell has an outer diameter of 1000 mm, thickness of 30 mm and length of 1800 mm. The top and bottom spherical shells of outer vessel have a thickness of 35 mm. The top spherical shell of inner pressure vessel has a thickness of 15 mm. The material for all the pressure experiencing components is chosen as per ASTM-A516 Gr. 70 material, which has the following properties: Young's modulus of 200 GPa, density of 7850 kg/m3, Poisson's ratio of 0.3,

tensile strength of 250 MPa and the ultimate strength of 460 MPa. It is primarily intended for use in welded pressure vessels. The popular chemical composition of this grade is Carbon 0.27 - 0.31%; Manganese 0.79 - 1.3%; Phosphorous 0.035% max; Sulphur 0.035% max; Silicon 0.13 - 0.45%. The other supporting fixtures and components material are chosen as per IS 2062 Gr. B structural steel. This code specifies requirements of design, fabrication, inspection and testing of pressure vessels.

Analysis of total pressure vessel assembly is done to evaluate equivalent stress, factor of safely and total deformation when application of 100x10s Pa pressure on internal surface of external pressure vessel, 50*105 Pa pressure applied on external surface of internal pressure vessel, self-weight and vertical force created by above mentioned pressurisation are applied on supporting structure.

In case of external pressure vessel cylindrical portion have six circular holes for connect six communicating chambers and these holes are created major stresses which are undesirable and effect tremendous damage to whole pressure vessel so this type of difficulty may avoided by two ways i.e. locally thickening the critical portion and by adding ribs. In present work we have done locally thickening the critical portion by adding patches to it.

Top and bottom spherical shells are have flanged edges which are welded to cover the main cylindrical shell by means of bolted joints. These types of welded joints are not able to withstand the higher pressures so this critical portion was strengthening by adding ribs. The present pressure vessel is designed to simulate various missile components at ground level so it is important to keep the factor of safety above 1.5 and in present design we achieved total assembly factor of safety of 2.75.

No of bolts required to join the spherical shells with cylindrical shell is calculated by following relation

Vertical load created by applied pressure (N)

Number of bolts required =

Max axial load withstand by each bolt (N)

Number of M36 bolts required = = 74

H 850000

Total 74Nos M36 bolts are required to with stand the given force. Fig. 4 shows complete pressure vessel assembly with total supporting structure. Fig. 5 shows sectional view of total pressure vessel assembly for better understanding of internal parts included in pressure vessel. The complete pressure vessel assembly is shown in Fig. 3 and 4. The entire assembly is designed in Solid Works package. The sectional view shown in Fig. 2 for clear understanding of the design. Designing and modelling of complete parts of pressure vessel are performed in Solid Works 2012 and analysis is performed in Ansys VI3.

Fig. 4. Complete pressure vessel assembly Fig. 5. Section view of complete pressure vessel assembly

(b) L.nli1f li'lPrrt,.. (C)

Fig. 6. (a) Quadrilateral tetrahedron FE mesh of the external cylinder, (b) Quadrilateral hexahedron FE mesh of the communicating chambers and ribs

and (c) factor of safety plot for the entire outer cylinder assembly

The complete external cylinder assembly design obtained through solid works is meshed and analyzed in ansys, by which the stresses resulted are higher. So to compensate this locally strengthening square shaped patches have been incorporated. As a result of this, the corner stresses are reduced which are shown in above figure. Fig. 6 shows meshing and factor of safety of external main cylinder. The types of elements used in this design are Quadratic Hexahedron, Quadratic Quadrilateral Contact, Quadratic Quadrilateral Target, Quadratic Tetrahedron, Quadratic Triangular Contact, Quadratic Triangular Target and Quadratic Wedge. In the above external cylinder meshing total nodes used are 425297, total elements are 2117600, total body elements are 208508, total contact elements are 1909092, total contacts are 334, and total element types are 7.

(a) (b) (c)

Fig. 8. (a) Quadrilateral tetrahedron FE mesh of the internal cylindrical shell and Quadrilateral hexahedron FE mesh of the ribs, (b) Equivalent stress distribution on internal vessel assembly and (c) Equivalent stress distribution on top dome of the internal cylindrical vessel assembly.

The top and bottom domes are designed analyzed to qualify the components of pressure vessel at design pressure loads and all other vertical loads generated by internal pressurization. The Fig.7 shows the equivalent stress plots of external cylinder top and bottom dome and Fig. 8 shows internal cylinder assembly and its top dome meshing and equivalent stress distribution. The high stresses obtained are compensated in the form of installing ribs at shell flange circumference. Finally after compensating all unwanted stresses the total factor of safety achieved is about 2.56 which is more than sufficient for human occupancy type pressure vessels.

The Fig. 9 shows the complete supporting structure for complete pressure vessel assembly is constructed by using Insertion, I-section and C-section beams according to Indian standard Code for unfired pressure vessel. In case of I-section beams ISMB-300 was used to withstand the design load conditions. The number of I-section beams which are directly connected to base plate are finalized by considering total vertical load generated by internal pressurization and self weight of total pressure vessel assembly. The high stresses which are induced in I- section beams are minimized by incorporating patches for locally strengthening the critical stress points. All beams are connected by bolted joints to form a complete rig structure.

Fig. 9. Equivalent stress distribution on the supporting fixture assembly for the pressure vessels

Fig. 10. Fatigue analysis of complete pressure vessels assembly: Safety factor achieved during working condition as per the fully reversed constant

amplitude loading of stress life design

The Fig. 10 shows results obtained after performing the fatigue analysis on the complete pressure vessel assembly which indicates that maximum number of working cycles the pressure vessel can resists without any considerable failures. The higher factor of safety is desirable for any human occupancy type pressure vessel so the present design is manipulated to achieve higher F.O.S. Finally by considering all forces acting on the present pressure vessel like design pressures, self weight and vertical load created by internal pressurization, the factor of safety achieved is 2.75.

5. Conclusions

From the present work about the design and analysis of the pressure vessel assemble the following conclusions are drawn.

• All the design factors are considered and designed the safe pressure vessel.

• The total unfired pressure vessel assembly is designed and analysed at required conditions and by considering all other loads generated by internal pressurization.

• The compensating high stresses which are undesirable during installation of various components.

• The total factor of safety achieved is 2.75.

• The number of cycles up to which the pressure vessel can withstand without any noticeable failure are obtained by performing fatigue analysis on complete pressure vessel assembly in ansys work bench are 4441 cycles stress based (Fully reversed) type fatigue analysis.

References

[1] Ellenberger, J., P., Chuse, R, Carson, B., E., Pressure Vessels, McGraw-Hill Professional Engineering, 2004.

[2] Unfired Pressure Vessel Code: IS 2825-1969.

[3] An International Code 2007 ASME Boiler & Pressure Vessel Code, The American Society of Mechanical Engineers, 2007.

[4] Chuanxiang, Z., 2000. Analysis of Controllable Stress Distribution and Optimal Design of Flat Steel Ribbon Wound Pressure Vessel, Journal of Pressure Vessel Technology, 122,186-191.

[5] Dong, P., Welding, F., W., B., 2000. Residual Stresses and Effects on Fracture in Pressure Vessel and Piping Components: A Millennium Review and Beyond, Journal of Pressure Vessel Technology, 122,329-338.

[6] Mayer, H., Stark, H., L., Ambrose S., 2000. Review of fatigue design procedure for pressure vessels, International Journal of Pressure Vessels and Piping 77,775-771.

[7] Petrovic, A., 2001. Stress analysis in cylindrical pressure vessel with loads applied to the free end of a nozzle, International Journal of Pressure Vessels and Piping 78,485^193.

[8] Liu, Y., H., Zhang, B., S., Xue, M., D., Liu, Y., Q., Limit pressure and design criterion of cylindrical pressure vessels with nozzles, International Journal of Pressure Vessels and Piping, 81,619-624.

[9] Diamantoudis, A., Th., Kermanidis, Th., 2005. Design by analysis versus design by formula of high strength steel pressure vessels: a comparative study, International Journal of Pressure Vessels and Piping 82,43-50.

[10] Gao, B., Chen, X., Shi, X., Dong, J., 2010. An Approach to Derive Primary Bending Stress From Finite Element Analysis for Pressure Vessels and Applications in Structural Design, Journal of Pressure Vessel Technology, 132,061101-1-8.

[11] Carrera, E., Soave, M., 2011. Use of Functionally Graded Material Layers in a Two-Layered Pressure Vessel, Journal of Pressure Vessel Technology, 133,051202-1-11.

[12] Walker, M., Tabakov, P., Y., 2013. Design optimization of anisotropic pressure vessels with manufacturing uncertainties accounted for, International Journal of Pressure Vessels and Piping 104,96-104.

[13] Kim, E., S., Choi, S., K., 2013. Risk analysis of CNG composite pressure vessel via computer-aided method and fractography, Engineering Failure Analysis 27, 84-98.

[14] Cai, B., Liu, Y., Liu, Z., Tian, X., Ren, C., Abulimiti, A., 2013. Exploratory study on load and resistance factor design of pressure vessel for subsea blowout preventers, Engineering Failure Analysis 27,119-129.