ISSN 2321-6441 STRESS ANALYSIS OF PRESSURE VESSEL WITH DIFFERENT END CONNECTIONS 1 APSARA C. GEDAM, 2 Dr. D. V. BHOPE 1 PG Student, M.Tech (CAD/CAM) R.C.E.R.T., Chandrapur (MH) 2 Professor, Department of mechanical engineering R.C.E.R.T., Chandrapur (MH) ABSTRACT A thin cylindrical pressure vessel has been analyzed for different end connections using analytical and finite element analysis. The main objective of project is to compare stress distribution in the pressure vessel for different end connections viz. hemispherical, flat circular, standard ellipsoidal and dished shape. The various dimensions of pressure vessel like internal diameter, thickness of vessel and end connections has been decided using analytical design and three dimensional model is prepared in modeling software Pro-E and analyzed using FE tool ANSYS. The analysis has been carried out for 2-D axysymmetric analysis, 3-D horizontal pressure vessel with saddle support and vertical pressure vessel over the stand. Keywords:-, hemispherical end, ellipsoidal end, flat circular end, dished end, ANSYS 1.INTRODUCTION Tanks, vessel and pipelines that carry, store or receive fluids are called pressure vessel. A pressure vessel is defined as a container with a pressure differential between inside and outside.the Pressure vessels are usually spherical or cylindrical with dome end. The cylindrical vessels are generally preferred because of the simple manufacturing process and make better use of the available space. Boiler, heat exchanger, chemical reactor and so on, are generally cylindrical. Cylindrical vessels are design and manufactured with different end connections viz. hemispherical, flat circular, ellipsoidal and dished shape. Analysis of cylindrical pressure vessel is done for internal pressure of 2 Mpa. Circumferential and longitudinal stresses are determined for given geometry. Analytical solution of the same is determined and Comparison of the result is carried out. Following data is used for the analysis. Inner dia. = 250 mm, thickness = 5 mm, internal Pressure = 2 Mpa, Material properties: Material selected is mild steel with E=200 Kpa & µ = 0.3. 2. ANALYTICAL SOLUTION Analytical solution is determined for cylindrical pressure with different end connections using following equations The hoop stress in cylinder is given by, given by, The Longitudinal stress in cylinder is a) Thickness of Dished shape cover plate b) Thickness of Standard Ellipsoidal shape cover plate c) Thickness of Hemispherical shape cover plate d) Thickness of Flat circular Coverplate Page 19
IPASJ International Journal of Mechanical Engineering (IIJME) ISSN 2321-6441 3. FINITE ELEMENT ANALYSIS Using the technical specification of vessel, the FE analysis has been carried out in ANSYS. A higher order 3-D, 10-node element having three degrees of freedom at each node ( translations in the nodal x, y, and z directions SOLID187) and 2-D, 8- node element having two degree of freedom at each node ( translation in the nodal x and y directions PLANE 183) are used. The Inner Diameter of cylinder is 250 mm, Internal Pressure is 2 Mpa and Thickness of vessel is5mm. Case-1: Finite element analysis of axysymmetric pressure vessel with different end connections The two dimensional model is prepared in the geometry environment of ANSYS which is meshed with 8-node PLANE 183 element. The FE analysis has been carried out for four end connections. The results computed for circumferential and longitudinal stresses are shown in figure 3.1(a), 3.1(b), 3.2(a), 3.2(b), 3.3(a), 3.3(b) 3.4(a) and 3.4(b) respectively. Fig 3.1 (a) Circumferential Fig 3.1 (b) Longitudinal Fig3.1: Circumferential and longitudinal stresses in hemispherical end pressure vessel Fig 3.2 (a) Circumferential Fig 3.2 (b) Longitudinal Fig3.2: Circumferential and longitudinal stresses in flat circular end pressure vessel Fig3.3 (a) Circumferential Fig.3.3 (b) Longitudinal Fig3.3 Circumferential and longitudinal stresses in dished end pressure vessel Page 20
IPASJ International Journal of Mechanical Engineering (IIJME) ISSN 2321-6441 Fig 3.4(a) Circumferential Fig.3.4(b) Longitudinal Fig.3.4 Circumferential and longitudinal stresses in ellipsoidal end pressure vessel Case-2: Finite element analysis of horizontal pressure vessel with saddle support. FE analysis of horizontal pressure vessel with saddle support having distance of 250 mm between two saddles has been carried out by applying boundary condition of fixed support at bottom and side face of saddle. The result so Obtained for circumferential and longitudinal stresses are shown in fig. 3.5(a), 3.5(b), 3.6(a), 3.6(b), 3.7(a), 3.7(b), 3.8(a) and 3.8(b) for hemispherical, flat circular, dished and ellipsoidal end vessels respectively. Fig 3.5 (a) Circumferential stress Fig.3.5 (b) Longitudinal stress Fig 3.5 Circumferential and longitudinal stresses in hemispherical end pressure vessel with saddle support Fig 3.6(a) Circumferential stress Fig.3.6 (b) Longitudinal stress Fig 3.6 Circumferential and longitudinal stresses in flat circular end pressure vessel with saddle support Page 21
ISSN 2321-6441 Fig 3.7(a) Circumferential stress Fig3.7 (b) Longitudinal stress Fig 3.7 Circumferential and longitudinal stresses in Dished end pressure vessel with saddle support Fig 3.8(a) Circumferential stress Fig 3.8 (b) Longitudinal stress Fig 3.8 Circumferential and longitudinal stresses in ellipsoidal end pressure vessel with saddle support Case-3: Finite element analysis of vertical pressure vessel with straight leg support FE analysis has been carried for vertical pressure vessel having three straight legs support. The legs are mounted at the interval of 1200 which are fixed at the bottom end. Due to internal pressure, circumferential and longitudinal stresses are shown in figure 3.9(a), 3.9(b), 3.10(a), 3.10(b), 3.11(a), 3.11(b), 3.12(a) and 3.12(b) respectively. Fig 3.9 (a) Circumferential stress Fig 3.9 (b) Longitudinal stress Fig 3.9 Circumferential and longitudinal stresses in hemispherical end vertical pressure vessel with three leg support Page 22
IPASJ International Journal of Mechanical Engineering (IIJME) ISSN 2321-6441 Fig 3.10 (a) Circumferential stress Fig 3.10 (b) Longitudinal stress Fig 3.10 Circumferential and longitudinal stresses in flat circular end vertical pressure vessel with three leg support Fig 3.11(a) Circumferential stress Fig 3.11 (b) Longitudinal stress Fig 3.11 Circumferential and longitudinal stresses in dished vertical pressure vessel with three leg support Fig 3.12 (a) Circumferentia Fig 3.12 (b) Longitudinal stress Fig 3.12 Circumferential and longitudinal stresses in ellipsoidal end vertical pressure vessel with three leg support 4. RESULTS AND DISCUSSION Results of FE axysymmetric analysis, horizontal pressure vessel with saddle support and vertical pressure vessel with straight leg support are tabulated in table 4.1, 4.2 & 4.3 respectively. Comparison of stresses for respective cases is shown in fig 4.1, 4.2 & 4.3 respectively. Compare to 2D axysymmetric analysis, 3D analysis of horizontal pressure vessel and vertical pressure vessel are in good agreement. The tabular representation of stress distribution for all these cases are shown in table 4.4 and graphical representation of stresses is shown in fig 4.4. Page 23
ISSN 2321-6441 Table 4.1 Finite element analysis of 2D axysymmetric pressure vessel Sr. No. Type of Pressure Vessel Von Mises Normal (x) Normal (y) Maximum Principal Minimum Principal es on End Connection 1 Hemispherical 71.35 106.63 60.372 125.05 41.95 48.075 2 Flat Circle 75.121 109.74 63.73 128.02 45.45 101.76 3 Dished 92.29 130.35 74.8 153.56 51.59 109.14 4 Ellipsoidal 66.53 106.22 58.389 118.15 46.45 91.48 Fig 4.1 Comparison of stresses in pressure vessel with different end connections. Table 4.2: Finite Element Analysis of Horizontal Pressure Vessel with Saddle Support Sr. No. Type of Pressure Vessel Von Mises Normal (x) Normal (y) Maximu m Principal Minimu m Principa l es on End Connection 1 Hemispherical 111.4 110.51 43.37 121.67 28.02 58.75 2 Flat Circle 516.45 522.37 128.1 565.14 66.81 501.46 3 Dished 124.06 124.16 58.238 130.47 16.68 97.48 4 Ellipsoidal 160.61 157.29 76.502 165.5 11.89 140.14 Page 24
ISSN 2321-6441 Fig 4.2 Comparison of stresses over horizontal pressure vessel with saddle Sr. No. Table 4.3: Finite Element Analysis of Vertical Pressure Vessel with three Leg Support Type of Von Normal Normal Maximum Minimum es on Pressure mises Principal Principal End Connection Vessel stress (x) (y) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) 1 Hemispherical 113.14 104.64 62.4 112.42 22 56.71 2 Flat Circular 478.9 466.21 91.88 520.19 36.38 480.46 3 Dished 127.28 118.98 55.56 128.3 11.74 132.14 4 Ellipsoidal 157.81 163.7 73.14 163.7 5.62 92.48 Fig 4.3 Comparison of stresses in vertical pressure vessel with three leg support Page 25
ISSN 2321-6441 Table 4.4 Comparison of FE analysis of 2-D axysmmetric analysis and 3-D analysis for horizontal and vertical pressure vessel : Sr. Type of Von Maximum Minimum Normal Normal No. Pressure Vessel Mises Principal Principal (x) (y) stress (MPa) (MPa) (MPa) (MPa) (MPa) (A) FE Analysis of 2-D Axysymmetric Pressure Vessel 1 Hemispherical 71.35 106.63 60.372 125.05 41.95 2 Flat Circular 75.121 109.74 63.73 128.02 45.45 3 Dished 92.29 130.35 74.8 153.56 51.59 4 Ellipsoidal 66.53 106.22 58.389 118.15 46.45 (B) FE Analysis of Horizontal Pressure Vessel with Saddle Support 1 Hemispherical 111.14 110.51 43.37 121.67 28.02 2 Flat Circular 516.45 522.37 128.1 565.14 66.81 3 Dished 124.06 124.16 58.238 130.47 16.68 4 Ellipsoidal 160.61 157.29 76.502 165.5 11.89 (C) FE Analysis of Vertical Pressure Vessel with three Leg Support 1 Hemispherical 113.14 104.64 62.4 112.42 22 2 Flat Circular 478.9 466.21 91.88 520.19 36.38 3 Dished 127.28 118.98 55.56 128.3 11.74 4 Ellipsoidal 157.81 163.7 73.14 163.7 5.62 The FE analysis for all cases shows that, the stresses are very high for flat circular end as compared to all other types of ends. The Von Mises stresses are is in the range of 57 to 160 MPa for hemispherical, dished and ellipsoidal end. The comparison of stresses for all cases is shown in figure 4.4. Page 26
ISSN 2321-6441 Fig 4.4 Comparison of von Mises stresses for 2-D axysymmetric analysis and 3-D analysis for horizontal and vertical pressure vessel. 5. CONCLUSION From FE analysis of horizontal pressure vessel it is observed that, the magnitude of stresses is very high for flat circular end pressure vessel while magnitude of stresses is lower in case of hemispherical and dished end pressure vessel. The results obtained for vertical pressure vessel is similar to horizontal pressure vessel having very high stresses in flat circular end vessel and lower stresses in hemispherical and dished end pressure vessel. From the complete analysis it can be concluded that, hemispherical end and dished ends are better end connections for pressure vessel and flat circular end is not preferable for pressure vessel. Also the arc length of saddle support does not have appreciable effect on stresses for horizontal pressure vessel and the length of leg support also have very marginal effect on stresses in vertical pressure vessel. REFERENCES [1] Adithya M. M, M. M. Patnaik, Finite Element Analysis of Horizontal Reactor Pressure Vessel Supported on Saddles, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 2, Issue 7, July 2013 [2] L. P. Zick, es in Large Horizontal Cylindrical Pressure Vessels on Two Saddle Supports, Reprinted from Welding Journal Research Supplement, 1971.Journal of Engineering Research and Applications, Vol. 2, Issue 3, May-Jun 2012. [3] Heckman, David, Finite element analysis of pressure vessels, MBARI 1998. [4] Yogesh Borse, Avadesh Sharma, Modelling of Pressure Vessels with differentend Connections using Pro Mechanics, International Journal of EngineeringResearch and Applications, Vol. 2, Issue 3, May-Jun 2012, pp.1493-1497. [5] D. Dinesh Babu, T JeganBalaji, Theoretical and Finite Element Analysis of High Pressure Components, www.iosrjen.org. Vol. 3, Issue 2, Feb 2013, PP 25-34. [6] Yashraj Jaywant SalunkeProf. K. S. Mangrulkar, Analysis of acomposite Cylinder for the Storage of Liquefied Gases, International Journal ofengineering Trends and Technology (IJETT) Volume 13 Number 8 Jul 2014. [7] Laxmikant D. Rangari, P. M. Zode, P.G. Mehar, Analysis of LPG Cylinder Using Ansys Software, International Journal of Engineering Researchand Applications, Vol. 2, Issue4, 2012, pp.2278-2281. Page 27