Research Article Volume 6 Issue No. 3

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1 DOI / ISSN IJESC Research Article Volume 6 Issue No. 3 Pressure Vessel Analysis by Using FEM Prof. Chaudhari P. Sandip 1, Prof.Bhirud Pankaj P. 2, Prof.Trinkle Y. Saindane 3 Lecturer 1, H.O.D 2, WS 3 Department of Mechancial K.V.N.NaikPolytechnic,Nashik,Maharashtra,India Abstract: Pressure vessel is a closed container designed to hold gases or liquids at a pressure substantially different from the ambient pressure Most of the pressure vessels are designed as per ASME Code Section VIII in which Division 1 and Division 2 are normally used in design. The Division 1 corresponds to design by rule where as the Division 2 correspond to Design by Analysis. The significance of the title of the project comes to front with designing structure of the pressure vessel for static loading and its assessment by ANSYS. The finite element analysis for different configurations of pressure vessel on saddle supports is done using ANSYS. The equivalent stresses and deformation under operating condition analyzed by using ansys software and the optimal location when the saddles are placed away from heads is considered as the most suitable design for the large horizontal vessels. The effect of ring provided on the pressure vessel shell is considered. The thickness of shell without rings is maximum than the shell with ring for the same volume and same capacity of pressure vessel. The optimization of thickness is done which results huge reduction of weight. Keywords: Pressure Vessel, Finite Element Analysis, Optimization, Analysis etc. I. INTRODUCTION Pressure vessel is a closed container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. These vessels are designed to store reactive fluids and sustain chemical reactions that may occur in the vessel. So these pressure vessels are to be designed carefully to avoid failures which are mostly stress dependent. For this reason it becomes necessary to obtain the stress distribution in the pressure vessels. Hence there is a need to evaluate the operating stresses due to the imposed conditions by analytical methods. Furthermore we also need to understand the significance of these stresses on the structural integrity of the pressure vessel by considering the material properties of the vessel. Knowledge of the material behavior is necessary not only to ensure that the vessel can withstand the loading but also to make sure that the material has been chosen and utilized in an optimum manner. The rings can be provided over the shell or not provided. The stress distributions need to be analyzed for the both configurations of shell in operating case by FEM. Then the optimal thickness of shell is decided by using rings. The two types of analysis are commonly applied to pressure vessels. The most common method is based on a simple mechanics approach and is applicable to thin wall pressure vessels which by definition have a ratio of inner diameter (d) to wall thickness (t) of d/t 20. The second method is based on elasticity solution and is always applicable regardless of the d/t ratio and can be referred to as the solution for thick wall pressure vessels. Both types of analysis are discussed here, although for most engineering applications, the thin wall pressure vessel can be used.the stress analysis of pressure vessel, having shell with or shell without. In this work approximate the solution by using analytical method and by FEM in order to verify the solution. II DESIGN OF PRESSURE VESSEL Design a Horizontal type of pressure vessel. The vessel is designed for a 50 bar of internal pressure, 1bar atmospheric external pressure, and a maximum working temperature of 70⁰C. It is the horizontal pressure vessel. 2.1 Selection of Code The American Society of Mechanical Engineers set up a committee in 1911 for the purpose of formulating standard rules for the construction of steam boilers and other pressure vessels. This committee is now called the Boilers and Pressure Vessel committee. ASME Boiler and Pressure Vessel Code Section VIII, Division-1, Rules for the construction of the pressure vessel is used to design the pressure vessel. 2.2 Material Selection Material subjected to stress due to pressure shall conform to one of the specification given in section -II.The material use for the construction of pressure vessel is SA516GR70 and its properties are, Table: 4.1 Properties of Material Sr. No. Properties Values 1 Yield strength 260 N/mm 2 2 Tensile strength 485 N/mm 2 3 Modules of elasticity 2 x 10 5 N/mm 2 4 Poison s ratio Density of material 7833Kg/m 3 International Journal of Engineering Science and Computing, March

2 2.3 Maximum Allowable Stress S = maximum allowable stress (ASME SA 516 GR 70) Ultimate Tensile Strength = 483 N/mm 2 Yield Strength =262 N/mm 2 According to ASME section-viii division-1 taking factor of safety = 3.5, Then, S (maximum allowable stress) = 483/ 3.5= 138 N/mm 2 For design at Yield stress taking factor of safety 1.5 Then S = 262 / 1.5 = 174 N/mm 2 Though this value (UTS) is lower than (yield stress), Then, taking S = maximum allowable stress = 138 N/mm Thin Shell Design Taking fabrication and inspection quality into account, ASME has suggested modified formula for finding thickness for given pressure. 1. Circumferential Stress (Longitudinal Joint) t = or P = 2. Longitudinal Stress (Circumferential Joint) t = or P = Design Data Operating pressure = N/mm 2 (shell side)design pressure = 5 N/mm 2 Inside diameter = 295 mm,shell material - SA 516 GR.70,Permissible stress, S = 138 N/mm 2 Welding efficiency, E = 1 t = PR / ( SE- 0.6 P) + C, = 5*147.5 / (138*1 0.6 *5) +0, = mm t s = PR / (2SE P) + C, = 5 * / (2*138* *5) + 0, = 2.65 mm 2.5 Weight Calculation [8] Weight of Shell without = = = Kg Weight of Shell with = Weight of shell + Weight of rings = + = + = Kg 2.6.Ellipsoidal Head (Thickness Calculation) Material use SA516 GR70,E =1,Allowable Stress, S = 138 N/mm 2,P = 5 N/mm 2 Thickness of Head t = + C Where K is spherical radius factor K =, K = ( 2 + (295/73.75) 2 ) / 6,K = 1 Therefore, Thickness of Head ( t h ) = (5*295*1)/ (2*138*1 0.2*5) + 0 Thickness of Head ( t h ) = 5.37 mm. 2.7 Stress Analysis of Pressure Vessel i. Total longitudinal stresses 1) f 1 + f a = = N/mm 2 2) f a + f 2 = = N/mm 2 3) f a + f 3 = = N/mm 2 The resultant longitudinal stresses are well within the limit of allowable stress (138 N / mm 2 ) Therefore support design is safe. Circumferential Stress σ hoop =,σ hoop =, σ hoop = MPa ii. Stress at crown in Ellipsoidal head σ c =, σ c =, σ c = N/mm 2 This is also within permissible limit. Hence design is safe. III. FINITE ELEMENT ANALYSIS OF PRESSURE VESSEL BY USING ANSYS FEM PACKAGE The finite element analysis is a numerical technique for finding approximate solutions of partial differential equations as well as of integral equations. The solution approach is based on either eliminating the differential equation completely(steady state problems) or rendering the partial differential equation into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler s method, Runge-Kutta method etc. In the finite element method, a structure is broken down into many small simple blocks or elements. The behaviour of an individual element can be described with a relatively simple set of equations. Just as the set of elements would be joined together to build the whole structure, the equations describing the behaviour of the individual elements are joined into an extremely large set of equations that describe the behaviour of the whole structure. 3.1 Analysis of Pressure Vessel by FEM [12] In today s competitive environment it has become essential to reduce the time as well as cost of the design and analysis of complex geometry components. There are many approaches for carrying out the stress analysis. Experimental stress analysis by using strain gauges would have been good approach. However complicated shape would need very large number of strain gauges. Also the International Journal of Engineering Science and Computing, March

3 direction of principle stresses being not known, one will have to use rosette analysis making the work completed. Strain gauge analysis will be quite highly sophisticated equipment. Because of the complicated shape of the shell, stress analysis by using photo-elasticity will also be difficult. Stress analysis by finite element method is obviously the best choice. Hence finite element technique has been selected for the analysis purpose. There are different types of commercial F.E.M. software s available in the market. ANSYS FEM software is one of the most popular commercial software is used for the Finite element analysis of the pressure vessel. In Ansys there are three processors that are used in finite element analysis, i. Pre-processor ii. Solution or Processor. iii. General postprocessor. Fig.1. Pressure Vessel Model without i. Pre-processor: in pre-processor following steps involved. 1) Define element type. 2) Define element real constant. 3) Define material properties 4) Create model or geometry. 5) Define meshing controls 6) Mesh the object created. ii. Solution or processor The solution processor has the commands that allow you to apply boundary conditions and loads and it solves for nodal solutions. iii. General Postprocessor It contains the commands that allow us to list and display the result of analysis. 3.2 Define the Element [5] Ansys provides more than 150 various elements to be used to analyze different problems. Selecting the correct element type is a very important part of the analysis process.in ANSYS each element type is identified by category name followed by a number. PLANE -42 is a four node quadrilateral element used to model structural solid problems. The element is defined by four nodes having two degrees of freedom at each node. Translation in x and y direction. Fig.2. Pressure Vessel Model with 3.4 Define Meshing Control In this step the created geometrical model is discretized into nodes and elements. The process is called meshing. The Ansys program can automatically generate the nodes and elements, provided that we specify the element size. The element size controls the fineness of the mesh. The smaller the element size the finer the mesh 3.3 Modelling: Rings having Uniform Thickness 6 mmrings having Uniform Thickness 4 mm Fig.3Meshing Model of Pressure Vessel. 3.5 Solution [6] In this phase the following steps involved. International Journal of Engineering Science and Computing, March

4 Von Mises Stress ( N/mm ) 3.5.1Loading and Boundary Conditions In this work applied boundary conditions are as per shown in fig 1.and those are at support. The pressure applied inside the shell is 5 MPa as shown in fig.4 Fig. 7. Equivalent Stresses in Pressure Fig. 4.Internal Pressure Applied General Postprocessor 3.6 Analysis of Pressure Vessel with Fig 8. Total Deformation of Pressure Vessel without without Rings Fig 5 Equivalent Stress in Pressure 3.8 FEA of Pressure Vessel with Different Types of Different Elements. 3.9Comparison of Different Elements: Fig. 6. Total Deformation of PressureVessel with Rings. 3.7Analysis Pressure Vessel without Ring Shell 281 plane 181 shell tetsolid Elements Von Mises Stresses at Head Von Mises stresses in shell without Von Mises stresses in shell with Fig. 9. Chart of Von Mises Stress in N/mm 2 vs different Elements International Journal of Engineering Science and Computing, March

5 Von-mises stress (N/mm²) Von -mises stresses (N/mm ) Von-mises Stress (N/mm ) By finite element analysis we get following results by considering internal pressure is 50 bar at 70⁰ Celsius. Von Mises Stresses in shell with observed MPa and Von Mises Stresses in shell without observed MPa. Fig no 9 shows that by varying element we get different result. For fine meshing we obt ained most close result Fig 10.Graph of Von Mises Stress at Head vs different elements. Fig no.10 shows a graph of Von Mises stress in head vs different elements. It shows that for element shell 281 Von Mises stress at head is 144 MPa, for element plane 181 Von Mises stress at head is 146 MPa and for element shell 181 Von Mises stress at head is MPa, Shell 281 plane 181 shell tetsolid Types of Elements Shell 281 plane 181 shell tetsolid Types of Elements Fig 11.Graph of Von Mises Stress in shell without vs different Elements Von Mises Stresses at Head Von Mises stresses in shell without Fig. 11. shows a graph of Von Mises stress in shell without vs different elements. It shows that for element shell 281 Von Mises stress in shell without is 96 MPa, for element plane 181 Von Mises stress in shell without is MPa and for element shell 181 Von Mises stress in shell without is 94 MPa. Fig 12. Graph of Von Mises Stress in Shell with vs different Elements Fig no. 12. shows a graph of Von Mises stress in shell with vs different elements. It showsthat for element shell 281 Von Mises stress in shell with is 92. MPa, for element plane 181 Von Mises stress in shell with Mises stress in shell with is 91 MPa. is MPa and for element shell 181 Von IV. RESULT AND DISCUSSION 4.1 Comparison of Shell Geometry Sr. No Element Types Shell 281 plane 181 shell 181 Types of Elements No. of Elements 4 tetsolid Von Mises stresses in shell with Von Mises Stress in Pressure vessel ( N/mm 2 ) Stresses At Head Stresses in shell without 1 Shell Stresses inshell with 2 Plane Shell tetsolid Table 3. shows the comparison FEA stresses between shell without and shell with. Maximum stress MPa is observed in shell without, Von-Mises stresses observed in shell without and shell with is MPa and MPa respectively. Stress intensity observed in shell without and shell with is MPa and MPa respectively. Total deformation in shell without and shell with observed 0.48 mm and 0.50 mm respectively. International Journal of Engineering Science and Computing, March

6 Weight (Kg) Deformation (mm) Table 3 Comparisons according to Shell Geometry Shell Geometr Thickness of Shell (mm) Weight (Kg) Max Stress (MPa) Von-Mises Stress (MPa) Stress Intensity (MPa) Total (mm) Defor-mation Shell without Shell With Shell Without Shell with Types of Shell Fig. 13.Bar Chart showing deformation of Shell without and Shell with From fig no 13. shows that deformation of shell without and shell with. From this graph total deformation occur during operating case in shell without is 0.48 mm andtotal deformation occur during operating case in shell with is 0.5 mm that is deformation is approximate same Shell without Types of Shell Fig.14 Graph of Weight Vs Shell types Shell with From Table 3. Weight of shell without and shell with is Kg and Kg respectively. Fig14shows graph of Weight verses shell geometry and from this it is clear that,for same volume and capacity shell with having weight is less up to 20%than shell without. Here reduction material is achieved with optimization of thickness. Total material cost is reduced by 20% and fabrication cost is same. Hence overall cost of pressure vessel is reduced by 14%. V. CONCLUSION: i. In the analytical stress analysis, it is found that the maximum stress in the pressure vessel is N/mm 2 which is less than allowable stress 260 N/mm 2.Hence design of pressure vessel using ASME codes is very safe. ii. From Table 2. it is found that different types of finite elements behavior is different for the same operating or load conditions and it is observed that PLANE-182 Element gives approximate close results at vessel shell and head. iii. By comparing analytical design and the finite element analysis of that design it is observed that there is 8-10% result variation between the both methods. iv. From Table no.3.stresses obtained in pressure vessel with ring and pressure vessel without ring is approximately same. Keeping the capacity of vessel constant the optimization of shell thickness is achieved by the provision of ring over the shell. 20% weight reduction is achieved for shell alone. v. Hence it is concluded that addition of rings helps to reduce the thickness of the shell by 25% compare to pressure vessel without s, which in turn helps in saving of material and cost associated with it. The overall cost reduction is achieved up to 14 %. REFERENCES: [1] Andrew P. F. Little, Carl T. F. Ross and David Flowers A Theoretical and Experimental Investigation of Externally Ring Stiffened Cylindrical Pressure Vessels Subjected to External Pressure, proceedings of the International Conference on Computing in Civil and Building Engineering, University of Portsmouth,, Issue 3, International Journal of Engineering Science and Computing, March

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