3-IJAEST-Volume-No-2-Issue-No-2-A-Study-on-the-Effect-of-Cross-Section-Approximation-on-the-Behaviou by ISERP ISERP

AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 2, Issue No. 2, 132 - 138

A Study on the Effect of Cross Section Approximation on the Behaviour of Pipe Bends with Ovality and Thinning T. Christo Michael

AR. Veerappan*

S. Shanmugam

Department of Mechanical Engineering, National Institute of Technology, Tiruchirappalli – 620 015, Tamilnadu, INDIA. * Corresponding author email: aveer@nitt.edu

Keywords- Axisymmetric, Bend angle, Bend radius, Ovality, Pipe bend, Thinning.

INTRODUCTION

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Pipe bends are critical components in piping systems and generally are the most economical means of changing directions while providing flexibility and end reactions to piping systems within the allowable limits [1]. The bend section may be a potential source of damage during service, due to internal pressure and other loads, particularly in the cases where significant ovality and wall thickness variation (thinning/thickening) exist, which are introduced during the manufacturing process[2 - 4]. The acceptability of pipe bends depends on the magnitude of these shape imperfections [5]. For numerical investigation when ovality is considered, the cross section of the pipe bend is often assumed to be perfectly oval or elliptical [6 - 9] as shown in Fig. 1(a). Distortion in cold bend tubes is usually limited to the outer half of the bend where flattening occurs and the distortion can be described by a semi-oval/semi-round section [10] as shown in Fig. 1(b). Both the aforesaid shapes do not represent the true cross section of pipe bend but are only approximated. In industries generally the contour of the pipe bend cross sections are captured in their first off trial test (FOT) to study and accept the pipe bends with ovality and thinning/thickening. The

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contours reveal that the cross section is neither elliptical nor semi oval. Nevertheless, as literatures propose, elliptical and semi oval cross sections are employed to analyse the pipe bend analytically and numerically. Analyses in pipe bends rely on the assumptions of constant wall thickness along the contour of the pipe’s cross section and no initial ovality [11]. However, the majority of shortradius curved pipes are made using a forming process, and, as a result, have variable wall thickness along the contour of the pipe’s cross section. The pipe wall is thinner than nominal on the convex side and is thicker on the concave one [11]. Bending of a curved pipe is accompanied by the flattening forces. They transform initial circular cross sections of a pipe into oval cross sections [12]. Ovality is a main defect in all pipe bending techniques [13]. The current study aims at determining the effect of shape approximation in cross section on induced stresses in pipe bend by comparing the stress induced in elliptical and semi oval cross sections of pipe bend with each other and with those obtained from actual cross section taken from FOT reports. The effect of ovality and thinning/thickening is studied for the assumed cross sections. Studying the combined effect of ovality and thinning/thickening is more significant in the stress analysis than studying the shape imperfections individually as the real geometry of pipe bend has both the irregularities. Previous study has shown that when internal pressure is the predominant load, in a 90° pipe bend, without considering initial ovality and variable wall thickness, 2D axisymmetric models provide accurate stress results compared with those obtained from 3D models [14]. The determination of the effect of ovality and thinning on the performance of 2D and 3D pipe bends was done and it was observed that they produce comparable results [15]. Hence 2D models have been used to determine the effect of shape approximation on the induced stresses in the present analysis. The effect of bend radius on the induced stress was also studied for the elliptic and semi elliptic sections by considering four different bend radii namely 101.6 mm, 152.4 mm, 203.2 mm and 304.8 mm.

Abstract— The effect of cross section approximation on the behaviour of pipe bends with shape imperfections under internal pressure was performed numerically. Two cross sections namely elliptical and semi oval were taken for analysis. FE analyses were performed on these cross sections. The hoop stress induced due to internal fluid pressure load was obtained for the models. On comparison, the stress induced in the elliptic and semi oval sections differed by a large amount. Five cross sections from first off trial report which is the actual cross section at the bend section were analysed and the stress induced was compared with the elliptic and semi oval cross sections. The results confirmed that approximation in cross section produces considerable effect on the induced stresses. The effect of bend radius and the combined effect of ovality and thinning/thickening on the stress developed were studied for the assumed (elliptic and semi oval) cross sections and compared

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AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 2, Issue No. 2, 132 - 138

DEFINITIONS

III

ASSUMPTIONS

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The following assumptions are made in the analysis: Linear behaviour, homogeneous isotropic material, and steady static state loading. The effects of the following are not considered in the present evaluation: Bourdon’s effect, external pressure, external forces, external moments, centrifugal forces due to change of fluid flow direction, effects of friction between the pipe inside fluid and the pipe bend inner surface, fluid turbulence, interfaces between the straight pipe and pipe bend, tolerances and deviations of the straight pipe before fabricating into pipe bend and pipe bend surface roughness [5, 6]. IV

INPUT DATA

The parameters considered for analysing the assumed cross sections (elliptic and semi elliptic) is given below. Pipe Parameters

Specification

Material

ASME SA234 WPB [19]

Internal Pressure

10 MPa

Outside Diameter

114.3 mm

Nominal Thickness

8.56 mm

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Bend Radii

101.6, 152.4, 203.2 and 304.8 mm

Percent Ovality

0% to 20% in steps of 5%

Percent Thinning/Thickening

0% to 20% in steps of 5%

Percent ovality C0, thinning Ct, and thickening Cth, are defined as follows [16 – 18]: Dmax  Dmin  (1) Co   100 Dmax  Dmin  2 t  t min   100 (2) Ct  t t  t (3) Cth  max  100 t

(b) Semi elliptic section (a) Elliptic section Fig. 1 Assumed pipe bend sections for the analysis

V ANALYSIS AND COMPARISON BETWEEN ELLIPTIC AND SEMI ELLIPTIC CROSS SECTIONS The elliptic cross section of a typical bend is assumed to become a perfect ellipse after bending as shown in Fig. 1(a). The major axis of the elliptical shape of pipe bend is assumed to be perpendicular to the plane of bending of the pipe bend. The minor axis of the elliptical shape of pipe bend is assumed to be in the plane of pipe bend. The pipe bend is assumed to be smooth, without ripples. The assumed semi elliptic cross section is shown in Fig. 1(b). 5.1 Stress Analysis The finite element method is a numerical analysis technique used by engineers, scientists, and mathematicians to obtain solutions to the differential equations that describe, or approximately describe a wide variety of physical and nonphysical problems. During the last three decades considerable advances have been made in the applications of numerical techniques to analyze pressure vessel and piping problems. Among the numerical procedures, finite element methods are the most frequently used [20]. 5.1 Methodology In this paper linear static analyses were carried out using the commercial FE program ANSYS v12. A scripting language, APDL (ANSYS Parametric Design Language) [21], was used to automate the common tasks and build the model in terms of parameters. By exploiting symmetry one half of the problem was modelled for the 2D models. The axisymmetric model was meshed with PLANE183 [22] quadrilateral elements. The FE models, after supplying necessary boundary and loading conditions, were solved. The required output results were

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AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 2, Issue No. 2, 132 - 138

5.2 Pre-Processing The 2D axisymmetric cross sections were modelled using PLANE183 element with axisymmetry option. PLANE183 is a higher order 2-D element. It has quadratic displacement behavior and is well suited to modeling irregular meshes. This element is defined by 8 nodes having two degrees of freedom at each node: translations in the nodal x and y directions. The element may be used as a plane element (plane stress, plane strain and generalized plane strain) or as an axisymmetric element. Material properties namely modulus of elasticity and Poisson’s ratio were specified to the models. The axisymmetric model was generated using mapped meshing ensuring proper aspect ratio. The total number of elements for the axisymmetric model is chosen as 60 with 3 elements across the thickness of the pipe cross section to develop the mesh model. Symmetry boundary condition was supplied to the models. Internal fluid pressure load was applied to the inner surface of the models.

aforementioned, apply the internal pressure load and solve the problem. Input diameter, thickness, bend radius and material properties

Ovality = 0

If Ovality ≤ 20

yes Thinning = 0

obtained, using APDL commands and directly written into an excel file.

If Thinning ≤ 20

5.3 FE Analysis

Yes

Model creation Constraints

Ct = 10 Co = 10 R = 152.4 mm

Load

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Solution

(a) Elliptic cross section

Thinning + 5 Ovality + 5

Ct = 10 Co = 10 R = 152.4 mm

Hoop stress at intrados and extrados written as an Excel file

(b) Semi elliptic Fig. 2 Meshed models with constraints and load The models were solved to obtain the required results. The programmes using APDL were written to create the models with various combinations of ovality and thinning/thickening from 0% to 20 % in steps of 5%, constraint the models as

Stop

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Fig. 3 Flow chart for the APDL program The hoop stress values obtained at intrados and extrados sections of the two cross sections of pipe bend were written into an excel file.

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AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 2, Issue No. 2, 132 - 138

5.5 Interpretation of Stress Analysis Results

20 15 10 5

25 20

Ovality, %

Fig. 6 Percent difference in hoop stress between elliptic and semi elliptic sections at the intrados for R = 152.4 mm

10 5 0 0

10 Ovality, %

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Fig. 4 Percent difference in hoop stress between elliptic and semi elliptic sections at the intrados for R = 101.6 mm 16

Hoop stress difference, %

5.4 The Computer Program A program was written in APDL to create the models, analyze and get the results into a separate file which is then plotted as graphs for all different problems. Fig. 3 shows the flowchart of the program. The program prompts the user to enter the pipe diameter, bend radius, thickness, internal pressure and material properties. On giving the required input, the program creates the models in sequence keeping ovality constant at 0% and varying thinning/thickening from 0% to 20 % in steps of 5%, applies the internal pressure load and solves the problem. Hoop stress values at intrados and extrados sections are obtained and written into an Excel file. The ovality is then incremented in steps of 5% up to 20% repeating all the other steps. The procedure is repeated for other bend radii.

Fig. 4 shows the absolute percentage difference in the hoop stress values at the intrados between elliptic and semi elliptic models for bend radius 101.6 mm. It can be observed that this difference increases with increase in ovality. For constant ovality, increase in thinning also causes an increase in this difference. At the extrados section (Fig. 5), the difference is less compared to the intrados section but still large in magnitude, the minimum and maximum being 9.62% and 14.75% respectively.

Hoop stress difference, %

Fig. 2 shows the meshed model of elliptic (Fig. 2(a)) and semi elliptic (Fig. 2(b)) cross sections with boundary conditions and internal pressure load.

20 15 10 5 0

8 6 4 2 0

Ovality, %

Fig. 5 Percent difference in hoop stress between elliptic and semi elliptic sections at the extrados for R = 101.6 mm

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10 Ovality, %

Fig. 7 Percent difference in hoop stress between elliptic and semi elliptic sections at the extrados for R = 152.4 mm

As the bend radius is increased to 152.4 mm, at the intrados, the difference increases with increase in thinning for 5% ovality alone. As ovality is increased beyond 5%, the difference decreases with increase in thinning keeping ovality constant (Fig. 6). At the extrados, increase in ovality keeping thinning constant causes an increase in the difference percentage (Fig. 7). The maximum and minimum percentage difference at the intrados are 28.77% and 6.99% respectively while it is 21.76% and 1.53% respectively at the extrados. As the bend radius is increased to 203.2 mm, 5% ovality produces a decrease in the difference with increase in thinning at the intrados (Fig. 8) and extrados (Fig. 9). As ovality is

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AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 2, Issue No. 2, 132 - 138

increased to 10% and beyond, increase in thinning causes an increase in the percentage difference in hoop stress between elliptic and semi elliptic cross sections. The maximum difference is as high as 38.28% at the intrados and 28.53% at the extrados while the minimum difference at these sections are 2.23% and 7.26% respectively, both occurring at 20% thinning and 5% ovality. 40 35

25 20 15 10 5 0 0

10 Ovality, %

40 30 20 10 0

Fig. 8 Percent difference in hoop stress between elliptic and semi elliptic sections at the intrados for R = 203.2 mm

10 Ovality, %

Fig. 10 Percent difference in hoop stress between elliptic and semi elliptic sections at the intrados for R = 304.8 mm

15 10 5 0

10 Ovality, %

Fig. 9 Percent difference in hoop stress between elliptic and semi elliptic sections at the extrados for R = 203.2 mm The percent difference in hoop stress increases with increase in bend radius. Figures 10 and 11 show the percent variation in the hoop stress values between elliptic and semi elliptic cross sections at the intrados and extrados respectively for bend radius of 304.8 mm. The maximum difference is observed at this bend radius. At the intrados, the difference is as high as 55.01% while at the extrados it is 38.37%. For all bend radii, the models with 0% ovality and thinning varying from 0% to 20% yield the same hoop stress for both the cross sections considered, since for these combinations of ovality and thinning, both the assumed cross sections become the same i.e. circular with thinning, hence validating the modeling and analysis procedure used.

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Hoop stress difference, %

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Hoop stress difference, %

It has been observed that the common assumptions of elliptic and semi elliptic cross sections found in literature do not give comparable results. The difference between the results is very high and therefore unacceptable. The general observation is that at the intrados, up to R = 203.2 mm, the semi elliptic models yielded higher values than the elliptic models while for R = 304.8 mm, the elliptic models gave higher hoop stress values than semi elliptic models. At the extrados, the elliptic cross section gives higher values for most of the combinations of bend radius, ovality and thinning.

35 30 25 20 15 10 5 0

10 Ovality, %

Fig. 11 Percent difference in hoop stress between elliptic and semi elliptic sections at the extrados for R = 304.8 mm VI

REAL CROSS SECTION ANALYSIS AND COMPARISON

The pipe manufacturing industries always accept or reject pipe bends based on the magnitude of shape imperfections obtained from the first off trial reports. The pipe after bending is cut at the bend section, the impression at this section is taken on a graph paper, thinning and ovality measurements are made from these impressions and based on the magnitude of these imperfections the pipe bend is accepted or rejected. Hence it would be realistic to analyse real time pipe bend cross sections

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AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 2, Issue No. 2, 132 - 138

obtained from these reports for the stresses induced. Five cross section impressions as shown in Fig. 12 were taken for the analyses. The details of these bend sections is given in table 1. Table 1 Details of the actual cross sections considered for analysis Id No. A B C D E

Diameter, mm

Thickness, mm

5.0

Bend Radius, mm 31.75 38.00 51.00 95.25 121.00

Thinning, %

Ovality, %

17.31 8.75 15.19 13.09 20.4

1.28 4.58 4.26 8.64 5.57

extrados sections were extracted. The elliptic and semi elliptic models were also modelled to the dimensions of the actual cross section and solved to obtain the hoop stress induced. Fig. 13 shows the steps involved in the creation of the actual model.

Id No. D

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Id. No. C

Id No. B

Id No. A

Id No. E Fig. 12 Scanned image of the actual cross sections considered for analysis The FOT reports of these cross sections were first scanned and the image was converted into an AutoCAD drawing file. Necessary corrections were made to the image in AutoCAD and the drawing was saved and converted into IGES file and imported into ANSYS and necessary corrections in the model was done. The ANSYS models were meshed with PLANE183 elements and solved after applying necessary constraints and internal pressure load. The hoop stress induced at intrados and

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(b) AutoCAD image

(a) Scanned image (Id No. E)

(c) Actual cross section imported into ANSYS, meshed, constrained and internal pressure applied Fig. 13 Steps involved in creation of the actual cross section Table 2 Percentage difference in hoop stress between actual and assumed cross sections Id No. A B C D E

Comparison Between Actual and Elliptic Cross Sections, %

Comparison Between Actual and Semi Elliptic Cross Sections, %

Intrados

75.08 72.00 22.02 22.72 37.89

Extrados

32.51 21.07 9.75 25.14 48.17

70.95 86.29 36.38 7.27 56.35

Extrados

29.46 33.98 23.03 45.94 57.74

The actual cross section was compared with elliptic and semi elliptic sections for the hoop stress induced due to internal fluid pressure load. Table 2 gives the absolute percentage difference in the stress values between actual cross section and assumed cross sections. It can be seen that the difference is large. It was observed that the stress induced in the actual cross section was higher than the assumed sections for Id No. A, B and C while for Id. No. D and E, it was lower than the assumed sections.

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AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 2, Issue No. 2, 132 - 138

CONCLUSIONS

Stress analysis carried out for the assumed and actual pipe bend cross sections show that they are not comparable. The actual cross sections taken from FOT reports gave results much different from the assumed sections. Therefore the pipe bend analysis needs to be necessarily carried out with actual cross section models to obtain its actual performance which will lead to a better design and will also improve the procedure involved in accepting/rejecting pipe bends based on the shape imperfection. Higher bend radii can cause a greater difference in the stresses induced between elliptic and semi elliptic sections. REFERENCES Reno C King, Piping Handbook, 5th ed., McGraw-Hill Book Company, 1973. [2] B.P. Patel, C.S. Munot, S.S. Gupta, C.T. Sambandam, M. Gunapathi, “Application of higher order finite element for elastic stability analysis of laminated cross-ply oval cylindrical shells” Finite Elements in Analysis and Design, vol. 40, pp. 1083 – 1104, 2004. [3] T.H. Hyde, W. Sun, J.A. Williams, “Life estimation of Pressurised Pipe Bends Using Steady-State Creep Reference Rupture Stress”, International Journal of Pressure Vessels & Piping, vol. 79, pp. 799805, 2002. [4] T.H. Hyde, A.A. Becker, W. Sun, J.A. Williams, “Influence of geometry change on creep failure life of 90° pressurised pipe bends with no initial ovality”, International Journal of Pressure Vessels & Piping, vol. 82, pp. 509-516, 2005. [5] AR. Veerappan, S. Shanmugam, “Analysis for Flexibility in the Ovality and Thinning Limits of Pipe Bends”, ARPN Journal of Engineering and Applied Sciences, vol. 3, pp. 31–41, 2008. [6] AR. Veerappan, S. Shanmugam, S. Soundrapandian, “The Accepting of Pipe Bends With Ovality and Thinning Using Finite Element Method” ASME Journal of Pressure Vessel Technology, vol. 132, pp. 031204-1–031204-9, 2010. [7] M.L. Nayyar, Piping handbook, 7th ed., McGraw-Hill, A269, 2000, [8] Dan Vlaicu. “The Influence of the Initial Ovality Tolerance on the Nonlinear Cycling Analysis of Piping Bends”, ASME Journal of Pressure Vessel Technology, 2009, vol. 131, 041203-1–041203-7. [9] V.B. Sarin, “The Steady Laminar Flow of an Elastico-Viscous Liquid in a Curved Pipe of Varying Elliptic Cross Section”, Mathl. Comput. Modelling, vol. 26, pp. 104-121, 1997. [10] J.T. Boyle, J.A. Spence, “Simple Stress Analysis for Out-of-Round, Pressurised Pipe Bends”, International Journal of Pressure Vessels and Piping, , vol. 9, pp. 251-261, 1981. [11] V.P. Cherniy, “The Bending of Curved Pipes with Variable Wall Thickness. Journal of Applied Mechanics, vol. 70, pp. 253–259, 2003. [12] V.P. Cherniy, Effect of Curved Bar Properties on Bending of Curved Pipes, Journal of Applied Mechanics, Vol. 68, pp. 650–655, 2001.

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[1]

[13] A.V. Kale, H.T. Thorat, “Effect of Precompression on Ovality of Pipe after Bending”, “Journal of Pressure Vessel Technology”, vol. 131, pp. 011207-1–011207-7, 2009. [14] T.H. Hyde, V. Yaghi, A.A. Becker, P.G. Earl, “Comparison of toroidal pipes and 90° pipe bends during steady state creep analysis”, Proceedings of the fifth international colloquium on ageing of materials and methods for the assessment of lifetimes of engineering plant Cape Town, pp. 305-317, 1999. [15] T. Christo Michael, AR. Veerappan, S. Shanmugam, “Effect of Bend Angle on Induced Stresses in Pipe Bends – Numerical Investigation” International conference on Frontiers in Mechanical Engineering, pp. 92–98, 2010. [16] LI Xue-tong, WANG Min-ting, DU Feng-shan, XU Zhi-qiang, “FEM Simulation of Large Diameter Pipe Bending Using Local Heating”, Journal of Iron and Steel Research, International, vol. 13, pp. 25-29, 2006. [17] Jochen Weber, A. Klenk, M. Rieke, “A new method of strength calculation and lifetime prediction of pipe bends operating in the creep range”, International Journal of Pressure Vessels and Piping, vol.. 82, 77–84, 2005. [18] Z. Hu, L.Q. Li, Computer simulation of pipe-bending processes with small bending radius using local induction heating”, Journal of Materials Processing Technology, vol. 91, 75–79, 1999. [19] ASME, 2008a. ASME Boiler and Pressure Vessel Code, Section II: Materials Part A- Ferrous Material Specifications, ASME New York, 376, 2008 [20] Jaroslav Mackerle. “Finite elements in the analysis of pressure vessels and piping, an addendum: a bibliography (2002-2004)”, International journal of Pressure Vessels and Piping, vol. 82, pp. 571-592, 2005. [21] ANSYS Help System. Mechanical APDL Documentation Descriptions, ANSYS Parametric Design Language Chapter 1: Introducing APDL. Canonsburg PA, Compact Disc, 2009. [22] ANSYS Help System. Mechanical APDL Documentation Descriptions, Element Reference, Part I Element Library, plane 183, Canonsburg, PA, Compact Disc, 2009.

VII

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NOMENCLATURE Co Ct Cth D Dmax Dmin t tmax tmin R

: percent ovality : percent thinning : percent thickening : pipe outside diameter, mm : maximum outside pipe diameter, mm : minimum outside pipe diameter, mm : nominal thickness of pipe bend, mm : maximum pipe thickness, mm : minimum pipe thickness, mm : bend radius to neutral axis, mm

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