Nonlinear Finite Element Analysis of Gasketed Flange Joints under Combined Internal Pressure and Different Thermal Loading Conditions

Transcription

1 Failure of Engineering Materials & Structures Code 50 UET TAXILA MECHNICAL ENGINEERING DEPARTMENT Nonlinear Finite Element Analysis of Gasketed Flange Joints under Combined Internal Pressure and Different Thermal Loading Conditions Muhammad Abid 1, Sajid Iqbal 2 and Shahab Khushnood 3 1 Faculty of Mechanical Engineering, GIK Institute of Engineering Sciences and Technology, Topi 2 MED UET Taxila and 3 Chairman MED UET Taxila ABSTRACT Conventional gasketed-flanged pipe joints have been widely used in industries for connecting pressure vessels and pipes since many decade. For bolted flange joints, the two main concerns are the joint strength and the sealing capability. Present available design methods and codes address only the structural strength of the flange joint under internal pressure only and do not consider the effect of steady state and transient temperature loadings. With the rapid advancement in technology for high temperature applications trends are changing. The leakage of bolted flange joints at high temperature or during transient thermal is a well recognized problem and makes the problem more complex under combined application of internal pressure and temperature. To investigate fundamental joint characteristics, joint strength and sealing capability under combined internal pressure and variable steady state, transient thermal loading, a nonlinear finite element analysis of gasketed flange joint is carried out using ANSYS commercial software. Reduced joint strength and sealing is concluded due to the flange rotation resulting in flange yielding under bolt up and applied operating conditions. Flange rotation, bolt bending and joint relaxation concluded fatigue and dynamic behaviour in the gasketed joint. These effects are observed more pronounced at higher temperatures. Finite element model is also verified with the available classical theories and discussed. INTRODUCTION When bolted connections with gaskets are used in mechanical structures such as pipe flange connections and covers of pressure vessels in nuclear engineering, chemical plants, and the cylinder head in combustion engines, they are usually under thermal conditions. Gasketed flange joints have been the subject of detailed research since many decades. The most significant contribution is by Waters et al [1], for the comprehensive flange design and became the basis of well-known Taylor Forge method. Wide acceptance and the relative simplicity in its application has made the Taylor Forge method the most widely used flange design technique and is the basis of BS 0 [2], ASME VIII [3] and many other codes. Sawa et al [4, 5] discussed the finite

2 Muhammad Abid et al FEMS (2007) difference method to determine the temperature distribution, the variation of bolt force, the stresses produced in the bolts and in the hub of the pipe flanges under transient temperature field. A number of numerical studies are available for internal pressure loading only [6, 7]. Extensive experimental studies for combined internal pressure, axial and bending loading are performed by Abid et al [8] to observe joint s behaviour. Nechache et al [9] using elastic interaction theory observed that pre-load loss in the bolts during bolt up and more than half of the initial operating gasket seating stress loss is observed at relatively high temperature in the gasketed joint. Abid et al [10] using 3-D non-linear finite element analysis concluded the results of thermal analysis that more heat transfer occurs from flange ring than from the pipe. Bouzid et al [] worked on the theoretical analysis used for the determination of the steady state operating temperature and deflections in bolted flanged joint. Flange rotation, bolt bending and joint relaxation concluded fatigue and dynamic behaviour in the gasketed joint. These effects are observed more pronounced at higher temperatures. Finite element model is also verified with the available classical theories and discussed. ALLOWABLE STRESSES AND FLANGE JOINT CONFIGURATION Allowable stresses and material properties for flange, pipe, bolt and gasket (as a solid ring) are given in Table-1. Material properties for flange is as per ASTM A105 [12, 13], for bolts is as per ASTM A193-B7 [12, 13] and for gasket is as per ASTM A182 [12, 14]. Bilinear kinematic hardening for elasto-plastic material properties was used during analysis. Finite Element Modeling In the previous work by Spence et al [15] and Abid et al [7, 18], only 2-D finite element modeling and analysis is performed for internal pressure loading only. In the present work, a detailed 2-D parametric FEA is performed using elasto-plastic material model for combined internal pressure steady state and thermal loadings. Half portion of combined bolt and gasket is modeled due to plane symmetry of bolt. The cross sectional area and resulted flange joint model is shown in Fig. 1a. Table 1: Material Properties Parts E (N/mm 2 ) Poisson s ratio (υ) Allowable Stress ( N/mm 2 ) K (W/mo C) Flange Bolt α (m/mo C) 12.5e e- 6 Density (ρ) (kg/mm 3 ) Specific Heat Cp (J/kg o C) e e Gasket e e-6 461

3 219 Muhammad Abid et al FEMS (2007) 50 Internal pressure Axial pressure component at pipe Temperature at inside of pipe, flange and gasket Temperature at outside of pipe, flange and gasket (a) (b) Figure 1: (a) 2-D Model, (b) Mesh and Boundary condition (Thermal and Structural) ELEMENT SELECTION AND MESH Plane structural element PLANE82 is used for the two-dimensional modeling of flange, bolt, and gasket and shell (pipe). Thermal elements (PLANE77) due to its compatibility with PLANE82 element are used to determine the temperature distribution and other related thermal fields. Twodimensional node-to-surface CONTAC48 contact elements are used to simulate contact distribution between the flange face and gasket surface, the top of the flange and the bottom of the bolt. Two-dimensional node-to-surface CONTA contact elements in combination with TARGE169 target elements are used between the flange face and gasket, the top of the flange and the bottom of the bolt, to simulate contact distribution in thermal analysis. In this study, no friction was employed between surfaces. Adaptive meshing is used in the regions of high stress distribution i.e. flange fillet, bolt-hole, bolt head and shank corner and gasket. [Fig. 1b]. BOUNDARY CONDITIONS Structural Boundary Conditions The flanges are free to move in either axial or radial direction. Symmetry conditions are applied to gasket lower portion, bolt cross sectional area, both sides of flange ring and attached pipe. Bolts are constrained in radial and tangential direction. A nominal pre-load of about 35% (254 MPa) of the yield strength of the bolt (723 MPa) is chosen as per the achieved maximum strain in the bolt at the applied torque of 505 Nm by Abid et al [6, 8, 10].

4 Muhammad Abid et al FEMS (2007) Thermal Boundary Conditions For steady state thermal analysis convection with internal fluid temperature at the inside surface of pipe, flange ring and gasket and with ambient temperature at the outer surface of pipe and flange ring is applied [Fig. 1b]. Steady state thermal boundary conditions with different internal temperatures ( o C) and external temperature of 20 o C, with convection heat transfer coefficient internal (150 W/m 2 o C) [12, 13] and external (20 W/m 2 o C) are applied to the model. For transient thermal analysis initial temperature of the joint was taken as 20 o C. Then internal fluid temperature was raised from o C with heat transfer co-efficient150 W/m 2o C. Ambient temperature was kept constant with heat transfer co-efficient 20 W/m 2o C. The change in the temperature of the joint was calculated for each second from the start of transient to reach steady state. ANALYSIS SOLUTION As a flange joint is a combination of bolts, flange, gasket and pipe. Contact is defined between flange ring and gasket, bolt head and flange ring making problem complex.. During solution each load step was further divided into number of small sub steps ranging from 10 to Sequential couple field analysis is performed in ANSYS in two steps. 1. First thermal analysis is performed to determine nodal temperature distribution. thermal analysis was run at different time of the process. Time was given to the transient thermal analysis to reach 25%, 35%, 45%, 55%, 95% and 100% of the steady state temperatures at different internal fluid temperatures o C at the flange outside surface node. Nodal temperature distribution at these times was stored. 2. During structural analysis, following multi-load step procedure is used. Step-1: Contact between flange top surface and bolt bottom and gasket is initiated by applying a small initial axial displacement at the bolt bottom. Step-2: Initial pre-stress in the bolt is achieved by applying a second value of displacement at bolt bottom. Step-3: Internal pressure is applied. Step-4: In case of steady state thermal analysis nodal temperatures from thermal analysis are directly applied as body loads. In case of transient thermal analysis Nodal temperatures from thermal analysis at different time of the process are directly applied as body loads. ANALYSIS RESULTS Fe Model Verification FEA results are compared with mathematically calculated radial, tangential and longitudinal stresses using Lames theory [19] as pipe is thick and are found in good agreement, providing model verification [Fig 2a].For steady state analysis mathematically calculated [20] and FEA results plotted show good agreement [Fig 2b]. For thermal analysis Comparison of the temperature at the outside surface of pipe for a given time is in good agreement [Fig 2b]. In thermal analysis a complete history of temperature 100 o C at the outside surface of the pipe with time and location of graphical results is shown in Fig. 3 in flange, bolt and gasket.

5 221 Muhammad Abid et al FEMS (2007) 50 FEA RESULTS DISCUSSION Stresses in Flange and Pipe The stress intensity of the flange in start of transient shows some decrease in stress at 25-45% and maximum relaxation at 100% of steady state temperature. At bolt up, maximum SI of 437 MPa is observed at hub flange fillet, which decreased to 410 MPa at internal pressure of 15.3 MPa and further decreased to ( MPa) at temperature o C [Fig. 4a-d]. Stress(Mpa) Tangential (OD) Theory FEA Radial (ID) Axial (OD) Type of Stress Temperature (oc) 350 Theory FEA ST-100 ST-200 ST-300 ST-400 TT-100 TT-200 TT-300 PO-400 Theory FEA and Temp (a) (b) Figure 2: Comparison of Mathematical and FEA results for model verification (a) Stresses, (b) Temperature (ST) and Thermal (TT) Temperature at pipe section L 5 L-6 (b) Locations for graphical results L-7 Figu re 3: Tem pera ture Vs Tim e at outs ide surf ace of pipe at o 100 C,

6 Muhammad Abid et al FEMS (2007) The axial stress of the flange in start of transient shows a maximum decrease in bending stress at 25% of steady state temperature and little relaxation at 35-95% of steady state temperature. In steady state boundary conditions, at bolt up, SY of 250 MPa is observed, which decreased to 238 MPa at internal pressure of 15.3 MPa. SY further decreased from ( MPa) at temperature of o C at hub flange fillet [Fig. 4d]. Overall, maximum SY is within the yield limit of the flange material under bolt up and operating conditions. Axial Stress (MPa) T-100 Max. SY Max. SI T-200 T-300 T-400 (a) (b) (c) (d) Figure 4: Flange SINT plots at (a) bolt up (b) internal pressure (c) combined loading at 100 o C (d) SINT and SY variation at o C () Bolt Stress Variation The stress intensity plots of bolt shows that in the start of transient process the bolt load increases because heat has not flown to the bolt yet hence increase the bolt load. At the end of the transient it relaxed. In steady state boundary conditions at bolt up, SI of 483 MPa is observed at the corner of the bolt head and shank [Fig. 5a]. Maximum SI of 486 MPa is observed at the application of internal pressure[fig.5b]. No local yielding was observed in the bolt head and shank due to the high yield stress of the bolt material. Additional thermal load produced some relaxation in the bolt load and the stress reduced to 483 MPa at 100 o C [Fig.5c]. SI further reduced from ( MPa) at temperature of o C [Fig.5d]. The axial stress plots of bolt shows that the bending stress of the bolt increases in start of transient because temperature has not reached the bolt yet. The bolt only relaxed at the end of the transient analysis when it reaches steady state temperatures. In steady state boundary conditions, during bolt up, a maximum SY of 440 MPa is observed under internal pressure loading. Additional thermal load produced some relaxation in the bolt load and the stress reduced to 438 MPa at 100 o C. The SI further reduced from ( MPa) at temperature of o C. [Fig.5d]. Bolt Axial Stress variation from inside to outside diameter in the shank At the start of transient the bending stress of bolt bottom at inside diameter increases till it reaches 95% of steady state but after this the bending stress reduces considerably thus showing

7 223 Muhammad Abid et al FEMS (2007) 50 relaxation of the bolt bottom line at inside diameter [Fig.6a]. The bending stress at bottom of the bolt at outside diameter at start of transient decreases till it reaches steady state condition and thus showing relaxation of the bolt bottom line at outside diameter. From results comparison it is concluded that the application of additional thermal load decreased the initial bolt up load resulting in a decrease of sealing capability of the joint [Fig.6b]. In steady state boundary conditions, the axial stress at the bolt bottom from inside diameter to outside diameter at bolt up is (341 to 143MPa) which reduced to (344 to 141MPa) by the application of internal pressures 15.3 MPa. Further bending stress was reduced to (123 to 138 MPa) with the application of steady state temperature from (100 to 400 o C).This reduction of the bending stress shows that the bolt was relaxed under the application of temperature. Due to this reduction of bending stress at the bolt bottom was reduced the contact pressure at the flange bottom and flange top that will ultimately prone the joint to leakage [Fig.7]. Axial Stress (MPa) Max. SY Max. SI 400 T-100 T-200 T-300 T-400 (a) (b) (c) (d) Figure 5: Bolt SINT plots (a) bolt up (b) internal pressure(c) combined loading at 100 o C (d) Axial Stress (MPa) Axial Stress (MPa) SINT and SY variation at o C ( ) (a) (b) Figure 6: Bolt bottom line at L-4 Axial Stress Vs Time (a) at inside diameter (b) at outside diameter

8 Muhammad Abid et al FEMS (2007) STRESS (MPa) DISPALCEMENT (mm) BOLT UP B-P B-P-T-100 B-P-T-200 B-P-T-300 B-P-T-400 Figure 7: Bolt axial stress (SY) variation (inside to outside diameter at L-4) Contact Stress Variation Between Flange and Gasket Maximum SI of 308 MPa is observed during bolt up, at the outside diameter of the raised face of flange and is more than the yield limit of the gasket resulting in local yielding. The SI decreased during the application of internal pressure from 308 to 2 MPa and from 2 to 165 MPa with additional thermal load from o C.The stress intensity plots shows that the stress intensity of the gasket start decreasing in start of transient and maximum decrese at the end of transient of steady state. [Fig.8a-d]. Maximum SY of 164 N/mm 2 is observed which reduced from N/mm 2 at internal pressure loading. At additional thermal load ( o C) it decreased from 138 to22 N/mm 2 resulting in relaxation in the bolt load and stress contact pressure.the Axial stress plots of gasket shows that the bending stress decreases with the passage of time and relaxed maximum at the end of transient state. [Fig.8d]. Stress Intensity (N/mm 2 ) Max. SI Max. SY T-100 T-200 T-300 T-400 (a) (b) (c) (d) Figure 8: Gasket SINT plots (a) bolt up (b) internal pressure(c) combined loading at 100 o C (d) SINT and SY variation at o C ( ) Gasket Contact Stress Variation From Inside to Outside Diameter (Sy) To observe the sealing capability of the joint the axial displacement of the flange raised face both at the inside and at the outside nodes was taken. The small rotation of the joint under bolt up occur but after the application of internal pressure, joint will tends to open at the inside diameter

9 225 Muhammad Abid et al FEMS (2007) 50 and it moves upward distance of ( mm) from the bolt up position and a distance of (+0.001mm) at the outside diameter of the raised face. This shows that at internal pressure there is more tendency of the joint to open up at the inside diameter of the flange. Application of the fluid temperature tends to open the gap more than at internal pressure at the inside diameter a values range from ( to mm) from the bolt up position.at the outside diameter fluid temperature will tends to open the gap and its value is very small ranges from ( mm to ) as shown in [Fig. 9] UY(mm) -0.5 CF- 100 CF- 200 CF- 300 CF- 400 Max. SI inside dia Max. SI outside dia -0.6 Figure 9: Contact pressure variation for combined operating conditions inside/ Outside diameter DISPLACEMENTS Axial Flange Displacement at Raised Face (L-1) From the result, it is observed that initial preload produces displacement which varies along radial direction. Thus flange rotates more about outside diameter of the raised diameter is shown in [Fig. 10b]. (a) (b) Figure 10: Flanged raised face L-1 Axial Displacement Vs Time (a) at inside dia (b) at outside dia Axial Displacement of Flange Top Surface (L-2): face and causes more compressive stress on the gasket. The application of thermal loading Axial Displacemnt (MPa) further allowing relaxation of gasket. Results show that at inside diameter the displacement of the flange is in downward direction. While that at the outer diameter is in upward direction causing a non-uniform behaviour of the joint and will result non uniform contact pressure Axial Displacement (mm)

10 Muhammad Abid et al FEMS (2007) distribution. The Axial displacement of the flange raised face at the inside diameter is shown in [Fig. 10a]. This graph sows that at the start of transient the joint tends to close the gap but at 95% of steady state it opens more than at the internal pressure. The Axial displacement of the flange raise face at the outside A flange rotation of about 0.16 o is observed, which remained same during all loading conditions at bolt up. However the difference of axial displacement at each loading condition is obvious. The application of internal pressure caused almost a negligible change, but a significant effect was observed when additional thermal load was applied. In transient thermal analysis [Fig. ], the axial displacement of flange top surface is taken both at inside diameter and outside diameter. Form the result it is observed that flange rotation increases at the end of transient analysis i.e. at steady state and more rotation is observed at outside diameter than at inside diameter. (a) (b) Axial Displacement (mm) Figure : Flanged top surface L-2 Axial Displacement Vs Time (a) at inside dia (b) at outside dia Flange Radial Displacement (L-3) Results shows that during initial bolt preload the radial displacement increases along the flange height up to hub and from hub onward it decreases and further along the pipe length the displacement dies out. The same behaviour is observed for pressure and the thermal load condition, but with more radial displacement. The increase of radial displacement during thermal loading is mainly due to thermal expansion of the joint material. In transient thermal analysis [Fig. 12], the radial displacement of flange is taken both at inside diameter and outside diameter. CONCLUSIONS A cyclic mode-of-load based on flange rotation during bolt up and applied loading conditions occurs which result in fatigue behaviour due to bolt bending and ultimately joint relaxation. This effect is more pronounced at thermal loading especially at high internal temperature and is concluded to be due to the different thermal expansions of the flange joint components. A joint s sealing capability is concluded to be related to the gasket seating or contact pressure, which varied with bolt load variation during bolt up and operating conditions providing possible leakage and ultimately joint s failure. The application of additional thermal load produced Axial Displacement (mm)

11 227 Muhammad Abid et al FEMS (2007) 50 decrease in bolt load and this effect was more pronounced with high internal fluid temperatures. Comparison of steady state and transient thermal results shows that the transient thermal model gives more realistic results than the steady state thermal model. Summarizing, a joint designed for internal pressure loading is found to be prone to failure, both in terms of its strength and sealing capability, under additional thermal loading. Therefore for the safe operating conditions, actual joint s capacity needs to be determined Axial Displacement (mm) Axial Displacement (mm) (a) (b) Figure 12: Flanged surface L-3 Radial Displacement Vs Time (a) at inside dia (b) at outside dia REFERENCES 1. Waters, E. O., Wesstrom, D. B., Rossheim, D. B., and Williams, F. S. G. (1937). Formulas for Stresses in Bolted Flanged Connections. Transactions of ASME, 59, BS 0.(1991) Unfired Fusion Welded Pressure Vessels British Standards Institution, UK. 3. ASME Boiler & Pressure Vessel Code,Section VIII,(1).American Society of Mech. Eng., New York, USA. 4. Sawa, T., Higurashi, N., and Akagawa, H., 1991, A Stress Analysis of Pipe Flange Connections, Journal of Pressure Vessel Technology, Vol. 3, pp Sawa, T., Hirose, T., and Kumano, H., 1993, Behavior of Pipe Flange Connection in Temperature Field, ASME J. Pressure Vessel Technol., 5_2_, pp ABID, M., NASH, D. H. (2004). Comparative study of the behaviour of conventional gasketed and compact non-gasketed flanged pipe joints under bolt up and operating conditions. 7. Power, D. J. (1997). A Study of Conventional and Unconventional Flanged Pipe Joint Styles Using Non Linear Finite Element Analysis Techniques. M.Phil. Thesis. 8. Abid, M. (2000). Experimental and Analytical studies of conventional (gasketed) and unconventional (non gasketed) flanged pipe joints (with special emphasis on the engineering of joint strength and sealing ). PhD Thesis.

12 Muhammad Abid et al FEMS (2007) Nechache, A. and Bouzid, A. (2003). The Determination of Load Changes in Bolted Gasketed Joints Subjected to Elevated Temperature. ASME International PVP Conference, USA. 4, 10. Abid, M, 2004, Determination of safe operating conditions for gasketed flange joint under combined internal pressure and temperature. ASME International PVP journal 2004, Vol 405,. Bouzid.A, Akli Nechache, November 2005 Thermally Induced Deflections in Bolted Flanged Connections 12. ASME Boiler and Pressure Vessel Code, Section II, Part D, (1). American Society of Mech. Eng., New York, USA. 13. Brown, W. and Derene, M. (2000). Determination of the Operating Temperature of Pressure Vessel Flange Components: Part 1- Analytical Method. ASME International PVP Conference, USA. 405, Brown, W. and Derene, M., Bouzid, A. (2001). Determination of Mechanical and Thermal Properties of selected Gasket Types.Proceedings of the ASME PVP, Atlanta, USA, 416, Spence, J., Macfarlane, D. M. and Tooth, A. S. (1). Metal-to-Metal full face taper hub flanges: finite element model evaluation and preliminary plastic analysis. 16. Bouzid,A.and Nechache, A.(2002). The Effect of Thermal Loading on the Deflections of Flanged Joint with a Cover Plate.ASME Intl. PVP Conference, USA,, ANSYS Inc., (2004) ANSYS Elements Manual, Seventh Edition. 18. Nash, D. H. and Abid, M. (2000). Combined external loads tests for standard and compact flanges. International Journal of Pressure Vessels and Piping, 77 (13), Spence, J. and Tooth, A.S. (1994). Pressure Vessel design Concepts and Principles. 20. Holman, J.P. (1986). Heat and Mass Transfer. ISBN