LCLS-II 2K Cold Box Transfer Line Nozzle. Analysis and Allowable Loads

Transcription

1 Author(s): Connor Kaufmann Page 1 of 12 LCLS-II 2K Cold Box Transfer Line Nozzle Analysis and Allowable Loads Revision History: Revision Date Released Description of Change - 01/03/2018 Original release, Issued for Project use Connor Kaufmann JLab Cryogenics Group Mechanical Engineer Nate Laverdure JLab Cryogenics Group Mechanical Engineering Lead Joe Matalevich JLab Cryogenics Group Lead LCLS-II Cold Design Fredrik Fors JLab Mechanical Engineering Group Mechanical Engineer Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 1

2 Author(s): Connor Kaufmann Page 2 of 12 Table of Contents 1.0 Introduction Nozzle Design and Analysis Approach Basis of Allowable Loads Vessel Nozzle Junction Stresses Calculation Using WRC 107/ Nozzle Stresses Weld Stresses at Vessel/Nozzle Junction Replacement Area Calculation Conclusion and Summary References Appendix A Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 2

3 Author(s): Connor Kaufmann Page 3 of Introduction The purpose of this Engineering Note is to document the analysis that was performed to ensure adequate nozzle design for the LCLS-II 2K Cold Box. A secondary motivation was also to calculate the allowable nozzle loads that the main transfer line may safely impart on the 2K Cold Box Vacuum Shell. Figure 1 provides a graphical representation of the 2K Cold Box nozzle that connects to the main transferline. This nozzle connection joins the vacuum jacket (clamshell) of the Sub-Atmospheric Return to the 2K Coldbox vacuum shell. This report discusses the nozzle connection design (Section 2), the basis of the analysis that was performed (Section 3), the calculations (Sections 4 through 7) and the summary / conclusion (Section 8). Nozzle Connection CP1 Main Transfer Line Clamshell Section CP1 2K Cold Box Vessel Figure 1: CP1 2K Cold Box Main Transfer Line Nozzle Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 3

4 2.0 Nozzle Design and Analysis Approach Pressure Systems Documentation-Calculations Author(s): Connor Kaufmann Page 4 of 12 In order to receive the incoming Sub-Atmospheric Helium return pipe to the suction of the cold compressors, a nozzle was designed on the 2K Cold Box vessel. As per standard cryogenic design, a vacuum jacket is required for process piping in order to minimize heat transfer to ambient temperature. The focus of this analysis is the nozzle which connects the main transfer line vacuum jacket to the cold box vacuum shell. As the 2K cold box is an internal JLab design and the main transfer line is an outside vendor design, it is necessary to limit the loads that the transfer line may transmit to the 2K coldbox. The 2K coldbox is designed to ASME BPVC 2013, and thus it is the responsibility of the designers (JLab) to determine a combination of forces and moments which satisfy code allowable stresses. To evaluate allowable external loads on the 2K cold box nozzle, the following approach was taken: 1. Analyze vessel stresses at nozzle/vessel junction using WRC 107/ Analyze nozzle stresses from external forces/moments 3. Analyze weld stresses at nozzle/vessel junction 4. Analyze replacement area required by ASME BPVC Relevant vessel/nozzle design data are listed in Table 2.1. Vessel and Nozzle Data Name Symbol Vessel Nozzle Unit Note Material Specification - SA 516 Gr. 70 SA 312 TP304/304L - Basic Allowable Stress in Tension S ksi ASME BPVC 2013 SII-D Table 1A Size Specification - 144" OD x 0.75" W 20 NPS Sch. 10S - Outside Diameter D in Wall Thickness T in 3.0 Basis of Allowable Loads Table 2.1: Vessel/Nozzle Design Data To analyze the effect of external forces and moments on a nozzle connection to a pressure vessel, it is industry standard practice to use finite element analysis or an analytical solution called WRC 107/537. Per ASME BPVC Section VIII Division (a), localized stress calculations from external loads may be calculated using WRC 107. WRC 107 is a graphical solution method developed by the Welding Research Council for stresses in the vessel based on forces/moments from the nozzle. In 2010, WRC 537 was released for polynomial fitting data on the WRC 107 graphs, allowing for programmable solutions. To this effect, the WRC 107/537 approach is conducive for parametrization of external loads and obtaining fast results for nozzle induced stresses. Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 4

5 Author(s): Connor Kaufmann Page 5 of 12 Typically for nozzle connections on vessels that are small and exert negligible loads, the WRC analysis can be ignored. However, for large nozzles with seismic loads, such as the main transfer line nozzle (24 NPS), it is reasonable to expect that vessel stresses are critical. Therefore, an allowable set of nozzle loads should be determined by the vessel designer as a safe upper limit. Determining the allowable loads for a nozzle connection is inherently a difficult mathematical problem, as one must determine a single linear combination of the load set {Fx, Fy, Fz, Mx, My, Mz} which results in a stress state less than or equal to the given allowable stress. Since there are an infinite number of solutions (nozzle loads) that satisfy this constraint, the load set should logically be parametrized. From mechanics is known that radial forces and non-torsional moments on the nozzle result in the highest primary stresses on the vessel, while shears and torsional moments result in secondary (shear) stresses. In terms of loading, the vessel is much more sensitive to primary stresses than secondary stresses, and therefore the loads that exert primary stresses are designated the driving variables for parametrization. For simplicity in the case of the 2K Cold Box Nozzle, the Radial Force (P) has been designated as the driving variable, and all other loads are a function of the Radial Force. Because the entire process has been parameterized, any particular force or moment can be the driving factor, or the relationship between the loads can be changed. From this point forward, WRC 107/537 can compute the stress and confirm it is below code allowable limits. For the sake of conservatism, the strengthening effect of the reinforcement pad was not considered when analyzing the external loads. 4.0 Vessel Nozzle Junction Stresses Calculation Using WRC 107/537 The first step of calculating the vessel nozzle junction stresses was to determine the loads on the nozzle end, and convert them into the WRC 537 coordinates. From the parametrization in Section 3, relationships were selected for the forces and moments as a function of the driving radial force. Table 4.1 illustrates this parametrization of loads. Figure 4.1 demonstrates the coordinate axes of the loads, and Figure 4.2 shows the conversion of these nozzle end loads into the WRC coordinated system which is in the plane of the vessel/nozzle junction. Nozzle Loads Definition at Nozzle End Name Symbol Vessel Nozzle Unit Parameterization Design Pressure psi Longitudinal Shear Fx - 7,500 lbf Fx = 0.5*Fz Circumferential Shear Fy - 7,500 lbf Fy = 0.5*Fz Radial Force Fz - 15,000 lbf Driving Variable Circumferential Moment Mx - 270,000 lbf-in Mx = 1.5*Fz*e Longitudinal Moment My - 270,000 lbf-in My = 1.5*Fz*e Torsional Moment Mz - 180,000 lbf-in Mz = 1.0*Fz*e Table 4.1: Nozzle Load Definition Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 5

6 Author(s): Connor Kaufmann Page 6 of 12 Figure 4.1: Global Axes for Nozzle Loads Figure 4.2: WRC 537 Loads in Plane of Vessel Junction Once the forces and moments have been determined in the correct coordinate system, nondimensional values for Primary Membrane (P M ), Local Membrane (P L ), Bending (P b ), and Secondary (Q) stresses are computed using WRC 537 polynomial fit parameters. These nondimensional parameters are multiplied by the appropriate loads to calculate stresses in the vessel. The stress classifications are totaled for the circumferential and longitudinal directions of the vessel, and then the scalar valued stress intensity is computed. Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 6

7 Author(s): Connor Kaufmann Page 7 of 12 As an example, to find the circumferential stress in the vessel borne only from the radial load (P), the local membrane induced stress and the bending load induced stress are algebraically totaled. Table 4.2 below depicts the tabulation of the WRC 537 calculation. As per WRC convention, the stress is calculated at eight points (A U,A L,B U,B L,C U,C L,D U,D L ) clocked around the nozzle, and the maximum stress classification result is taken. σ φ (P) = N φ P P/R m R m T ± M φ P 6P T 2 Local Membrane Bending Figure Parameter Stress Category Value A U A L B U B L C U C L D U D L Unit Notes 3C N φ /(P/Rm) P L ,679 2,679 2,679 2,679 psi 4C N φ /(P/Rm) P L ,930 3,930 3,930 3,930 psi 1C M φ /P Pb ,773-11,773 11,773-11,773 psi 2C-1 M φ /P Pb ,722-6,722 6,722-6,722 psi 3A N φ /[M c /(Rm 2 β)] P L ,500-1,500 1,500 1,500 psi 1A M φ /[M c /(Rm-β)] Q ,051 17,051 17,051-17,051 psi 3B N φ /[M L /(Rm 2 β)] P L ,106 8,106-8,106-8,106 psi 1B-1 M φ /[M L /(Rm-β)] Q ,806-11,806-11,806 11,806 psi Circumferential Pressure Stress P M - 1,425 1,425 1,425 1,425 1,425 1,425 1,425 1,425 psi Primary Memb. Circ. Stress P M + P L - 13,461 13,461-2,751-2,751 2,604 2,604 5,604 5,604 psi Primary Memb. + Bend. Circ. Stress P M + P L + Pb - 20,183 6,740 3,970-9,473 14,377-9,169 17,377-6,169 psi Total Circumferential Stress P M + P L + Pb + Q - 31,989-5,066-7,835 2,333-2,674 7,882 34,428-23,220 psi 3C N x /(P/Rm) P L ,679 2,679 2,679 2,679 psi 4C N x /(P/Rm) P L ,930 3,930 3,930 3,930 psi 1C-1 M x /P Pb ,025-12,025 12,025-12,025 psi 2C M x /P Pb ,687-6,687 6,687-6,687 psi 4A N x /[M c /(Rm 2 β)] P L ,750-2,750 2,750 2,750 psi 2A M x /[M c /(Rm-β)] Q ,354 8,354 8,354-8,354 psi 4B N x /[M L /(Rm 2 β)] P L ,958 2,958-2,958-2,958 psi 2B-1 M x /[M L /(Rm-β)] Q ,039-16,039-16,039 16,039 psi Longitudinal Pressure Stress P M psi Primary Membrane Longitudinal Stress P M + P L - 6,349 6, ,892 1,892 7,393 7,393 psi Primary Memb. + Bend. Long. Stress P M + P L + Pb - 18,375-5,676 12,458-11,592 8,579-4,795 14, psi Total Longitudinal Stress P M + P L + Pb + Q - 34,414-21,715-3,581 4, ,559 22,435-7,649 psi Shear Stress from M T psi Shear Stress from V C psi Shear Stress from V L psi Total Shear Stress psi Total Primary Membrane P M + P L - 13,462 13,462 3,479 3,479 3,033 3,033 7,395 7,395 psi * Stress Intensity Total Primary Memb. + Bending P M + P L + Pb - 20,185 12,416 12,516 2,540 14,460 4,592 17,378 6,876 psi * Stress Intensity Total Combined P M + P L + Pb + Q - 34,416 16,649 4,479 4,658 3,220 7,993 34,428 15,572 psi * Stress Intensity Table 4.2: WRC 107/537 Stress Calculation Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 7

8 Author(s): Connor Kaufmann Page 8 of 12 In this case, the stress classifications are compared with to ASME BPVC Section VIII Division 1 and 2 allowable limits. A comparison of calculated stresses and allowable limits is shown in Table 4.3. Name Maximum Calculated Values ASME BPVC 2013 Section VIII Division 1 Allowable Limits Acceptable Vessel Shell Stress per Div. 1 ASME BPVC 2015 Section VIII Division 2 Allowable Limits Acceptable Vessel Shell Stress per Div. 2 Stress Category Symbol Value Unit P M + P L ksi P M + P L + Pb ksi P M + P L + Pb + Q ksi - S ksi ASME BPVC 2013 SII-D Table 1A P M + P L S PM ksi ASME BPVC 2013 SVIII D1 UG-23(d) P M + P L + Pb S PM + S B ksi ASME BPVC 2013 SVIII D1 UG-23(c) P M + P L + Pb + Q S PS ksi ASME BPVC 2013 SVIII D1 UG-23(e) TRUE - - S ksi ASME BPVC 2013 SII-D Table 1A P M + P L S PL =1.5S ksi ASME BPVC 2015 Section VIII D (a) P M + P L + Pb S PL =1.5S ksi ASME BPVC 2015 Section VIII D (a) P M + P L + Pb + Q S PS = 3S ksi ASME BPVC 2015 Section VIII D (d)(1) TRUE - Table 4.3: Comparison of Calculated Vessel Stresses to Allowable Limits Since calculated stresses are below allowable limits with an additional safety factor of about 1.5, the 2K cold box nozzle is sufficiently designed to withstand the allowable loads from Table 4.1. The loads from Table 4.1 shall form the allowable limit for the transfer line loads on the 2K Cold Boxes. As the WRC 537 calculation process is tedious and complicated, the complete calculation process was coded into MS Excel Visual Basic in order to automate the routine. For reference, both the calculation workbook and the code are in Appendix A. In order to verify the accuracy of the developed WRC 537 nozzle Excel program, the intermediate and final results were compared to a commercially available product Bentley AutoNozzle. The differences in the results were less than 5% and well within the margin for acceptable error in what was originally a hand-calculated graphical method. Note 5.0 Nozzle Stresses Since the WRC 107/537 calculates stresses in the vessel only, there must be additional verification to ensure that stresses from external loads are not exceeded in the nozzle itself. To this end, by using basic solid mechanics equations for axial loads, bending, shear and torsion, one can calculate the induced stresses in the nozzle from external loads. All the external loads from Table 4.1 result in nozzle stresses lower than allowable limits, and thus are acceptable. These calculations have been documented in Table 4.4. Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 8

9 Author(s): Connor Kaufmann Page 9 of 12 Nozzle Stress Analysis from UG-22 External Loading Name Symbol Value Unit Notes Long. Stress from Pressure ksi = P*Ri/(2t) Long. Stress from Radial Force ksi = F/(π(Ro 2 -Ri 2 ) Long. Stress from Bending Mom ksi = (M 2 C +M 2 L ) 0.5 R o /I xx Long. Primary Stress (Max Compressive) ksi Long. Primary Stress (Max Tensile) 5.30 ksi Allowable Primary Memb. Stress S PM ksi (Compressive) Acceptable Primary Stress - TRUE - Nozzle Shear Stresses Name Symbol Value Unit Notes Shear Stress from Shear Forces ksi = (V L 2 +V C 2 ) 0.5 /(π*r i* t) Shear Stress from Torsion ksi = M T /(2π*R 2 i *t) Shear Stress in Total τ 2.96 ksi Allowable Shear Stress τ* 16.8 ksi Acceptable Shear Stress - TRUE - Table 4.4: Nozzle Stresses Induced by External Loads 6.0 Weld Stresses at Vessel/Nozzle Junction The nozzle is a set-through nozzle with a penetration of 1 inch past the vessel wall. As the weld is a full penetration weld per ASME BPVC Section VIII Division 1 UW-16(s), with a 3/8 fillet cap weld, it is necessary to verify the weld can withstand these external forces and moments. The calculation for the weld strength due to nozzle loads is shown below in Table 6.1 and Figure 6.1. The analysis technique is per Blodgett s Weld as a Line method, which resolves are forces and moments into unit forces per length onto a fictitious weld represented by line elements. By assuming the resolved unit force acts as pure shear on the fillet weld, the minimum size for the weld is calculated as about 1/16. As the specified weld size is 3/8, the weld has been sufficiently sized. Also conservatively, only the externally facing weld was considered, and not the interior vessel weld on the set-through nozzle which has the same size. 7.0 Replacement Area Calculation For any type of nozzle, regardless of external loading, it is important to verify that it is in conformance with ASME replacement area calculations. The replacement area calculations are shown in Table 7.1 below. As the replacement area exceeds the required area, the nozzle has been sufficiently designed. Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 9

10 Author(s): Connor Kaufmann Page 10 of 12 Nozzle/Vessel Fillet Weld Stress Analysis Name Symbol Nozzle A Unit Notes Nozzle Material Specification - SA /304L - Nozzle Allowable Stress S 20 ksi ASME BPVC 2013 SVIII D1 UG-23(a) Nozzle Size - 20 NPS Sch. 10S - Nozzle Outside Diameter in Nozzle Wall Thickness in Nozzle Length/Eccentricity e in Fillet Weld Specified Size (Leg) w 3/8 in Fillet Weld Acting Diameter D w in Fillet Weld Total Length L in = π Dw CG to Fiber Distance Cx in = Dw/2 CG to Fiber Distance Cy in = Dw/2 CG to Fiber Distance Cz in Fillet Weld Inertia Ix in 3 = (π/8) Dw 3 Fillet Weld Inertia Iy in 3 = (π/8) Dw 3 Fillet Weld Inertia Iz in 3 = Ix + Iy Fillet Weld Allowable Stress S w 9.8 ksi Conservatively assume fillet weld in shear per UW-15(c)(3) Radial Force P -15,000 lbf Circumferential Moment M C 180,000 lbf-in Circumferential Shear V C -7,500 lbf Longitudinal Moment M L -360,000 lbf-in Longitudinal Shear V L -7,500 lbf Torsional Moment M T 180,000 lbf-in Force in X-Direction Fx 7,500 lbf Please note, origin of coordinate axis not per original nozzle Force in X-Direction Fy 7,500 lbf axis, but translated to be in the plane of the fillet weld Force in X-Direction Fz 15,000 lbf Moment in X-Direction Mx 180,000 lbf-in Moment in Y-Direction My 360,000 lbf-in Moment in Z-Direction Mz 180,000 lbf-in Lineal Force in X-Direction fx -167 lbf/in Lineal Force in Y-Direction fy -167 lbf/in Lineal Force in Z-Direction fz -334 lbf/in Total Force on Weld f 409 lbf/in Required Weld Leg Size w req 1/16 in Rounded up to nearest 32nd Specified Weld Leg Size w 3/8 in Acceptable Fillet Weld Size - TRUE - Table and Figure 6.1: Nozzle Weld Analysis Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 10

11 Author(s): Connor Kaufmann Page 11 of 12 Basic Design Vessel Shell Characteristics Nozzle Penetration Characteristics Reinforcement Pad Characteristics Attachment Weld Characteristics UG-37(c) Reinforcement Required for Opening in Shell (Internal Pressure) Nozzle Analysis per ASME BPVC 2013 Section VIII Division 1 UG-37 Name Symbol w/ Pad Unit Note Design Criteria Pass - TRUE - Internal Design Pressure P 15 psig External Design Pressure P ext 15 psid Outside Diameter D o 144 in Nominal Wall Thickness t in Corrosion Allowance c 0 in Allowable Stress S 20 ksi ASME BPVC 2013 II-D Table 1A Joint Efficiency E Type (1) Category D Joint, No Radiography per Table UW-3 Orientation Type - Radial - Size Specification - 20 NPS Sch. 10S Outside Diameter D in Nominal Wall Thickness t n in Wall Undertolerance % ASTM A312 Internal Projection h in Internal Proj.Thickness t i in Inside Nozzle Radius R n in Corrosion Allowance c n 0 in Shell Axis to Nozzle CL L - in Shell Inside Radius R in Required Shell Thickness t r in As defined in UG-37 Midsurface Shell Radius R m in Angle Parameter α - rad Opening Chord d in ASME BPVC 2013 Section VII Division 1 Fig. L Allowable Stress S n 20 ksi ASME BPVC 2013 SII-D Table 1A Joint Efficiency E Does Not Pass Through Cat. A Joint - TRUE - Per Table UW-3 Classification Allowable Stress S p 20 ksi ASME BPVC 2013 SII-D Table 1A Pad Diameter D p in Pad Thickness t e in Outward Weld Leg Leg 41 3/8 in Outer Pad Weld Leg Leg 42 9/16 in Inward Weld Leg Leg 43 3/8 in Parallel Reinf. Limit L R in UG-40(b) Normal Reinf. Limit L H in UG-40(c) Nozzle Req. Thickness t rn in UG-27(c)(1) Shell Req. Thickness t r in UG-37(a) Strength Reduction Factor f r f r f r f r Correction Factor F Fig. UG-37 / UW-16(c)(1) & UW-16(c)(2) Joint Efficiency E UG-37(a) Area Available in Shell A in 2 Area Available for Outward Projection A in 2 Area Available for Inward Projection A in 2 Area Available for Outward Weld A in 2 Area Available for RePad Weld A in 2 Area Available for Inward Weld A in 2 Area Available for RePad A in 2 Total Available Area A avail in 2 Required Area A in 2 Sufficient Reinforcement - TRUE - Table 7: Nozzle Replacement Area Calculation Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 11

12 Author(s): Connor Kaufmann Page 12 of Conclusion and Summary In conclusion, the allowable loads for the 2K Cold Box Transfer Line nozzle have been established. These established allowable loads meet the allowable stress standards of ASME BPVC 2013 Section VIII Division 1 and Division 2, and thus the design is acceptable. 9.0 References [1] Rules for Construction of Pressure Vessels, ASME BPVC 2013 Section VIII Division 1 [2] Rules for Construction of Pressure Vessels: Alternative Rules, ASME BPVC 2015 Section VIII Division 2 [3] Local Stresses in Spherical and Cylindrical Shells Due to External Loads, WRC Bulletin 107, 2002 Update to 1965 Original version [4] Precision Equations and Enhanced Diagrams for Local Stresses in Spherical and Cylindrical Shells Due to External Loadings for Implementation of WRC Bulletin 107, WRC Bulletin 537, 2013 Update to 2010 Original version [5] Design of Welded Structures, Blodgett, 1966 Appendix A The calculations, code and supporting files for this technical report are located at: Document Report Excel Calculations AutoNozzle Model Location M:\cryo\LCLS II ANALYSIS FOLDER\SCB - TL Nozzle\Reports M:\cryo\LCLS II ANALYSIS FOLDER\SCB - TL Nozzle\Excel M:\cryo\LCLS II ANALYSIS FOLDER\SCB - TL Nozzle\AutoNozzle Pressure Systems Documentation - 2K Cold Box Transfer Line Nozzle Analysis Page 12