ASME Boiler & Pressure Vessel Code Analysis of the 1497 MHz High-Current Cryomodule Helium Vessel

1.0 Introduction ASME Boiler & Pressure Vessel Code Analysis of the 1497 MHz High-Current Cryomodule Helium Vessel Katherine Wilson 28 May 2007 To minimize the hazards associated with vacuum and pressure vessels, section 6151 in the JLab EH&S manual requires documentation of all pressure and vacuum vessel designs. Appendix 6151-T1, Vessel Design Documentation, provides detail. Required documentation for the design of the High-Current Cryomodule helium vessel follows. The helium vessel was analyzed using the 2001 edition of the ASME Boiler and Pressure Vessel Code (BPVC), Section VIII, Division 1. 1.1 Design The High-Current Cryomodule helium vessel, shown in Helium Vessel Assembly A, CRM-910-5000-0000 and Helium Vessel Assembly B, CRM-910-5000-0001, is designed with six integral waveguides and a bellows; these are neglected in the analysis and only the vessel itself is considered. Since the helium vessel has flat heads, the length of the shell is taken from one end to the other, per Paragraph UG-28. The maximum internal pressure of 5 atm is determined by rounding up from the pressure to which the burst disks are set, 4.1 atm; the helium vessel would only experience this much pressure in case of a loss of beamline vacuum. A maximum external pressure of 3 atm was used for this analysis; that value is conservative. A more accurate value, arrived at after completing the analysis, would be 2 atm. However, the helium vessel is shown to be acceptable for an external pressure of 3 atm. (For comparison, normal operational pressure is 0.041 atm). The stub connecting the helium vessel to the beam pipe was not considered in this analysis as the BPVC does not provide guidance for niobium or niobium-titanium. See section 3.0 of this document entitled Exceptions for a discussion of the titanium-toniobium-titanium weld. 1.2 Assumptions The following assumptions were made for the purposes of this analysis. a. It was assumed that Grade 2 titanium (UNS R50400) would be used for the helium vessel. It is acceptable to use a different grade of titanium (most likely Grade 3, UNS R50550), as long as the tensile and yield strengths exceed those used in this analysis for Grade 2 titanium. Page 1 of 19

b. The design temperature is assumed to be 70º F. Section UG-20 of the BPVC states that the maximum temperature used in design shall not be less than the mean metal temperature (through the thickness) expected under operation conditions for the part, and the minimum metal temperature used in design shall be the lowest expected in service. However, as complete BPVC data is not available down to the operating temperature of 2 K, it is not possible to design for the lowest expected operational temperature. In addition, paragraph UNF-23 states that For vessels designed to operate at a temperature colder than -20º F (- 29º C), the allowable stress values to be used in design shall not exceed those given for temperatures of 20º F to 100 º F (-29º C to 38 º C). Since modulus and maximum allowable stress increase as temperature decreases, using a higher temperature should be conservative. It should be noted that the BPVC justifies the use of titanium at cryogenic temperatures in paragraph UNF-65: The materials listed in Table UNF-23, together with deposited weld material within the range of composition for material in that Table, do not undergo a marked drop in impact resistance at subzero temperature. Therefore, no additional requirements are specified for titanium or zirconium and their alloys used at temperatures down to -75ºF (- 59ºC). The materials listed in Table UNF-23 may be used at lower temperatures than those specified herein and for other weld metal compositions provided the user satisfied himself by suitable test results that the material has suitable ductility at the design temperature. c. The minimum joint efficiency given in the code, 0.45, was used throughout this analysis to be conservative. A joint with a higher efficiency would, of course, be an acceptable substitute. The efficiency of various weld joints, per Table UW-12 (p. 120-121), assuming no radiographic examination, is as follows: Type of Joint Efficiency Double-welded butt joints 0.70 Single welded butt joints with backing strip 0.65 Single welded butt joints without backing strip 0.60 Double full fillet lap joint 0.55 Single full fillet lap joint with plug welds 0.50 Single full fillet lap joint without plug welds 0.45 Corner joints or angle joints NA It should be noted that this involves disregarding code requirements. By code, every weld on the helium vessel must be either a double-welded butt joint or a single-welded butt joint with backing strip in order for the helium vessel to meet the requirements of the BPVC. A justification for this is provided in section 3.0 of this document entitled Exceptions. Page 2 of 19

d. It is assumed that the helium supply and return nozzles are grade 2 titanium along their entire lengths. In fact, both are titanium stubs welded to titanium-stainless steel explosion bonded connectors, which in turn are welded to stainless steel stubs. The BPVC provides no explicit guidance on evaluating bimetallic pipes. According to the BPVC, the length used in the analysis is the length from support to support; as the supply and return nozzles are not supported at the explosionbonded joint, it would be incorrect to use only the length of the titanium section. A conservative method to analyze this is the assume that the entire length of the nozzle is titanium, since this is a weaker material than stainless steel. The length used, therefore, is the longest length (as the welds are not planar) from the helium vessel to the supply or return header. 1.3 Specifications and Dimensions The following specifications and dimensions were used in the analysis. Internal Pressure......... 5 atm (73.5 psi) External Pressure... 3 atm (44.1 psi) Material.... Grade 2 Titanium Total length... 27.24 inches Outside Diameter... 10 inches Shell Thickness... 0.125 inches Head Thickness... 0.7 inches Weld Construction... Electron beam, TIG; joint type as described in 1.2.c above Shell Geometry...... Cylindrical Head Geometry...... Flat head Design Temperature... 70F (300 K) Stub to Supply Line... 0.75 IPS schedule 10, length 2.28 Stub to Return Line... 3 IPS schedule 10, length 3.67 2.0 Code Analysis 2.1 UG-23 Maximum Allowable Stress s This section of the code gives the maximum unit stress allowed in a given material in the pressure vessel. t design Actual thickness of helium vessel shell 0.125 in r o Outside radius of helium vessel shell 5.0 in t design Actual thickness of helium supply nozzle 0.083 in r o Outside radius of helium supply nozzle 0.525 in t design Actual thickness of helium return nozzle 0.120 in Page 3 of 19

r o Outside radius of helium return nozzle 1.750 in The code states that the maximum allowable tensile stress value permitted in a given material used in a vessel constructed under the rules of the BPVC shall be the smaller of the values calculated by methods (1) and (2), as shown below. (1) From table 1B (Section II, part D, page 246) the maximum allowable stress for the design temperature is given as 12.1 ksi. This is the maximum allowable stress for Grade 2 welded pipe at -20 to 100º F. The maximum allowable stresses for other forms of Grade 2 and Grade 3 titanium are higher; therefore, this is conservative. (2) For the helium vessel: r_o := 5.0 in := 0.125in A := 0.125 r_o A = 0.0031 (2) For the helium supply nozzle: r_o := 0.525 in := 0.083in A := 0.125 r_o A = 0.0198 (2) For the helium return nozzle: r_o := 1.75 in := 0.120in A := 0.125 r_o A = 0.0086 Page 4 of 19

Using Fig. NFT-2 (Section II, part D, page 716.1) and interpolating, the factor B is found to be about 16 ksi. Likewise, for the helium supply nozzle, A is 0.0198 and B is 19.5 ksi; for the helium return nozzle, A is 0.0086 and B is 19 ksi. Therefore the value for maximum allowable stress (S) to be used in this design will be 12.1 ksi, as found in (1) above. 2.2 UG-27 Thickness of Shells Under Internal Pressure This section gives the minimum required thickness of the shell, t, under internal pressure. For the helium vessel: t design Actual thickness of shell 0.125 in t Minimum required thickness 0.066 in / 0.033 in R Inside radius 4.875 in P design Internal design pressure 73.5 psi P Maximum allowable internal pressure 137.5 psi / 282.1 psi S Maximum allowable stress value 12.1 ksi E Joint efficiency of appropriate joint 0.45 s in italics are calculated. (c.1) Circumferential stress := 0.125in R := 4.875in P_design := 73.5psi S := 12100psi E := 0.45 P_design R t := E 0.6 P_design t = 0.066in E R + 0.6 P = 137.5psi The calculated value for the minimum required thickness (t) is smaller than the actual thickness value, and the calculated value for the maximum allowable internal pressure (P) is larger than the actual pressure. Therefore, the design of the vessel meets the BPVC requirements for circumferential stress. Page 5 of 19

(c.2) Longitudinal stress := 0.125in R := 4.875in P_design := 73.5psi S := 12100psi E := 0.45 P_design R t := 2S E + 0.4 P_design t = 0.033in 2 E R 0.4 P = 282.1psi The calculated value for the minimum required thickness (t) is smaller than the actual thickness value, and the calculated value for the maximum allowable internal pressure (P) is larger than the actual pressure. Therefore, the design of the vessel meets the BPVC requirements for longitudinal stress. For the helium supply nozzle: t design Actual thickness of shell 0.083 in t Minimum required thickness 0.006 in / 0.003 in R Inside radius 0.442 in P design Internal design pressure 73.5 psi P Maximum allowable internal pressure 918.9 psi / 2211 psi S Maximum allowable stress value 12.1 ksi E Joint efficiency of appropriate joint 0.45 s in italics are calculated. (c.1) Circumferential stress := 0.083in R := 0.442in P_design := 73.5psi S := 12100psi E := 0.45 P_design R t := E 0.6 P_design t = 0.006in E R + 0.6 P = 918.9psi The calculated value for the minimum required thickness (t) is smaller than the actual thickness value, and the calculated value for the maximum allowable internal pressure (P) Page 6 of 19

is larger than the actual pressure. Therefore, the design of the helium supply nozzle meets the BPVC requirements for circumferential stress. (c.2) Longitudinal stress := 0.083in R := 0.442in P_design := 73.5psi S := 12100psi E := 0.45 P_design R t := 2S E + 0.4 P_design t = 0.003in 2 E R 0.4 P = 2211psi The calculated value for the minimum required thickness (t) is smaller than the actual thickness value, and the calculated value for the maximum allowable internal pressure (P) is larger than the actual pressure. Therefore, the design of the helium supply nozzle meets the BPVC requirements for longitudinal stress. For the helium return nozzle: t design Actual thickness of shell 0.120 in t Minimum required thickness 0.022 in / 0.011 in R Inside radius 1.630 in P design Internal design pressure 73.5 psi P Maximum allowable internal pressure 383.9 psi / 826 psi S Maximum allowable stress value 12.1 ksi E Joint efficiency of appropriate joint 0.45 s in italics are calculated. (c.1) Circumferential stress := 0.12in R := 1.63in P_design := 73.5psi S := 12100psi E := 0.45 P_design R t := E 0.6 P_design t = 0.022in E R + 0.6 P = 383.9psi The calculated value for the minimum required thickness (t) is smaller than the actual thickness value, and the calculated value for the maximum allowable internal pressure (P) Page 7 of 19

is larger than the actual pressure. Therefore, the design of the helium return nozzle meets the BPVC requirements for circumferential stress. (c.2) Longitudinal stress := 0.12in R := 1.63in P_design := 73.5psi S := 12100psi E := 0.45 P_design R t := 2S E + 0.4 P_design t = 0.011in 2 E R 0.4 P = 826psi The calculated value for the minimum required thickness (t) is smaller than the actual thickness value, and the calculated value for the maximum allowable internal pressure (P) is larger than the actual pressure. Therefore, the design of the helium return nozzle meets the BPVC requirements for longitudinal stress. 2.3 UG-28 Thickness of Shells and Tubes Under External Pressure This section regulates the design of cylindrical shells and tubes under external pressure, with or without stiffening rings, tubes and spherical shells. These equations require iterating based on an assumed value of t. (See Fig. G, p. 682, and Fig. NFT-2, p. 716.1, of Section II, Part D.) For the helium vessel: D o Outside diameter of cylindrical shell 10.0 in L Total length of shell 27.24 in P design External design pressure 44.1 psi P Calculated value of maximum allowable external pressure 91.7 psi t design Actual thickness of shell 0.125 in t Minimum required thickness of cylindrical shell 0.09 in s in italics are calculated. Page 8 of 19

(c)(1) L := 27.24in := 10.0in := 0.125in L = 2.724 = 80 A 0.00065 B 5500 3 4 B P = 91.7 Minimum allowable thickness: t := 0.09in L = 2.724 t = 111.111 A 0.00045 B 3750 3 4 B t P = 45 Page 9 of 19

P is greater than the external design pressure. Therefore, the design thickness of the vessel is acceptable. The minimum allowable thickness of the pipe was determined to be approximately 0.09 inches. For the helium supply nozzle: D o Outside diameter of cylindrical shell 1.050 in L Total length of shell 2.28 in P design External design pressure 44.1 psi P Calculated value of maximum allowable external pressure 2055.2 psi t design Actual thickness of shell 0.083 in t Minimum required thickness of cylindrical shell 0.009 in s in italics are calculated. The total length of the shell (nozzle) was assumed to be the maximum length from the helium vessel to the supply header. Page 10 of 19

(c)(1) L := 2.28in := 1.050in := 0.083in L = 2.171 = 12.651 A 0.015 B 19500 3 4 B P = 2055.2 Minimum allowable thickness: t := 0.009in L = 2.171 t = 116.667 A 0.00055 B 4250 3 4 B t P = 48.6 Page 11 of 19

Based on the assumption of a 0.083-inch thick pipe, P is significantly greater than the external design pressure. Therefore, the design thickness of the supply nozzle is acceptable. The minimum allowable thickness of the pipe was determined to be approximately 0.009 inches. For the helium return nozzle: D o Outside diameter of cylindrical shell 3.5 in L Total length of shell 3.67 in P design External design pressure 44.1 psi P Calculated value of maximum allowable external pressure 868.6 psi t design Actual thickness of shell 0.12 in t Minimum required thickness of cylindrical shell 0.022 in s in italics are calculated. The total length of the shell (pipe) was assumed to be the maximum length from the helium vessel to the return header. Page 12 of 19

(c)(1) L := 3.67in := 3.5in := 0.12in L = 1.049 = 29.167 A 0.008 B 19000 3 4 B P = 868.6 Minimum allowable thickness: t := 0.022in L = 1.049 t = 159.091 A 0.0007 B 5750 3 4 B t P = 48.2 Page 13 of 19

Based on the assumption of a 0.12-inch thick pipe, P is greater than the external design pressure. Therefore, the design thickness of the return nozzle is acceptable. The minimum allowable thickness of the pipe was determined to be approximately 0.022 inches. 2.4 UG-34 Unstayed Flat Heads And Covers This section gives the minimum required thickness of unstayed flat heads, cover plates and blind flanges. t design Actual thickness of shell 0.125 in t Minimum allowable thickness of the head 0.651 in P design Internal design pressure 73.5 psi S Maximum allowable stress value in tension 12.1 ksi E Lowest efficiency of any joint in the head 0.45 d Outer diameter of flat head 9.75 in C Factor as listed in UG-34(d) and shown in Fig. UG-34 0.33 s in italics are calculated. This head appears to best fit the case described in sketch (h) of Fig. UG-34. C is therefore 0.33. C := 0.33 P_design := 73.5psi d := 9.75in S := 12100psi E := 0.45 t := d C P_design E t = 0.651in The minimum thickness of the head must therefore be 0.651 inches. Other requirements of this section are as follows: 1. t s must be at least 1.25 times t r. t s, the shell thickness, is 0.125 inches. The greatest required value for the thickness is taken from section UG-28 (Thickness of Shells and Tubes Under External Pressure) and is 0.09 inches. Therefore, this requirement is met. 2. The weld must conform to the requirements of UW-13e and Fig. UW-13.2, sketches (a) to (g) inclusive, and also to UG-93(d)(3). Page 14 of 19

The design appears to be closest to example (c) of Fig. UW-13.2. This requires that dimension a (the height of the weld) plus dimension b (half the thickness of the weld) be at least 2t s. 2t s is 0.25 inches. The height of the weld (a) cannot be less than t s, or 0.125 inches. t p, the distance from the edge of the weld to the edge of the head, must be greater than 0.125 in. 3. Per UW-93(d)(3), when a flat plate thicker than 0.5 inches is to be used to form a corner joint in a pressure vessel, before welding the weld joint preparation in the flat plate must be examined by either magnetic particle (if a magnetic material) or liquid penetrant methods as described in UW-93(d)(4). After welding, the exposed area of the flat plate and the weld must be reexamined by this method. 2.7 UG-37: Reinforcement Required for Openings in Shells and Formed Heads This section determines whether additional reinforcements are required for the nozzle attachments which are welded to the pressure vessel. For the helium supply nozzle: A Total cross-sectional area of reinforcement required in the plane under consideration A avail Total area available for reinforcement with no reinforcing element d Finished diameter of circular opening 1.050 in t Specified vessel wall thickness 0.125 in t r Required thickness of seamless shell for pressure 0.09 in, for external pressure t n Nozzle wall thickness 0.083 in t rn Required thickness of seamless nozzle wall 0.009 in, for external pressure f r1 Strength reduction factor = S n /S v 1.0 f r2 S n /S v 1.0 F Correction factor 1.0 E 1 Weld factor 1.0 S n Allowable stress in nozzle 12.1 ksi S v Allowable stress in vessel 12.1 ksi (c) A pressure vessel which is subject to either internal pressure or both internal and external pressure must meet the requirements given by the equations below (Fig. UG- 37.1, page 47). A avail must be greater than A. Page 15 of 19

d := 1.9in t := 0.25in t_r := 0.09in t_n := 0.083in t_rn := 0.009in f_r1 := 1.0 f_r2 := 1.0 F := 1.0 E1:= 1.0 S_n := 12100psi S_y := 12100psi t_e := 0.3in A := d t_r F + 2 t_n t_r F ( 1 f_r1) A = 0.171in 2 A1 is the larger of: A1_1 := d ( E1 t F t_r) 2 t_n ( E1 t F t_r) ( 1 f_r1) A1_1 = 0.304in 2 A1_2 := 2 ( t + t_n) ( E1 t F t_r) 2 t_n ( E1 t F t_r) ( 1 f_r1) A1_2 = 0.107in 2 Therefore A1 := A1_1 A2 is the smaller of: A2_1 := 5 ( t_n t_rn) f_r2 t A2_1 = 0.093in 2 A2_2 := 5 ( t_n t_rn) f_r2 t_n A2_2 = 0.031in 2 Therefore A2 := A2_2 A_avail := A1 + A2 A_avail 0.335in 2 = A_avail > A -- YES For the helium return nozzle: A Total cross-sectional area of reinforcement required in the plane under consideration A avail Total area available for reinforcement with no reinforcing element d Finished diameter of circular opening 3.5 in t Specified vessel wall thickness 0.25 in t r Required thickness of seamless shell for pressure 0.09 in, for external pressure t n Nozzle wall thickness 0.12 in t rn Required thickness of seamless nozzle wall 0.022 in, for external and internal pressure Page 16 of 19

f r1 Strength reduction factor = S n /S v 1.0 f r2 S n /S v 1.0 F Correction factor 1.0 E 1 Weld factor 1.0 S n Allowable stress in nozzle 12.1 ksi S v Allowable stress in vessel 12.1 ksi (c) A pressure vessel which is subject to either internal pressure or both internal and external pressure must meet the requirements given by the equations below (Fig. UG- 37.1, page 47). A avail must be greater than A. d := 3.5in t := 0.25in t_r := 0.09in t_n := 0.12in t_rn := 0.022in f_r1 := 1.0 f_r2 := 1.0 F := 1.0 E1:= 1.0 S_n := 12100psi S_y := 12100psi t_e := 0.3in leg := 0.1875in A := d t_r F + 2 t_n t_r F ( 1 f_r1) A = 0.315in 2 A1 is the larger of: A1_1 := d ( E1 t F t_r) 2 t_n ( E1 t F t_r) ( 1 f_r1) A1_1 = 0.56in 2 A1_2 := 2 ( t + t_n) ( E1 t F t_r) 2 t_n ( E1 t F t_r) ( 1 f_r1) A1_2 = 0.118in 2 Therefore A1 := A1_1 A2 is the smaller of: A2_1 := 5 ( t_n t_rn) f_r2 t A2_1 = 0.123in 2 A2_2 := 5 ( t_n t_rn) f_r2 t_n A2_2 = 0.059in 2 Therefore A2 := A2_2 A_avail := A1 + A2 A_avail = 0.619in 2 A_avail > A -- YES Page 17 of 19

3.0 Exceptions 3.1 Use of Niobium and Niobium-Titanium Paragraph UNF-5 states that [a]ll nonferrous materials subject to stress due to pressure shall conform to one of the specifications given in Section II and shall be limited to those listed in Table UNF-23 except as otherwise provided in UG-10 and UG-11. This allows Grades 2 (UNS R50400) and 3 (UNS R50550) titanium, but not niobium or niobium-titanium alloy. However, paragraph UNF-15 further states that (a) Other materials, either ferrous or nonferrous, may be used for parts of the vessels provided that they are suitable for the purpose intended. Both niobium and niobium-titanium, though not discussed in the BPVC, are commonly used in cryogenic accelerator design and have proven themselves over years of service. For both materials, the modulus and the yield strength increase at cryogenic temperatures. Based on these factors, it is judged that niobium and niobium-titanium are acceptable materials for use in the cryomodule. 3.2 Titanium-to-Niobium-Titanium Weld According to paragraph UNF-19, Titanium or zirconium and their alloys shall not be welded to other materials. In this helium vessel, titanium is welded to a 55-45 niobium-titanium alloy transition piece which is in turn welded to a niobium piece. Titanium-to-NbTi welds have been used in previous helium vessel designs (see, for instance CRM9007010-0047 and 115400-1020) and have proven durable. Because this weld could not be analyzed using the BPVC, a finite element analysis was performed to verify the strength of the weld joint. Results showing that that the stresses in the weld are no higher than in the surrounding base metal are shown below. For the analysis, an internal pressure load of 5 psi was applied. Note that resulting stresses should be compared to the cryogenic yield strengths of Ti, Nb, and NbTi. Page 18 of 19

Figure 1: Stress and displacement of helium vessel head under a 5 atm internal pressure load. 3.2 Use of Fillet Welds According to the specific requirements for titanium given in paragraph UNF-19, For vessels constructed of titanium or zirconium and their alloys, all joints of Categories A and B shall be of Type No. (1) or No. (2) of Table UW-12. That is, all titanium welds must be either a double-welded butt joint or a single-welded butt joint with backing strip. Nevertheless, fillet welds were used in locations in which butt welds were not feasible. The use of these is supported by past experience: previous helium vessels made of titanium have often used fillet welds in similar locations. See for example, CRM9007020-1001, Probe End Head Weldment, and CRM9007020-0002, Top Assembly (W/o Liq Lvl Probes) for comparable fillet welds used on the SNS Helium Vessels. 4.0 Conclusion The above analysis verifies that the High-Current Cryomodule helium vessel design meets the requirements of the BPVC with the exception of those instances noted in Section 3.0. Justification has been provided for these discrepancies. Page 19 of 19