helium vessel design documentationtnweb.jlab.org/tn/2006/06-017.pdfjlab-tn-06-017 renascence...

JLAB-TN-06-017 Renascence Cryomodule

Helium Vessel Design Documentation W. R. Hicks

Introduction To minimize the hazards associated with vacuum and pressure loads, section 6151

in the JLab EH&S manual [1] requires documentation of the Renascence cryomodule helium vessel design. Appendix 6151-T1, Vessel Design Documentation, provides guidance for the documentation. The following information serves to verify and document the design for the Renascence cryomodule helium vessel.

The Renascence cryomodule helium vessel design [2][3] is based on the 1998 cryomodule helium vessel design. The differences are a 3 inch helium outlet transition and an 8.25 inch bore in the helium vessel head for the Renascence design. The 1998 design had a 1.5 inch helium outlet transition with no bore in the elliptical head. This analysis covers that portion of the helium vessel between the head extensions. The transition plate between the head extension and the beam pipe does not qualify for the simple calculations in the 2001 edition of the ASME Boiler and Pressure Vessel Code (the code) [4]. A finite element analysis was performed on the transition plate as part of the tuner design. Analysis

This analysis should serve as a reference while following the design process in the code. While reading the code one can turn to the appropriate UG-part in this document for the specifics of the calculation and results. Components were analyzed using the applicable paragraphs in the code, see Figure 1 for details. Due to the iterative nature of the calculations, only one calculation per UG-part is shown with the results for all calculations tabulated. The specifications, Table 1, needed for this analysis were the same as the Jefferson Lab 1998 Cryomodule Helium Vessel [5].

Figure 1: BPVC Section / Component

Helium vessel (Shell)

8

7

8

7

Head Extension

Helium Outlet

s 6

UG-28

UG-27

Head

Pa

UG-32

UG-33

Appendix 2

UG-27

UG-2

UG-2

UG-2

UG-37
UG-3 Transition Plate
Bellow

ge 1 of 13



Description Specification

Internal Pressure 5 atm (73.45 psi) External Pressure 2 atm (29.38 psi) Material Titanium Grade 2 - Unalloyed Titanium Total length ~22 inches Outside Diameter 10 inches Shell Thickness 0.125 inches Head Thickness 0.1875 inches Head Extension Thickness 0.1 inches Weld Construction Electron Beam, TIG Shell Geometry Cylindrical Head Geometry Ellipsoidal head with 8.25 inch bore Design Temperature 70°F (294.26 K)

Table 1: Specifications for Renascence Cryomodule Helium Vessel UG-23 Maximum Allowable Stress Values (a)

Using table 1B (Section II, part D page #246), the maximum allowable stress for the design temperature is given as 14.3 ksi. (b)(2) Using the geometry in Table (2), the factor A was calculated from Equation (1). t* (in) Ro

** (in) Shell 0.125 5.00Head Extension 0.100 4.11Helium Outlet 0.120 1.75

Table 2: Geometry for Calculating Maximum Allowable Stress *t= Minimum required thickness of shell **Ro= Outside radius of cylindrical shell

( ) 0031.0125.==

tRA

oshell Equation (1)

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Figure 2: NFT-2 (Section II, part D, subpart 3, page #716.1)

Titanium at 70°F has a Young’s modulus of 15.5 ksi (Section II, part D, subpart 2,

table TM-5, page #676). Using Figure (2) and interpolating between 12.5 ksi and 16 ksi, the factor B was found to be 14.25 ksi. This procedure was also done for the head extension and helium outlet transition, see Table (3) for results summary. The lowest value for the maximum allowable stress found from paragraphs (a) and (b) was 14.25 ksi, therefore this is the required for design verification process.

B (ksi) Shell 14.25Head Extension 14.75Helium Outlet 17

Table 3: Maximum Allowable Stress Values UG-27 Thickness of Shells Under Internal Pressure tdesign *(in) R **(in) Shell 0.125 4.875Head Extension 0.100 3.985Helium Outlet 0.120 1.625

Table 4: Geometry for Calculating Thickness for Internal Pressure *tdesign= Actual thickness of shell **R= Inside radius Variable Definition:

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t = Minimum required thickness P= Internal design pressure S= Maximum allowable stress value E= Joint efficiency of appropriate joint (c)(1) Circumferential Stress The values for the required thickness and allowable internal pressure for the shell based on circumferential stress are calculated below in Equation (2) and Equation (3).

inpsipsi

inpsiPES

RPt 036.45.736.07.14250

875.445.736.0

=⋅−⋅

⋅=

⋅−⋅⋅

= Equation (2)

psiinininpsi

tRtES

Pdesign

design 89.251125.06.0875.4125.07.14250

6.0=

⋅+⋅⋅

=⋅+

⋅⋅= Equation (3)

The above calculations were performed for all components. The results are shown

in Table (5). The calculated values for the required thickness (t) and the allowable internal pressure (P) are smaller and larger, respectively, than the actual values. Therefore the design meets the code requirements for circumferential stress.

t (in) P (psi) Design Status Shell 0.036 251.89 OKAY Head Extension 0.029 246.60 OKAY Helium Outlet 0.012 733.46 OKAY

Table 5: Calculated Values for UG-27 (c)(1) (c)(2) Longitudinal Stress

The values for the required thickness and allowable internal pressure for the shell based on longitudinal stress are calculated below in Equation (4) and Equation (5).

inpsipsi

inpsiPES

RPt 028.45.734.045.142502

875.445.734.02

=⋅+⋅⋅

⋅=

⋅+⋅⋅⋅

= Equation (4)

psiinin

inpsitRtES

Pdesign

design 25.332125.04.0875.4

125.045.1425024.0

2=

⋅−⋅⋅⋅

=⋅−

⋅⋅⋅= Equation (5)

The above calculations were performed for all components. The results are shown

in Table (6). The calculated values for the required thickness (t) and the allowable internal pressure (P) are smaller and larger, respectively, than the actual values. Therefore the design meets the code requirements for longitudinal stress.

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t (in) P (psi) Design Status

Shell 0.028 332.25 OKAY Head Extension 0.023 325.10 OKAY Helium Outlet 0.009 1017.86 OKAY

Table 6: Calculated Values for UG-27 (c)(2) UG-28 Thickness of Shells and Tubes Under External Pressure L *(in) Do

**(in) Shell 22.00 10.00Head Extension 1.20 8.22Helium Outlet 1.75 3.50

Table 7: Geometry for Calculating Thickness for External Pressure *L= Total length of shell **Do= Outside diameter of cylindrical shell Variable Definition: P= External design pressure (29.38psi) Pa= Calculated value of maximum allowable working pressure t= Minimum required thickness of cylindrical shell (c)(1) Cylinders having Do/t ≥10 Using Equation (6) and Equation (7) along with Section II Subpart 3 Figure G page #682 the Factor A can be found.

2.21022

==inin

DL

o

Equation (6)

12508.0

10==

inin

tDo Equation (7)

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Figure 3: Section II Subpart 3 Figure G

Factor A was found to be approximately 0.00042. Using Figure (4) and

interpolating between 3500 and 3000, the factor B is found to be 3350.

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Using the value of B from above, the maximum allowable working pressure can be calculated from Equation (8).

( ) ( ) psiinintD

BPo

a 33.3708.103

335043

4=

⋅== Equation (8)

Based on the assumption of a 0.08 inch thick shell, Pa is greater than the external design pressure 29.38 psi and the actual thickness of the shell (0.125 inches) is greater than the minimum allowable thickness of ~0.08 inches. The above calculations were also done for the helium outlet transition and head extension. The results are shown below in Table (8).

t (in) Pa (psi) Design Status Shell 0.080 37.33 OKAY Head Extension 0.019 34.20 OKAY Helium Outlet 0.014 31.47 OKAY

Table 8: Calculated Values for UG-28 (c)(1) UG-32 Formed Heads, and Sections, Pressure on the Concave Side tdesign *(in) D **(in) Ellipsoidal Head 0.187 9.75

Table 9: Geometry for Calculating Thickness for Formed Heads, Pressure on Concave Side *tdesign= Minimum required thickness of head after forming **D= Inside diameter of head skirt

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Variable Definition: P = Internal design pressure (73.45psi) S = Maximum allowable stress value in tension (14.25ksi) E = Lowest efficiency of any joint in the head (0.6) L = Inside spherical crown radius (8.775 inch) t = minimum required thickness of head Pa = maximum allowable internal pressure (d) Ellipsoidal Heads with t/L≥0.002

021.=Ltdesign Equation (9)

inpsipsi

inpsiPES

DPt 042.45.732.06.0142502

75.945.732.02

=⋅−⋅⋅

⋅=

⋅−⋅⋅⋅

= Equation (10)

psiinin

inpsitDtES

Pdesign

designa 72.326

1875.2.075.91875.6.01425002

2.02

=⋅+

⋅⋅⋅=

⋅+


t (in) Pa (psi) Design Status Ellipsoidal Head 0.042 326.72 OKAY

Table 10: Calculated Values for UG-32 UG-33 Formed Heads, Pressure on Convex Side D*(in) Do

**(in) ho***(in)

Ellipsoidal Head 9.75 10.125 2.56Table 11: Geometry Values for UG-33

*D= Inside diameter of head skirt **Do= Outside diameter of head skirt ***ho= One-half of the length of the outside minor axis of the ellipsoidal head Variable definition: t= Minimum required thickness of head after forming P= External design pressure (29.38psi) Pa= Calculated value of maximum allowable working pressure based on t S= Maximum allowable stress value in tension (14.25 ksi) E = Lowest efficiency of any joint in the head (1) Ko= Factor depending on ellipsoidal head proportions (see table UG-33.1) Ro= Equivalent outside spherical radius The required thickness of the heads per UG-33 is the greater value found from paragraphs (a) and (d). (a)General (1)(a)

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psipsiP 4938.2967.1 =⋅= Equation (12)

inpsipsi

inpsiPES

DPt 017.0492.01143002

75.9492.02

=⋅−⋅⋅

⋅=

⋅−⋅⋅⋅

= Equation (13)

psiinininpsi

tDtES

Pdesign

designall 545

1875.2.075.91875.1142502

2.02

=⋅+⋅⋅⋅

=⋅+


(d) Ellipsoidal Heads Using Equation (15) and Table UG-33.1, the value of Ko was found to be 0.88.

97.12

=⋅ o

o

hD

Equation (15)

Equations (16) and (17) along with Figure (4) were used to determine the value of Factor B to be 5900.

inDKR ooo 91.8=⋅= Equation (16)

00077.0055.091.8

125.0125.0===

inintRA

o

Equation (17)


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The maximum allowable pressure determined by Equation (18) is based on an initial guess for the minimum required thickness. For ellipsoidal heads the minimum required thickness for external pressure is the larger of the two values found in UG-33 (a) General (1)(a) and (d). The minimum required thickness is 0.055 inches from Equation (18).

psiinintR

BPo

a .36055.91.8

5900=== Equation (18)

UG-37 Reinforcement Required for Openings in Shells and Formed Heads

Figure 6: Nomenclature for Reinforced Openings

(c) Design for Internal Pressure

Nomenclature Value t (Actual Thickness of shell ) 0.125 inches tr (Required thickness of shell) 0.036 inches tn (Actual thickness of helium outlet) 0.125 inches trn (Required thickness of helium outlet) 0.012 inches d (Inside diameter of helium outlet) 3.26 inches

Table 12: Geometry Values for Solving UG-37 (c), Design for Internal Pressure Variable definition: A = total cross-sectional area of reinforcement required in the plane under consideration A1 = area available in shell for reinforcement A2 = area available in the nozzle for reinforcement Aavail = total area available for reinforcement with no reinforcing element F = correction factor is .5 since the opening is perpendicular to longitudinal axis of shell

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fr1 = fr2 = Strength reduction factors are all unity since the nozzle, vessel, and reinforcement are all the same material E1= 1, Joint efficiency assuming that the opening is in solid plate and not on a weld or seam

( )112 rrnrrequired fFttFdtA −+= Equation (19a)

( ) 2059.115.0036.0125.025.0036.026.3 inArequired =−⋅⋅⋅+⋅⋅= Equation (19b)

( ) ( )( )1111 12 rrnr fFttEtFttEdA −−−−= Equation (20a)

( ) ( )( ) 21 349.011036.5.125.125.2036.5.125.26.3 inA =−⋅−⋅−⋅−= Equation (20b)

( ) tfttA rrnn 22 5 −= Equation (21a)

( ) 2

2 071.0125.1012.125.5 inA =⋅⋅−⋅= Equation (21b)

221 419.0 inAAAavail =+= Equation (22)

The reinforcement area required for internal pressure, Equation (19), is less than the area available in the helium vessel shell and helium outlet, Equation (22). No additional reinforcement is required. The calculations were also done for the opening in the helium vessel head. The results for paragraph (c) are shown below in Table (13).

Arequired (in2) Aavailable (in2) Design Status Shell 0.059 0.419 OKAY Head opening 0.335 1.260 OKAY

Table 13: Calculated Values for UG-37 (c) (d) Design for External Pressure

Nomenclature Value t (Actual Thickness of shell ) 0.125 inches tr (Required thickness of shell) 0.080 inches tn (Actual thickness of helium outlet) 0.125 inches trn (Required thickness of helium outlet) 0.014 inches d (Inside diameter of helium outlet) 3.260 inches

Table 14: Geometry Values for Solving UG-28 (c)(1), Design for External Pressure Variable definition (same as in (c) except for the following): F = correction factor is 1 for all external pressure reinforcement calculations

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([ 11221

rrnrrequired fFttFdtA −+= )] Equation (23a)

( )[ ] 213.0111080.125.21080.26.321 inArequired =−⋅⋅⋅+⋅⋅= Equation (23b)

( ) ( )( )1111 12 rrnr fFttEtFttEdA −−−−= Equation (24a)

( ) ( )( ) 2

1 147.01108.1125.1125.208.1125.126.3 inA =−⋅−⋅⋅−⋅−⋅= Equation (24b)

( ) tfttA rrnn 22 5 −= Equation (25a)

( ) 22 069.0125.1014.125.5 inA =⋅⋅−= Equation (25b)

2

21 216.0 inAAAavail =+= Equation (26)

The reinforcement area required for external pressure, Equation (23) is less than the area available in the helium vessel shell and helium outlet, Equation (26). No additional reinforcement is required. The calculations were also done for the opening in the helium vessel head. The results for paragraph (d) are shown below.

Arequired (in2) Aavailable (in2) Design Status

Shell 0.130 0.216 OKAY Head opening 0.319 0.965 OKAY

Table 15: Calculated Values for UG-37 (d) Mandatory Appendix 26

Figure 7: Typical Bellows Type Expansion Joint

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Nomenclature Value w (convolution depth) 0.75 inches q (convolution pitch) 0.50 inches S (maximum allowable stress value) 14.25 ksi d (inside diameter of bellows) 8.00 inches

Table 16: Geometry Values for Appendix 26 Variable definition: P = internal design pressure (73.45 psi) tm = minimum thickness of bellows sheet material before forming (0.008 inches) t = minimum thickness of bellows after forming

( ) ( ) in

qwS

wdPt 006.0

5.75.4114250

75.845.7341

≥⎟⎠⎞

⎜⎝⎛ ⋅+

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+≥ Equation (27)

Equation (27) shows that the required thickness, 0.006 inches, of the bellows is less than the actual thickness, 0.008. Therefore, the bellows meets the requirements of the code. Conclusion In all cases the Renascence cryomodule helium vessel design meets the requirements of the ASME Boiler and Pressure Vessel Code. References:

1. Jefferson Lab EH&S Manual 2. JLab DWG# CRM1007020-1000 Rev. B, HELIUM VESSEL ASSY LOW LOSS 3. JLab DWG# CRM1007020-0000 Rev. B, HELIUM VESSEL ASSY HIGH

GRADIENT 4. 2001 edition of the ASME Boiler and Pressure Vessel Code 5. Hogan, J., 1998 Cryomodule Helium Vessel Design Criteria and Calculations,

JLAB-TN-99-028

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helium vessel design documentationtnweb.jlab.org/tn/2006/06-017.pdfjlab-tn-06-017 renascence...

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