JLB-TN-06-07 Renascence Crymdule Intrductin T minimize the hazards assciated with vacuum and pressure lads, sectin 65 in the JLab EH&S manual [] requires dcumentatin f the Renascence crymdule helium vessel design. ppendix 65-T, Vessel Design Dcumentatin, prvides guidance fr the dcumentatin. The fllwing infrmatin serves t verify and dcument the design fr the Renascence crymdule helium vessel. The Renascence crymdule helium vessel design [][3] is based n the 998 crymdule helium vessel design. The differences are a 3 inch helium utlet transitin and an 8.5 inch bre in the helium vessel head fr the Renascence design. The 998 design had a.5 inch helium utlet transitin with n bre in the elliptical head. This analysis cvers that prtin f the helium vessel between the head extensins. The transitin plate between the head extensin and the beam pipe des nt qualify fr the simple calculatins in the 00 editin f the SME Biler and Pressure Vessel Cde (the cde) [4]. finite element analysis was perfrmed n the transitin plate as part f the tuner design. nalysis This analysis shuld serve as a reference while fllwing the design prcess in the cde. While reading the cde ne can turn t the apprpriate UG-part in this dcument fr the specifics f the calculatin and results. Cmpnents were analyzed using the applicable paragraphs in the cde, see Figure fr details. Due t the iterative nature f the calculatins, nly ne calculatin per UG-part is shwn with the results fr all calculatins tabulated. The specificatins, Table, needed fr this analysis were the same as the Jeffersn Lab 998 Crymdule Helium Vessel [5]. Bellws ppendix 6 Helium vessel (Shell) UG-7 UG-8 Head UG-3 UG-33 Helium Outlet UG-7 UG-8 Head Extensin UG-7 UG-8 UG-37 UG-37 Figure : BPVC Sectin / Cmpnent Transitin Plate Page f 3
JLB-TN-06-07 Descriptin Specificatin Internal Pressure 5 atm (73.45 psi) External Pressure atm (9.38 psi) Material Titanium Grade - Unallyed Titanium Ttal length ~ inches Outside Diameter 0 inches Shell Thickness 0.5 inches Head Thickness 0.875 inches Head Extensin Thickness 0. inches Weld Cnstructin Electrn Beam, TIG Shell Gemetry Cylindrical Head Gemetry Ellipsidal head with 8.5 inch bre Design Temperature 70 F (94.6 K) Table : Specificatins fr Renascence Crymdule Helium Vessel UG-3 Maximum llwable Stress Values (a) Using table B (Sectin II, part D page #46), the maximum allwable stress fr the design temperature is given as 4.3 ksi. (b)() Using the gemetry in Table (), the factr was calculated frm Equatin (). t * (in) ** R (in) Shell 0.5 5.00 Head Extensin 0.00 4. Helium Outlet 0.0.75 Table : Gemetry fr Calculating Maximum llwable Stress *t= Minimum required thickness f shell **R = Outside radius f cylindrical shell.5 shell = = 0.003 Equatin () ( R t) Page f 3
JLB-TN-06-07 Figure : NFT- (Sectin II, part D, subpart 3, page #76.) Titanium at 70 F has a Yung s mdulus f 5.5 ksi (Sectin II, part D, subpart, table TM-5, page #676). Using Figure () and interplating between.5 ksi and 6 ksi, the factr B was fund t be 4.5 ksi. This prcedure was als dne fr the head extensin and helium utlet transitin, see Table (3) fr results summary. The lwest value fr the maximum allwable stress fund frm paragraphs (a) and (b) was 4.5 ksi, therefre this is the required fr design verificatin prcess. B (ksi) Shell 4.5 Head Extensin 4.75 Helium Outlet 7 Table 3: Maximum llwable Stress Values UG-7 Thickness f Shells Under Internal Pressure t * design (in) R ** (in) Shell 0.5 4.875 Head Extensin 0.00 3.985 Helium Outlet 0.0.65 Table 4: Gemetry fr Calculating Thickness fr Internal Pressure *t design = ctual thickness f shell **R= Inside radius Variable Definitin: Page 3 f 3
t = Minimum required thickness P= Internal design pressure S= Maximum allwable stress value E= Jint efficiency f apprpriate jint JLB-TN-06-07 (c)() Circumferential Stress The values fr the required thickness and allwable internal pressure fr the shell based n circumferential stress are calculated belw in Equatin () and Equatin (3). P R 73.45 psi 4.875in t = = =. 036in S E 0.6 P 450 psi.7 0.6 73.45 psi Equatin () S E tdesign 450 psi.7 0.5in P = = = 5.89 psi R + 0.6 t 4.875in + 0.6 0.5in Equatin (3) design The abve calculatins were perfrmed fr all cmpnents. The results are shwn in Table (5). The calculated values fr the required thickness (t) and the allwable internal pressure (P) are smaller and larger, respectively, than the actual values. Therefre the design meets the cde requirements fr circumferential stress. t (in) P (psi) Design Status Shell 0.036 5.89 OKY Head Extensin 0.09 46.60 OKY Helium Outlet 0.0 733.46 OKY Table 5: Calculated Values fr UG-7 (c)() (c)() Lngitudinal Stress The values fr the required thickness and allwable internal pressure fr the shell based n lngitudinal stress are calculated belw in Equatin (4) and Equatin (5). P R 73.45 psi 4.875in t = = =. 08in Equatin (4) S E + 0.4 P 450 psi.45 + 0.4 73.45 psi S E tdesign 450 psi.45 0.5in P = = = 33.5 psi Equatin (5) R 0.4 t 4.875in 0.4 0.5in design The abve calculatins were perfrmed fr all cmpnents. The results are shwn in Table (6). The calculated values fr the required thickness (t) and the allwable internal pressure (P) are smaller and larger, respectively, than the actual values. Therefre the design meets the cde requirements fr lngitudinal stress. Page 4 f 3
JLB-TN-06-07 t (in) P (psi) Design Status Shell 0.08 33.5 OKY Head Extensin 0.03 35.0 OKY Helium Outlet 0.009 07.86 OKY Table 6: Calculated Values fr UG-7 (c)() UG-8 Thickness f Shells and Tubes Under External Pressure L * (in) D ** (in) Shell.00 0.00 Head Extensin.0 8. Helium Outlet.75 3.50 Table 7: Gemetry fr Calculating Thickness fr External Pressure *L= Ttal length f shell **D = Outside diameter f cylindrical shell Variable Definitin: P= External design pressure (9.38psi) P a = Calculated value f maximum allwable wrking pressure t= Minimum required thickness f cylindrical shell (c)() Cylinders having D /t 0 Using Equatin (6) and Equatin (7) alng with Sectin II Subpart 3 Figure G page #68 the Factr can be fund. L in = =. D 0in Equatin (6) D 0in = = 5 t 0.08in Equatin (7) Page 5 f 3
JLB-TN-06-07 Figure 3: Sectin II Subpart 3 Figure G Factr was fund t be apprximately 0.0004. Using Figure (4) and interplating between 3500 and 3000, the factr B is fund t be 3350. Page 6 f 3
JLB-TN-06-07 Figure 4: NFT- (Sectin II, part D, subpart 3, page #76.) Using the value f B frm abve, the maximum allwable wrking pressure can be calculated frm Equatin (8). 4B 4 3350 P = = = 37. 33 psi Equatin (8) a 3 ( D t) 3( 0in.08in) Based n the assumptin f a 0.08 inch thick shell, P a is greater than the external design pressure 9.38 psi and the actual thickness f the shell (0.5 inches) is greater than the minimum allwable thickness f ~0.08 inches. The abve calculatins were als dne fr the helium utlet transitin and head extensin. The results are shwn belw in Table (8). t (in) P a (psi) Design Status Shell 0.080 37.33 OKY Head Extensin 0.09 34.0 OKY Helium Outlet 0.04 3.47 OKY Table 8: Calculated Values fr UG-8 (c)() UG-3 Frmed Heads, and Sectins, Pressure n the Cncave Side t * design (in) D ** (in) Ellipsidal Head 0.87 9.75 Table 9: Gemetry fr Calculating Thickness fr Frmed Heads, Pressure n Cncave Side *t design = Minimum required thickness f head after frming **D= Inside diameter f head skirt Page 7 f 3
Variable Definitin: P = Internal design pressure (73.45psi) S = Maximum allwable stress value in tensin (4.5ksi) E = Lwest efficiency f any jint in the head (0.6) L = Inside spherical crwn radius (8.775 inch) t = minimum required thickness f head P a = maximum allwable internal pressure JLB-TN-06-07 (d) Ellipsidal Heads with t/l 0.00 t design L =.0 Equatin (9) P D 73.45psi 9.75in t = = =. 04in Equatin (0) S E 0. P 450 psi 0.6 0. 73.45psi S E tdesign 4500 psi 0.6.875in Pa = = = 36. 7 psi Equatin () D + 0. t 9.75in + 0..875in design t (in) P a (psi) Design Status Ellipsidal Head 0.04 36.7 OKY Table 0: Calculated Values fr UG-3 UG-33 Frmed Heads, Pressure n Cnvex Side D * (in) D ** (in) h *** (in) Ellipsidal Head 9.75 0.5.56 Table : Gemetry Values fr UG-33 *D= Inside diameter f head skirt **D = Outside diameter f head skirt ***h = One-half f the length f the utside minr axis f the ellipsidal head Variable definitin: t= Minimum required thickness f head after frming P= External design pressure (9.38psi) P a = Calculated value f maximum allwable wrking pressure based n t S= Maximum allwable stress value in tensin (4.5 ksi) E = Lwest efficiency f any jint in the head () K = Factr depending n ellipsidal head prprtins (see table UG-33.) R = Equivalent utside spherical radius The required thickness f the heads per UG-33 is the greater value fund frm paragraphs (a) and (d). (a)general ()(a) Page 8 f 3
JLB-TN-06-07 Renascence Crymdule P =.67 9.38 psi = 49 psi Equatin () P D 49 psi 9.75in t = = = 0. 07in Equatin (3) S E 0. P 4300 psi 0. 49 psi P (d) Ellipsidal Heads S E tdesign 450 psi.875in = = = psi Equatin (4) D + 0. t 9.75in + 0..875in all 545 design Using Equatin (5) and Table UG-33., the value f K was fund t be 0.88. D h =.97 Equatin (5) Equatins (6) and (7) alng with Figure (4) were used t determine the value f Factr B t be 5900. R = K D = 8. 9in Equatin (6) = 0.5 0.5 = R t 8.9in 0.055in = 0.00077 Equatin (7) Figure 5: NFT- (Sectin II, part D, subpart 3, page #76.) Page 9 f 3
JLB-TN-06-07 Renascence Crymdule The maximum allwable pressure determined by Equatin (8) is based n an initial guess fr the minimum required thickness. Fr ellipsidal heads the minimum required thickness fr external pressure is the larger f the tw values fund in UG-33 (a) General ()(a) and (d). The minimum required thickness is 0.055 inches frm Equatin (8). B 5900 P = = = 36 psi a R t 8.9in.055in. Equatin (8) UG-37 Reinfrcement Required fr Openings in Shells and Frmed Heads (c) Design fr Internal Pressure Figure 6: Nmenclature fr Reinfrced Openings Nmenclature Value t (ctual Thickness f shell ) 0.5 inches t r (Required thickness f shell) 0.036 inches t n (ctual thickness f helium utlet) 0.5 inches t rn (Required thickness f helium utlet) 0.0 inches d (Inside diameter f helium utlet) 3.6 inches Table : Gemetry Values fr Slving UG-37 (c), Design fr Internal Pressure Variable definitin: = ttal crss-sectinal area f reinfrcement required in the plane under cnsideratin = area available in shell fr reinfrcement = area available in the nzzle fr reinfrcement avail = ttal area available fr reinfrcement with n reinfrcing element F = crrectin factr is.5 since the pening is perpendicular t lngitudinal axis f shell Page 0 f 3
JLB-TN-06-07 Renascence Crymdule f r = f r = Strength reductin factrs are all unity since the nzzle, vessel, and reinfrcement are all the same material E =, Jint efficiency assuming that the pening is in slid plate and nt n a weld r seam required r ( f ) = dt F + Equatin (9a) t ntr F r ( ).059 required = 3.6 0.036 0.5 + 0.5 0.036 0.5 = in Equatin (9b) ( E t Ft ) t ( E t Ft )( f ) d r n r r = Equatin (0a) (.5.036).5 (.5.5.036)( ) 0. = 3.6.5 = 349in Equatin (0b) ( t t ) f t = 5 n rn r Equatin (a) (.5.0).5 0. = 5 = 07in Equatin (b) avail = = + 0. 49in Equatin () The reinfrcement area required fr internal pressure, Equatin (9), is less than the area available in the helium vessel shell and helium utlet, Equatin (). N additinal reinfrcement is required. The calculatins were als dne fr the pening in the helium vessel head. The results fr paragraph (c) are shwn belw in Table (3). required (in ) available (in ) Design Status Shell 0.059 0.49 OKY Head pening 0.335.60 OKY Table 3: Calculated Values fr UG-37 (c) (d) Design fr External Pressure Nmenclature Value t (ctual Thickness f shell ) 0.5 inches t r (Required thickness f shell) 0.080 inches t n (ctual thickness f helium utlet) 0.5 inches t rn (Required thickness f helium utlet) 0.04 inches d (Inside diameter f helium utlet) 3.60 inches Table 4: Gemetry Values fr Slving UG-8 (c)(), Design fr External Pressure Variable definitin (same as in (c) except fr the fllwing): F = crrectin factr is fr all external pressure reinfrcement calculatins Page f 3
JLB-TN-06-07 Renascence Crymdule = dt F + t t F( f )] Equatin (3a) required [ r n r r required = [ 3.6.080 +.5.080 ( ) ] = 0.3in Equatin (3b) ( E t Ft ) t ( E t Ft )( f ) d r n r r = Equatin (4a) (.5.08).5(.5.08)( ) 0. = 3.6 = 47in Equatin (4b) ( t t ) f t = 5 n rn r Equatin (5a) (.5.04).5 0. = 5 = 069in Equatin (5b) avail = = + 0. 6in Equatin (6) The reinfrcement area required fr external pressure, Equatin (3) is less than the area available in the helium vessel shell and helium utlet, Equatin (6). N additinal reinfrcement is required. The calculatins were als dne fr the pening in the helium vessel head. The results fr paragraph (d) are shwn belw. required (in ) available (in ) Design Status Shell 0.30 0.6 OKY Head pening 0.39 0.965 OKY Table 5: Calculated Values fr UG-37 (d) Mandatry ppendix 6 Figure 7: Typical Bellws Type Expansin Jint Page f 3
JLB-TN-06-07 Renascence Crymdule Nmenclature Value w (cnvlutin depth) 0.75 inches q (cnvlutin pitch) 0.50 inches S (maximum allwable stress value) 4.5 ksi d (inside diameter f bellws) 8.00 inches Table 6: Gemetry Values fr ppendix 6 Variable definitin: P = internal design pressure (73.45 psi) t m = minimum thickness f bellws sheet material befre frming (0.008 inches) t = minimum thickness f bellws after frming ( d w) 73.45( 8 +.75) P + t = 0. 006in Equatin (7) 4w 4.75 S + 450 + q.5 Equatin (7) shws that the required thickness, 0.006 inches, f the bellws is less than the actual thickness, 0.008. Therefre, the bellws meets the requirements f the cde. Cnclusin In all cases the Renascence crymdule helium vessel design meets the requirements f the SME Biler and Pressure Vessel Cde. References:. Jeffersn Lab EH&S Manual. JLab DWG# CRM00700-000 Rev. B, HELIUM VESSEL SSY LOW LOSS 3. JLab DWG# CRM00700-0000 Rev. B, HELIUM VESSEL SSY HIGH GRDIENT 4. 00 editin f the SME Biler and Pressure Vessel Cde 5. Hgan, J., 998 Crymdule Helium Vessel Design Criteria and Calculatins, JLB-TN-99-08 Page 3 f 3