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Theoretical and experimental investigation of magnetic field related helium leak in helium vessel of a large superconducting magnet
Cryogenics 84 (2017) 1–6
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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Theoretical and experimental investigation of magnetic field related helium leak in helium vessel of a large superconducting magnet Pranab Bhattachryya a,b,⇑, Anjan Dutta Gupta a,b, S. Dhar c, P.R. Sarma b, Paramita Mukherjee a,b a
Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata 700064, India Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India c Jadavpur University, Kolkata 700032, India b
a r t i c l e
i n f o
Article history: Received 25 November 2016 Received in revised form 2 March 2017 Accepted 17 March 2017 Available online 18 March 2017
a b s t r a c t The helium vessel of the superconducting cyclotron (SCC) at the Variable Energy Cyclotron centre (VECC), Kolkata shows a gradual loss of insulation vacuum from 107 mbar to 104 mbar with increasing coil current in the magnet. The insulation vacuum restores back to its initial value with the withdrawal of current. The origin of such behavior has been thought to be related to the electromagnetic stress in the magnet. The electromagnetic stress distribution in the median plane of the helium vessel was studied to figure out the possible location of the helium leak. The stress field from the possible location was transferred to a simplified 2D model with different leak geometries to study the changes in conductance with coil current. The leak rate calculated from the changes in the leak geometry was compared with the leak rate calculated from the experimental insulation vacuum degradation behavior to estimate the initial leak shape and size. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Superconducting cyclotrons at high energy cyclotron facilities at Michigan State University [1], Texas A&M University [2], Milano [3] and VECC [4] use large superconducting magnets for producing high magnetic fields. These magnets operate at bath-cooled mode with LHe at 4 K. An insulation vacuum (107 mbar) jacket encompasses the cold mass of these magnets to minimize heat load to the LHe. At 4 K temperature, most of the gases in the insulation vacuum jacket space are effectively cryopumped by the cold mass of the magnet. Any rise in pressure in the vacuum jacket is generally due to helium leak from the LHe vessel [5]. These internal helium leaks may originate from the propagation of small cracks due to thermal stress during cool down of the coil to cryogenic temperature. The thermal stress can introduce a crack in the weld or more likely open a leak which was plugged by contamination (e.g. dirt, weld impurities, or water) [6]. During the first LHe filling of the VECC magnet, a small but significant deterioration of insulation vacuum was observed. This degradation occurred when the LHe level reached near the median plane (i.e. the horizontal symmetry plane of the magnet) [7]. It confirmed the opening of some cold leaks in the median plane near ⇑ Corresponding author at: Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata 700064, India. E-mail address: [email protected] (P. Bhattachryya). http://dx.doi.org/10.1016/j.cryogenics.2017.03.005 0011-2275/Ó 2017 Elsevier Ltd. All rights reserved.
the weld zone. Moreover, it was observed, during operation, that the insulation vacuum further degraded significantly with the increase of coil current. However, the insulation vacuum improved and reverted to its initial value (i.e. the insulation vacuum value with filled up LHe) once the magnet was de-energized. The magnet could be operated up to 550 A (about 70% of the maximum value of 800 A), as the existing refrigeration plant could not handle increased heat load due to degraded insulation vacuum. The magnet of SCC at VECC has two coils, viz., a-coil and b-coil (Fig. 1). It was further observed that the effect of the a-coil on the degradation of vacuum is much higher than the b-coil. It is very difficult to locate and repair any leak of the inner helium vessel after constructing the vacuum jacket around it. It requires a major disassembly of the cryostat to access to the leak location. Previous studies were carried out for addressing several aspects of the problem. Dutta et al. [8] mentioned the existence of unapproachable critical leaks which were related to the magnetic field. Bhunia et al. [9] discussed their operational experience about the satisfactory performance of the magnet cryostat coupled with the liquid helium refrigerator with moderate currents (550 A) in both the coils and subsequent slow dump at higher current. Naser et al. [10] concluded that the electro-magnetic stress due to Lorentz force increased with current but did not report any detailed stress analysis of the helium vessel. Bhattacharyya et al. [7,11] quantified the amount of excess heat load arising due to degraded insulation vacuum through experiments and theoretical analysis.
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Fig. 1. Schematic view of K500 superconducting cyclotron (SCC) magnet.
In the present work, a coupled electromagnetic and structural analysis has been made for finding out the magnetic field distribution and the stress pattern at the inner and outer wall weld joints near the median plane of the helium vessel at several different combinations of coil current. It is seen that near median plane, there exists a tensile stress pattern which may open up any existing crack. The stress field from the possible location was transferred to a simplified 2D model with different leak geometries to study the change in conductance. The leak rate calculated from the change in the leak geometry was compared with the leak rate that was calculated from experimental insulation vacuum degradation behavior to estimate the initial leak shape and size. The maximum allowable coil current was determined based on the estimated initial leak size and crack tip stress. 2. Effect of coil current on degradation of insulation vacuum The superconducting magnet of K500 SCC at VECC uses Nb-Ti superconducting coils. The coil consists of two halves (upper and lower sides of the median plane), and each half is again split into a large (b-coil) and a short (a-coil) coil as shown in Fig. 1. The superconducting coil is housed in an annular liquid helium vessel made of SS 316L material. It is surrounded by a copper thermal shield at 80 K, cooled by liquid nitrogen. The shield and the helium vessel is wrapped with multiple layers of superinsulation and is placed inside an outer vacuum enclosure (AISI 1020) to insulate it from the ambient heat. A high insulation vacuum (107 mbar) is maintained in the vessel by continuous pumping via. a turbo-molecular pump backed by a scroll pump. The pump is located 2.5 m away from the magnet to keep the pump away from the high magnetic field. During operation, it is observed that the insulation vacuum deteriorates with increase in coil current. A similar turbomolecular pump with a small experimental vacuum chamber was placed separately there (i.e. adjacent to the actual insulation vacuum turbo-molecular pump), and the pumping speed was found to be uninfluenced by the local magnetic field present there due to energization of the superconducting magnet. Thereby reconfirms that a leak was present in the helium chamber, and it is not that the pumping speed is getting reduced due to the magnetic field. This degradation of insulation vacuum finally limits the operation of the magnet well below the rated operating current.
Operational experience further shows that the effect of the bcoil on the deterioration of vacuum is much less than that of the a-coil [7]. The operational data has been analyzed, and it has been found that 0.4 A current in a-coil (Ia) produces the same insulation vacuum degradation as 1 A current in b-coil (Ib) does. Around 250 operational data points of loss of insulation vacuum with different current combination have been further studied, and an empirical relation (Eq. (1)) is proposed to fit with the experimental data within ±10% error. 2
LogðPÞ ¼ a þ by þ cy4 þ dy
6
ð1Þ
where P = insulation vacuum (mbar), a = 5.587, b = 7.21 107, c = 1.609 1011, d = 1.26 1017 and y = Ia + 0.4 Ib. Using Eq. (1), the full surface (Fig. 2) has been generated for predicting vacuum degradation at different current combinations. Fig. 2 clearly shows that the effect of a-coil is more dominant on insulation vacuum degradation than that of the b-coil. In the earlier work [7], we made an attempt to correlate the coil current with the extent of vacuum degradation. We surmised that an increase in the coil current raises the stress in the weld zone which, in turn, opens up the cold-leak and thus degrades the vacuum.
Fig. 2. Degradation of insulation vacuum at different coil currents in a- and b-coils.
P. Bhattachryya et al. / Cryogenics 84 (2017) 1–6
3
3. Effect of coil current on helium vessel stress In this section, we aimed at analyzing how the helium vessel weld zone stresses depend on the different combinations of coil currents. The median plane iron has a lot of cut outs of different sizes which are needed to accommodate different radial penetrations for the cyclotron operation (Fig. 1). However, we’ve used a simplified axisymmetric finite element model of the magnet made up of a 1/4th sector by incorporating an air volume in the median plane representing the equivalent median plane cut out volumes. The commercially available ANSYS finite element software was used for this purpose. The main steps carried out in this analysis have been: 1. Coil current: a. Ia = 0, Ib varied (Case-I) b. Ib = 0, Ia varied (Case-II) 2. Magnetic forces were estimated 3. Stress was calculated using the Lorentz force data obtained from step 2. The dominant stress, i.e. circumferential stress, at the outer wall and inner wall was plotted (Fig. 3). The stress values in the other directions are rather small than the circumferential stress value and were not considered assuming that they cannot produce any significant changes in the crack size. Comparative plot of the helium vessel circumferential (hoop) stress component has been summarized in Fig. 4. Fig. 4 reveals that the inner wall hoop stress due to b-coil is more than a-coil. Hence the b-coil should have more effect than the a-coil in case any weld zone leak is present there. But it is already experimentally known that the a-coil is dominating from insulation vacuum degradation point of view [7]. So, it can be inferred that the weld zone on the inner wall is probably not the place where the leak is present. On the other hand, the hoops stress due to the a-coil is more than the b-coil in the outer wall. This result supports the experimental observation that the a-coil is more dominating. It may, therefore, be concluded that the probable leak is in the outer wall. Further simulations for the outer wall median plane weld zone stress for different coil current combinations (including Ia = Ib) were carried out. It was observed that 1 A current in b coil produces the same stress as generated by 0.63 A current in a coil.
Fig. 4. Circumferential stress in the median plane weld zone.
Therefore one can invoke an equivalent current Ia_eqv which is a combination of currents in a and b coils as shown below -
Ia
eqv
¼ Ia þ 0:63Ib
ð2Þ
Here, Ia_eqv means that a current of Ia_eqv passing solely through
a coil (with Ib = 0) will result in the same value of circumferential
stress at the outer wall weld zone as when currents Ia and Ib are set in individual coils concurrently. In a magnetic system, the magnetic stress is expected to be dependent on the square of the magnetic field, and, hence, on the square of the current. Using the equivalence, two curves for the outer wall of Fig. 4 are plotted with abscissa as I2a_eqv in Fig. 5. Additionally, a case of Ia = Ib has been converted to Ia_eqv using the mentioned equivalence and plotted in Fig. 5. It can be clearly seen that all the three curves coincide. Hence, 100 A of coil current sent in both the a and b coils will produce same stress at the outer wall weld zone as solely 163 A current passing in the a-coil. It is interesting to note that this result agrees qualitatively with that of the vacuum degradation results. The difference is that in the degradation case, the effect of bcurrent is a little less, 1 A of b-current is equivalent to 0.4 A of acurrent. This difference may be attributed to the fact that though the opening of the crack size depends upon the stress value, the flow through the crack also depends on the flow-regime (viscous or molecular or mixed) of the flow. During development of this superconducting magnet, the inner wall of the annular helium vessel has been thoroughly cryoshocked separately and examined before coil winding. Hence it is almost a rare possibility that the defect will be in the inner wall weld. After coil winding and welding of the outer wall of the helium chamber, no such cryoshocking test was carried out, and vacuum leak testing was done only at room temperature. Hence, the probability of the presence of a cold leak in the weld zone is more reasonable for outer wall. This observation agrees with the conclusion of stress analysis simulation. 4. Growth of leak size with current and comparison with experimental result 4.1. Estimation of initial leak size at 4.2 K without current
Fig. 3. Helium vessel circumferential stress at Ia = 500 A & Ib = 0 A.
The helium vessel was checked for global leak rate at room temperature after closure welding of the outer wall of helium vessel, and the leak rate was found to be 1.15 107 mbar-lit/s. The theoretically expected leak rate at 4.2 K would be 4620 times [12]
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Fig. 5. Dependence of the circumferential stress (r) on the effective coil current Ia_eqv.
more than the room temperature value. So, the calculated value of leak rate at LHe temperature is expected to be 5 104 mbar-lit/s at 4.2 K. Again, experimentally observed leak rate at 500 A (Q500 A) is 1 102 mbar-lit/s [7]. From the characteristics graph of turbomolecular vacuum pump [13], it can be reasonably assumed that the pumping speed (S) of the turbomolecular pump remains constant within our calculation zone (till 3 104 mbar). Hence we can write-
Hence for the practical purpose, the initial leak rate of the cryogenic vessel at 4.2 K without any current in the coil is considered to be 1.2 105 mbar-lit/s. Also from Section 3, it has been concluded that the probable leak is in the outer wall which is 6 mm thick. With these inputs, the theoretical equivalent cylindrical leak diameter has been calculated. It has been predicted that the initial leak size for a cylindrical leak is of 1.08 lm diameter assuming viscous flow and 6.5 lm considering molecular flow.
Q 500 A =Q 0 A ¼ S P 500 A =S P0 A
4.2. Estimation of change in leak size with current
ð3Þ
Using values of P500 A = 3 104 mbar, P0 A = 3.7 107 mbar in Eq. (3), leak rate at no current (Q0 A) becomes 1.2 105 mbar-lit/s, which is approximately 50 times less than the value (5 104 mbar-lit/s) expected at 4.2 K estimated from the global leak rate value. This leak rate variation is very much consistent with the work of Mallory and Laumer [6], who observed similar discrepancy in a similar type of system for the unknown type of leak and found it to be consistent with their calculation based on two-phase flow model.
The helium vessel can be simplified to a schematic model shown in Fig. 6. We can write, [14]
Q ¼ C ðP1 P 2 Þ ¼ S P2
ð4Þ
where Q = leak rate, C = Conductance, P2 = Insulation Vacuum, P1 = helium vessel pressure, S = effective pumping speed of pumping system.
Fig. 6. Simplified schematic model of helium vessel.
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Fig. 8. Schematic of elliptical leak under tensile stress.
Fig. 7. Change of normalized diameter with coil current.
From Eq. (4), for a constant Pumping speed (S), the Insulation vacuum (P2) is proportional to leak rate (Q). The term (P1-P2) of Eq. (5) can be fairly assumed to be constant since P1(=1.2 bar) P2 (10n mbar, n varying from 7 to 4). Hence P2 becomes directly proportional to C. Thus, for two different regimes of gas flow, we have
P2 ad for viscous flow
ð5Þ
P2 ad for Molecular flow
ð6Þ
4
3
where d ¼ leak diameter assuming a cylindrical leak: Using Eqs. (5) and (6) the possible normalized leak diameter Instantaneous diameter; D (assuming both viscous flow and molecular Initial leak diameter; d0
flow) has been found out from the different insulation vacuum values corresponding to various coil currents. The results have been plotted in Fig. 7. It is understood that for an assumed viscous flow through the opening the final leak size increased 4.5 times of the initial size and could be 7.2 times for a molecular flow at 500 A coil current.
lowering the value of the parameter
4.3. Estimation of leak rate variation with current The electromagnetic stress analysis simulation results reveal that the weld region stress is tensile. As a result, the size of any prior weld defects may increase due to the presence of circumferential tensile stress. The main aim of this section is to predict the shape and size of the leak by comparing the trend in the change of leak rate with current for different cases and comparing it with available experimental data. The actual leak need not necessarily be of regular cylindrical geometry. Rather the leak is expected to be of irregular shape. Also, the flow (Fig. 6) through the leak is neither purely viscous nor purely molecular [15]. Comparison of leak diameter with the mean free path corresponding to 1.2 bar inlet pressure suggests that the flow is viscous in the upstream of the leak. But when the leak diameter is correlated to the mean free path corresponding to the downstream vacuum condition, it indicates that the flow is molecular. Actually, the total flow (Qt) may be assumed to be partly viscous flow (Qv) and partly molecular flow (Qm). So we can write:
Q t ¼ f Q v þ ð1 f Þ Q m
cylindrical leak diameter, which is the diameter of a circle that has the same cross-sectional area as of the deformed geometry of simulated elliptical area of interest, is derived. It basically conserves the mass flow conservation equation assuming that the entire leak path is of uniform cross section. Finally, the leak rate has been calculated based on the equivalent cylindrical diameter. Simulation has been done using ANSYS software. It is understood that the crack becomes wider when the wall is stretched. Hence, the defect in the weld zone was modeled as linear crack, perpendicular to the stress field, on a simplified flat plate geometry. Accordingly, an elliptical leak was modeled as shown in Fig. 8. Many iterations were made assuming various elliptical leak size that will match the initial leak rate as well as fit the trend of the rise of leak rate with the current. Finally, the width of an elliptical opening (of major diameter 350 lm) were varied, and the change in equivalent diameter of the leak geometry has been estimated. Using Q = SP2 (Eq. (4)) and assuming S to be constant, the leak rate was obtained from experimental data of different insulation vacuum (corresponding to different coil currents). Thus we could compare the actual leak rate with simulated one. A typical plot for two extreme flow (f = 0 i.e. molecular flow and f = 1, i.e. viscous flow) conditions through the leak is shown in Fig. 9. For the fixed upstream and downstream boundary conditions, the nature of flow though the leak depends on the defect geometry, mainly the pinhole diameter. For the same upstream and downstream pressure boundary condition, the mean free path in both the upstream and downstream remains unchanged. However, with mean free path , pinhole diameter of the leak
the flow
through the leak approaches viscous zone. With the higher current in the coil the pinhole diameter of the leak increases and thus from Fig. 9 it appears that the flow approaches towards viscous zone at higher current. To estimate the closeness between the simulated leak rate (Qs) and experimental leak rate (Qe) data, we also calculated goodness qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi parameter (E), ¼ RðQe QsÞ2 , which measures the least square
ð7Þ
where f is a factor between 0 and 1 indicating the proportion of viscous flow. A quarter symmetry model was used for simulating the leak size change with current. The obtained values of circumferential stress from the magneto-structural analysis was applied as far field stress on a flat plate with assumed initial elliptical leak. From the deformed geometry of simulated leak under stress, an equivalent
Fig. 9. Leak rate comparison between the experiment and a typical simulation (Crack length 350 lm & width 0.0053 lm).
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leak gets influenced by the electromagnetic stress generated by the superconducting magnet. Consequent degradation of insulation vacuum is seen to be larger when a-coil is energized. The interaction between magnetic field induced stresses and mechanical deformation of an existing leak has been investigated. The predicted behavior of leak opening from the simulated model is consistent with the experimental results. The results allow us to summarize as follows.
Fig. 10. Error estimation.
1. Both experimental data and modeling were used to locate a vacuum leak in a large superconducting magnet system. Such an approach may well be applied to other complicated leak questions. 2. Prior cryoshocking of all the weld zone of a cryogenic vessel after completion of welding is a must if one wants to avoid generation of the cold leak during operation. The cryoshocking will amplify any existing defects and detection of it will enable to fix it during fabrication stage itself. If the cold mass is too heavy to handle, alternatively, liquid nitrogen may be sprayed in the weld zone locally instead of immersing the whole mass in a cryogenic liquid. 3. For the first cool-down and excitation of the superconducting coils, a simplified dummy vacuum chamber (without the radial penetrations) may be used. This arrangement will help in easy and quick disassembly and overhaul of the helium vessel in the case of failure of the cryogenic components. In future, this work may be extended further for determination of acceptable crack size at room temperature for any high field superconducting magnet to minimize chances of cold leak. The permissible thermal shock (cooling rate) allowed may also be calculated considering the allowed crack size at room temperature. References
Fig. 11. Leak rate comparison between simulation and experiment.
difference between two sets of data. Fig. 10 shows a 3D plot of the E as a function of the initial crack width and the viscous flow proportion f. The parameter, E is found to be minimum (= 1.1) for elliptical opening (major diameter = 350 lm) with aspect ratio of 0.0000015 (i.e. 350 0.000015 = 0.0053 lm) and f = 0.23 (i.e. the total flow is assumed to be 23% viscous). The change in leak rate for this particular simulated case (i.e. minimum E) has been plotted and compared with the experimental results in Fig. 11. We have operated the magnet up to a current of 550 A and found the insulation vacuum restores back to its initial value once the coil current is made zero. Therefore no permanent damage sets in. The crack tip stress of this defect geometry at 740 A of current in both the coils just exceeds the elastic limit of SS316L at 4 K (431 MPa [16]). Hence it ensures no permanent change in the size of the leak up to 740 A of operating current. The limitation comes from the increased cryogenic cost due to degraded insulation vacuum. 5. Conclusion The present work indicates that during installation, a cold leak developed in the outer wall of the cryogenic vessel. The size of the
[1] Blosser HG, The Michigan State University superconducting cyclotron program. In: Proc of the 8th int conf on cyclotrons and their applications, Bloomington, USA; 1979. p. 2040–47. [2] May DP et al. Status of the Texas A&M K500 superconducting cyclotron. In: Proc of the 10th int conf on cyclotrons and their applications, East Lansing, Michigan, USA; 1984. p. 267–70. [3] Acerbi E et al. Progress report on the Milan superconducting cyclotron. In: Proc of the 12th int conf. on cyclotrons and their applications, Berlin; 1989. p. 26– 29. [4] Bhandari RK, Sinha Bikash, Status of K500 superconducting cyclotron project at Kolkata. In: proc of 18th int conf on cyclotron and their applications, Giardini Naxos, Italy; 2007. p. 51–3. [5] Davis R et al. Measurement of helium leak rates with temperature and pressure in RHIC. Vacuum 2001:131–5. [6] Mallory M et al. Cryogenic leak test procedure for a large superconducting cyclotron helium vessel. Nucl Instr Meth Phys Res 1985;A241:14–6. [7] Bhattacharyya P et al. Electro-magnetic stress-induced degradation of insulation vacuum of a large cryo-magnetic system. Cryogenics 2016;77:8–14. [8] Dutta M, Polley A. Detection of unapproachable leaks in VECC K-500 superconducting cyclotron, Indian national particle accelerator conf, InPAC India; 2013. p. 597–9. [9] Bhunia U et al. Operational experience of superconducting cyclotron at VECC, Kolkata. In: Proc of CYCLOTRONS 2010, China; 2010. p. 203–5. [10] Naser et al. Study of vacuum related problems during the energization of K500 superconducting cyclotron. In: Proc of the Asian particle accelerator conf, India 2007; 2007. p. 694–6. [11] Bhattacharyya P et al. Experiment and analysis: partial loss of insulation vacuum in K-500 superconducting cyclotron during energization. In: Proc of CYCLOTRONS 2010, China; 2010. p. 248–50. [12] Olmes JL, Palmy C. Cryogenics, CERN accelerator school: superconductivity in particle accelerators. CERN 1989:89–104. [13] Varian Vacuum Technology, Instruction Manual-87-900-934-01(D), September 2003. p. 30. [14] Rath A. Vacuum technology, 2nd ed., North-Holland; 1976. p. 65. [15] Hucknall DJ, Morris A. Vacuum technology calculations in chemistry. The Royal society of chemistry; 2003. p. 116. [16] Suzuki Kenichi, Fukakura Juichi, Kashiwaya Hideo. Near threshold fatigue crack growth of austenitic stainless steel at liquid helium temperature. Advances in cryogenics engineering, vol. 38A, 1992. p. 149–58.
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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Theoretical and experimental investigation of magnetic field related helium leak in helium vessel of a large superconducting magnet Pranab Bhattachryya a,b,⇑, Anjan Dutta Gupta a,b, S. Dhar c, P.R. Sarma b, Paramita Mukherjee a,b a
Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata 700064, India Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India c Jadavpur University, Kolkata 700032, India b
a r t i c l e
i n f o
Article history: Received 25 November 2016 Received in revised form 2 March 2017 Accepted 17 March 2017 Available online 18 March 2017
a b s t r a c t The helium vessel of the superconducting cyclotron (SCC) at the Variable Energy Cyclotron centre (VECC), Kolkata shows a gradual loss of insulation vacuum from 107 mbar to 104 mbar with increasing coil current in the magnet. The insulation vacuum restores back to its initial value with the withdrawal of current. The origin of such behavior has been thought to be related to the electromagnetic stress in the magnet. The electromagnetic stress distribution in the median plane of the helium vessel was studied to figure out the possible location of the helium leak. The stress field from the possible location was transferred to a simplified 2D model with different leak geometries to study the changes in conductance with coil current. The leak rate calculated from the changes in the leak geometry was compared with the leak rate calculated from the experimental insulation vacuum degradation behavior to estimate the initial leak shape and size. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Superconducting cyclotrons at high energy cyclotron facilities at Michigan State University [1], Texas A&M University [2], Milano [3] and VECC [4] use large superconducting magnets for producing high magnetic fields. These magnets operate at bath-cooled mode with LHe at 4 K. An insulation vacuum (107 mbar) jacket encompasses the cold mass of these magnets to minimize heat load to the LHe. At 4 K temperature, most of the gases in the insulation vacuum jacket space are effectively cryopumped by the cold mass of the magnet. Any rise in pressure in the vacuum jacket is generally due to helium leak from the LHe vessel [5]. These internal helium leaks may originate from the propagation of small cracks due to thermal stress during cool down of the coil to cryogenic temperature. The thermal stress can introduce a crack in the weld or more likely open a leak which was plugged by contamination (e.g. dirt, weld impurities, or water) [6]. During the first LHe filling of the VECC magnet, a small but significant deterioration of insulation vacuum was observed. This degradation occurred when the LHe level reached near the median plane (i.e. the horizontal symmetry plane of the magnet) [7]. It confirmed the opening of some cold leaks in the median plane near ⇑ Corresponding author at: Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata 700064, India. E-mail address: [email protected] (P. Bhattachryya). http://dx.doi.org/10.1016/j.cryogenics.2017.03.005 0011-2275/Ó 2017 Elsevier Ltd. All rights reserved.
the weld zone. Moreover, it was observed, during operation, that the insulation vacuum further degraded significantly with the increase of coil current. However, the insulation vacuum improved and reverted to its initial value (i.e. the insulation vacuum value with filled up LHe) once the magnet was de-energized. The magnet could be operated up to 550 A (about 70% of the maximum value of 800 A), as the existing refrigeration plant could not handle increased heat load due to degraded insulation vacuum. The magnet of SCC at VECC has two coils, viz., a-coil and b-coil (Fig. 1). It was further observed that the effect of the a-coil on the degradation of vacuum is much higher than the b-coil. It is very difficult to locate and repair any leak of the inner helium vessel after constructing the vacuum jacket around it. It requires a major disassembly of the cryostat to access to the leak location. Previous studies were carried out for addressing several aspects of the problem. Dutta et al. [8] mentioned the existence of unapproachable critical leaks which were related to the magnetic field. Bhunia et al. [9] discussed their operational experience about the satisfactory performance of the magnet cryostat coupled with the liquid helium refrigerator with moderate currents (550 A) in both the coils and subsequent slow dump at higher current. Naser et al. [10] concluded that the electro-magnetic stress due to Lorentz force increased with current but did not report any detailed stress analysis of the helium vessel. Bhattacharyya et al. [7,11] quantified the amount of excess heat load arising due to degraded insulation vacuum through experiments and theoretical analysis.
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Fig. 1. Schematic view of K500 superconducting cyclotron (SCC) magnet.
In the present work, a coupled electromagnetic and structural analysis has been made for finding out the magnetic field distribution and the stress pattern at the inner and outer wall weld joints near the median plane of the helium vessel at several different combinations of coil current. It is seen that near median plane, there exists a tensile stress pattern which may open up any existing crack. The stress field from the possible location was transferred to a simplified 2D model with different leak geometries to study the change in conductance. The leak rate calculated from the change in the leak geometry was compared with the leak rate that was calculated from experimental insulation vacuum degradation behavior to estimate the initial leak shape and size. The maximum allowable coil current was determined based on the estimated initial leak size and crack tip stress. 2. Effect of coil current on degradation of insulation vacuum The superconducting magnet of K500 SCC at VECC uses Nb-Ti superconducting coils. The coil consists of two halves (upper and lower sides of the median plane), and each half is again split into a large (b-coil) and a short (a-coil) coil as shown in Fig. 1. The superconducting coil is housed in an annular liquid helium vessel made of SS 316L material. It is surrounded by a copper thermal shield at 80 K, cooled by liquid nitrogen. The shield and the helium vessel is wrapped with multiple layers of superinsulation and is placed inside an outer vacuum enclosure (AISI 1020) to insulate it from the ambient heat. A high insulation vacuum (107 mbar) is maintained in the vessel by continuous pumping via. a turbo-molecular pump backed by a scroll pump. The pump is located 2.5 m away from the magnet to keep the pump away from the high magnetic field. During operation, it is observed that the insulation vacuum deteriorates with increase in coil current. A similar turbomolecular pump with a small experimental vacuum chamber was placed separately there (i.e. adjacent to the actual insulation vacuum turbo-molecular pump), and the pumping speed was found to be uninfluenced by the local magnetic field present there due to energization of the superconducting magnet. Thereby reconfirms that a leak was present in the helium chamber, and it is not that the pumping speed is getting reduced due to the magnetic field. This degradation of insulation vacuum finally limits the operation of the magnet well below the rated operating current.
Operational experience further shows that the effect of the bcoil on the deterioration of vacuum is much less than that of the a-coil [7]. The operational data has been analyzed, and it has been found that 0.4 A current in a-coil (Ia) produces the same insulation vacuum degradation as 1 A current in b-coil (Ib) does. Around 250 operational data points of loss of insulation vacuum with different current combination have been further studied, and an empirical relation (Eq. (1)) is proposed to fit with the experimental data within ±10% error. 2
LogðPÞ ¼ a þ by þ cy4 þ dy
6
ð1Þ
where P = insulation vacuum (mbar), a = 5.587, b = 7.21 107, c = 1.609 1011, d = 1.26 1017 and y = Ia + 0.4 Ib. Using Eq. (1), the full surface (Fig. 2) has been generated for predicting vacuum degradation at different current combinations. Fig. 2 clearly shows that the effect of a-coil is more dominant on insulation vacuum degradation than that of the b-coil. In the earlier work [7], we made an attempt to correlate the coil current with the extent of vacuum degradation. We surmised that an increase in the coil current raises the stress in the weld zone which, in turn, opens up the cold-leak and thus degrades the vacuum.
Fig. 2. Degradation of insulation vacuum at different coil currents in a- and b-coils.
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3
3. Effect of coil current on helium vessel stress In this section, we aimed at analyzing how the helium vessel weld zone stresses depend on the different combinations of coil currents. The median plane iron has a lot of cut outs of different sizes which are needed to accommodate different radial penetrations for the cyclotron operation (Fig. 1). However, we’ve used a simplified axisymmetric finite element model of the magnet made up of a 1/4th sector by incorporating an air volume in the median plane representing the equivalent median plane cut out volumes. The commercially available ANSYS finite element software was used for this purpose. The main steps carried out in this analysis have been: 1. Coil current: a. Ia = 0, Ib varied (Case-I) b. Ib = 0, Ia varied (Case-II) 2. Magnetic forces were estimated 3. Stress was calculated using the Lorentz force data obtained from step 2. The dominant stress, i.e. circumferential stress, at the outer wall and inner wall was plotted (Fig. 3). The stress values in the other directions are rather small than the circumferential stress value and were not considered assuming that they cannot produce any significant changes in the crack size. Comparative plot of the helium vessel circumferential (hoop) stress component has been summarized in Fig. 4. Fig. 4 reveals that the inner wall hoop stress due to b-coil is more than a-coil. Hence the b-coil should have more effect than the a-coil in case any weld zone leak is present there. But it is already experimentally known that the a-coil is dominating from insulation vacuum degradation point of view [7]. So, it can be inferred that the weld zone on the inner wall is probably not the place where the leak is present. On the other hand, the hoops stress due to the a-coil is more than the b-coil in the outer wall. This result supports the experimental observation that the a-coil is more dominating. It may, therefore, be concluded that the probable leak is in the outer wall. Further simulations for the outer wall median plane weld zone stress for different coil current combinations (including Ia = Ib) were carried out. It was observed that 1 A current in b coil produces the same stress as generated by 0.63 A current in a coil.
Fig. 4. Circumferential stress in the median plane weld zone.
Therefore one can invoke an equivalent current Ia_eqv which is a combination of currents in a and b coils as shown below -
Ia
eqv
¼ Ia þ 0:63Ib
ð2Þ
Here, Ia_eqv means that a current of Ia_eqv passing solely through
a coil (with Ib = 0) will result in the same value of circumferential
stress at the outer wall weld zone as when currents Ia and Ib are set in individual coils concurrently. In a magnetic system, the magnetic stress is expected to be dependent on the square of the magnetic field, and, hence, on the square of the current. Using the equivalence, two curves for the outer wall of Fig. 4 are plotted with abscissa as I2a_eqv in Fig. 5. Additionally, a case of Ia = Ib has been converted to Ia_eqv using the mentioned equivalence and plotted in Fig. 5. It can be clearly seen that all the three curves coincide. Hence, 100 A of coil current sent in both the a and b coils will produce same stress at the outer wall weld zone as solely 163 A current passing in the a-coil. It is interesting to note that this result agrees qualitatively with that of the vacuum degradation results. The difference is that in the degradation case, the effect of bcurrent is a little less, 1 A of b-current is equivalent to 0.4 A of acurrent. This difference may be attributed to the fact that though the opening of the crack size depends upon the stress value, the flow through the crack also depends on the flow-regime (viscous or molecular or mixed) of the flow. During development of this superconducting magnet, the inner wall of the annular helium vessel has been thoroughly cryoshocked separately and examined before coil winding. Hence it is almost a rare possibility that the defect will be in the inner wall weld. After coil winding and welding of the outer wall of the helium chamber, no such cryoshocking test was carried out, and vacuum leak testing was done only at room temperature. Hence, the probability of the presence of a cold leak in the weld zone is more reasonable for outer wall. This observation agrees with the conclusion of stress analysis simulation. 4. Growth of leak size with current and comparison with experimental result 4.1. Estimation of initial leak size at 4.2 K without current
Fig. 3. Helium vessel circumferential stress at Ia = 500 A & Ib = 0 A.
The helium vessel was checked for global leak rate at room temperature after closure welding of the outer wall of helium vessel, and the leak rate was found to be 1.15 107 mbar-lit/s. The theoretically expected leak rate at 4.2 K would be 4620 times [12]
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Fig. 5. Dependence of the circumferential stress (r) on the effective coil current Ia_eqv.
more than the room temperature value. So, the calculated value of leak rate at LHe temperature is expected to be 5 104 mbar-lit/s at 4.2 K. Again, experimentally observed leak rate at 500 A (Q500 A) is 1 102 mbar-lit/s [7]. From the characteristics graph of turbomolecular vacuum pump [13], it can be reasonably assumed that the pumping speed (S) of the turbomolecular pump remains constant within our calculation zone (till 3 104 mbar). Hence we can write-
Hence for the practical purpose, the initial leak rate of the cryogenic vessel at 4.2 K without any current in the coil is considered to be 1.2 105 mbar-lit/s. Also from Section 3, it has been concluded that the probable leak is in the outer wall which is 6 mm thick. With these inputs, the theoretical equivalent cylindrical leak diameter has been calculated. It has been predicted that the initial leak size for a cylindrical leak is of 1.08 lm diameter assuming viscous flow and 6.5 lm considering molecular flow.
Q 500 A =Q 0 A ¼ S P 500 A =S P0 A
4.2. Estimation of change in leak size with current
ð3Þ
Using values of P500 A = 3 104 mbar, P0 A = 3.7 107 mbar in Eq. (3), leak rate at no current (Q0 A) becomes 1.2 105 mbar-lit/s, which is approximately 50 times less than the value (5 104 mbar-lit/s) expected at 4.2 K estimated from the global leak rate value. This leak rate variation is very much consistent with the work of Mallory and Laumer [6], who observed similar discrepancy in a similar type of system for the unknown type of leak and found it to be consistent with their calculation based on two-phase flow model.
The helium vessel can be simplified to a schematic model shown in Fig. 6. We can write, [14]
Q ¼ C ðP1 P 2 Þ ¼ S P2
ð4Þ
where Q = leak rate, C = Conductance, P2 = Insulation Vacuum, P1 = helium vessel pressure, S = effective pumping speed of pumping system.
Fig. 6. Simplified schematic model of helium vessel.
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Fig. 8. Schematic of elliptical leak under tensile stress.
Fig. 7. Change of normalized diameter with coil current.
From Eq. (4), for a constant Pumping speed (S), the Insulation vacuum (P2) is proportional to leak rate (Q). The term (P1-P2) of Eq. (5) can be fairly assumed to be constant since P1(=1.2 bar) P2 (10n mbar, n varying from 7 to 4). Hence P2 becomes directly proportional to C. Thus, for two different regimes of gas flow, we have
P2 ad for viscous flow
ð5Þ
P2 ad for Molecular flow
ð6Þ
4
3
where d ¼ leak diameter assuming a cylindrical leak: Using Eqs. (5) and (6) the possible normalized leak diameter Instantaneous diameter; D (assuming both viscous flow and molecular Initial leak diameter; d0
flow) has been found out from the different insulation vacuum values corresponding to various coil currents. The results have been plotted in Fig. 7. It is understood that for an assumed viscous flow through the opening the final leak size increased 4.5 times of the initial size and could be 7.2 times for a molecular flow at 500 A coil current.
lowering the value of the parameter
4.3. Estimation of leak rate variation with current The electromagnetic stress analysis simulation results reveal that the weld region stress is tensile. As a result, the size of any prior weld defects may increase due to the presence of circumferential tensile stress. The main aim of this section is to predict the shape and size of the leak by comparing the trend in the change of leak rate with current for different cases and comparing it with available experimental data. The actual leak need not necessarily be of regular cylindrical geometry. Rather the leak is expected to be of irregular shape. Also, the flow (Fig. 6) through the leak is neither purely viscous nor purely molecular [15]. Comparison of leak diameter with the mean free path corresponding to 1.2 bar inlet pressure suggests that the flow is viscous in the upstream of the leak. But when the leak diameter is correlated to the mean free path corresponding to the downstream vacuum condition, it indicates that the flow is molecular. Actually, the total flow (Qt) may be assumed to be partly viscous flow (Qv) and partly molecular flow (Qm). So we can write:
Q t ¼ f Q v þ ð1 f Þ Q m
cylindrical leak diameter, which is the diameter of a circle that has the same cross-sectional area as of the deformed geometry of simulated elliptical area of interest, is derived. It basically conserves the mass flow conservation equation assuming that the entire leak path is of uniform cross section. Finally, the leak rate has been calculated based on the equivalent cylindrical diameter. Simulation has been done using ANSYS software. It is understood that the crack becomes wider when the wall is stretched. Hence, the defect in the weld zone was modeled as linear crack, perpendicular to the stress field, on a simplified flat plate geometry. Accordingly, an elliptical leak was modeled as shown in Fig. 8. Many iterations were made assuming various elliptical leak size that will match the initial leak rate as well as fit the trend of the rise of leak rate with the current. Finally, the width of an elliptical opening (of major diameter 350 lm) were varied, and the change in equivalent diameter of the leak geometry has been estimated. Using Q = SP2 (Eq. (4)) and assuming S to be constant, the leak rate was obtained from experimental data of different insulation vacuum (corresponding to different coil currents). Thus we could compare the actual leak rate with simulated one. A typical plot for two extreme flow (f = 0 i.e. molecular flow and f = 1, i.e. viscous flow) conditions through the leak is shown in Fig. 9. For the fixed upstream and downstream boundary conditions, the nature of flow though the leak depends on the defect geometry, mainly the pinhole diameter. For the same upstream and downstream pressure boundary condition, the mean free path in both the upstream and downstream remains unchanged. However, with mean free path , pinhole diameter of the leak
the flow
through the leak approaches viscous zone. With the higher current in the coil the pinhole diameter of the leak increases and thus from Fig. 9 it appears that the flow approaches towards viscous zone at higher current. To estimate the closeness between the simulated leak rate (Qs) and experimental leak rate (Qe) data, we also calculated goodness qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi parameter (E), ¼ RðQe QsÞ2 , which measures the least square
ð7Þ
where f is a factor between 0 and 1 indicating the proportion of viscous flow. A quarter symmetry model was used for simulating the leak size change with current. The obtained values of circumferential stress from the magneto-structural analysis was applied as far field stress on a flat plate with assumed initial elliptical leak. From the deformed geometry of simulated leak under stress, an equivalent
Fig. 9. Leak rate comparison between the experiment and a typical simulation (Crack length 350 lm & width 0.0053 lm).
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leak gets influenced by the electromagnetic stress generated by the superconducting magnet. Consequent degradation of insulation vacuum is seen to be larger when a-coil is energized. The interaction between magnetic field induced stresses and mechanical deformation of an existing leak has been investigated. The predicted behavior of leak opening from the simulated model is consistent with the experimental results. The results allow us to summarize as follows.
Fig. 10. Error estimation.
1. Both experimental data and modeling were used to locate a vacuum leak in a large superconducting magnet system. Such an approach may well be applied to other complicated leak questions. 2. Prior cryoshocking of all the weld zone of a cryogenic vessel after completion of welding is a must if one wants to avoid generation of the cold leak during operation. The cryoshocking will amplify any existing defects and detection of it will enable to fix it during fabrication stage itself. If the cold mass is too heavy to handle, alternatively, liquid nitrogen may be sprayed in the weld zone locally instead of immersing the whole mass in a cryogenic liquid. 3. For the first cool-down and excitation of the superconducting coils, a simplified dummy vacuum chamber (without the radial penetrations) may be used. This arrangement will help in easy and quick disassembly and overhaul of the helium vessel in the case of failure of the cryogenic components. In future, this work may be extended further for determination of acceptable crack size at room temperature for any high field superconducting magnet to minimize chances of cold leak. The permissible thermal shock (cooling rate) allowed may also be calculated considering the allowed crack size at room temperature. References
Fig. 11. Leak rate comparison between simulation and experiment.
difference between two sets of data. Fig. 10 shows a 3D plot of the E as a function of the initial crack width and the viscous flow proportion f. The parameter, E is found to be minimum (= 1.1) for elliptical opening (major diameter = 350 lm) with aspect ratio of 0.0000015 (i.e. 350 0.000015 = 0.0053 lm) and f = 0.23 (i.e. the total flow is assumed to be 23% viscous). The change in leak rate for this particular simulated case (i.e. minimum E) has been plotted and compared with the experimental results in Fig. 11. We have operated the magnet up to a current of 550 A and found the insulation vacuum restores back to its initial value once the coil current is made zero. Therefore no permanent damage sets in. The crack tip stress of this defect geometry at 740 A of current in both the coils just exceeds the elastic limit of SS316L at 4 K (431 MPa [16]). Hence it ensures no permanent change in the size of the leak up to 740 A of operating current. The limitation comes from the increased cryogenic cost due to degraded insulation vacuum. 5. Conclusion The present work indicates that during installation, a cold leak developed in the outer wall of the cryogenic vessel. The size of the
[1] Blosser HG, The Michigan State University superconducting cyclotron program. In: Proc of the 8th int conf on cyclotrons and their applications, Bloomington, USA; 1979. p. 2040–47. [2] May DP et al. Status of the Texas A&M K500 superconducting cyclotron. In: Proc of the 10th int conf on cyclotrons and their applications, East Lansing, Michigan, USA; 1984. p. 267–70. [3] Acerbi E et al. Progress report on the Milan superconducting cyclotron. In: Proc of the 12th int conf. on cyclotrons and their applications, Berlin; 1989. p. 26– 29. [4] Bhandari RK, Sinha Bikash, Status of K500 superconducting cyclotron project at Kolkata. In: proc of 18th int conf on cyclotron and their applications, Giardini Naxos, Italy; 2007. p. 51–3. [5] Davis R et al. Measurement of helium leak rates with temperature and pressure in RHIC. Vacuum 2001:131–5. [6] Mallory M et al. Cryogenic leak test procedure for a large superconducting cyclotron helium vessel. Nucl Instr Meth Phys Res 1985;A241:14–6. [7] Bhattacharyya P et al. Electro-magnetic stress-induced degradation of insulation vacuum of a large cryo-magnetic system. Cryogenics 2016;77:8–14. [8] Dutta M, Polley A. Detection of unapproachable leaks in VECC K-500 superconducting cyclotron, Indian national particle accelerator conf, InPAC India; 2013. p. 597–9. [9] Bhunia U et al. Operational experience of superconducting cyclotron at VECC, Kolkata. In: Proc of CYCLOTRONS 2010, China; 2010. p. 203–5. [10] Naser et al. Study of vacuum related problems during the energization of K500 superconducting cyclotron. In: Proc of the Asian particle accelerator conf, India 2007; 2007. p. 694–6. [11] Bhattacharyya P et al. Experiment and analysis: partial loss of insulation vacuum in K-500 superconducting cyclotron during energization. In: Proc of CYCLOTRONS 2010, China; 2010. p. 248–50. [12] Olmes JL, Palmy C. Cryogenics, CERN accelerator school: superconductivity in particle accelerators. CERN 1989:89–104. [13] Varian Vacuum Technology, Instruction Manual-87-900-934-01(D), September 2003. p. 30. [14] Rath A. Vacuum technology, 2nd ed., North-Holland; 1976. p. 65. [15] Hucknall DJ, Morris A. Vacuum technology calculations in chemistry. The Royal society of chemistry; 2003. p. 116. [16] Suzuki Kenichi, Fukakura Juichi, Kashiwaya Hideo. Near threshold fatigue crack growth of austenitic stainless steel at liquid helium temperature. Advances in cryogenics engineering, vol. 38A, 1992. p. 149–58.