Pressure drop of twophase helium along long cryogenic flexible transfer lines to support a superconducting RF operation at its cryogenic test stand
 M. H. Chang^{1}Email authorView ORCID ID profile,
 M. H. Tsai^{1},
 Ch. Wang^{1},
 M. C. Lin^{1},
 F. T. Chung^{1},
 M. S. Yeh^{1},
 L. H. Chang^{1},
 C. H. Lo^{1},
 T. C. Yu^{1},
 L. J. Chen^{1} and
 Z. K. Liu^{1}
Received: 21 June 2016
Accepted: 21 November 2016
Published: 5 December 2016
Abstract
Background
Establishing a standalone cryogenic test stand is of vital importance to ensure the highly reliable and available operation of superconducting radiofrequency module in a synchrotron light source. Operating a cryogenic test stand relies strongly on a capability to deliver twophase helium along long cryogenic transfer lines. A newly constructed cryogenic test stand with flexible cryogenic transfer lines of length 220 m at National Synchrotron Radiation Research Center is required to support a superconducting radiofrequency module operated at 126.0 kPa with a 40W dynamic load for a longterm reliability test over weeks. It is designed based on a simple analytical approach with the introduction of a socalled tolerance factor that serves to estimate the pressure drops in transferring a twophase helium flow with a substantial transfer cryogenic heat load. Tolerance factor 1.5 is adopted based on safety factor 1.5 commonly applied in cryogenic designs to estimate the total mass flow rate of liquid helium demanded. A maximum 60W dynamic load is verified with experiment measured with heater power 60 W instead after the cryogenic test stand has been installed.
Results
Aligning the modeled cryogenic accumulated static heat load with the results measured in situ, actual tolerance factor 1.287 is obtained. The feasibility and validity of our simple analytical approach with actual tolerance factor 1.287 have been scrutinized by using five test cases with varied operating conditions. Calculated results show the discrepancies of the pressure drops between the estimated and measured values for both liquid helium and cold gaseous helium transfer lines have an underestimate 0.11 kPa and an overestimate 0.09 kPa, respectively. A discrepancy is foreseen, but remains acceptable for engineering applications from a practical point of view.
Conclusions
The simple analytical approach with the introduction of a tolerance factor can provide not only insight into optimizing the choice of each lossy cryogenic piping element of the transfer lines in the design phase but also firm guidance for upgrading the present cryogenic transfer lines for its subsequent application.
Keywords
Background
Since its first introduction in Taiwan Light Source (TLS) at National Synchrotron Radiation Research Center (NSRRC) (Jensen 2011), 500MHz superconducting radiofrequency (SRF) modules are currently widely selected as RF accelerating cavities for newly constructed or upgraded thirdgeneration synchrotron light sources including Canadian Light Source (CLS, Canada), SOLEIL synchrotron (SOLEIL, France), Diamond Light Source (DLS, UK), Shanghai Synchrotron Radiation Facility (SSRF, China), Pohang Light Source II (PLSII, Korea), National Synchrotron Light Source II (NSLSII, USA) and Taiwan Photon Source (TPS, Taiwan). These SRF modules are all operated with dedicated closedloop 4.5K helium cryogenic plants. To fulfill the strict requirements of operational reliability and availability for users of synchrotron light sources, continuously improving or upgrading the operational performance of a SRF module has been considered necessary. Considering also the limited operational life expectancy of a SRF module, developing a standalone cryogenic test stand in house is commonly necessary to verify both the performance and the expected improvements, or a reliable examination of a SRF module that might be either newly constructed or repaired or to serve as a spare.
The cryogenic plant placed in service for the SRF module(s) on duty used in a synchrotron light source is typically oversized, following a standard rule of thumb commonly adopted to select a cryogenic plant with safety factor 1.5 for its refrigeration capacity. The inclusion of this safety factor opens a possibility to support a cryogenic test stand in a parasitic mode while maintaining an uninterrupted operation of the SRF modules on duty. The location of the cryogenic plant is commonly selected to be as near the SRF modules on duty as practical for the light source to benefit the routine operational efficiency, but the cryogenic test stand might be compelled to be located some distance from the main Dewar (MD) of the cryogenic plant because of space limitations. Under these circumstances, it becomes unavoidable to deliver liquid helium (LHe) from MD of a cryogenic plant to the tested SRF module at the cryogenic test stand to maintain the level balance of the SRF module and to send the evaporated cold gaseous helium (CGHe) from the tested SRF module to the cold box (CB) of a cryogenic plant to maintain the pressure balance of a SRF module over a long distance. Some operational challenges are consequently expected, such as insufficient pressure drops and a deterioration of the refrigeration capacity of the cryogenic plant. Both situations are induced mainly by the unexpected heat loads in the LHe and CGHe transfer lines. Such unexpected heat loads are easily introduced into a longdistance cryogenic transfer line. It might be questioned whether the guideline with safety factor 1.5 to account for the uncertainty of the heat load in the cryogenic designs is applicable also to the design of a longdistance cryogenic transfer line. Its validity must be verified for a design concept of this kind applied to longdistance cryogenic transfer lines of twophase helium flow.
The maximum deliverable rate of flow of LHe reserved for the operation of the tested SRF modules relies strongly on the available budget of the pressure drop. The acceptable operating pressure of the tested SRF module places a constraint on the pressure drops of the cryogenic transfer lines. As these lines suffer from unexpected pressure drops resulting from a transfer heat load or other causes, the maximum deliverable rate of helium flow falls short. An unaccountable heat load is easily introduced through various constraints at the cryogenic piping interfaces, an inappropriate piping path from constraints in civil engineering, assembly defects from human negligence etc. This extra heat load might transcend the original expectation to neglect the existence of a twophase fluid during the transfer of LHe and oversimplify the calculation of the pressure drop with a singlephase flow model. A twophase flow model must thus be considered in evaluating the pressure drop that becomes much larger than that obtained with a singlephase flow model. If the pressure drops of LHe and CGHe transfer lines are underestimated with a large error, the maximum accelerating gradient of the tested SRF module to be examined at the cryogenic test stand becomes significantly compromised because of either an unacceptable overpressure operation or an insufficient cooling capacity. In the worst case, a test of the longterm reliability of the tested SRF module becomes prohibitive because of a conflict with the cryogenic operation of the SRF modules on duty in the synchrotron light source. To avoid the abovementioned problems, we must ensure that the pressure drops of longdistance cryogenic transfer lines are designed to assure a total mass flow rate of LHe to meet the requirement of the cryogenic test stand. How to design cryogenic transfer lines over a long distance is an important challenge in establishing a cryogenic test stand. Three important factors must be taken into consideration: first, the maximum allowable pressure drops of cryogenic transfer lines must be specified depending on the operating pressure of the tested SRF module; second, plausible values of heat loads in the LHe supply lines must be estimated because they dominate the magnitude of the total mass flow rate; third, a twophase flow model to calculate the pressure drops of long cryogenic transfer lines with acceptable uncertainty must be available or developed.
The complication of calculating the pressure drop of a transfer line arises from the dynamic behavior of a twophase helium flow along the cryogenic transfer line. There exist two available theoretical models for a calculation of the pressure drop of twophase flow in a pipe, namely the classical Martinelli–Nelson equation (Martinelli and Nelson 1948) and the homogeneous equilibrium model (Collier 1981). The pressure drop of a turbulent twophase helium flow in a horizontal channel has been addressed with these two methods; experiments have been conducted to verify the same (Vishnev et al. 1982). Another relevant paper by Rane et al. (2011) reports a successful use of numerical simulation to modify the classical Martinelli–Nelson equation, and demonstrates the equivalence between the classical Martinelli–Nelson equation and the homogeneous equilibrium model. It also reproduces the pressure drop in helium transfer lines in experimental tests by Vishnev et al. (1982) and Mamedov et al. (1983). With the rapid development of computational speed in a computer, a homogenous twophase dynamic model based on continuity of mass, momentum and energy with pressure–volumetemperature relations (Regiera et al. 2011) is directly solvable after numerical discretization, which provides a theoretically reliable and accurate approach but at the cost of heavy computational resources. We prefer to apply a reliable, and approximate but efficient, approach involving only algebraic formulae to predict the pressure drop to minimize the design cost. Our theoretical model to calculate the frictional pressure drop of twophase flow adopts a homogeneous equilibrium model with a new definition of Reynolds number and the frictional factor of twophase flow, which was proposed by Shannak (2008), as presented in “Theoretical model for varied pressure drops” section below.
One must still determine the total heat load, i.e. the total mass flow rate, demanded under the test of a SRF module, which is used in the calculation of pressure drops of longdistance cryogenic transfer lines. The uncertainty of an estimate of the total heat load arises mainly from the heat loads of the LHe transfer lines. We aligned the accumulated static heat load from the engineering specifications of each LHe supply line provided by vendors with the measured value of a cryogenic transfer system as built. A tolerance factor is introduced in our alignment effort to take into consideration all construction uncertainties of the heat load and is also an effective merit of figure to verify the applicability of our calculational approach. Tolerance factor 1.5 is adopted as the safety margin of heat load of a LHe supply line to determine the total mass flow rate demanded in the test of a SRF module in the design phase, as is commonly used in cryogenic designs. After the transfer system is installed, the value of the actual tolerance factor can be verified on aligning the modeled accumulated static heat load with the results measured in situ. Additionally, after the actual accumulated static heat load from the LHe supply line is obtained, the actual total heat load at varied heater power applied on the tested SRF module will be deduced. In this paper, we take the 220m flexible cryogenic transfer lines as built at NSRRC as an example to introduce how to design long cryogenic transfer lines for a cryogenic test stand. This transfer system is originally designed with tolerance factor 1.5; the actual tolerance factor is found to be 1.287 by experiment after the system installation. The feasibility and validity of our simple analytical approach with actual tolerance factor 1.287 are verified using five test cases with varied operating conditions.
The structure of this paper is as follows. “Cryogenic test stand and its configurations” section describes the cryogenic layout to be discussed in this work. “Design process and test results of the cryogenic test stand” section explains the design process and the test results of the cryogenic test stand at NSRRC. “Results of experimental measurements” section summarizes the measured results from the cryogenic transfer lines as built. “Theoretical model for varied pressure drops” section presents our computational approach to determine algebraically the pressure drops of the twophase helium flow along a LHe supply line. “Heat loads of the cryogenic transfer lines” section introduces the concept of a tolerance factor and describes how to align it with the measured results. We discuss the results in “Results and discussion” section before a conclusion in “Conclusions” section.
Cryogenic test stand and its configurations
NSRRC operates two 470W, 4.5K helium cryogenic plants (Hsiao et al. 2008) simultaneously for the electron storage ring of TLS. During the standard operational scenario, CB #1 is to support the routine operation of the SRF module on duty (named S1) and CB #2 for five superconducting magnets. The latter serves also as a backup cryogenic plant for the SRF module on duty. This redundant design ensures a highly reliable and uninterrupted cryogenic operation of the SRF module and for the light source. The unloaded refrigeration capacity was originally designed to be sufficient to support one additional tested SRF module (named S0) operated at a large accelerating gradient for a longterm test run at its cryogenic test stand.
Rigid multichannel lines are commonly selected to transfer LHe over a long distance to take advantage of a small pressure drop and transfer heat load, but the piping path from the TLS cryogenic plant to the cryogenic test stand must pass through three separate buildings with varied piping elevation over a total piping length greater than 220 m. LN_{2}shielded, flexible cryogenic transfer lines of corrugated type were eventually chosen as a compromise considering several factors including the availability of the piping path, and quick, easy and cheap installation (Laeger et al. 1978; Blessing et al. 1990).
Cryogenic transfer lines L1 to L4, L12, g2, and g10 to g13, are solid pipes with smooth surfaces, but L5 to L11 and g3 to g9, between the first valve box, VB #1, and the second valve box, VB #2, are all corrugated flexible transfer lines. Lines L7 and L9, as well as g5 and g7, are concentric lines of fourtube design (CRYOFLEX) (Laeger et al. 1978; Blessing et al. 1990) with integrated length 205 m, whereas L6, L8, L10, g4, g6 and g8 are bayonet joints. Because of the varied piping elevation from the experimental hall of TLS to the building of the SRF laboratory, LHe supply lines L4–L12 and the CGHe return lines g2–g10 have cryogenic piping with ascending and descending sections. Figure 1 shows also the complicated piping path between VB #1 and VB #2, with details available in the article presented by Lin et al. (2010).
During the operation of the SRF module under test, the cryogenic valves at VB #1, for both LHe and CGHe, are operated in a manual mode with a fixed opening, typically fully open. The LHe valve at VB #2 regulates the LHe supply flow rate to maintain the SRF module with liquid at a constant level; the CGHe valve at VB #2 regulates the CGHe return flow rate from the SRF module to maintain constant its operational pressure at the LHe vessel. These two cryogenic regulating valves are controlled with independent controllers.
Design process and test results of the cryogenic test stand
A 500MHz superconducting cavity has a bellshaped shell structure with nominal thickness 3 mm and is made of highly pure niobium; its mechanical structure is thus weak and soft. The warm cavity itself has a susceptibility to buckle. Taking the TLS 500MHz SRF module as an example (shown in Fig. 1), its threshold buckling pressure is about 150–200 kPa (21.75–29 psia, 1500–2000 mbar) for the cavity when warm. This condition forces the operational pressure of a SRF module not to exceed 130.0 kPa (18.85 psia, 1300 mbar), but the routine operational pressure is further decreased to 126.2 kPa (18.3 psia = 1262 mbar) because of other operational concerns. The operating pressure of MD #1 is thus optimized at 140–150 kPa (1400–1500 mbar), even possibly to increase its operational pressure to 200 kPa, which is appreciably less than the critical point, 227.5 kPa. The fully loaded pressure drop must thus be within the range 13.8–23.8 kPa (1380–2380 mbar) for the LHe supply line from MD #1 to the SRF module of S1. The suction line of the first compressor, Comp #1, with warm gaseous helium returned from CB #1 has a pressure designed to be slightly above atmospheric pressure to avoid sucking air into the cryogenic plant, i.e. 105 kPa (1050 mbar). The CGHe return pressure drop of the heat exchangers inside CB #1 of medium size is about 15–20 kPa (150–200 mbar), dependent on the operational mass flow rate from the CGHe return line. CB #1 takes a pressure drop 17.5–19.0 kPa (175–190 mbar) when fully loaded; i.e. when both the onduty and tested SRF modules are in operation concurrently. An acceptable pressure drop within 3.7–2.2 kPa is consequently reserved for the CGHe return line from the SRF module on duty back to the cold return port of CB #1. Such a tight constraint on the maximum allowable pressure drop creates extreme difficulty for the transfer of twophase helium fluid if the cryogenic flexible transfer lines are long.
The performance of the 500MHz SRF modules (Lo et al. 2013) of KEKBtype (Bfactory accelerator at High Energy Accelerator Research Organization, Japan) for newly constructed synchrotron light source Taiwan Photon Source at NSRRC is examined at the cryogenic test stand in the SRF laboratory. The acceptance test includes maximum RF gap voltage 2.4 MV for a shorttime operation of several minutes and RF gap voltage 1.6 MV for a test of longterm reliability over weeks. The dynamic load of a tested SRF module with a cavity quality factor 7.0 × 10^{8} at RF gap voltage 2.4 MV is about 90 W, and at RF gap voltage 1.6 MV is about 40 W. The KEKBtype SRF module can be operated only at a pressure not greater than 126.2 kPa (18.3 psia). Our objective is hence to design the cryogenic transfer lines to transfer the dynamic load 40 W to the KEKBtype SRF module operated at 126.0 kPa when the SRF module on duty at TLS operates routinely. As for the acceptance test with maximum RF gap voltage 2.4 MV, it is not an issue because it is just a shorttime test and can be achieved in several ways without interfering with the operation of the SRF module on duty in TLS.
The 220m flexible cryogenic transfer lines were originally designed with our simple analytical approach with the introduction of tolerance factor 1.5, applied to avoid a possible underestimate in the pressure drops of long cryogenic transfer lines. The maximum dynamic load available at the cryogenic test stand is about 60 W when the tested SRF module is operated at pressure 126.0 kPa after the experimental verification with the equivalent heater power. The KEKBtype SRF modules were successfully examined at RF gap voltage 1.6 MV over weeks; the impact on routine operation of the TLS SRF module is shown to be sustainable under the acceptance test. The maximum dynamic load available exceeds design objective 20 W, which implies that an actual tolerance factor for the 220m flexible cryogenic transfer lines as built should be less than 1.5. It becomes verified on performing the experimental measurement for the accumulated static heat load of the LHe supply line.
On trying to impel the dynamic load of a tested SRF module up to 90 W, or even more, a phenomenon is observed. The extra pressure drop along the CGHe return line prevents sending the evaporated CGHe back to CB #1. After that, the LHe vessel pressure of the tested SRF module cannot be maintained and increases gradually, which prevents the delivery of LHe to the tested SRF module. Effective solutions have been found according to which, first, the operating pressure of MD #1 is increased to compensate the extra pressure drop from the LHe supply line, and, second, the speed of the turbines of the CB #1 is decreased (for example, slowing one step of speed so as to decrease the pressure drop of the heat exchangers inside CB #1 by about 5 kPa) or guiding partial CGHe flows directly to the suction line through the bypass line, so that less CGHe flows back to CB #1; the operating pressure of the tested SRF module can consequently stay at the expected condition. Both slowing the turbines of CB #1 and decreasing the quantity of the CGHe return to CB#1 can decrease the pressure drop of the heat exchangers inside CB #1 but at a cost of degrading the refrigeration capacity of CB #1. The LHe level of MD #1 might decline slowly whether or not the cooling capacity at the cryogenic test stand is greater than the refrigeration capacity of CB #1. For the acceptance test with maximum RF gap voltage 2.4 MV, we adopted to guide partial CGHe directly to the suction line to compensate the extra pressure drop from the CGHe return line to regulate the LHe vessel pressure operated at 126.0 kPa and to elevate the pressure of MD #1 from 140 to 146 kPa to compensate the extra pressure drop from the LHe supply line to balance the LHe level of the tested SRF module. During the test period, the decay of the LHe level of MD #1 is nearly imperceptible.
Results of experimental measurements
During the measurements of the pressure drops, the contribution of the static heat load to the cryogenic transfer lines is invariably present; the mass flow rate induced by the static heat load of the LHe supply line is thus essential for the corresponding computation. The pressure drops related to the 220m LHe and CGHe transfer lines are directly measurable with pressure transducers available in VB #1 and VB #2, indicated with diamond symbols in Fig. 1. The Venturitype flow meters (Forster and Graber 1996) are located at the CGHe return line upstream of both VB #1 and VB #2, as shown in Fig. 1. The pressure transducers and Venturitype flow meters on VB #1 and VB #2 and the electric power of a heater inside the LHe vessel of S0 were well calibrated before measurement. On maintaining constant both the level and pressure of the LHe vessel of S0 and varying the electric power of a heater inside the LHe vessel, both the total mass flow rate and the accumulated static heat load of the LHe supply line from MD #1 to S0, with static heat load of S0 included, can be deduced from the differential pressure of the CGHe flow read from the Venturitype flow meter with the technique developed; refer to Lin et al. (2013). The range of the applied heater power is limited by several operating parameters, such as the pressure of MD #1, the pressure of S0, the openings of the LHe valves at VB #1 and of the CGHe valves at VB #1, the speed of turbines in CB #1 etc. The LHe supply valve directly after MD #1, the valves inside the SVB, and the cold return valve of the CB #1 are fixed openings. For every setting of a new heater power for S0, the corresponding total mass flow rate and pressure drops of the 220m flexible cryogenic transfer lines are measured from the average readout of the Venturitype flow meter at VB #2 and of the pressure transducers at VB #1 and VB #2 after the system attains a new thermal equilibrium. The duration to achieve another equilibrium state is much greater than what is taken for the measurement.
Operating conditions and ranges of the applied heater power for five test cases
Case  MD #1 average pressure (kPa)  S0 average pressure (kPa)  LHe valve at VB #1 (%)  CGHe valve at VB #1 (%)  S0 heater power (W) 

1  145  126.33  86.0  90  30–70 
2  145  127.66  86.0  90  30–80 
3  145  127.04  86.0  90  40–85 
4  150  127.70  98.5  100  40–100 
5  150  129.08  98.0  100  50–100 
Theoretical model for varied pressure drops
A theoretical model for pressure drops of various kinds of the piping elements of the cryogenic transfer lines shown in Fig. 1 follows. The pressure drop of an inclined pipe flow is induced mainly by both the friction between the fluids and the pipe wall and the elevation head; the latter is an effect of gravity from an altered elevation along the cryogenic piping path. The effects of the twophase helium flow in the LHe supply line are treated with a simple theoretical model with consideration of the effect of gravity. Included also is the pressure drop caused by the resistance of cryogenic valves to the twophase flow. Various pressure drops of the CGHe return line can be analyzed with the corresponding twophase flow formula with vapor quality set to 1, whereas those of the assumed conditions on the LHe supply line with pure liquid are also computed with vapor quality set to 0. The LHe supply line is operated at a saturated state, but the CGHe return line is operated at a gaseous state.
Inclined pipe pressure drop
Valve pressure drop
Heat loads of the cryogenic transfer lines
General assumptions and working parameters
 1.
We suppose that the entire upstream heat load of transfer lines L1 to L4 flows to S0.
 2.
The fluid pressure is approximated as a constant value in the LHe and CGHe transfer lines to calculate the required properties, viscosity and density, at each cryogenic piping element. The pressure at S0 is assigned to be the common pressure of the LHe supply lines from L1 to L13; the return pressure of CB #1, P _{ CB#1}, measured downstream from the SVB is assigned to be the common pressure of the CGHe return lines from g1 to g13.
 3.
The surface is assumed to be smooth for cryogenic transfer lines L4, L6, L8, L10, L12, g2, g4, g6, g8 and g10 that are made of noncorrugated pipes (solid tubes with smooth surfaces) with the corresponding friction factor calculated with Eq. (7).
 4.
Another way to obtain the surface roughness ε of a corrugated pipe is available in the literature (Laeger et al. 1978; Jaiman et al. 2010; Uslu and Ahn 2013). We chose estimated value 0.08 for our calculation in corrugated pipes according to the paper (Laeger et al. 1978) for a fluid with Reynolds number about 10^{5}, as both LHe and CGHe transfer lines, L5, L7, L9, L11, g3, g5, g7 and g9, have Reynolds numbers between 1 × 10^{5} and 4 × 10^{5} for all simulated cases.
 5.
The effect of an elbow, a bend of the corrugated pipe, a sudden enlargement and a sudden contraction on the pressure drop are also considered. For their loss coefficient, K _{ L }, we referred to the literature (Munson et al. 2001). The values for the 90° elbow, common elbow and corrugated bends with ε = 0.08 are 1.1, 0.3 and 0.65, respectively.
 6.
The pressure drop across a Venturitype flow meter is typically between 10 and 20% of the measured differential pressure (Forster and Graber 1996); a pressure drop 15% of the measured differential pressure of the Venturitype flow meter at VB #2 is thus added to the calculated pressure drop for the CGHe return line to simulate the pressure drop across the Venturitype flow meter at VB #1.
 7.
The outlet temperature from the LHe vessel is assumed to be 5 K. The saturated temperature at the LHe vessel is about 4.5 K for these five test cases.
Twophase LHe supply line
List of type, length, inner diameter (regarded as hydraulic diameter) and heatload specification for each cryogenic piping element of the LHe supply line. Note that the vacuumjacketed solid line of L1 includes two vertical bayonets; the multichannel line of L1 includes one cryogenic value
Element  L1  L2  L3  L4  L5  L6  L7  L8  L9  L10  L11  L12  L13  

Type  +  ■  +  ■  +  ○  Horizontal bayonet  ●  Horizontal bayonet  ●  Horizontal bayonet  ○  +  ○ 
Size [ℓ (m), D_{h} (mm)]  (3.1,22.45)  (3.8,22.45)  (1.5,22.45)  (4,22.45)  (1,13.85)  (5,20.2)  (0.6,22.45)  (67,21)  (0.6,22.45)  (138,21)  (0.6,22.45)  (2.5,17.12)  (1,17.12)  (8,27.86) 
Heat load (W)  8.95  1.14  6.1  1.2  1.4  7.5  4.75  4.02  4.75  8.28  4.75  3.5  1.4  14.6 
In our case, tolerance factor F _{ B } is thus obtained as 93.1/72.34 = 1.287. The measured accumulated static heat load of the entire LHe supply line is hence 28.7% greater than the sum of the specified values provided by the vendors, which is still less than commonly adopted safety factor 1.5 for cryogenicrelated designs. Being unable to identify the actual tolerance factor element by element of the cryogenic piping, we considered it reasonable to proceed to multiply this tolerance factor F _{ B } by the engineering static heat load of each piping element of the LHe supply line to approach the measured accumulated static heat load. Given the heat load of the LHe supply line, the various pressure drops are obtainable according to the theoretical model given in “Theoretical model for varied pressure drops” section. The information related to each cryogenic piping element for the calculation is also listed in Table 2.
CGHe return line
List of type, length, inner diameter (regarded as hydraulic diameter) and heatload specification for each cryogenic piping element of the CGHe return line
Element  g1  g2  g3  g4  g5  g6  g7  g8  g9  g10 

Type  ○  +  ○  Horizontal bayonet  ●  Horizontal bayonet  ●  Horizontal bayonet  ○  + 
Size [ℓ (m), D_{h} (mm)]  (8,38.2)  (1,27.86)  (2.5,27.86)  (0.6,22.45)  (138,38.9)  (0.6,22.45)  (67,38.9)  (0.6,22.45)  (5,40.1)  (1,22.45) 
Heat load (W)  17.8  2.8  4.75  4.75  16.56  4.75  8.04  4.75  11.5  2.8 
Results and discussion
Verification of theoretical model for frictional pressure drop
Twophase LHe supply line
A quick estimate of the pressure drops of the pure liquid on the LHe supply line between VB #1 and VB #2 with the same mass flow rate was made, but Fig. 6 shows that the pressure drops were significantly underestimated. This effect illustrates that the oversimplified method of estimation is unsuitable to calculate the pressure drop of the twophase LHe supply line.
CGHe return line
An improved agreement between the measured and calculated results is obtained for the gaseous flow, as shown in Fig. 7. The straightline fit for the measured pressure drops of cases 1–5 has slope 0.0244 kPa/W and a constant term −1.351 kPa, for comparison with 0.0308 kPa/W and −2.3579 kPa for cases 1–3 and 0.0274 kPa/W and −2.07 kPa for cases 4 and 5, for the calculated results. The relative errors of the slope between the measured and calculated results for these two groups are 26.2 and 12.3%, respectively. ME and MPE between the individual measured and calculated total pressure drops are 0.29 kPa and 7.9% for cases 1–3 and −0.11 kPa and −3.2% for cases 4 and 5 within the applied total heatload range, 180–250 W. If the valve pressure drop is neglected, the slope of the calculated total pressure drop becomes 0.0224 kPa/W for cases 1 to 3; the error of the slope decreases from 26.2 to 8.2%. These data reveal that the slope of the calculated total pressure drops is affected mainly by the valve pressure drop calculated from the empirical formula of the gas valve in Eq. (9).
The actual tolerance factor is unknown in the design phase; the validity of a sufficient safety margin using tolerance factor 1.5 is demonstrated with the measured results of the 220m flexible cryogenic transfer lines as built at NSRRC. The calculated result of cases 1 to 5 for the twophase flow in the LHe supply line neglecting the effect of gravity has an overestimate 0.76 kPa relative to measured results; similarly, the tolerance factor has a minor effect on the pressure drop in the CGHe return line. As a result of these comparisons, value 1.5 of the tolerance factor is explained to suit well the present longdistance helium transfer line in the design phase.
Remarks
Conclusions
A cryogenic transfer system including flexible cryogenic transfer lines of corrugated type of total length 220 m has been installed at NSRRC (Lin et al. 2010) to deliver LHe for a cryogenic test stand. This system might be the longest cryogenic flexible lines ever implemented for similar applications. A successful design of cryogenic transfer lines has been made to provide the demanded cooling capacity at the cryogenic test stand based on our simple analytical approach with tolerance factor 1.5 in the estimate of pressure drops of the cryogenic transfer lines. The objective of a longterm reliability test of a KEKBtype SRF module examined at gap voltage 1.6 MV over weeks when the SRF module on duty at TLS operates routinely was also achieved. The test result proves also that value 1.5 of tolerance factor suits well a longdistance helium transfer line of this kind during a design phase.
Five test cases with varied heater power were applied to simulate the corresponding dynamic loads from the tested SRF modules operating at varied accelerating RF voltages after the installation of the helium transfer system. Actual value 1.287 of the tolerance factor is obtained from the heat load measurements of these five test cases. The corresponding rates of mass flow and pressure drops under varied operating conditions were measured concurrently. We reconfirm the feasibility and validity of our analytical approach with actual tolerance factor 1.287. Our calculated results are found to agree satisfactorily with the measured data after applying actual tolerance factor 1.287, which is less than safety factor 1.5 commonly adopted in cryogenicrelated designs. The discrepancies of the pressure drops between the measured and calculated values for the LHe and CGHe transfer lines are an underestimate 0.11 kPa and an overestimate 0.09 kPa, respectively, which are much smaller than the measurement uncertainty.
Our model reveals also that roughly one sixth (17.0%) of the static heat load comes from the 200m concentric flexible cryogenic transfer lines of corrugated type, one fifth (19.7%) from the horizontally oriented bayonet joints, and onethird (35.4%) from the short but nonLN_{2}shielded flexible lines for easy piping. The upstream rigid multichannel lines as well as two cryogenic valve boxes, VB #1 and VB #2, account for 27.9% of the static heat load. This information provides one direction to upgrade or to optimize the present cryogenic transfer lines for a subsequent application. The design concept and the calculation approach of a pressure drop for a long helium transfer line developed herein is verified in the example of the 220m flexible cryogenic transfer lines as built at NSRRC; we suggest that it is extensible to applications of varied cryogenic loads subject to similar operational constraints.
Abbreviations
 A :

crosssectional area of a pipe
 Comp:

compressor
 CB:

cold box
 CGHe:

cold gaseous helium
 D _{ h } :

hydraulic diameter of a pipe
 f :

friction factor
 F _{ B } :

tolerance factor
 \( \bar{g} \) :

acceleration of gravity
 \( \bar{G} \) :

mass flux
 h :

enthalpy
 K _{ L } :

loss coefficient, K _{ L } = ∆P/(1/2ρu ^{2})
 \( K_{{\nu ,\max }} \) :

maximum valve coefficient
 \( \ell \) :

length of a pipe
 LHe:

liquid helium
 \( \dot{m} \) :

mass flow rate
 M :

number of experimental data
 ME:

mean error
 MPE:

mean percentage error
 MD:

main Dewar
 P _{1} :

upstream pressure of a valve
 q :

heat load
 R :

rangeability of a valve
 Re:

Reynolds number
 SRF:

superconducting radio frequency
 SVB:

switching valve box
 S0:

tested SRF module
 S1:

SRF module operated routinely in Taiwan Light Source
 T _{1} :

upstream temperature of a valve
 u :

velocity of a fluid
 VB:

valve box
 \( \dot{V} \) :

volumetric flow rate
 x :

vapor quality
 X :

flash ratio
 z :

direction along an inclined pipe
Greek symbols
 ∆P :

pressure drop
 ε :

surface roughness of a pipe
 θ :

inclined angle of a pipe
 μ :

dynamic viscosity of a fluid
 ρ :

density of a fluid
 Φ :

twophase frictional multiplier term
Superscripts
 \( \bar{L} \) :

effective valve opening
Subscripts
 1φ :

singlephase flow
 2φ :

twophase flow
 calc :

calculation
 f :

frictional
 g:

gaseous phase
 G:

saturated gas of twophase flow
 L:

saturated liquid of twophase flow
 meas :

measurement
 s :

static
 T :

total
 val :

valve
 Ven :

Venturitype flow meter
Declarations
Authors’ contributions
MHC developed the calculation approach, performed the measurement and drafted the manuscript. CW and MCL participated in the measurement, gave advice on the calculation and modified the manuscript. MHT and CHL were responsible for the mechanical installation and system assembly. FTC, MSY and LJC were responsible for the control system assembly and test. LHC, TCY and ZKL helped to maintain the cryogenic system. All authors have read and approved the final manuscript.
Acknowledgements
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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