“…The accuracy of frictional pressure drops in a horizontal pipe with a smooth surface calculated with our theoretical model of two-phase helium flow is verified with available experimental data (Rane et al 2011) and other theoretical models, for example, the homogenous flow model (Collier 1981) and the Martinelli–Nelson equation with improved correlation term (Rane et al 2011). Figure 5 shows a comparison for calculated Φ
2 vs vapor quality x at flow pressures 1.1, 1.2, 1.3 and 1.4 bar.…”
Section: Resultssupporting
confidence: 78%
“…The experimental data are unavailable at x = 1 for pressures 1.1 and 1.2 bara, but the calculated results for pressures 1.3 and 1.4 bara agree approximately with the experimental data.Fig. 5Calculated results of two-phase frictional multiplier term Φ
2 varying with vapor quality × with our theoretical model are compared with the experimental data, the modified Martinelli–Nelson equation and the homogenous model (Rane et al 2011) (Courtesy Cryogenics 2011)
…”
Section: Resultsmentioning
confidence: 57%
“…Calculated results of two-phase frictional multiplier term Φ
2 varying with vapor quality × with our theoretical model are compared with the experimental data, the modified Martinelli–Nelson equation and the homogenous model (Rane et al 2011) (Courtesy Cryogenics 2011)…”
Section: Resultsmentioning
confidence: 99%
“…The two-phase frictional multiplier term Φ (Rane et al 2011) is defined asWithin which is the frictional pressure drop for a single-phase flow. Here a single-phase flow means that pure liquid flows along a pipe.…”
Section: Resultsmentioning
confidence: 99%
“…The pressure drop of a turbulent two-phase 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).…”
BackgroundEstablishing a stand-alone cryogenic test stand is of vital importance to ensure the highly reliable and available operation of superconducting radio-frequency module in a synchrotron light source. Operating a cryogenic test stand relies strongly on a capability to deliver two-phase 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 radio-frequency module operated at 126.0 kPa with a 40-W dynamic load for a long-term reliability test over weeks. It is designed based on a simple analytical approach with the introduction of a so-called tolerance factor that serves to estimate the pressure drops in transferring a two-phase 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 60-W dynamic load is verified with experiment measured with heater power 60 W instead after the cryogenic test stand has been installed.ResultsAligning 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.ConclusionsThe 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.
“…The accuracy of frictional pressure drops in a horizontal pipe with a smooth surface calculated with our theoretical model of two-phase helium flow is verified with available experimental data (Rane et al 2011) and other theoretical models, for example, the homogenous flow model (Collier 1981) and the Martinelli–Nelson equation with improved correlation term (Rane et al 2011). Figure 5 shows a comparison for calculated Φ
2 vs vapor quality x at flow pressures 1.1, 1.2, 1.3 and 1.4 bar.…”
Section: Resultssupporting
confidence: 78%
“…The experimental data are unavailable at x = 1 for pressures 1.1 and 1.2 bara, but the calculated results for pressures 1.3 and 1.4 bara agree approximately with the experimental data.Fig. 5Calculated results of two-phase frictional multiplier term Φ
2 varying with vapor quality × with our theoretical model are compared with the experimental data, the modified Martinelli–Nelson equation and the homogenous model (Rane et al 2011) (Courtesy Cryogenics 2011)
…”
Section: Resultsmentioning
confidence: 57%
“…Calculated results of two-phase frictional multiplier term Φ
2 varying with vapor quality × with our theoretical model are compared with the experimental data, the modified Martinelli–Nelson equation and the homogenous model (Rane et al 2011) (Courtesy Cryogenics 2011)…”
Section: Resultsmentioning
confidence: 99%
“…The two-phase frictional multiplier term Φ (Rane et al 2011) is defined asWithin which is the frictional pressure drop for a single-phase flow. Here a single-phase flow means that pure liquid flows along a pipe.…”
Section: Resultsmentioning
confidence: 99%
“…The pressure drop of a turbulent two-phase 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).…”
BackgroundEstablishing a stand-alone cryogenic test stand is of vital importance to ensure the highly reliable and available operation of superconducting radio-frequency module in a synchrotron light source. Operating a cryogenic test stand relies strongly on a capability to deliver two-phase 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 radio-frequency module operated at 126.0 kPa with a 40-W dynamic load for a long-term reliability test over weeks. It is designed based on a simple analytical approach with the introduction of a so-called tolerance factor that serves to estimate the pressure drops in transferring a two-phase 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 60-W dynamic load is verified with experiment measured with heater power 60 W instead after the cryogenic test stand has been installed.ResultsAligning 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.ConclusionsThe 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.
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