Heat transfer in a liquid helium cooled vacuum tube following sudden vacuum loss Ram C. Dhuley Steven W. Van Sciver National High Magnetic Field Laboratory, Tallahassee, FL 32310 Mechanical Engineering Department, FAMU-FSU College of Engineering, Tallahassee, FL 32310 June 29, 2015 | Cryogenic Engineering Conference | Tucson, AZ

Overview Objective: To study heat transfer in a LHe cooled vacuum tube resulting from accidental vacuum loss to atmosphere The scenario resembles sudden vacuum loss in the beam-line of a SRF accelerator air vacuum LHe We have obtained from experiments and have analyzed: Condensation heat transfer to the tube Heat transfer to liquid helium

Experimental apparatus and procedure gas tank fast opening valve Starting conditions Valve closed; N2 gas in the supply tank (295 K); Copper vacuum tube (≈10-4 Pa) immersed in LHe (4.2 K), He II (2.1 K) Open the valve Loss of vacuum, gas flows and condenses in the cold vacuum tube Record data at four stations Pressure and temperature rise in the vacuum tube; Duration of experiment = 5 s

Tube pressurizes uniformly after the front is stopped by the rigid end Tube pressure profiles from the 4.2 K LHe experiment uniform pressurization Tube pressurizes uniformly after the front is stopped by the rigid end A pressure front propagates down the tube immediately after loss of vacuum

Tube pressure profiles from the 4.2 K LHe experiment Tube pressurizes uniformly after the front is stopped by the rigid end A pressure front propagates down the tube immediately after loss of vacuum As more gas flows in, the tube pressurizes to atmosphere

Tube temperature profiles from the 4.2 K LHe experiment The tube initially carries a temperature gradient, but stabilizes to ≈50 K after the tube gets to atmospheric pressure tube at atmospheric pressure gas reaches the rigid end

Heat transfer processes in the tube Energy conservation over dx: : rate of energy rise in the tube wall Calculated using the tube temperature traces : axial heat conduction (the procedure is illustrated using T2) : heat transfer to LHe

Calculating condensation heat transfer Calculating the RHS of energy conservation at station #2 Rate of energy rise in the tube wall T(t) c[1], d/dt 1NIST Cryogenic Material Properties Database

Calculating condensation heat transfer Calculating the RHS of energy conservation at station #2 Derivative of axial heat conduction T(t) k[1], d/dx T-Δx(t) TΔx(t) 1NIST Cryogenic Material Properties Database

Calculating condensation heat transfer Calculating the RHS of energy conservation at station #2 Heat transfer to LHe T(t) [2] 2S. W. Van Sciver, Helium Cryogenics, 2nd ed., Springer NY, 2012

Condensation heat transfer from a propagating gas front uniform pressurization results in spatially uniform qdep station #1 #2 #3 #4 I) Rising pressure - > faster condensation I >> II I << II Two competing processes II) Rising tube temperature - > slower condensation All the peaks in qdep occur when local Ttube = 24-28 K; local ptube < 0.5 kPa

Comparing qdep with qLHe tube at atmospheric pressure qdep qLHe qLHe is limited by film boiling! qLHe ≈ 25 kW/m2 Cold tube, faster condensation: qdep >> qLHe (tube accumulates the incident heat) Warm tube, slower condensation: qdep ≈ qLHe (LHe absorbs the incident heat)

Temperature profiles from the He II experiment Tbath = 2.1 K at start, remains below 2.17 K for the entire duration (5 s) station #1 not actively cooled by He II Propagation -> temperature gradient qdep shows similar behavior as in the case of the 4.2 K LHe experiment * He II heat transfer controlled by film boiling No sure way to determine qHeII - hydrostatic head varies along the tube - mode of phase change (He II -> vapor or He II -> He I -> vapor) LHe I film boiling will onset when Tbath will exceed 2.17 K (this was not observed in our experiment)

Conclusions A gas pressure front propagates in the tube following sudden vacuum loss Condensation heat transfer to the tube is largely controlled by the tube temperature - highest when the tube temperature is in the 24-28 K range - rapidly drops as the tube warms above this temperature High instantaneous heat fluxes (>200 kW/m2) are deposited on to the tube by the propagating pressure front Heat transfer to LHe is limited by film boiling

Acknowledgement Department of Energy Grant DE-FG02-96ER40952 Dr. Wei Guo and Dr. Ernesto Bosque of NHMFL-FSU Colleagues at NHMFL Cryogenics lab - Dr. Mark Vanderlaan, Jian Gao, Brian Mastracci, and Andrew Wray NHMFL is supported by the US National Science Foundation and the State of Florida.

Extra slides Instrumentation