Ram C. DhuleySteven W. Van Sciver

Heat transfer in a liquid helium cooled vacuum tube following

sudden vacuum loss

June 29, 2015 | Cryogenic Engineering Conference | Tucson, AZ

National High Magnetic Field Laboratory,Tallahassee, FL 32310

Mechanical Engineering Department,FAMU-FSU College of Engineering, Tallahassee, FL 32310

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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

We have obtained from experiments and have analyzed:

• Condensation heat transfer to the tube

• Heat transfer to liquid helium

air vacuum

LHe

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Experimental apparatus and procedure

Starting conditionsValve 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 valveLoss of vacuum, gas flowsand condenses in the coldvacuum tube

Record data at four stationsPressure and temperature rise inthe vacuum tube;Duration of experiment = 5 s

gas tank

fast opening valve

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Tube pressure profiles from the 4.2 K LHe experiment

A pressure front propagates down the tube immediately after loss of vacuum

uniform pressurization

Tube pressurizes uniformly after the front is stopped by the rigid end

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As more gas flows in, the tube pressurizes to atmosphere

Tube pressure profiles from the 4.2 K LHe experiment

A pressure front propagates down the tube immediately after loss of vacuumTube pressurizes uniformly after the front is stopped by the rigid end

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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 reachesthe rigid end

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Heat transfer processes in the tube

Energy conservation over dx:

dTcdt

dTkdx

: rate of energy rise in the tube wall: axial heat conduction

: heat transfer to LHe

Calculated using the tube temperature traces

(the procedure is illustrated using T2)

2 2

4dep LHe

OD ID dT d dT ODq c k q

ID dt dx dx ID

LHeq

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Calculating the RHS of energy conservation at station #2

Rate of energy rise in the tube wall

T(t)

c[1], d/dt

Calculating condensation heat transfer

1NIST Cryogenic Material Properties Database

2 2

4dep LHe

OD ID dT d dT ODq c k q

ID dt dx dx ID

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2 2

4dep LHe

OD ID dT d dT ODq c k q

ID dt dx dx ID

Derivative of axial heat conduction

T(t)

k[1], d/dx

TΔx(t)T-Δx(t)

Calculating condensation heat transfer

1NIST Cryogenic Material Properties Database

Calculating the RHS of energy conservation at station #2

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Heat transfer to LHe

T(t)

[2]

Calculating condensation heat transfer

2S. W. Van Sciver, Helium Cryogenics, 2nd ed., Springer NY, 2012

Calculating the RHS of energy conservation at station #2

2 2

4dep LHe

OD ID dT d dT ODq c k q

ID dt dx dx ID

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I) Rising pressure - > faster condensation

I >> II

I << II

Two competing processes

II) Rising tube temperature - > slower condensation

uniform pressurizationresults in spatially uniform qdep

station #1

#2

#3#4

Condensation heat transfer from a propagating gas front

All the peaks in qdep occur when local Ttube = 24-28 K; local ptube < 0.5 kPa

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Comparing qdep with qLHe

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)

tube at atmospheric pressureqdep

qLHe

qLHe is limited by film boiling!

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Temperature profiles from the He II experiment

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)

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

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Conclusions

• Condensation heat transfer to the tube is largely controlled by the tube temperature

• High instantaneous heat fluxes (>200 kW/m2) are deposited on to the tube by the propagating pressure front

• A gas pressure front propagates in the tube following sudden vacuum loss

- highest when the tube temperature is in the 24-28 K range- rapidly drops as the tube warms above this temperature

• Heat transfer to LHe is limited by film boiling

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• 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

Acknowledgement

• NHMFL is supported by the US National Science Foundation and the State of Florida.

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Extra slides

Instrumentation