1. Beam Tube Vacuum Break
Thermal Fluid Design
Nov 15, 2016
Luis Figueroa
Austin Houser
Denitsa Kurteva

2. Presentation Outline
• Motivation
• Introduction
• Apparatus
• Theory
• Evaluation
• Future Work

3. Motivation
• Rupture in the cold beam
line of a superconducting
particle accelerators
• CERN~ Large Hadron
Collider
• Atmospheric gas enters,
causing cryogen to
evaporate outside the tube
-> expensive
LHC in Switzerland [4]
Schematic [1]

4. Introduction
• Straight beam tube project in Maglab
• Experiment: Nitrogen gas used as a
substitute for air
• Pressure difference causes atmospheric gas
to enter at a high velocity
• Temperature difference causes
condensation on the sides of the tube
-> thermocouples & pressure sensors
Schematic [1]

5. Apparatus
• Problem: Critical length and time for complete
propagation
• Compare results with straight tube
• Helix tube instead of straight tube to obtain more data
points
• Venturi to be used

6. Theory
0 = 𝑚𝑖𝑛 −
𝑑𝑚
𝑑𝑡
− 𝑚 𝑜𝑢𝑡
Conservation of Mass
𝑚𝑖𝑛 = 𝜌 𝑁 𝐴𝑉𝑖𝑛 𝑚 𝑑𝑒𝑝
𝑔
𝑚2 𝑠
𝑚 𝑜𝑢𝑡 = 𝜌 𝑚𝑖𝑛 𝐴𝑉𝑜𝑢𝑡
𝑉𝑖𝑛 = 25.56 𝑚/𝑠

7. Calculations
= 𝜌 𝑁 𝑔 +
2𝑓𝑐 𝜌 𝑁 𝑉2
𝑑
+
2𝜌 𝑁 𝑉2 𝑑
𝐷
𝑑𝑃
𝑑𝐿
= 𝜌 𝑁 𝑔 +
𝑑𝑃
𝑑𝐿 𝑓
+
𝑑𝑃
𝑑𝐿 𝑟𝑎𝑑
Additional helical pressure drop
= 245.1 𝑃𝑎
𝑅𝑒 𝐻 = 𝑅𝑒𝑆 1 + 12
𝑑
2𝐷
= 193,384
𝑓𝑐 =
7.0144
𝑅𝑒 𝐻
𝐷𝑒 = 7.975 ∗ 10−3
𝐷𝑒 = 𝑅𝑒 𝐻
𝑑
2𝐷
= 48,345
𝑅𝑒𝑆 =
𝜌 𝑁 𝑉𝑑
𝜇 𝑁
= 48,345

8. Results
Pressure Drop
(kPa)
Inlet Velocity
(m/s)
Inlet Mass Flow
rate (kg/s)
Linear
Tube
100 25.56 0.01909
Helical
Tube
100.25 25.63 0.01914
• Inlet Mass Flow rate of helical
tube increase by 0.26%

9. Future Work
• Determine 𝑚 𝑜𝑢𝑡(𝑉𝑜𝑢𝑡, 𝜌 𝑜𝑢𝑡)
• Calculate 𝓍 𝑜𝑢𝑡
• Compare Results of the Straight
and Helical Tubes
0 = 𝑚𝑖𝑛 −
𝑑𝑚
𝑑𝑡
− 𝑚 𝑜𝑢𝑡
𝓍 𝑜𝑢𝑡 =
𝑚𝑖𝑛 − 𝑚 𝑜𝑢𝑡
𝜋𝐷 𝑚 𝑑𝑒𝑝,𝑎𝑣𝑔

10. references
1. Ram C. Dhuley, “Gas propagation in a liquid helium cooled vacuum tube following a sudden vacuum loss,” Ph.D.
dissertation, Dept. Mech. Eng., Florida State Univ., Tallahassee, FL, 2016.
2. Thandlam, Mandal, and Majumder. "Asia-Pacific Journal of Chemical EngineeringVolume 10, Issue 3, Version of Record
Online: 31 MAR 2015." Flow Pattern Transition, Frictional Pressure Drop, and Holdup of Gas Non-Newtonian Fluid Flow in
Helical Tube. Wiley Online Library, 31 Mar. 2015. Web. 15 Nov. 2016.
3. "Pressure Drop Correlations for Flow through Regular Helical Coil Tubes." Iopscience.iop.org. N.p., 11 Oct. 2000. Web.
4. "CERN Accelerating Science." The Large Hadron Collider | CERN. N.p., n.d. Web. 15 Nov. 2016.