Heat Transfer In Helium Injected Liquid Nitrogen
Fenner Colson1,2, Dogan Celik2,3, Steven W. Van Sciver2,3
1Department of Physics and Astronomy, Minnesota State University College of Social and Natural Sciences, Moorhead, MN 56563 USA
2National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
3Mechanical Engineering Department, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA
ABSTRACT
Define the coefficients:
RESULTS AND CONCLUSIONS
Liquid nitrogen boiling suppression is a known phenomenon occurring when
gaseous helium is injected directly into boiling nitrogen. The heat transfer coefficient,
which determines how efficiently heat is transmitted from a heat source to a material, is not
the same in boiling liquid nitrogen and helium injected liquid nitrogen. This change is not
due to the temperature drop of the nitrogen, nor from the chemical interaction of helium
gas and liquid nitrogen, but because of some other mechanism not covered by the scope
of this project.
c L ΔT
Ja =
= Jakob number
i fg
The change in temperature due to heat flux through the aluminum disk was measured
for a number of different power inputs. The ∆T is illustrated in the graph below.
pSAT
KP =
[gσ L ( ρ L − ρG )]1/ 2
Helium Injected at 17 Watts
85
Bath Temperature
Heater Temperature
83
Heater
turned
on.
Tempertature (K)
81
INTRODUCTION
Suppression of boiling in liquid nitrogen is valuable in experiments where the
optical or vibrational disturbances should be minimized. Once the helium is injected into
the liquid nitrogen, the nitrogen drops several degrees. Thus the injection of helium
causes the liquid nitrogen to cool down beyond its boiling point, which then allows
absorbed heat to increases nitrogen temperature, rather than changing the state.
As the helium is injected, the liquid nitrogen evaporates directly into the helium
bubbles [1],[2]. Evaporation of the nitrogen is the mechanism by which the temperature
decreases.
∆T 79
€
Helium
injected.
77
ρL
ρG
µL
cL
g
PrL
σL
ifg
= liquid density
= vapor density
= liquid viscosity
= liquid specific heat
= gravitational acceleration
= liquid Prandtl no.
= surface tension
= heat of vaporization.
Evaluation of the above equation with the appropriate values yields the power
transfer per unit area as a function of ∆T. Using those values with Newton’s
Law of Cooling produces a set of heat transfer coefficients that we can
compare to the helium injected data.
Heat Transfer Coefficient (W/m2!K)
75
73
0 500 1000 1500 2000 2500 3000 Time (s)
Figure 3: Data showing temperature difference due to heater and helium injection.
The method of extracting ∆T, as demonstrated above, was replicated for all data runs
with plain liquid nitrogen as well as helium injected. Power input per unit area is known since
the disk was held at a measured voltage.
∆T = 6.51 K
∆T = 8.08 K
∆T = 9.51 K
He injected
848.54
2906.34
9085.27
Boiling correlation
855.79
804.00
672.06
Liquid Nitrogen
∆T = 2.43 K
∆T = 3.84 K
∆T = 4.99 K
∆T = 5.75 K
∆T = 6.53 K
3452.32
7247.40
10079.92
12040.57
13895.17
Figure 6: Summary of heat transfer coefficients. The helium and nitrogen
values are calculated by direct division of data from Figure 4.
Heat Transfer Rates
10
9
6
5
Liquid Nitrogen
4
LN2 with Helium
3
This reaction has the potential to change certain physical properties, let’s consider
Newton’s Law of Cooling:
Q
= hΔT [4].
A
2
1
0
0 1 2 3 4 5 6 7 8 9 10 ∆T (K)
The heat transfer coefficient for helium injected liquid nitrogen agrees
nicely with the equivalent super-cooled nitrogen at low ∆T, but as ∆T
increases, the difference rises dramatically. Thus ∆T cannot be the only factor
in changing the heat transfer coefficient.
F i g u r e 7 :
Heluim Injected Hydrogen Injected 85 Comparison of
84 83 82 81 helium and
80 79 78 77 76 hydrogen injected
75 74 73 72 into nitrogen.
-­‐100 400 900 1400 1900 2400 2900 3400 0 500 1000 1500 2000 Temperature (K) Figure 1:Boiling liquid nitrogen and result of helium injected into liquid nitrogen [3] .
Q/A (W/cm^2)
7
Figure 4: Summary of data
analysis. Power inputs are
plotted as a function of ∆T
so the heat transfer
coefficient can be evaluated
directly from the data.
Temperature (K) 8
Time (s) (W/m2ŸK),
Our interest lies in the proportionality constant h
and how it behaves under the condition of helium injection.
the heat transfer coefficient,
Our area of interest lies in the ∆T values, which define how the heat transfer coefficient is
behaving. Evaluating the quotient of Q/A and ∆T at a point will be the means that the heat
transfer coefficient is calculated. The accepted format to present the data is on a logarithmic
scale graph.
Heat Transfer Rates (Log Scale)
€EXPERIMENTAL METHODS
10
Q/A (W/cm^2)
Our measurement apparatus consisted of a bulb
shaped glass dewar into which we suspended a rod to
which we attached an aluminum disk. This aluminum disk
is surrounded by G-10 insulation, with one face being open
to the liquid nitrogen, and the other face having a resistive
heater and insulation. Two thermocouples were run down
the rod to monitor the temperature of the nitrogen bath and
the temperature of the disk.
Helium and hydrogen were both used in the
research, and were supplied to the liquid nitrogen by direct
injection from a metal tube. A flow meter was connected in
series to the hose. A constant flow was applied to assure
Figure 2:
that the amount of gas being injected was not a factor in
Experimental setup.
the experiments.
The heat transfer coefficient of liquid nitrogen was experimentally verified first. The
aluminum disk was subject to a certain amount of heat, which allowed it to remain at a
different temperature than the nitrogen bath.
By observing the behavior of the
temperature of both the disk and nitrogen, the heat transfer coefficient can be calculated
using Newton’s Law of Cooling. The coefficient for liquid nitrogen can be compared with
known values to verify the quality of experiment. The same process was applied to helium
injected nitrogen, and the heat transfer coefficient for liquid nitrogen at the equivalent
super-cooled temperature was used for comparison.
100
Liquid Nitrogen
LN2 with Helium
1
0.01 0.1 1 10 100 Figure 5: Logarithmic
scale of Figure 4 with
experimental nucleate/
film boiling for nitrogen
superimposed.
∆T (K)
From Figure 5 we can conclude that the heat transfer coefficient does change between liquid
nitrogen and helium injected liquid nitrogen since there is a horizontal shift from left to right.
This fact, however, is not necessarily a shocking discovery, because we expect a change of
coefficient due to the change of ∆T. Comparing the equivalent super-cooled liquid nitrogen
heat transfer coefficient to observed helium injected coefficient will reveal reason for
coefficient change. For this purpose we can use the boiling correlation
Ja
(PrL ) 0.65
Calculations from Figure 7 reveal that the gas itself has no effect on
the heat transfer coefficient, since the results are the same if helium or
hydrogen is used. Therefore the reason for the coefficient change cannot be
related to molecular interactions with the gas, nor can the coefficient change
be explained by ∆T. One possibility is that film boiling, which occurs at higher
∆T, is affected by the helium injection. This interaction may reduce film
boiling, which would normally increase the heat transfer coefficient.
Implications of this include helium injected nitrogen being used as a coolant,
since its ability to transfer heat is improved. The scope of the project did not
investigate this avenue, but future exploration should consider that possibility.
REFERENCES
1000 0.1
0.3
Time (s) 0.7
%(Q / A)
(
% ρG (
σL
= 0.0007'
[5].
* ' KP *
)
& µL i fg g( ρ L − ρG ) ) & ρ L
[1] S. Takayoshi, W. Kokuyama, H. Fukyama The Boiling Suppresion of Liquid
Nitrogen Cryogenics 49 (2009) pg 221
[2] G. Minkoff, F. Scherber, A. Stober Suppression of Bubbling in Boiling
Refrigerants Nature Vol. 180 pg 1414
[3] S. Takayoshi, et. al. pg 222
[4] F. Incropera and D. DeWitt Fundamentals of Heat and Mass Transfer 4th
Ed. © 1996 John Wiley & Sons pg 8
[5] R. Barron Cryogenic Heat Transfer © 1999 Taylor and Francis pgs 164-166
ACKNOWLEDGEMENTS
Special thanks to Dr. Dogan Celik, Dr. Steven W. Van Sciver, and the entire
Cryogenics Laboratory Group for their guidance and assistance in running the
experiment; Mr. Jose Sanchez, and the staff of the National High Magnetic
Field Laboratory Center for Integrated Research and Learning; Work funded by
the NSF Cooperative Agreement DMR-0654118, NSF DMR-0645408, Florida
State University