Experimental study of the evaporation of spreading liquid nitrogen
*Duy Nguyen1), Myungbae Kim2), Byungil Choi3) and Taehoon Kim4)
1), 2), 3), 4)
Department of Plant System and Machinery, Korea Institute of Machinery and
Materials campus, Korea University of Science and Technology, Daejeon, Korea.
2)
[email protected]
ABSTRACT
The investigation of cryogenic liquid pool spreading is an essential procedure to assess
the hazard of cryogenic liquid usage. There is a wide range of models used to describe the
spreading of a cryogenic liquid pool. Many of these models require the evaporation
velocity, which has to be determined experimentally because the heat transfer process
between the liquid pool and the surroundings is too complicated to be modeled. In this
experimental study, to measure the evaporation velocity when the pool is spreading, liquid
nitrogen was continuously released onto unconfined concrete ground. Almost all of the
reported results are based on a non-spreading pool in which cryogenic liquid is
instantaneously poured onto bounded ground for a very short period of time. For the
precise measurement of pool spreading and evaporation weight with time, a cone-type
funnel was designed to achieve a nearly constant liquid nitrogen release rate during
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discharge. Specifically, three release flow rates of 3.4×10 kg/s, 5.6×10 kg/s and
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9.0×10 kg/s were used to investigate the effect of the release rate on the evaporation
velocity. A simultaneous measurement of the pool location using thermocouples and of the
pool mass using a digital balance was carried out to measure the evaporation velocity and
the pool radius. A greater release flow rate was found to result in a greater average
evaporation velocity, and the evaporation velocity decreased with the spreading time and
the pool radius.
1. INTRODUCTION
Cryogenic liquids, such as liquefied natural gas, liquid hydrogen and liquid nitrogen, are
commonly used. However, accidents during transportation and storage are a serious
problem.
When cryogenic liquid leaks out of its container unwantedly, a liquid pool is created and
spreads rapidly. At the same time, the boiling process occurs violently because the
1)
Graduate student
Professor
3)
Professor
4)
Professor
2)
ambient temperature is much greater than the boiling temperature of the cryogenic liquid.
As a result, a vapor cloud is formed due to heat flux into the pool from various sources:
conduction heat flux from the ground, convection heat flux from the air and radiation heat
flux from the sun. Moreover, if the cryogenic liquid is flammable, the potential of a pool fire
and explosion are obvious. Additionally, if the leaked cryogenic liquid is toxic and is spilled
with large flow rate, the air will be polluted and people’s health may be put in danger.
Therefore, a study of the spreading and vaporization of a cryogenic liquid pool is not only
an important procedure for hazard assessment but also contributes to the design
optimization of an energy plant and the cryogenic liquid storage and transportation
methods.
There have been a number of different studies, including analytical work (Briscoe 1980)
and numerical work (Brandeis 1983, Stein 1980). Regarding the analytical and the
numerical work, models have been created to predict and calculate pool spread. However,
to make the models solvable, the authors neglected radiation heat flux from the sun and
convection from the ambient air and only considered one-dimensional heat conduction
from the ground. Another approximation was the introduction of the evaporation velocity,
defined as the evaporated volume of liquid per unit area of the liquid pool per unit time. In
this case, the evaporation velocity should be determined experimentally. This is the reason
why experiments, which can precisely measure the evaporation velocity, are still important.
In many experimental studies (Reid 1978, Takeno 1994, Olewski 2013), to measure the
evaporation velocity, cryogenic liquid was poured onto bounded ground instantaneously so
that the discharge time was much smaller than the evaporation time. In other words,
measurements were made for a non-spreading pool. As a result, heat flux into the nonspreading pool decreased continuously due to a decrease in the ground temperature. In
real accidents, a cryogenic liquid spills and spreads over a large or unbounded ground
such that the pool spreading process should be taken into account. In contrast with a nonspreading pool, a spreading pool is continuously in contact with new warm ground in front
of the pool. Therefore, the heat flux into the spreading pool is obviously greater than the
heat flux of the non-spreading pool with the same release volume of liquid.
For the present work, a cone-type-funnel was designed to maintain a constant release
rate during discharge so that the evaporation velocity for the spreading pool could be
measured. Additionally, we required a simultaneous measurement of the pool boundary
arrival time using thermocouples and the weight of the spreading pool using a digital
balance.
2. EXPERIMENTAL SET UP AND PROCEDURE
The experiment was set up within a laboratory with five main components: a funnel, a
concrete flat plate, a balance, thermocouples and a computer. The funnel was insulated to
avoid conduction through the funnel wall and was placed above the flat concrete plate,
which had a diameter of 0.8 m and a thickness of 0.025 m, as shown in Fig. 1. Liquid
nitrogen spread on the concrete ground which was placed on the digital balance.
To measure the arrival time of the pool front, there were 24 thermocouples that were
mounted along four concurrent horizontal lines from the concrete plate center. Along each
line, the thermocouples were spaced 0.05 meters apart starting at the center of the plate.
The thermocouple arrangement is shown in detail in Fig. 2. A thermocouple is considered
to be within the liquid pool if the thermocouple temperature falls below -190 °C because
the boiling point of liquid nitrogen is -195 °C. The thermocouples were connected to the
computer to record the temperature data.
A precise digital balance with a resolution of 0.1 g was used to measure the mass of
the liquid nitrogen that was spreading over the concrete plate. The balance was also
connected to the computer to record the spreading mass simultaneously with the
temperature data.
A cone-type funnel was designed as the liquid nitrogen supplier. The key factor in
maintaining an approximately constant release flow rate during the experiment is the
design of the funnel with a large cone angle and high throat. Three nozzles with a
diameter of 6 mm, 8 mm and 10 mm were utilized to change the release flow rate to
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values of 3.4×10 kg/s, 5.6×10 kg/s and 9.0×10 kg/s, respectively.
Fig. 1 General schematic of the experiment apparatus
The outlet of the funnel was blocked using a pad before 7.5 liters of liquid nitrogen was
poured into the funnel from the tank. Once the liquid nitrogen was poured into the funnel, it
boiled violently for a few seconds due to the significant difference in temperature between
the liquid nitrogen and the funnel. After several minutes, the liquid nitrogen became very
stable. This is because the funnel is well isolated and the temperature difference between
the funnel and the liquid nitrogen becomes small. The stability of the liquid nitrogen in the
funnel is very important because of the influence on the release flow rate. Next, the pad
stopping the outlet was removed and the liquid nitrogen was released onto the concrete
plate. The thermocouple T0 at the center of the concrete plate was used to determine the
moment when the experiment started. Six experiments were carried out and were
recorded with a video camera to observe the experimental process.
Fig. 2 Concrete ground with the thermocouples
3. RESULTS AND DICUSSION
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Two experiments were conducted for release flow rates of 3.4×10 kg/s (Case1, Case
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2), 5.6×10 kg/s (Case 3, Case 4), and 9.0×10 kg/s (Case 5, Case 6). In each
experiment, the period of time that the liquid nitrogen pool required to reach a particular
radius was calculated by averaging the four times corresponding to the four thermocouples
in four directions to compensate for several non-isotropic conditions caused by
manufacturing.
A model was built to determine the spill rate
(kg/s), which is a function of spill time t1.
When the outlet stop pad was removed, t1 is zero.
The potential release volume, V, of the liquid nitrogen lined area in the funnel, as
shown in Fig. 3, is a function of h only.
Fig. 3 Design parameters of the funnel
(
For
(
For
),
)
(
)
( )
,
( )
From the conservation of mass,
̇
̇
√
√
(
)
√
√
( )
∫
(
)
√
√
∫
Finally, we obtain
√
Substituting
( )
into Eq. (4), we obtain
√
[
]
( )
The discharge time,
is measured experimentally. Subsequently, the discharge
coefficient, , was calculated to be 0.56, 0.52, and 0.54 for the release flow rates of
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3.4×10 kg/s, 5.6×10 kg/s and 9.0×10 kg/s, respectively.
The spill rate,
(kg/s) was determined as the following:
( )
√
which is determined according to the spreading time, t2,
The pool spreading weight,
was recorded by the digital balance. When the liquid nitrogen arrived at thermocouple T0, t2
was zero. Actually, t1 and t2 were not coincident, but the difference between them was
small (0.1 s), so we can approximately equate t1=t2=t. The increase rate in the nitrogen
mass spreading on the plate,
(kg/s), from
to can be calculated as follows:
( )
Here
and
and are the spreading times of the pool at thermocouple i-1 and i, and
are the pool spreading weights at spreading times at
and , respectively.
Additionally, the top side of the funnel was open. Therefore, the evaporation rate
(kg/s) of the liquid nitrogen through the top side should be considered. This liquid nitrogen
evaporated amount is calculated using the following formula:
[
(
)]
( )
Here, = 1.77x10-5 m/s, which is the evaporation velocity of a non-spreading pool, was
determined from other separate experiments. This value is much less than results from
other works with non-spreading pools (Olewski 2013). This result was because liquid
nitrogen remained in the funnel with a thin and well-isolated wall, which means that the
latent heat source for evaporation is from the convective heat flux coming from ambient air
to the top side of the funnel. Obviously, this convective heat flux is much less than heat
flux applied to the pool in the work of Olewski (2013), which also included the conductive
heat flux from the ground. As recorded in some studies (Verfondern 2007), the conductive
heat flux from the ground is increased to be more than 80% of the total heat flux to the
pool.
The actual spill rate
side of the funnel
(kg/s) was adjusted considering the evaporation from the top
( )
The actual release rate during the experiment changed with time because of the funnel
design, as shown in Fig. 4. The evaporation velocity (m/s) at spreading time was then
calculated
(
0.10
0.09
Case 5,6
Spill rate Qs (kg/s)
0.08
0.07
0.06
Case 3,4
0.05
0.04
Case 1,2
0.03
0.02
0.01
0.00
0
20
40
60
80
100
120
140
Time (s)
Fig. 4 Spill rate Qs with time for the three flow rates
)
The measurement results are summarized
Table 1 Pool radius and evaporation velocity with time (to be continued…)
Case
No.
Q1 (kg/s)
Q2 (kg/s)
Q3 (kg/s)
Evaporation
velocity E
(m/s)
7.85E-03
3.43E-02
1.26E-03
1.41E-03
4.96E-03
0.1
3.14E-02
3.41E-02
5.44E-03
1.34E-03
1.24E-03
40.75
0.15
7.07E-02
3.38E-02
3.33E-03
1.26E-03
5.48E-04
4
52.88
0.2
1.26E-01
3.35E-02
3.30E-03
1.19E-03
3.05E-04
5
90.84
0.25
1.96E-01
3.25E-02
2.63E-03
9.44E-04
1.93E-04
6
126.16
0.3
2.83E-01
3.13E-02
1.42E-03
6.93E-04
1.30E-04
1
16.23
0.05
7.85E-03
3.43E-02
1.23E-03
1.41E-03
4.97E-03
2
25.05
0.1
3.14E-02
3.42E-02
4.54E-03
1.36E-03
1.24E-03
3
37.67
0.15
7.07E-02
3.39E-02
4.75E-03
1.28E-03
5.45E-04
4
57.15
0.2
1.26E-01
3.34E-02
2.57E-03
1.16E-03
3.06E-04
5
98.25
0.25
1.96E-01
3.23E-02
2.43E-03
8.93E-04
1.92E-04
6
135.11
0.3
2.83E-01
3.09E-02
1.36E-03
6.24E-04
1.29E-04
1
14.59
0.05
7.85E-03
5.64E-02
2.06E-03
1.36E-03
8.47E-03
2
26.22
0.1
3.14E-02
5.57E-02
2.58E-03
1.25E-03
2.10E-03
3
42.53
0.15
7.07E-02
5.46E-02
4.90E-03
1.08E-03
9.18E-04
4
51.53
0.2
1.26E-01
5.40E-02
6.67E-03
9.83E-04
5.12E-04
5
66.80
0.25
1.96E-01
5.26E-02
7.20E-03
8.09E-04
3.22E-04
6
79.68
0.3
2.83E-01
5.13E-02
5.43E-03
6.51E-04
2.18E-04
i
Time(s)
Radius(m)
1
15.86
0.05
2
28.72
3
Pool
2
Area(m )
Case 1
Case 2
Case 3
Table 1 Pool radius and evaporation velocity with time (continued)
Case
No.
Q1 (kg/s)
Q2 (kg/s)
Q3 (kg/s)
Evaporation
velocity E
(m/s)
7.85E-03
5.64E-02
2.66E-03
1.36E-03
8.47E-03
0.1
3.14E-02
5.53E-02
2.31E-03
1.19E-03
2.09E-03
41.53
0.15
7.07E-02
5.47E-02
5.43E-03
1.09E-03
9.19E-04
4
52.73
0.2
1.26E-01
5.39E-02
6.25E-03
9.69E-04
5.10E-04
5
62.74
0.25
1.96E-01
5.30E-02
5.99E-03
8.57E-04
3.23E-04
6
82.24
0.3
2.83E-01
5.10E-02
5.64E-03
6.18E-04
2.18E-04
1
14.15
0.05
7.85E-03
9.08E-02
3.53E-03
1.28E-03
1.39E-02
2
26.51
0.1
3.14E-02
8.86E-02
3.24E-03
1.07E-03
3.41E-03
3
34.89
0.15
7.07E-02
8.69E-02
9.55E-03
9.26E-04
1.49E-03
4
42.00
0.2
1.26E-01
8.52E-02
1.55E-02
7.94E-04
8.22E-04
5
48.14
0.25
1.96E-01
8.35E-02
1.14E-02
6.71E-04
5.20E-04
6
59.06
0.3
2.83E-01
7.91E-02
1.37E-02
4.13E-04
3.42E-04
1
13.79
0.05
7.85E-03
9.08E-02
3.63E-03
1.29E-03
1.39E-02
2
25.79
0.1
3.14E-02
8.87E-02
3.33E-03
1.09E-03
3.41E-03
3
34.50
0.15
7.07E-02
8.70E-02
8.04E-03
9.34E-04
1.49E-03
4
45.04
0.2
1.26E-01
8.44E-02
1.14E-02
7.34E-04
8.14E-04
5
52.00
0.25
1.96E-01
8.23E-02
1.01E-02
5.90E-04
5.12E-04
6
60.89
0.3
2.83E-01
7.85E-02
1.35E-02
3.82E-04
3.40E-04
i
Time(s)
Radius(m)
1
15.01
0.05
2
32.33
3
Pool
2
Area(m )
Case 4
Case 5
Case 6
The evaporation velocity decreases during pool spreading, as shown in Fig. 5 because
the overall temperature difference between the pool and the concrete ground decreases
with time.
1.4x10-2
Case 1
Case 2
Evaporation velocity, E (m/s)
1.2x10-2
1.0x10-2
Case 3
Case 4
8.0x10-3
Case 5
Case 6
-3
6.0x10
4.0x10-3
2.0x10-3
0.0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Pool radius, R (m)
Fig. 5 Evaporation velocity with time
To obtain useful data for engineering purposes, the average evaporation velocity is
calculated using the flow rates and the polynomial fitting given in Table 2.
Table 2 The average evaporation velocity E (m/s)
Flow rate (kg/s)
3.4E-2
5.6E-2
9E-2
E (m/s)
4.99E-04
8.33E-04
1.35E-03
To compare the results of the present work with previous studies, the results from
several studies are listed in Table 3. It is worth noting that all of the studies in Table 3 were
carried out using a non-spreading pool. From the comparison, the average evaporation
velocity in this study is greater than the evaporation velocities listed in Table 3 because
the pool in this work spreads continuously to new warm ground while the heat flux into the
pool deteriorates continuously due to the temperature decreasing gap between the
environment and the non-spreading pool in previous experiments.
Table 3 Other experimental results
Author


Zabetakis
1960




Takeno 1994



Olewski
2013




Olewski
2014





Reid 1978


Contents
Cryogenic liquid: Liquid
Hydrogen
Ground material: Paraffin
wax.
Release method:
Instantaneous.
Pool characteristic: Nonspreading.
Cryogenic liquid: Liquid
hydrogen and liquid oxygen
Ground material: Limestone
concrete.
Release method:
Instantaneous.
Pool characteristic: Nonspreading.
Cryogenic liquid: Liquid
nitrogen
Ground material: Concrete.
Release method:
Instantaneous.
Pool characteristic: Nonspreading.
Cryogenic liquid: Liquid
nitrogen
Ground material: Concrete.
Release method: Not
determined
Pool characteristic: Nonspreading.
Cryogenic liquid: Liquefied
Natural Gas
Ground material: Insulating
concrete, soil, sand, dry
polyurethane.
Release method:
Instantaneous.
Pool characteristic: Nonspreading.
Results
E= 1 ~ 3 in/s
(4.23x10-4 ~ 12.7x10-4 m/s)
Estimated evaporation velocity :
Cryogenic
liquid
Liquid
hydrogen
Liquid
oxygen
Evaporation velocity
(m/s)
1.80x10-3 ~ 3.10x10-4
from 0 ~ 250s
1.36x10-3 ~ 4.11x10-5
from 0 ~ 500s
Conductive heat flux: q= 135.2t-0.5
(kJ/m2s)
Estimated evaporation velocity E:
8.38x10-4 ~ 5.92x10-5 m/s from 1 ~
200s
Conductive heat flux: q= 130t-0.5
(kJ/m2s)
Estimated evaporation velocity E:
8.05x10-4 ~ 5.70x10-5 m/s from 1 ~
200s
Rate of boiling:
̇
(
)
Estimated evaporation velocity E:
1.20x10-3 ~ 8.50x10-5 m/s from 1 ~
200s
4. CONCLUSIONS
In this study, the evaporation velocity was measured for a spreading liquid nitrogen pool
with continuous release. Because it is known that a spreading pool with continuous
release is much more probable than a non-spreading pool with instantaneous release with
respect to accidents, the method developed in this study for the measurement of the
evaporation velocity is meaningful.
To perform this experiment, we required information about the spill flow rate and a
simultaneous measurement of the pool boundary and the liquid nitrogen weight with time.
For the measurement of the evaporation velocity for a non-spreading pool, the weight
change with time is the only parameter required because the pool area is a constant value.
The funnel is designed so that the spill flow rate was nearly constant.
A greater release flow rate was found to result in a greater evaporation velocity, and the
evaporation velocity decreased with the spreading time. The measured evaporation
velocities are greater than the evaporation velocities from other studies because the
spreading pool in the present work receives heat more effectively from the ground
compared with a non-spreading pool.
NOMENCLATURE
E: Evaporation velocity [m/s]
: Liquid nitrogen density [kg/m3]
V: Release volume [m3]
: Spill weight without considering the evaporation from the top side of the funnel [kg]
: Pool spreading weight [kg]
: Evaporation weight form the top side of the funnel [kg]
Ai: Pool area at thermocouple i [m2]
= 0.375 m: Initial high level of liquid nitrogen from the outlet
h: Instantaneous high level of liquid nitrogen at time t [m]
: Cone- angle of the funnel
: Initial radius of top surface area at high level
[m]
: Nozzle radius [m]
: Discharge coefficient [-]
ACKNOWLEDGEMENT
This research was supported by the Converging Research Center Program funded by
the Ministry of Education, Science and Technology of Korea (Grant number: 2012K001437)
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