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Available online at www.sciencedirect.com
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Thermodynamic analysis of the emptying process
of compressed hydrogen tanks
Lei Zhao a,*, Fenggang Li a, Zhiyong Li b, Lifang Zhang c, Guangping He a,
Quanliang Zhao a, Junjie Yuan a, Jiejian Di a, Chilou Zhou d
a
School of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, China
School of Civil Engineering, North China University of Technology, Beijing 100144, China
c
Beijing JONTON Hydrogen Tech. Co., Ltd, Beijing 102299, China
d
School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641,
China
b
article info
abstract
Article history:
During the driving of fuel cell vehicles, the fast depressurization of compressed hydrogen
Received 10 July 2018
tanks plus the high storage pressure and the low thermal conductivity of carbon fiber
Received in revised form
reinforced plastic (CFRP) can lead to significant cooling of the tank. This can result in a
4 December 2018
temperature below 40 C inside the compressed hydrogen tanks and cause safety prob-
Accepted 12 December 2018
lems. In this paper, a thermodynamic model that incorporates the nature of external
Available online 5 January 2019
natural convection was developed to describe the emptying process of compressed
hydrogen tanks and was validated by experiments. Thermodynamic analyses of the
Keywords:
emptying process were performed to study the global heat transfer characteristics and the
Compressed hydrogen tanks
effects of ambient temperature, defueling rate, defueling pattern, initial and final density of
Emptying
hydrogen gas, liner and CFRP thickness and the crosswind velocity on the final tempera-
Thermodynamic analysis
ture decreases of hydrogen gas, the inner wall and the outer wall.
Heat transfer
© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Temperature decrease
Introduction
Fuel cell vehicles (FCVs) provide a promising solution to air
pollution and the increasing fossil fuel scarcity because of the
cleanness, high energy efficiency and wide availability of
hydrogen [1e3]. To achieve a comparable mileage as the fossil
fuel vehicles, high pressure (35 or 70 MPa) composite tanks are
widely used for onboard hydrogen storage [4,5]. Such tanks
usually consist of a metal (type III tank) or polymer (type IV
tank) liner and a carbon fiber reinforced plastic (CFRP) wrapped over the liner. With the high storage pressure and the low
thermal conductivity of CFRP, the fast depressurization of
such tanks during the driving of fuel cell vehicles can lead to
significant cooling inside the tanks. This can result in a gas
temperature below the lower temperature limit of 40 C [6,7]
inside the compressed hydrogen tanks and cause safety
problems. For this reason, the emptying process of compressed hydrogen tanks should be carefully studied.
The temperature rise during fast filling of compressed
hydrogen tanks has been a hot topic over the past 10 years and
there have been many studies on the fast filling process,
including experimental studies [8e11], computational fluid
dynamics (CFD) simulations [12e20] and thermodynamic analyses [21e26]. This subject has been extensively reviewed by
Bourgeois [27]. From the above studies, the gas flow in the
* Corresponding author.
E-mail addresses: zhaolei@ncut.edu.cn, 04gczbzl@163.com (L. Zhao).
https://doi.org/10.1016/j.ijhydene.2018.12.091
0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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tanks is dominated by forced convection for fast filling and by
mixed convection for slow filling. The forced convection
component during filling is mainly caused by the jet flowing
into the tank. In contrast to the fast filling process, only a few
studies have been devoted to the emptying process of compressed hydrogen tanks [28e32]. Winters reviewed the
convective heat transfer correlations for gas flow in tanks
during the emptying process and indicated that the gas flow in
the tank is mainly dominated by natural convection during
the emptying process since there is no jet flow in the tanks
and the gas velocities are extremely low except near the exit of
the tanks. He developed a thermodynamic model and a CFD
model of the fast emptying process of a low pressure spherical
hydrogen vessel by assuming a constant wall temperature
throughout the emptying process [28]. Rothuizen [23] and Guo
[29] proposed thermodynamic models of the emptying process by treating the average heat transfer coefficient over the
outer wall of the tank as a constant. Melideo developed a CFD
model of the emptying process of compressed hydrogen tanks
and numerically studied the temperature distribution during
defueling at two different defueling rates [30]. In the experimental studies, the thermal stratification in the tank during
defueling were investigated [31,32]. The thermal stratification
appears to be vertical in the compressed hydrogen tanks
during defueling [31,32] and the maximum top-to-bottom
temperature difference during defueling was found to be
positively correlated with defueling rate [32]. However, none
of the above-mentioned thermodynamic models consider the
inherent dependence of the convection heat transfer coefficient on the temperature difference between ambient air and
the outer wall of the tank, which is an important feature of
natural and mixed convection [33]. Moreover, the effects of
parameters other than defueling rate on temperature decreases have not been investigated, and the global heat
transfer characteristics of the emptying process have not been
discussed. Therefore, a comprehensive thermodynamic
analysis of the emptying process is urgently needed.
In this paper, a thermodynamic model of the emptying
process of compressed hydrogen tanks was developed by
considering the real gas effects of compressed hydrogen gas,
the nature of internal natural convection, and further, by
including the nature of external natural convection, which
has not been considered by other authors. The proposed
thermodynamic model was verified by the defueling
experiments presented in Ref. [32]. Thermodynamic analyses
of the emptying process were conducted for both type III and
type IV tanks to study the global heat transfer characteristics
and the effects of ambient temperature, defueling rate, defueling pattern, initial and final pressure of hydrogen gas, liner
and CFRP thickness and the crosswind velocity on the final
temperature decreases of hydrogen gas, the inner wall and the
outer wall.
Modeling
Governing equations
A thermodynamic model was developed to describe the
emptying process of compressed hydrogen tanks. The heat
transfer mechanisms involved in the thermodynamic model
were illustrated in Fig. 1. During the emptying process, the
expansion of hydrogen gas results in cooling of the tank [34]
and leads to temperature differences among hydrogen, tank
wall and ambient air. Because the length of the tank and the
perimeter of its cross section are much larger than the
thickness of the tank wall, the directional derivative of wall
temperature in the radial direction is much larger than those
in the axial and circumferential directions. For this reason,
heat conduction through the tank wall is assumed to occur
only along the thickness direction. The heat transfer at the
inner wall is dominated by natural convection because the gas
velocities within the tank are extremely low except near the
exit region [28]. The heat transfer at the outer wall is natural or
mixed convection depending on the velocity of ambient air
and the temperature difference between the outer wall and
ambient air [33]. The convective heat transfer at the inner wall
and the outer wall are described by Newton's cooling law and
convective heat transfer correlations. The hydrogen gas in the
tank was treated as a bulk. The aim of the thermodynamic
model is to study the global thermal behavior during the
emptying process.
The governing equations for the hydrogen gas in tank are:
Continuity equation :
dmg
¼ m_ g
dt
(1)
Energy equation : mg
dug
¼ m_ g pg vg Q_ i
dt
(2)
Fig. 1 e Schematic diagram of the thermodynamic model for the emptying process of compressed hydrogen tanks.
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where m, t, u, p, v and Q_ are mass, time, specific internal energy, pressure, specific volume and heat transfer rate
respectively. Subscript g represents hydrogen gas, and
subscript i denotes the inner tank wall. Thermodynamic
properties of hydrogen were derived from the fundamental
equation of state (EOS) for normal hydrogen [35] according to
approaches given in Ref. [36]. The adopted EOS is explicit in
the Helmholtz free energy as given by Eqs. (3)e(5). The reason
for using this EOS is the high accuracy of the thermodynamic
properties calculated from it in a wide range of pressures and
temperatures.
a ¼ a0 þ a t
(3)
where,a is the reduced Helmholtz free energy, which is
composed of two parts, the ideal gas contribution a0 and the
residual contribution at . The reduced Helmholtz free energy is
a
. a is the Helmholtz free energy, R is
defined as a ¼ RT
the molecular gas constant, 8.314472 J/(mol.K) and T is the
temperature. The ideal gas contribution and the residual
contribution to the reduced Helmholtz free energy are
expressed as
a0 ¼ lnrr þ 1:5 lnTr þ b1 þ b2 Tr þ
7
X
(4)
l
X
j¼1
þ
d
m X
t
Nj rr k;j Trk;j þ
n X
d
t
p
Nj rr k;j Trk;j exp rr k;j
j¼lþ1
d
t
Nj rr k;j Trk;j exp
2 2
4j rr Dk;j þ bj Tr gk;j
(2) Boundary conditions
During defueling, the mass flow rate (defueling rate) is
specified and the hydrogen gas at the exit of the tank is
assumed to have the same pressure and temperature as the
bulk gas inside the tank. The liner and CFRP are assumed to
have the same temperature at their interface. Heat transfer at
the inner wall and the outer wall of the tank are described by
the Newton's law of cooling and are given by the following
equations:
For the inner wall:
Q_ i ¼ hi Ai Tg Twi
For the outer wall:
(5)
where rr and Tr are the reduced density and reduced tem¼ TTc . rc and Tc are the critical density and
3
critical temperature of normal hydrogen, rc ¼ 31:263 kg=m ,
Tc ¼ 33:145 K. In Eqs. (4) and (5), aj , bj , cj , Nj , dk;j , tk;j , pk;j , 4j , bj ,
Dk; j and gk; j are constants and specified in Ref. [35].
The expressions for other thermodynamic properties can
be derived by combining Eqs. (3)e(5) and the relations between
the reduced Helmholtz free energy and other thermodynamic
properties as given in Ref. [36].
The governing equations for the tank wall are shown as
follows:
For the interior of the wall:
vTw
v2 Tw
¼ aw 2
vt
vr
(6)
(8)
Where h is the convective heat transfer coefficient and A is the
surface area. Subscripts i, o and amb denote the inner wall, the
outer wall and the ambient air, respectively. The heat transfer
at the inner wall are dominated by natural convection because
of the extremely low velocities of the gas within the tank and
the Nusselt number can be estimated using the correlations
suggested by Clark [37]:
j¼mþ1
perature, rr ¼ rrc , Tr
(7)
Q_ o ¼ ho Ao ðTamb Two Þ
bj ln 1 exp cj Tr
j¼3
at ¼
and the ambient temperature are specified for each simulation. The advantage of specifying initial density instead of
initial pressure is that the State of Charge (SOC, the ratio between the actual gas density and the rated gas density which
equals to 40.2 g/L for 70 MPa tanks) at the beginning of defueling remains unchanged at different ambient temperatures.
Nui ¼
1:15Rai0:22 ; Rai < 108
0:14Rai0:333 ; Rai 108
(9)
In Eq. (9), Nu and Ra are the Nusselt number and Rayleigh
number, respectively. Rai , which represents the Rayleigh
r2 D3 bg;f gðTwi Tg ÞCpjg;f
number at the inner wall is defined as Rai ¼ g;f i
mg;f lg;f
.
Where D is the diameter of tank, b is the volumetric thermal
expansion coefficient, Cp is the specific heat capacity at constant pressure, m is the dynamic viscosity and l is the thermal
conductivity. Subscript f denotes the film temperature, which
is the average temperature of a gas and its adjacent wall. The
dynamic viscosity and thermal diffusivity of hydrogen were
calculated with the empirical formulas presented in Ref. [38]
and Ref. [39], respectively.
The heat transfer coefficient at the outer wall can be represented by the following equations:
where Tw is the wall temperature, aw is the thermal diffusivity
of the material of wall and r is the radial distance from the
inner wall.
14
Nuo ¼ Nu4o;free þ Nu4o;forced
Initial and boundary conditions
outer wall of the tank and can be calculated using the
approach described in Ref. [14], Nuo;forced is the Nusselt number
(1) Initial conditions
In this study, the hydrogen gas and the tank wall are
assumed to have the same temperature with the ambient at
the beginning of defueling. The initial density of hydrogen gas
(10)
Where Nuo;free is the Nusselt number for free convection at the
for forced convection due to cross wind at the outer wall of the
tank and can be estimated by the surface average of
Nucylinder;forced and Nusphere;forced , which are the Nusselt Numbers
for cross flow over cylinder and sphere, and can be estimated
using Eqs. 11 and 12, respectively [40].
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Nucylinder;forced ¼
Nusphere;forced ¼
8 0;
>
>
<
0:3 þ h
>
>
:
1 þ 0:4 Pramb;f
ReDo ¼ 0
"
1=3
0:62Re1=2
Do Pramb;f
1þ
2=3 i1=4
5=8 #4=5
ReDo
282000
;
(11)
Numerical schemes
8
0;
>
<
1=2
ReDo
>
:2 þ
þ 3 104 Re1:6
;
Do
4
ReDo ¼ 0
(12)
ReDo >0
where Re and Pr denote the Reynold number and Prandtl
r
c
wind
number, respectively. ReDo is defined by ReDo ¼ amb;f
m
Do
amb;f
and
m
Cpjamb;f
Pramb; f is defined by Pramb;f ¼ amb;f
. c is the velocity, and
lamb;f
subscript wind represents the cross wind. The density of
ambient air can be determined by the idea gas law, while the
specific heat capacity of ambient air at constant pressure and
the transport coefficients of ambient air were calculated using
Eqs. 13e15, which were obtained by fitting the property data
from Ref. [41].
Tamb;f 4:789
þ 1002
Cp amb;f ¼ 0:01514
100
mamb;f ¼4:127107
(13)
Tamb;f 2
Tamb;f
þ4:094107
þ7:258106
100
100
(14)
lamb;f ¼ 3:77 104
ReDo > 0
Tamb;f 2
Tamb;f
4:776
þ 1:004 102
100
100
104
(15)
In Eqs. 13e15, the international system of units is used.
Tank parameter
For the numerical solution of Eqs. 1e12, the tank wall was
radially discretized into a number of sub-volumes using the
finite volume method. The partial differential heat conduction
equation for the tank wall was then converted into ordinary
differential equations (ODEs) for each sub-volume by applying
the method of lines [42]. The obtained ODEs were solved using
the Classical Runge-Kutta method [43]. The numerical simulations have been performed with MATLAB R2013a.
Model validation
For the validation of the proposed model, defueling experiments for the 29 L type IV tank with constant mass flow rates
of 1.8 g/s and 0.2 g/s [32] were used. The 1.8 g/s corresponds to
a fast defueling with a total defueling time much less than
that of FCVs and the 0.2 g/s corresponds to a slow defueling
with a total defueling time comparable to that of FCVs. These
two defueling rates were selected to examine the ability of our
model to predict both fast and slow emptying process. The
above defueling experiments were numerically simulated
using the proposed thermodynamic model. Comparisons
were made among the mass-averaged hydrogen temperatures
calculated from the proposed thermodynamic model, from
the thermodynamic model that assumes a constant convective heat transfer coefficient and from experimental data of
Ref. [32]. The comparison results for the 1.8 g/s and 0.2 g/s
defueling are shown in Fig. 2 and Fig. 3 respectively. In Fig. 2,
comparison between the thermodynamic model proposed in
The simulated tanks include a commercial type IV tank with
High-density polyethylene (HDPE) liner and an imaginary type
III tank with Aluminum (Al) liner. The latter was assumed to
have the same dimensions as the former one and was used for
comparison. The default size of these tanks [32] and the
physical properties of tank materials [7] are given in Table 1.
Table 1 e Parameters of the simulated tanks.
Simulated tanks
Volume (L)
Internal diameter (mm)
External diameter (mm)
External length (mm)
Thermal conductivity of liner (W/m.K)
Heat capacity of liner (J/kg.K)
Density of liner (kg/m3)
Thermal conductivity of CFRP (W/m.K)
Heat capacity of CFRP (J/kg.K)
Density of CFRP (kg/m3)
Type III
tank
Type IV
tank
29
230
279
827
164
1106
2700
0.74
1120
1494
29
230
279
827
0.5
2100
945
0.74
1120
1494
Fig. 2 e Comparison of the mass-averaged hydrogen
temperatures calculated from the proposed
thermodynamic model and from experimental results for
the 1.8 g/s defueling.
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and the end of defueling are specified such that the mileage of
FCVs can be maintained at a certain value. In the following
section, each parameter takes its default value as given in
Table 2 unless otherwise specified.
Results and discussion
In this Chapter, the tank parameters and defueling parameters take their default values as given in Tables 1 and 2 unless
otherwise specified.
Global heat transfer characteristics of the emptying process
Fig. 3 e Comparison of the mass-averaged hydrogen
temperatures calculated from the proposed
thermodynamic model, from the thermodynamic model
that assumes a constant convective heat transfer
coefficient of 6 W/K.m2 at the outer wall and from
experimental results for the 0.2 g/s defueling.
this paper and that assumes a constant convective heat
transfer coefficient at the outer wall is not shown since the
effect of the outer-wall heat transfer coefficient is small for
short-time defueling. As is shown in Figs. 2 and 3, the thermodynamic model proposed in this paper is in good agreement with experiments and has much better performance
than the thermodynamic model that assumes a constant
convective heat transfer coefficient of 6 W/K.m2 at the outer
wall [23,29]. The reason for this is that our model incorporates
the nature of external free convection.
The default defueling condition
The default defueling condition used in Section Results and
discussion are given in Table 2.
In this study, the temperature of the tank and the hydrogen
gas are assumed to be equal to the ambient temperature at the
beginning of the defueling. The gas density at the beginning
Thermodynamic analyses of the emptying process were performed for the type III and type IV tank specified in Table 1 under
the default defueling condition to understand the global heat
transfer characteristics of the emptying process. The temporal
variation of the temperatures of hydrogen gas, the inner wall and
the outer wall during defueling are shown in Fig. 4. According to
Fig. 4, the hydrogen temperature falls with a decreasing rate at
the beginning and middle of defueling, but with an increasing
rate near the end, while the temperatures of the inner and outer
wall fall with decreasing rates throughout the emptying process.
The increased hydrogen cooling rate near the end of defueling
can result from the high ratio of mass flow rate to the mass of
hydrogen gas remaining in the tank at that time.
The temporal variation of Rayleigh numbers at the inner
and outer wall are shown in Fig. 5. The temporal variation of
the temperature differences between the inner wall and
hydrogen gas and between ambient air and the outer wall are
described in Fig. 6. As shown in Figs. 5 and 6, the Rayleigh
number at the inner wall increases to a peak at the onset of
defueling because of the increase in temperature difference
between the inner wall and hydrogen gas, and then decreases
due to the reduced hydrogen density. The Rayleigh number at
the inner wall appears to be larger than 108 during most of the
time of defueling, implying that the interior of the tank is
mainly dominated by turbulent natural convection during
defueling [33]. The Rayleigh number at the outer wall increases
Table 2 e The default defueling condition.
Defueling parameter
Volume (L)
Internal diameter (mm)
External diameter (mm)
Liner thickness (mm)
CFRP thickness (mm)
Defueling rate (g/s)
Defueling pattern
Ambient temperature (K)
Initial gas temperature (K)
Initial wall temperature (K)
Initial hydrogen density (g/L)
Final hydrogen density (g/L)
Ambient wind
Default value
29
230
279
5
19.5
0.4
Constant defueling rate
288.15
Equal to ambient temperature
Equal to ambient temperature
40.2 (The density value at 70 MPa,
288.15 K)
1.68 (The density value at 2 MPa,
288.15 K)
None
Fig. 4 e The temporal variation of the temperatures of
hydrogen gas, the inner wall and the outer wall during
defueling.
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Fig. 5 e The temporal variation of the Rayleigh numbers at
the inner and outer wall during defueling.
from below 107 to 107~109 during defueling, suggesting that the
free convection on the outer wall experiences a flow transition
from the laminar regime to the transitional regime [33].
The temporal variation of heat transfer coefficients at the
inner and outer wall are shown in Fig. 7. According to Figs. 5
and 7, the heat transfer coefficient has similar trend as the
Rayleigh number at the inner wall, but with an earlier peak
due to the decreasing thermal conductivity of hydrogen gas,
which results from the density and temperature decrease
during defueling. The heat transfer coefficient at the outer
wall increases throughout the defueling process because of
the continuously increasing temperature difference between
ambient air and the outer wall as shown in Fig. 6.
The temporal variation of heat transfer rate at the inner
and outer wall are shown in Fig. 8. According to Fig. 8, the heat
transfer rate at the inner wall increases to a maximum at the
beginning of defueling, and then decreases slowly till the end.
Compared with the heat transfer coefficient at the inner wall,
the much slower decrease of the heat transfer rate at the inner
wall after its maximum can be explained by the increasing
temperature difference between the inner wall and hydrogen
gas (Fig. 6).
Fig. 7 e The temporal variation of the heat transfer
coefficients at the inner and outer wall during defueling.
Fig. 8 e The temporal variation of the heat transfer rates at
the inner and outer wall during defueling.
The temperature distribution along the thickness of the
tank wall at different times during defueling are given in Fig. 9
(a) and (b). As can be seen from Fig. 9 (a) and (b), the temperature is almost uniform along the thickness of the Al liner
because of the high thermal conductivity of aluminum alloy,
while the temperature varies along the thickness of the HDPE
liner and the CFRP laminate because of the low thermal conductivity of HDPE and CFRP.
The heat transfer rate along the thickness of the tank wall
at different times during defueling are shown in Fig. 10 (a) and
(b). According to Fig. 10 (a) and (b), the heat transfer rate exhibits a decrease along the thickness of the tank wall because
the heat output must be higher than the heat input at a certain
point to maintain the cooling process.
Influencing factors on final temperature decreases
(1) Ambient temperature
Fig. 6 e The temporal variation of the temperature
differences between the inner wall and hydrogen gas and
between ambient air and the outer wall during defueling.
With the assumption that the tank and gas are in thermal
equilibrium with ambient, the effects of ambient temperature
on the final temperature decreases of the hydrogen gas, the
inner wall and the outer wall were studied by varying the
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 3 9 9 3 e4 0 0 5
Fig. 9 e Temperature distribution along the thickness of
the tank wall at different times during defueling: (a) 465,
930 and 1395 s; (b) 1860, 2325 and 2790 s.
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Fig. 10 e Heat transfer rate along the thickness of the tank
wall at different times during defueling: (a) 465, 930 and
1395 s; (b) 1860, 2325 and 2790 s.
ambient temperature from 233.15 K to 323.15 K using the
proposed thermodynamic model and the results are shown in
Fig. 11. According to Fig. 11, the final temperature decreases of
the hydrogen gas, the inner wall and the outer wall all increase almost linearly with the increase in ambient temperature. This can be explained by the expansion power increase
resulting from the increase in gas pressure due to the increase
in ambient temperature and gas temperature.
(2) Defueling rate
The effects of defueling rate on the final temperature decreases of the hydrogen gas, the inner wall and the outer wall
were studied by varying the defueling rate from 0.1 g/s to 2 g/s
using the proposed thermodynamic model and the results are
shown in Fig. 12. According to Fig. 12, the increase in the final
temperature decreases of the hydrogen gas and the inner wall
Fig. 11 e Variation of the final temperature decreases with
ambient temperature.
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Fig. 12 e Variation of the final temperature decreases with
defueling rate.
Fig. 14 e The temporal variation of the mass of hydrogen
gas for different defueling patterns.
slow down with the increase in defueling rate. The reason for
this slowdown is that the final temperature decreases of
hydrogen gas and the inner wall are negatively proportional to
the total heat transfer, which is positively proportional to the
total defueling time and inversely proportional to defueling
rate. As the defueling rate increases, the final temperature
decrease of the outer wall increases first and then decreases
(Fig. 12). Such decrease can be explained by the decreasing and
near-unity Fourier number of the CFRP layer at higher defueling rates as shown in Fig. 13, since thermal diffusion is the
determinant for a conjugate heat transfer problem at a nearunity Fourier number.
(3) Defueling pattern
The defueling history varies with the driving condition. For
this reason, the effect of defueling pattern on temperature
decreases was studied using the proposed thermodynamic
model. Four typical defueling patterns were discussed in this
paper. The temporal variation of the mass of hydrogen gas for
these defueling patterns are shown in Fig. 14.
Fig. 13 e Variation of defueling rate and the final
temperature decrease of the outer wall with Fourier
number.
Fig. 15 e The temporal variation of hydrogen temperature
for different defueling patterns: (a) The type III tank; (b) the
type IV tank.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 3 9 9 3 e4 0 0 5
The temporal variation of the temperature of hydrogen gas
and the inner wall are shown in Fig. 15 and Fig. 16, respectively. For the “fast-slow” defueling pattern (defueling pattern
2), the temperature of hydrogen gas and the inner wall first
decreases with time to a minimum during the fast defueling
phase and then begins to recover during the slow defueling
phase. Compared with the constant-rate defueling pattern
(defueling pattern 1), the “fast-slow” defueling pattern exhibits a higher final temperature of hydrogen gas and inner
wall, but a similar minimum temperature. The higher final
temperature for the “fast-slow” defueling pattern can be
explained by the enhanced heat transfer due to the high
temperature difference established at the beginning of defueling. For the “slow-fast” defueling pattern (defueling pattern
3), the temperature of hydrogen gas and the inner wall show
moderate decrease with time during the slow defueling phase
and a rapid decrease during the fast defueling phase. The
“slow-fast” defueling pattern exhibits lower final temperature
of hydrogen gas and inner wall for reasons similar to the “fastslow” defueling pattern. The “defuel-stop alternate” defueling
Fig. 16 e The temporal variation of the inner wall
temperature for different defueling patterns: (a) The type III
tank; (b) the type IV tank.
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pattern (defueling pattern 4) is composed of a series of defuelstop sub-processes, and thus shows temperature oscillation
around the temperature profile for the constant-rate defueling
pattern. From the above findings, changing defueling pattern
may not be an effective way to reduce the temperature decreases of hydrogen gas and the inner wall.
(4) Initial and final hydrogen density
The effects of initial hydrogen density on the final temperature decreases of hydrogen gas, the inner wall and the outer
wall were studied by varying the initial hydrogen density from
14.9 g/L (the density value at 20 MPa, 288.15 K) to 47.3 g/L (the
density value at 90 MPa, 288.15 K) with a constant final
hydrogen density of 1.68 g/L (the density value at 2 MPa,
288.15 K) using the proposed thermodynamic model. The results are shown in Fig. 17. According to Fig. 17, the final temperature decreases of hydrogen gas, the inner wall and the
outer wall all increase with the increase in initial hydrogen
density. This is because the total expansion work increases
with the increase in initial hydrogen density (initial pressure)
while the final heat capacity of hydrogen is roughly the same
with the same final hydrogen density.
The effects of final hydrogen density on the final temperature decreases of hydrogen gas, the inner wall and the outer
wall were studied by varying the final hydrogen density from
0.42 g/L (the density value at 0.5 MPa, 288.15 K) to 16.1 g/L (the
density value at 51.1 MPa, 288.15 K) with a constant initial
hydrogen density of 40.2 g/L and are described in Fig. 18. As
shown in Fig. 18, the final temperature decrease of hydrogen
gas declines with the increase in final hydrogen density, while
those of the inner and outer wall show a clear decrease with
the increase in final hydrogen density only when the final
density is higher than 4.02 g/L. The drop of the final temperature decreases can be ascribed to the decrease in total
expansion work and the increase in heat capacity of the
remaining hydrogen gas at the end of defueling, while the
insensitivity of the final temperature decreases of the inner
and outer wall to the final hydrogen density when such density is lower than 4.02 g/L can be ascribed to the almost
Fig. 17 e Variation of final temperature decreases with
initial hydrogen density.
4002
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 3 9 9 3 e4 0 0 5
Fig. 18 e Variation of final temperature decreases with final
hydrogen density.
negligible effect of the final hydrogen density on the total
expansion work and the low heat capacity of hydrogen gas at
the end defueling compared with the liner and CFRP because
of the low final density of hydrogen gas.
(5) Liner and CFRP thickness
The effects of liner thickness on the final temperature decreases of hydrogen gas, the inner wall and the outer wall
were studied by varying the liner thickness from 1 mm to
8 mm with an interval of 1 mm. The results are shown in
Fig. 19. As can be seen from Fig. 19, the final temperature decreases of hydrogen gas, the inner wall and the outer wall all
decrease with the increase in liner thickness for type III tanks,
because of the increased heat capacity of the Al liner and the
almost unchanged total thermal resistance due to the high
thermal conductivity of aluminum alloy. The effects of CFRP
thickness on the final temperature decreases of hydrogen gas,
the inner wall and the outer wall were studied by varying the
CFRP thickness from 10 mm to 28 mm with an interval of
Fig. 19 e Variation of final temperature decreases with
liner thickness.
Fig. 20 e Variation of final temperature decreases with
CFRP thickness.
2 mm. The results are shown in Fig. 20. Combining Figs. 19 and
20, the thickness of HDPE liner and CFRP have similar effect on
the final temperature decreases. The final temperature decreases of the hydrogen gas and the inner wall increase with
the increase in the thickness of HDPE liner and CFRP because
of the non-negligible increase in total thermal resistance due
to the low thermal conductivity of HDPE and CFRP, while the
final temperature decrease of the outer wall shows the
opposite trend for the same reason.
(6) Cross-wind velocity
The effects of cross-wind velocity on the final temperature
decreases of the hydrogen gas, the inner wall and the outer
wall were studied by varying the ambient cross-wind velocity
from 0 to 20 m/s with an interval of 1 m/s. The results are
described in Fig. 21. It can be seen that the final temperature
decreases of the hydrogen gas and the inner wall only
decrease by ~4 K when the cross-wind velocity increases from
0 to 20 m/s.
Fig. 21 e Variation of final temperature decreases with
cross-wind velocity.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 3 9 9 3 e4 0 0 5
4003
tanks. For this purpose, a thermodynamic model that incorporates the nature of external natural convection was
developed. Thermodynamic analyses of the emptying process
were performed for both type III and type IV tanks to study the
global heat transfer characteristics and the effects of ambient
temperature, defueling rate, defueling pattern, initial and final
hydrogen density, liner and CFRP thickness and the crosswind
velocity on the final temperature decreases. The conclusions
of this research are summarized as follows:
Fig. 22 e Comparison of the convective heat transfer
coefficients at the outer wall without cross-wind and with
a cross-wind velocity of 20 m/s.
Fig. 23 e Comparison of the total thermal resistances per
unit area without cross-wind and with a cross-wind
velocity of 20 m/s.
For a comprehensive understanding of the cross-wind effect, comparisons on heat transfer coefficient at the outer wall
and the total thermal resistance per unit area were made between the defueling without cross-wind and that with a crosswind velocity of 20 m/s. The comparison results are shown in
Fig. 22 and Fig. 23. Combining Figs. 22 and 23, the heat transfer
at the outer wall can be enhanced by cross-wind (Fig. 22), but
the effect of cross-wind in reducing the total thermal resistance appears to be limited because the convective thermal
resistance at the outer wall and the conductive thermal resistance of CFRP are on the same order of magnitude (Fig. 23). The
above findings implies that the final temperature decreases
may not be effectively reduced by enhanced ventilation.
Conclusions
The main objective of this paper was to study the thermal
effects during the emptying process of compressed hydrogen
(1) During defueling, the natural convection within the
tank is predominantly turbulent, while the natural
convection on the outer wall experiences a flow transition from the laminar regime to the transitional
regime. The Rayleigh number, the heat transfer coefficient and the heat transfer rate at the inner wall all increase to their maximum first because of the increases
in temperature difference between the inner wall and
hydrogen gas, and then decrease because of the
decrease in hydrogen densities; while those at the outer
wall increase throughout the defueling process because
of the continuously increasing temperature difference
between ambient air and the outer wall.
(2) When the hydrogen gas, the tank wall and the ambient
air are in thermal equilibrium at the beginning of
defueling, the final temperature decreases of hydrogen
gas, the inner wall and the outer wall are all positively
proportional to ambient temperature because the total
expansion power is positively proportional to the initial
gas pressure which is positively proportional to the
ambient temperature.
(3) The increase in the final temperature decreases of
hydrogen gas and the inner wall slow down with the
increase in defueling rate because those temperature
decreases are negatively proportional to the total heat
transfer, which is positively proportional to the total
defueling time and inversely proportional to defueling
rate. As the defueling rate increases, the temperature
decrease of the outer wall first increases because of the
increased temperature decrease of hydrogen gas, and
then decreases due to the decreasing and near-unity
Fourier number of the CFRP layer.
(4) Compared with the constant-rate defueling pattern, the
“fast-slow” and “slow-fast” defueling pattern exhibit
similar and lower minimum temperatures respectively,
while the “on-off alternate” defueling pattern shows
temperature oscillation around the temperature profile
for the constant-rate defueling. Changing defueling
pattern may not be an effective way to reduce the
temperature decreases of hydrogen gas and the inner
wall.
(5) The final temperature decreases of hydrogen gas, the
inner wall and the outer wall all increase with the increase in initial hydrogen density because of the
increased total expansion work. The final temperature
decrease of hydrogen gas declines with the increase in
final hydrogen density, while those of the inner and
outer wall show a clear decrease with the increase in
final hydrogen density only when the final density is
higher than 4.02 g/L. The drop of the final temperature
4004
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 3 9 9 3 e4 0 0 5
decreases can be ascribed to the reduced total expansion work and the increased heat capacity of the
remaining hydrogen gas at the end of defueling, while
the insensitivity of the final temperature decreases of
the inner and the outer wall to the final hydrogen density when such density is lower than 4.02 g/L can be
ascribed to the almost negligible effect of the final
density on the total expansion work and the low gas-towall heat capacity ratio at the end of defueling when the
final gas density is low.
(6) For type III tanks, the final temperature decreases of the
hydrogen gas, the inner wall and the outer wall all
decrease with the increase in liner thickness because of
the increased heat capacity and the almost unchanged
total thermal resistance because of the high thermal
conductivity of aluminum alloy. The final temperature
decreases of the hydrogen gas and the inner wall increase with the increase in the thickness of HDPE liner
and CFRP because of the increased total thermal resistance, while that of the outer wall shows the opposite
trend for the same reason.
(7) Enhanced ventilation appears to be ineffective in
reducing the final temperature decreases due to the
high thermal resistance of the CFRP layer.
Acknowledgements
This research is supported by the Beijing Municipal Natural
Science Foundation (Grant Number: L172001 and 3194047), the
National Natural Science Foundation of China (Grant Number:
51705157) and the New Staff Research Start-up Fund of North
China University of Technology.
Nomenclature
a
A
c
Cp
Helmholtz free energy
Surface area
Velocity
Isobaric specific heat capacity
D
Fo
g
h
m
Nu
p
Pr
Q_
Diameter
Fourier number
Gravitational acceleration
Heat transfer coefficient
Mass
Nusselt number
Pressure
Prandtl number
r
Ra
Re
t
T
Tc
Tr
Tw
Heat transfer rate
Radial distance from the inner wall
Rayleigh number
Reynold number
Time
Temperature
The critical temperature of normal hydrogen
The reduced temperature
Wall temperature
u
v
Specific internal energy
Specific volume
Greek letters
a
The reduced Helmholtz free energy
a0
at
aw
b
l
m
r
rc
rr
The ideal gas contribution to the reduced Helmholtz
free energy
The residual contribution to the reduced Helmholtz
free energy
Thermal diffusivity of the wall
Thermal expansion coefficient
Thermal conductivity
Dynamic viscosity
Density
The critical density of normal hydrogen
The reduced density
Subscripts
amb
Ambient air
D
Diameter
f
Film temperature, which is the mean temperature of
fluid and its adjacent wall
cylinder Cylinder
forced
Forced convection
free
Free convection
g
Hydrogen gas
i
Inner wall
o
Outer wall
sphere
Sphere
wind
Cross wind
references
[1] Johnston B, Mayo MC, Khare A. Hydrogen: the energy source
for the 21st century. Technovation 2005;25:569e85.
€ m M. On optimal investment strategies
[2] Forsberg P, Karlstro
for a hydrogen refueling station. Int J Hydrogen Energy
2007;32:647e60.
[3] Maus S, Hapke J, Ranong C, Wüchner E, Friedlmeier G,
Wenger D. Filling procedure for vehicles with compressed
hydrogen tanks. Int J Hydrogen Energy 2008;33:4612e21.
[4] Hua TQ, Ahluwalia RK, Peng JK, et al. Technical assessment of
compressed hydrogen storage tank systems for automotive
applications. Int J Hydrogen Energy 2011;36(4):3037e49.
[5] Zheng J, Liu X, Xu P, et al. Development of high pressure
gaseous hydrogen storage technologies. Int J Hydrogen
Energy 2011;37(1):1048e57.
[6] ISO/DIS 15869. Gaseous hydrogen and hydrogen blends land vehicle fuel tanks. 2009.
[7] SAE J2601. Fuelling protocols for light duty gaseous hydrogen
surface vehicles. SAE International. 2016. December.
[8] Dicken CBJ, Merida W. Measured effects of filling time and
initial mass on the temperature distribution within a hydrogen
cylinder during refuelling. J Power Sources 2007;165(1):324e36.
[9] Liu YL, Zhao YZ, Zhao L, et al. Experimental studies on
temperature rise within a hydrogen cylinder during
refueling. Int J Hydrogen Energy 2010;35(7):2627e32.
[10] Galassi MC, Acosta-Iborra B, Baraldi D, et al. Onboard
compressed hydrogen storage: fast filling experiments and
simulations. Energy Procedia 2012;29(13):192e200.
[11] Ortiz Cebolla R, Acosta B, De Miguel N, et al. Effect of
precooled inlet gas temperature and mass flow rate on final
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 3 9 9 3 e4 0 0 5
state of charge during hydrogen vehicle refueling. Int J
Hydrogen Energy 2015;40(13):4698e706.
[12] Dicken CJB, Merida W. Modeling the transient temperature
distribution within a hydrogen cylinder during refueling.
Numer Heat Tran 2007;53(7):685e708.
[13] Matthias H, Daniele B, Pietro M. Numerical investigations on
the fast filling of hydrogen tanks. Int J Hydrogen Energy
2011;36(3):2606e12.
[14] Galassi MC, Acosta-Iborra B, Baraldi D, et al. Onboard
compressed hydrogen storage: fast filling experiments and
simulations. Energy Procedia 2012;29(13):192e200.
[15] Galassi MC, Baraldi D, Iborra BA, et al. CFD analysis of fast
filling scenarios for 70MPa hydrogen type IV tanks. Int J
Hydrogen Energy 2012;37(8):6886e92.
[16] Suryan A, Kim HD, Setoguchi T. Three dimensional
numerical computations on the fast filling of a hydrogen
tank under different conditions. Int J Hydrogen Energy
2012;37(9):7600e11.
[17] Melideo D, Baraldi D, Galassi MC, et al. CFD model
performance benchmark of fast filling simulations of
hydrogen tanks with pre-cooling. Int J Hydrogen Energy
2014;39(9):4389e95.
[18] Galassi MC, Papanikolaou E, Heitsch M, et al. Assessment of
CFD models for hydrogen fast filling simulations. Int J
Hydrogen Energy 2014;39(11):6252e60.
[19] Melideo D, Baraldi D. CFD analysis of fast filling strategies for
hydrogen tanks and their effects on key-parameters. Int J
Hydrogen Energy 2015;40(1):735e45.
[20] Optimization of hydrogen vehicle refuelling requirements.
Int J Hydrogen Energy 2017;42(19):13789e809.
[21] Hosseini M, Dincer I, Naterer GF, et al. Thermodynamic
analysis of filling compressed gaseous hydrogen storage
tanks. Int J Hydrogen Energy 2012;37(6):5063e71.
[22] Monde M, Woodfield P, Takano T, et al. Estimation of
temperature change in practical hydrogen pressure tanks
being filled at high pressures of 35 and 70 MPa. Int J Hydrogen
Energy 2012;37(7):5723e34.
rida W, Rokni M, et al. Optimization of
[23] Rothuizen E, Me
hydrogen vehicle refueling via dynamic simulation. Int J
Hydrogen Energy 2013;38(11):4221e31.
[24] Ruffio E, Saury D, Petit D. Thermodynamic analysis of
hydrogen tank filling. Effects of heat losses and filling rate
optimization. Int J Hydrogen Energy 2014;39(24):12701e14.
[25] Bourgeois T, Ammouri F, Weber M, et al. Evaluating the
temperature inside a tank during a filling with highlypressurized gas. Int J Hydrogen Energy 2015;40(35):11748e55.
[26] Simonovski I, Baraldi D, Melideo D, et al. Thermal
simulations of a hydrogen storage tank during fast filling. Int
J Hydrogen Energy 2015;40(36):12560e71.
[27] Bourgeois T, Ammouri F, Baraldi D, et al. The temperature
evolution in compressed gas filling processes: a review. Int J
Hydrogen Energy 2018;43(4).
4005
[28] Winters WS, Evans GH, Rice SF, et al. An experimental and
theoretical study of heat and mass transfer during the
venting of gas from pressure vessels. Int J Heat Mass Tran
2012;55(1e3):8e18.
[29] Guo J, Yang J, Zhao Y, et al. Investigations on temperature
variation within atype III cylinder during the hydrogen
gas cyclingtest. Int J Hydrogen Energy 2014;39(25):
13926e34.
[30] Melideo D, Baraldi D, Acosta-Iborra B, et al. CFD simulations
of filling and emptying of hydrogen tanks. Int J Hydrogen
Energy 2016;42(11):7304e13.
[31] Hirohiko Itoi, Maeda Yasumasa, Yohsuke Tamura,
Watanabe Shogo. Temperature change of container and
fittings during hydrogen discharging. Jari Research Journal
2007;29:299e302.
[32] Miguel ND, Acosta B, Moretto P, et al. The effect of defueling
rate on the temperature evolution of on-board hydrogen
tanks. Int J Hydrogen Energy 2015;40(42):14768e74.
[33] Incropera FP, Dewitt D. Fundamentals of heat and mass
transfer. 7th ed. New York: John Wiley & Sons; 2011. chap.9.
[34] Moran MJ, Shapiro HN, Boettner DD, Bailey MB.
Fundamentals of engineering thermodynamics. 8th ed. New
York: John Wiley & Sons; 2014. chap. 2.
[35] Leachmana J, Jacobsen R, Penoncello S, Lemmon E.
Fundamental equations of state for parahydrogen, normal
hydrogen, and orthohydrogen. J Phys Chem Ref Data
2009;38:721e48.
[36] Jacobsen R, Penoncello S, Lemmon E. Thermodynamic
properties of cryogenic fluids. New York: Plenum; 1997.
chap.3.
[37] Clark GL. Zero-dimensional model of compressible gas flow
in networks of pressure vessels: program TRIC. Sandia
Laboratories Report. 1983. p. 84. SAND 83-8226.
[38] Yusibani E, Nagahama Y, Kohno M, Takata Y,
Woodfield PL, Shinzato K, et al. A capillary tube viscometer
designed for measurements of hydrogen gas viscosity at
high pressure and high temperature. Int J Thermophys
2011;32:1111e24.
[39] Moroe S, Woodfield PL, Kimura K, Kohno M, Fukai J, Fujii M,
et al. Measurements of hydrogen thermal conductivity at
high pressure and high temperature. Int J Thermophys
2011;32:1887e917.
[40] Kreith F, Manglik RM, Bohn MS. Principles of heat transfer.
Stamford: Cengage Learning; 2011. chap. 7. 7th end.
[41] https://www.engineeringtoolbox.com/air-properties-d_156.
html.
[42] Hamdi S, Schiesser W, Griffiths G. Method of lines.
Scholarpedia 2009;2(7):2859e69.
[43] Burden R, Faires J. Numerical analysis. 6th ed. Pacific Grove:
Brooks/Cole; 1997. chap.5.