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Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer
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Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer Tao Jin a,b, Yuanliang Liu b,**, Jianjian Wei b,*, Dengyang Zhang b, Xiaoxue Wang c, Gang Lei a, Tianxiang Wang a, Yuqi Lan d, Hong Chen a a
State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing, 100028, China Institute of Refrigeration and Cryogenics/Key Laboratory of Refrigeration and Cryogenic Technology of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China c Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China d Beijing Institute of Aerospace Testing Technology, Beijing, 100074, China b
highlights Dispersion
of
graphical abstract
hydrogen
vapor
cloud in presence of atmospheric inversion layer was analyzed. The inversion layer restrains the upward
movement
of
the
hydrogen vapor cloud. Increasing the temperature lapse rate strengthens the restraining effect. A higher ground air temperature is also adverse for the cloud dilution.
article info
abstract
Article history:
Characterization of the dispersion behaviors of spilled liquid hydrogen is necessary from
Received 17 May 2019
the safety prospective. In this study, the two-phase flow of liquid hydrogen spill is pre-
Received in revised form
dicted with the mixture multiphase model, Lee model and Realizable k-ε model, and the
26 June 2019
dispersion of hydrogen vapor cloud with the atmospheric inversion layer is numerically
Accepted 1 July 2019
analyzed. The inversion layer restrains the upward movement of the cloud and the mixing
Available online xxx
of the cloud with air, increasing its ground-level hydrogen concentration. The heights of the flammable cloud can be reduced by 5.71%, 10.49% and 12.86%, respectively, with the
Keywords:
temperature lapse rates of 0.03, 0.06 and 0.10 K/m in our investigated scenarios. Besides,
Liquid hydrogen
the restraining effect is strengthened by increasing the ground air temperature if the
Vapor cloud
temperature lapse rate remains unchanged.
Inversion layer
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Two-phase flow
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Liu), [email protected] (J. Wei). https://doi.org/10.1016/j.ijhydene.2019.07.004 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Introduction Liquid hydrogen has been widely used as the new generation of aerospace propellant [1,2], and also shows promising application potentials in fuel cells and vehicles [3e6]. Upon the handling and application of hydrogen, safety is one of the primary concerns. The accidental spill of liquid hydrogen threats the safety of life and property. The boiling point of liquid hydrogen is extremely low, which may cause frostbite. Moreover, the vapor cloud formed by liquid hydrogen spill is highly flammable or explosive [7]. It is necessary to investigate the dispersion behaviors of spilled liquid hydrogen from the safety prospective. In the past decades, several institutions have carried out experiments on liquid hydrogen spill in the atmosphere, including National Aeronautics and Space Administration (NASA) in USA [8,9], Federal Institute for Materials Research and Testing (BAM) in Germany [10], Health and Safety Laboratory (HSL) in U.K. [11,12], etc. The scenarios included the large-scale spill into the open environment, the spill in the presence of building and the small-scale spill resulting from pipe rupture, respectively. The experimental results showed that the vapor cloud rises because of buoyancy and the wind starts to dominate in its dispersion as it travels far from the spill source. Numerical studies were also reported by a number of researchers. Sklavounos et al. [13] performed numerical investigation on liquid hydrogen spill using the CFX code, and found that the cryogenic vapor cloud behaved as heavy gas. Middha et al. [14] used FLACS to model the liquid hydrogen spill experiment by NASA, and the stable atmosphere gave best results in comparison with the experiments. Jin et al. [15] numerically investigated the effect of wind speed and wind temperature on the concentration distribution of hydrogen cloud. Increasing the wind speed enlarged the streamwise distance, while increasing the air temperature restrained the cloud dispersion process. By investigating the cloud dispersion under different weather conditions, Shao et al. [16] found that air entrainment into the cloud was promoted with the increased wind speed, or the decreased atmospheric pressure. Besides, the cloud dispersion process shows different trends in four seasons. Upon modeling the liquid hydrogen spill between buildings, Statharas [17] found that the dispersion could be characterized by the complex wind patterns, the back flow near the source, the heavy gas dispersion behavior in the near field and the buoyancy behavior in the far field. The partial condensation or freezing of oxygen and nitrogen [18,19], or the phase change of water [19e21] in the atmosphere, increased the buoyancy of the flammable cloud, and promoted the upward movement. The previous researches show that the atmosphere condition can influence the dispersion behavior of hydrogen vapor cloud to a great extent. Temperature inversion is the layer of atmosphere where the potential temperature rises with height [22,23], which can occur at any height. The potential temperature is the temperature of the dry air when brought adiabatically and reversibly from its initial state to a standard pressure. Various topographic landscapes and meteorological factors can induce the formation of inversion layer, including the radiation inversion, the advective inversion, and the subsidence inversion, etc. [24].
The inversion layer has been found to constrain the vertical airflow, and to trap aerosols and air pollutants at the ground level [22,24,25]. For instance, upon the statistical analysis of the pollutants in the atmosphere in Hanoi City in 2011, the average concentration of SO2 was found to reach 16.2 mg/m3 in the inversion days in comparison with 10.5 mg/m3 in normal days [22]. However, the air temperature was commonly modeled as a constant in previous numerical studies on liquid hydrogen spill. The present work is intended to investigate the effect of inversion layer on the dispersion of hydrogen vapor cloud, where the inversion is supposed to start from the ground. The cloud is considered to be diluted out of flammability when the volume concentration of hydrogen in the vapor cloud is below 4%, i.e., the lower flammability limit (LFL).
Numerical methods Governing equations The dispersion of liquid hydrogen can be divided into the following stages: (1) liquid hydrogen spill from the source, (2) the spread and evaporation of liquid pool, (3) the formation and dispersion of hydrogen vapor cloud. The two-phase flow is predicted by solving the following transient conservation equations for mixture mass, mixture momentum and mixture enthalpy, vrm þ V$ðrm vm Þ ¼ 0 vt
(1)
v ðr vm Þ þ V$ðrm vm vm Þ ¼ Vp þ V$ mm Vvm þ VvTm þ rm g vt m ! 2 X þ V$ ai ri vdr;i vdr;i
(2)
i¼1 n n X v X ðai ri hi Þ þ V$ ðai vi ðri hi þ pÞÞ ¼ V$ðlVTÞ þ SE vt i¼1 i¼1
(3)
where r, v, m, h, p and T are the density, velocity, kinetic viscosity, enthalpy, pressure and temperature, respectively. The subscript “m” refers to mixture phase, and “i” represents liquid or gas phase. a is the volume fraction, l is the effective heat conductivity, and SE is the volumetric heat source. vdr,i is the drift velocity for phase i, which is defined as vdr;i ¼ vi vm . The slip velocity between liquid/gas phases (vlg) takes the relation proposed by Mikko et al. [26]. The mass transfer rate between phases is predicted by Lee model [27], which has been widely used in flow boiling and condensation conditions [28], 8 < m_ ¼ g $a r ðT T Þ=T ; if T > T lg l l l sat sat l sat ev : m_ gl ¼ gcon $ag rg Tg Tsat Tsat ; if Tg < Tsat
(4)
The local mass fraction of species i in gas phase is calculated by the convection-diffusion equation,
v m rg ag Yg;i þ V$ rg ag ! v Yg;i ¼ V$ag rDg;i þ t VYg;i vt Sct þ m_ ilg m_ igl
(5)
where m_ lg and m_ gl are the mass transfer rates due to evaporation and condensation, respectively. The subscripts “l”
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Fig. 1 e Illustration of the computational domain for liquid hydrogen spill. represents liquid phase, “g” represents gas phase, and “sat” represents saturation. Yg,i is the local mass fraction of species i in the gas phase. The evaporation coefficient gev and the condensation coefficient gcon are both specified with the value 0.25 s1 for the hydrogen. Realizable k-ε model [29] is adopted for turbulent closure, with the generation of turbulent kinetic energy due to buoyancy considered. Power-law wind flow field proposed by Architectural Institute of Japan [30] is used to model the atmospheric boundary layer. In addition, the radiation heat is ignored in the simulation, and the phase changes of water and air components are not taken into consideration. The above numerical model for predicting the two-phase flow of liquid hydrogen spill in neutral atmosphere has been validated by comparisons with the NASA Test 6 in the previous work [31].
Computational domain and boundary conditions Fig. 1 illustrates the computational domain for liquid hydrogen spill in our simulation, with the dimensions of 200 m, 60 m and 80 m in x, y and z directions, respectively. The spill source is located at (20.25, 0, 0.5), which is modeled as mass flow inlet condition. The spill rate of liquid hydrogen is 9.52 kg/s and the spill time is 38 s. The domain outlet is modeled as pressure outlet with the pressure of 101325 Pa. The ground is modeled as no-slip wall [31]. The planes of y ¼ 0 m, z ¼ 80 m, and y ¼ 60 m are adopted as symmetry to reduce the calculation cost; the latter two planes are far enough from the hydrogen vapor cloud, where normal gradients of all variables are regarded as zero. Velocity inlet condition is specified at the domain inlet, with the power-law velocity profile [30]. The wind speed at 10 m height is 2.2 m/s. The vertical distribution of air temperature is given as T ¼ T0þJz, assuming that the inversion starts from ground surface, with a height larger than 80 m, as illustrated in Fig. 1. T0 is the ground air temperature (air temperature at the ground level). J is the temperature lapse rate with the expression of dT/dz, representing the temperature gradient in
vertical direction. The simulation is performed with ANSYS FLUENT 14.5. Second-order upwind scheme is adopted, with the time step of 0.001 s and the convergence criteria of 104. A steady wind field is calculated before liquid hydrogen spill, and afterwards the dispersion of hydrogen vapor cloud formed by liquid hydrogen spill is predicted.
Results and discussions The simulated conditions for the atmospheric inversion layer are listed in Table 1. The dispersion of hydrogen vapor cloud in the atmosphere with or without inversion layer (Case 2 or Case 1) is analyzed firstly to investigate the effect of inversion layer on the hydrogen concentration distribution, the vertical velocity, and the spread dimensions. Then, Cases 1e4 are adopted to investigate the effects of temperature lapse rate. In addition, Cases 2, 5 and 6 are used to investigate the effects of ground air temperature. A temperature lapse rate up to 0.10 K/ m has been reported in the literature [32]. The present study adopts the values of 0.03, 0.06 and 0.10 K/m for comparison.
Effect of the presence of atmospheric inversion layer Effect of atmospheric inversion layer is firstly investigated by comparing Case 1 (dT/dz ¼ 0) and Case 2 (dT/dz ¼ 0.10 K/m).
Table 1 e Simulated conditions for the atmospheric inversion layer in the present work. Case label 1 2 3 4 5 6
Ground air temperature (K)
Temperature lapse rate (K/m)
273 273 273 273 253 308
0 0.10 0.03 0.06 0.10 0.10
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Fig. 2 shows the hydrogen concentration contours on the symmetry plane (y ¼ 0) at the end of spill. The hydrogen concentration distribution near the source is found insensitive to the inversion layer, where strong turbulence caused by the spill and evaporation of liquid hydrogen plays a dominating role. Away from the source, the inversion layer plays a more important role in affecting the cloud spread, restraining its upward movement and making the cloud less lifted, due to the constraining effect in vertical airflow. The vertical velocity contour of the vapor cloud is illustrated in Fig. 3. The vertical velocity is decreased by the inversion layer, with the
maximum value dropping from 1.76 m/s to 1.54 m/s. The range of the cloud with high vertical velocity is also reduced. The air is entrained into the hydrogen vapor cloud as the cloud disperses in the atmosphere. The hydrogen concentration of the cloud decreases till being diluted below the flammability limit of 4%. Fig. 4 shows the hydrogen concentration contour on the symmetry plane at t ¼ 56 s, when the source has been terminated for 18 s. The inversion layer restrains the cloud dilution process, with a higher hydrogen concentration in the vapor cloud. Also, the cloud rises with a smaller upward angle with inversion layer. The time needed for the vapor
Fig. 2 e Hydrogen concentration contour on the symmetry plane at the end of spill (t ¼ 38 s).
Fig. 3 e Vertical velocity contour on the symmetry plane at t ¼ 38 s.
Fig. 4 e Hydrogen concentration contour on the symmetry plane at t ¼ 56 s. Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
international journal of hydrogen energy xxx (xxxx) xxx
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Fig. 5 e Vertical velocity contour on the symmetry plane at t ¼ 56 s.
Fig. 6 e Variation of ground-level hydrogen concentration with time. cloud to be diluted below the flammability limit increases from 31 s to 35 s, compared with the case without inversion. The vertical velocity contour of the vapor cloud is shown in Fig. 5. The configuration of the high vertical velocity region is consistent with that of the flammable cloud, i.e., the configuration is more upward without inversion. The maximum vertical velocity decreases when the inversion layer is present, similar with the result at the end of spill. The effect of inversion layer on the hydrogen concentration on the ground where human activity commonly takes place is specifically focused on. Fig. 6 shows the variations of hydrogen concentration at different distances downwind the source. The inversion layer increases the hydrogen concentration for most of the hazard duration. At the location of 10 m downwind the source, the hydrogen concentration is 11.54% at 38 s with inversion layer, while it is 10.59% without inversion. Similarly, the hydrogen concentration increases from 4.04% to 4.47% at the location of 20 m downwind the source. In addition, the spread dimensions of the flammable vapor cloud are investigated. Fig. 7 illustrates the dimensions of the flammable cloud relative to the source at the end of spill, which is obtained from the 4% LFL concentration contour depicted in Fig. 2. The length is defined as the largest streamwise distance of the flammable cloud, the detachment distance is the distance that the front of the cloud begins to detach from the ground, and the height refers to the maximum distance of the cloud above the ground. hB is
bottom height of the cloud at the largest streamwise distance, or the height at the same streamwise distance with inversion layer. The presence of the inversion layer reduces the height of flammable cloud from 35.00 m to 30.50 m, with a reduction rate of 12.86%. The inversion layer also increases the cloud detachment distance from 30.15 m to 34.15 m, which worsens
Fig. 7 e Dimensions of the flammable cloud at the end of spill (t ¼ 38 s).
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Fig. 8 e Variation of the dimensions of flammable vapor cloud with time.
Fig. 9 e Turbulent kinetic energy of the cloud at t ¼ 38 s.
the situations near the ground. The cloud reaches the maximum streamwise distance at the bottom height of 25.40 m without inversion, while it decreases by 7.70 m in the presence of inversion layer. The variation of the cloud dimensions with time is shown in Fig. 8, including the length, the detachment distance, the height, and the bottom height. The length of flammable vapor cloud varies little with the presence of inversion layer before 50 s, but afterwards it deviates from the trajectory without inversion due to the restraining effect in cloud dilution. In the presence of inversion layer, the detachment distance of the cloud increases while the cloud height decreases. The maximum height difference is 5.40 m with the relative deviation of 14.03% at the time of 48 s. In addition, the difference in bottom height (DhB) for the cases without and with inversion
Fig. 10 e Spread of flammable vapor cloud at t ¼ 38 s.
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Table 2 e Dimensions of the flammable vapor cloud at t ¼ 38 s with different temperature lapse rates. Temperature lapse rate (K/m) 0 0.03 0.06 0.10
Length (m)
Detachment distance (m)
Height (m)
Bottom height (m)
74.73 75.19 75.84 76.64
30.15 31.56 32.27 34.15
35.00 33.00 31.33 30.50
25.40 21.93 20.06 17.70
weaken the effects of inversion layer on the dispersion of hydrogen cloud.
Effect of temperature lapse rate
Fig. 11 e Vertical velocity and dilution time of hydrogen vapor cloud with different temperature lapse rates.
layer increases with time in the beginning and reaches 12.20 m at the time of 52 s. From the above analysis, the inversion layer restrains the cloud from moving upwards and then increases the groundlevel hydrogen concentration, which is detrimental to the safety of life and property. Meanwhile, the cloud dilution process slows down and the hazardous duration increases in the presence of inversion layer. The temperature gradient induces the density gradient of the air, i.e., the upper air is lighter and the upward movement of the airflow is constrained. Moreover, the mixing of the cloud with the air is restrained, and the cloud will be less turbulent, as shown in Fig. 9. However, due to the buoyancy of the hydrogen vapor cloud, the cloud rises at the velocity of 1.54 m/s in the presence of inversion layer, as shown in Fig. 3(a). The strong turbulence near the spill source, and the buoyancy of the cloud
The inversion layers with the intensities of 0, 0.03, 0.06 and 0.10 K/m are investigated. The spread dimensions of the flammable vapor cloud at the end of spill (t ¼ 38 s) are compared, as shown in Fig. 10, with the detailed dimensions listed in Table 2. The restraining effect in cloud upward movement is strengthened by increasing the temperature lapse rate, with the cloud being less lifted. In details, the length and detachment distance of the flammable cloud increase with the increased temperature lapse rate. Compared with the case without inversion, the heights of the cloud are reduced by 5.71%, 10.49% and 12.86%, and the bottom heights are reduced by 13.66%, 21.02% and 30.32%, respectively, with the temperature lapse rates of 0.03, 0.06 and 0.10 K/m. Moreover, the clouds with various temperature lapse rates intersect at the location where the flammable cloud reaches the maximum streamwise distance without inversion. The vertical velocity of the cloud and the time needed for the cloud to be diluted out of flammability with different temperature lapse rates are also investigated, as shown in Fig. 11. With increasing temperature lapse rate, the vertical velocity of the vapor cloud decreases, while the dilution time increases.
Effect of ground air temperature The ground air temperature varies with seasons, weather, or time of day, etc. In this study, three typical temperatures are chosen, i.e., 253 K (winter), 273 K (spring or autumn) and 308 K (summer).
Fig. 12 e Hydrogen concentration contours on the symmetry plane at t ¼ 38 s without inversion layer.
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Table 3 e Dimensions of the flammable cloud at t ¼ 38 s with different air temperatures. Air temperature (K)
Length (m)
Detachment distance (m)
Height (m)
71.30 74.73 76.87
23.17 30.15 35.04
47.39 35.00 32.36
253 273 308
Table 4 e Dimensions of flammable cloud at t ¼ 38 s with different ground air temperatures in the presence of inversion layer. Ground air temperature (K) 253 273 308
Detachment distance (m)
Detachment distance variation (m)
Height (m)
Height variation (m)
24.39 33.84 39.68
1.22 3.69 4.64
44.27 30.29 29.79
3.12 4.71 2.57
The effects of air temperature on cloud dispersion without inversion layer are analyzed firstly. The hydrogen concentration contours on the symmetry plane at the end of spill are shown in Fig. 12 and Fig. 2(b) (T0 ¼ 273 K), with the spread dimensions listed in Table 3. With increasing air temperature, the range of the high concentration region near the source decreases, and the cloud becomes less buoyant. The length and detachment distance of the cloud are increased by 7.81% and 51.23%, respectively, when increasing the air temperature from 253 K to 308 K. A reduction of 31.72% in cloud height is also observed. The air density decreases with increasing air temperature, and more rapid evaporation of liquid hydrogen under warmer atmospheric environment leads to more rapid cooling of the hydrogen vapor cloud. The lighter surrounding ambient air and heavier vapor cloud result in the restraining effect in cloud upward movement. The effects of ground air temperature on the dimensions of flammable vapor cloud with the given temperature lapse rate of 0.10 K/m are then analyzed. The dimensions and their variations relative to the case without inversion layer are listed in Table 4. With increasing ground air temperature, the detachment distance and its variation are increased. The
Fig. 13 e Location of the maximum vertical velocity region with different ground air temperatures.
result shows that the cloud will be less lifted in a hotter day, as listed in Table 3, and the presence of inversion layer worsens the situation due to the larger variation in detachment distance. Similarly, the height of the cloud also decreases with the ground air temperature. However, the height variation with the ground air temperature is not monotonous. The possible reason is that the locations of the high vertical velocity region with various ground air temperatures are different, as illustrated in Fig. 13. When the air temperature is 253 K, the region is close to the ground and the source, and the presence of inversion layer has less influence on the region location and the subsequent height variation of the cloud. For the air temperature of 273 K, the maximum vertical velocity region is higher than that of 308 K, and the variation in cloud height is more obvious. Thus, the effect of inversion layer on the cloud height is more obvious if the high vertical velocity region is away from the source or the ground.
Conclusions The effects of the presence of inversion layer, the temperature lapse rate and the ground air temperature in the dispersion of hydrogen cloud are numerically analyzed. The main conclusions are: The inversion layer influences the cloud spread in the far field, which makes the cloud less lifted, and increases the ground-level hydrogen concentration. In the presence of inversion layer (dT/dz ¼ 0.10 K/m), the height of the flammable cloud reduces from 35.00 m to 30.50 m, with a reduction rate up to 12.86%, which is due to the restraining effect in the vertical airflow and the mixing of the cloud with air. By increasing the temperature lapse rate, the effects of inversion layer on cloud spread, vertical velocity and dilution time are strengthened. Compared with the case without inversion, the cloud heights are reduced by 5.71%, 10.49% and 12.86%, respectively, with the temperature lapse rates of 0.03, 0.06 and 0.10 K/m. The restraining effect in cloud dispersion is strengthened by increasing the ground air temperature. The effect of inversion layer on the cloud height is more obvious if the high vertical velocity region is away from the source or the ground.
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
international journal of hydrogen energy xxx (xxxx) xxx
Acknowledgement [16]
This study is financially supported by the State Key Laboratory of Technologies in Space Cryogenic Propellants (SKLTSCP1911), and the Fundamental Research Funds for the Central Universities.
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Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer Tao Jin a,b, Yuanliang Liu b,**, Jianjian Wei b,*, Dengyang Zhang b, Xiaoxue Wang c, Gang Lei a, Tianxiang Wang a, Yuqi Lan d, Hong Chen a a
State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing, 100028, China Institute of Refrigeration and Cryogenics/Key Laboratory of Refrigeration and Cryogenic Technology of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China c Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China d Beijing Institute of Aerospace Testing Technology, Beijing, 100074, China b
highlights Dispersion
of
graphical abstract
hydrogen
vapor
cloud in presence of atmospheric inversion layer was analyzed. The inversion layer restrains the upward
movement
of
the
hydrogen vapor cloud. Increasing the temperature lapse rate strengthens the restraining effect. A higher ground air temperature is also adverse for the cloud dilution.
article info
abstract
Article history:
Characterization of the dispersion behaviors of spilled liquid hydrogen is necessary from
Received 17 May 2019
the safety prospective. In this study, the two-phase flow of liquid hydrogen spill is pre-
Received in revised form
dicted with the mixture multiphase model, Lee model and Realizable k-ε model, and the
26 June 2019
dispersion of hydrogen vapor cloud with the atmospheric inversion layer is numerically
Accepted 1 July 2019
analyzed. The inversion layer restrains the upward movement of the cloud and the mixing
Available online xxx
of the cloud with air, increasing its ground-level hydrogen concentration. The heights of the flammable cloud can be reduced by 5.71%, 10.49% and 12.86%, respectively, with the
Keywords:
temperature lapse rates of 0.03, 0.06 and 0.10 K/m in our investigated scenarios. Besides,
Liquid hydrogen
the restraining effect is strengthened by increasing the ground air temperature if the
Vapor cloud
temperature lapse rate remains unchanged.
Inversion layer
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Two-phase flow
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Liu), [email protected] (J. Wei). https://doi.org/10.1016/j.ijhydene.2019.07.004 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Introduction Liquid hydrogen has been widely used as the new generation of aerospace propellant [1,2], and also shows promising application potentials in fuel cells and vehicles [3e6]. Upon the handling and application of hydrogen, safety is one of the primary concerns. The accidental spill of liquid hydrogen threats the safety of life and property. The boiling point of liquid hydrogen is extremely low, which may cause frostbite. Moreover, the vapor cloud formed by liquid hydrogen spill is highly flammable or explosive [7]. It is necessary to investigate the dispersion behaviors of spilled liquid hydrogen from the safety prospective. In the past decades, several institutions have carried out experiments on liquid hydrogen spill in the atmosphere, including National Aeronautics and Space Administration (NASA) in USA [8,9], Federal Institute for Materials Research and Testing (BAM) in Germany [10], Health and Safety Laboratory (HSL) in U.K. [11,12], etc. The scenarios included the large-scale spill into the open environment, the spill in the presence of building and the small-scale spill resulting from pipe rupture, respectively. The experimental results showed that the vapor cloud rises because of buoyancy and the wind starts to dominate in its dispersion as it travels far from the spill source. Numerical studies were also reported by a number of researchers. Sklavounos et al. [13] performed numerical investigation on liquid hydrogen spill using the CFX code, and found that the cryogenic vapor cloud behaved as heavy gas. Middha et al. [14] used FLACS to model the liquid hydrogen spill experiment by NASA, and the stable atmosphere gave best results in comparison with the experiments. Jin et al. [15] numerically investigated the effect of wind speed and wind temperature on the concentration distribution of hydrogen cloud. Increasing the wind speed enlarged the streamwise distance, while increasing the air temperature restrained the cloud dispersion process. By investigating the cloud dispersion under different weather conditions, Shao et al. [16] found that air entrainment into the cloud was promoted with the increased wind speed, or the decreased atmospheric pressure. Besides, the cloud dispersion process shows different trends in four seasons. Upon modeling the liquid hydrogen spill between buildings, Statharas [17] found that the dispersion could be characterized by the complex wind patterns, the back flow near the source, the heavy gas dispersion behavior in the near field and the buoyancy behavior in the far field. The partial condensation or freezing of oxygen and nitrogen [18,19], or the phase change of water [19e21] in the atmosphere, increased the buoyancy of the flammable cloud, and promoted the upward movement. The previous researches show that the atmosphere condition can influence the dispersion behavior of hydrogen vapor cloud to a great extent. Temperature inversion is the layer of atmosphere where the potential temperature rises with height [22,23], which can occur at any height. The potential temperature is the temperature of the dry air when brought adiabatically and reversibly from its initial state to a standard pressure. Various topographic landscapes and meteorological factors can induce the formation of inversion layer, including the radiation inversion, the advective inversion, and the subsidence inversion, etc. [24].
The inversion layer has been found to constrain the vertical airflow, and to trap aerosols and air pollutants at the ground level [22,24,25]. For instance, upon the statistical analysis of the pollutants in the atmosphere in Hanoi City in 2011, the average concentration of SO2 was found to reach 16.2 mg/m3 in the inversion days in comparison with 10.5 mg/m3 in normal days [22]. However, the air temperature was commonly modeled as a constant in previous numerical studies on liquid hydrogen spill. The present work is intended to investigate the effect of inversion layer on the dispersion of hydrogen vapor cloud, where the inversion is supposed to start from the ground. The cloud is considered to be diluted out of flammability when the volume concentration of hydrogen in the vapor cloud is below 4%, i.e., the lower flammability limit (LFL).
Numerical methods Governing equations The dispersion of liquid hydrogen can be divided into the following stages: (1) liquid hydrogen spill from the source, (2) the spread and evaporation of liquid pool, (3) the formation and dispersion of hydrogen vapor cloud. The two-phase flow is predicted by solving the following transient conservation equations for mixture mass, mixture momentum and mixture enthalpy, vrm þ V$ðrm vm Þ ¼ 0 vt
(1)
v ðr vm Þ þ V$ðrm vm vm Þ ¼ Vp þ V$ mm Vvm þ VvTm þ rm g vt m ! 2 X þ V$ ai ri vdr;i vdr;i
(2)
i¼1 n n X v X ðai ri hi Þ þ V$ ðai vi ðri hi þ pÞÞ ¼ V$ðlVTÞ þ SE vt i¼1 i¼1
(3)
where r, v, m, h, p and T are the density, velocity, kinetic viscosity, enthalpy, pressure and temperature, respectively. The subscript “m” refers to mixture phase, and “i” represents liquid or gas phase. a is the volume fraction, l is the effective heat conductivity, and SE is the volumetric heat source. vdr,i is the drift velocity for phase i, which is defined as vdr;i ¼ vi vm . The slip velocity between liquid/gas phases (vlg) takes the relation proposed by Mikko et al. [26]. The mass transfer rate between phases is predicted by Lee model [27], which has been widely used in flow boiling and condensation conditions [28], 8 < m_ ¼ g $a r ðT T Þ=T ; if T > T lg l l l sat sat l sat ev : m_ gl ¼ gcon $ag rg Tg Tsat Tsat ; if Tg < Tsat
(4)
The local mass fraction of species i in gas phase is calculated by the convection-diffusion equation,
v m rg ag Yg;i þ V$ rg ag ! v Yg;i ¼ V$ag rDg;i þ t VYg;i vt Sct þ m_ ilg m_ igl
(5)
where m_ lg and m_ gl are the mass transfer rates due to evaporation and condensation, respectively. The subscripts “l”
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Fig. 1 e Illustration of the computational domain for liquid hydrogen spill. represents liquid phase, “g” represents gas phase, and “sat” represents saturation. Yg,i is the local mass fraction of species i in the gas phase. The evaporation coefficient gev and the condensation coefficient gcon are both specified with the value 0.25 s1 for the hydrogen. Realizable k-ε model [29] is adopted for turbulent closure, with the generation of turbulent kinetic energy due to buoyancy considered. Power-law wind flow field proposed by Architectural Institute of Japan [30] is used to model the atmospheric boundary layer. In addition, the radiation heat is ignored in the simulation, and the phase changes of water and air components are not taken into consideration. The above numerical model for predicting the two-phase flow of liquid hydrogen spill in neutral atmosphere has been validated by comparisons with the NASA Test 6 in the previous work [31].
Computational domain and boundary conditions Fig. 1 illustrates the computational domain for liquid hydrogen spill in our simulation, with the dimensions of 200 m, 60 m and 80 m in x, y and z directions, respectively. The spill source is located at (20.25, 0, 0.5), which is modeled as mass flow inlet condition. The spill rate of liquid hydrogen is 9.52 kg/s and the spill time is 38 s. The domain outlet is modeled as pressure outlet with the pressure of 101325 Pa. The ground is modeled as no-slip wall [31]. The planes of y ¼ 0 m, z ¼ 80 m, and y ¼ 60 m are adopted as symmetry to reduce the calculation cost; the latter two planes are far enough from the hydrogen vapor cloud, where normal gradients of all variables are regarded as zero. Velocity inlet condition is specified at the domain inlet, with the power-law velocity profile [30]. The wind speed at 10 m height is 2.2 m/s. The vertical distribution of air temperature is given as T ¼ T0þJz, assuming that the inversion starts from ground surface, with a height larger than 80 m, as illustrated in Fig. 1. T0 is the ground air temperature (air temperature at the ground level). J is the temperature lapse rate with the expression of dT/dz, representing the temperature gradient in
vertical direction. The simulation is performed with ANSYS FLUENT 14.5. Second-order upwind scheme is adopted, with the time step of 0.001 s and the convergence criteria of 104. A steady wind field is calculated before liquid hydrogen spill, and afterwards the dispersion of hydrogen vapor cloud formed by liquid hydrogen spill is predicted.
Results and discussions The simulated conditions for the atmospheric inversion layer are listed in Table 1. The dispersion of hydrogen vapor cloud in the atmosphere with or without inversion layer (Case 2 or Case 1) is analyzed firstly to investigate the effect of inversion layer on the hydrogen concentration distribution, the vertical velocity, and the spread dimensions. Then, Cases 1e4 are adopted to investigate the effects of temperature lapse rate. In addition, Cases 2, 5 and 6 are used to investigate the effects of ground air temperature. A temperature lapse rate up to 0.10 K/ m has been reported in the literature [32]. The present study adopts the values of 0.03, 0.06 and 0.10 K/m for comparison.
Effect of the presence of atmospheric inversion layer Effect of atmospheric inversion layer is firstly investigated by comparing Case 1 (dT/dz ¼ 0) and Case 2 (dT/dz ¼ 0.10 K/m).
Table 1 e Simulated conditions for the atmospheric inversion layer in the present work. Case label 1 2 3 4 5 6
Ground air temperature (K)
Temperature lapse rate (K/m)
273 273 273 273 253 308
0 0.10 0.03 0.06 0.10 0.10
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Fig. 2 shows the hydrogen concentration contours on the symmetry plane (y ¼ 0) at the end of spill. The hydrogen concentration distribution near the source is found insensitive to the inversion layer, where strong turbulence caused by the spill and evaporation of liquid hydrogen plays a dominating role. Away from the source, the inversion layer plays a more important role in affecting the cloud spread, restraining its upward movement and making the cloud less lifted, due to the constraining effect in vertical airflow. The vertical velocity contour of the vapor cloud is illustrated in Fig. 3. The vertical velocity is decreased by the inversion layer, with the
maximum value dropping from 1.76 m/s to 1.54 m/s. The range of the cloud with high vertical velocity is also reduced. The air is entrained into the hydrogen vapor cloud as the cloud disperses in the atmosphere. The hydrogen concentration of the cloud decreases till being diluted below the flammability limit of 4%. Fig. 4 shows the hydrogen concentration contour on the symmetry plane at t ¼ 56 s, when the source has been terminated for 18 s. The inversion layer restrains the cloud dilution process, with a higher hydrogen concentration in the vapor cloud. Also, the cloud rises with a smaller upward angle with inversion layer. The time needed for the vapor
Fig. 2 e Hydrogen concentration contour on the symmetry plane at the end of spill (t ¼ 38 s).
Fig. 3 e Vertical velocity contour on the symmetry plane at t ¼ 38 s.
Fig. 4 e Hydrogen concentration contour on the symmetry plane at t ¼ 56 s. Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Fig. 5 e Vertical velocity contour on the symmetry plane at t ¼ 56 s.
Fig. 6 e Variation of ground-level hydrogen concentration with time. cloud to be diluted below the flammability limit increases from 31 s to 35 s, compared with the case without inversion. The vertical velocity contour of the vapor cloud is shown in Fig. 5. The configuration of the high vertical velocity region is consistent with that of the flammable cloud, i.e., the configuration is more upward without inversion. The maximum vertical velocity decreases when the inversion layer is present, similar with the result at the end of spill. The effect of inversion layer on the hydrogen concentration on the ground where human activity commonly takes place is specifically focused on. Fig. 6 shows the variations of hydrogen concentration at different distances downwind the source. The inversion layer increases the hydrogen concentration for most of the hazard duration. At the location of 10 m downwind the source, the hydrogen concentration is 11.54% at 38 s with inversion layer, while it is 10.59% without inversion. Similarly, the hydrogen concentration increases from 4.04% to 4.47% at the location of 20 m downwind the source. In addition, the spread dimensions of the flammable vapor cloud are investigated. Fig. 7 illustrates the dimensions of the flammable cloud relative to the source at the end of spill, which is obtained from the 4% LFL concentration contour depicted in Fig. 2. The length is defined as the largest streamwise distance of the flammable cloud, the detachment distance is the distance that the front of the cloud begins to detach from the ground, and the height refers to the maximum distance of the cloud above the ground. hB is
bottom height of the cloud at the largest streamwise distance, or the height at the same streamwise distance with inversion layer. The presence of the inversion layer reduces the height of flammable cloud from 35.00 m to 30.50 m, with a reduction rate of 12.86%. The inversion layer also increases the cloud detachment distance from 30.15 m to 34.15 m, which worsens
Fig. 7 e Dimensions of the flammable cloud at the end of spill (t ¼ 38 s).
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Fig. 8 e Variation of the dimensions of flammable vapor cloud with time.
Fig. 9 e Turbulent kinetic energy of the cloud at t ¼ 38 s.
the situations near the ground. The cloud reaches the maximum streamwise distance at the bottom height of 25.40 m without inversion, while it decreases by 7.70 m in the presence of inversion layer. The variation of the cloud dimensions with time is shown in Fig. 8, including the length, the detachment distance, the height, and the bottom height. The length of flammable vapor cloud varies little with the presence of inversion layer before 50 s, but afterwards it deviates from the trajectory without inversion due to the restraining effect in cloud dilution. In the presence of inversion layer, the detachment distance of the cloud increases while the cloud height decreases. The maximum height difference is 5.40 m with the relative deviation of 14.03% at the time of 48 s. In addition, the difference in bottom height (DhB) for the cases without and with inversion
Fig. 10 e Spread of flammable vapor cloud at t ¼ 38 s.
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Table 2 e Dimensions of the flammable vapor cloud at t ¼ 38 s with different temperature lapse rates. Temperature lapse rate (K/m) 0 0.03 0.06 0.10
Length (m)
Detachment distance (m)
Height (m)
Bottom height (m)
74.73 75.19 75.84 76.64
30.15 31.56 32.27 34.15
35.00 33.00 31.33 30.50
25.40 21.93 20.06 17.70
weaken the effects of inversion layer on the dispersion of hydrogen cloud.
Effect of temperature lapse rate
Fig. 11 e Vertical velocity and dilution time of hydrogen vapor cloud with different temperature lapse rates.
layer increases with time in the beginning and reaches 12.20 m at the time of 52 s. From the above analysis, the inversion layer restrains the cloud from moving upwards and then increases the groundlevel hydrogen concentration, which is detrimental to the safety of life and property. Meanwhile, the cloud dilution process slows down and the hazardous duration increases in the presence of inversion layer. The temperature gradient induces the density gradient of the air, i.e., the upper air is lighter and the upward movement of the airflow is constrained. Moreover, the mixing of the cloud with the air is restrained, and the cloud will be less turbulent, as shown in Fig. 9. However, due to the buoyancy of the hydrogen vapor cloud, the cloud rises at the velocity of 1.54 m/s in the presence of inversion layer, as shown in Fig. 3(a). The strong turbulence near the spill source, and the buoyancy of the cloud
The inversion layers with the intensities of 0, 0.03, 0.06 and 0.10 K/m are investigated. The spread dimensions of the flammable vapor cloud at the end of spill (t ¼ 38 s) are compared, as shown in Fig. 10, with the detailed dimensions listed in Table 2. The restraining effect in cloud upward movement is strengthened by increasing the temperature lapse rate, with the cloud being less lifted. In details, the length and detachment distance of the flammable cloud increase with the increased temperature lapse rate. Compared with the case without inversion, the heights of the cloud are reduced by 5.71%, 10.49% and 12.86%, and the bottom heights are reduced by 13.66%, 21.02% and 30.32%, respectively, with the temperature lapse rates of 0.03, 0.06 and 0.10 K/m. Moreover, the clouds with various temperature lapse rates intersect at the location where the flammable cloud reaches the maximum streamwise distance without inversion. The vertical velocity of the cloud and the time needed for the cloud to be diluted out of flammability with different temperature lapse rates are also investigated, as shown in Fig. 11. With increasing temperature lapse rate, the vertical velocity of the vapor cloud decreases, while the dilution time increases.
Effect of ground air temperature The ground air temperature varies with seasons, weather, or time of day, etc. In this study, three typical temperatures are chosen, i.e., 253 K (winter), 273 K (spring or autumn) and 308 K (summer).
Fig. 12 e Hydrogen concentration contours on the symmetry plane at t ¼ 38 s without inversion layer.
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Table 3 e Dimensions of the flammable cloud at t ¼ 38 s with different air temperatures. Air temperature (K)
Length (m)
Detachment distance (m)
Height (m)
71.30 74.73 76.87
23.17 30.15 35.04
47.39 35.00 32.36
253 273 308
Table 4 e Dimensions of flammable cloud at t ¼ 38 s with different ground air temperatures in the presence of inversion layer. Ground air temperature (K) 253 273 308
Detachment distance (m)
Detachment distance variation (m)
Height (m)
Height variation (m)
24.39 33.84 39.68
1.22 3.69 4.64
44.27 30.29 29.79
3.12 4.71 2.57
The effects of air temperature on cloud dispersion without inversion layer are analyzed firstly. The hydrogen concentration contours on the symmetry plane at the end of spill are shown in Fig. 12 and Fig. 2(b) (T0 ¼ 273 K), with the spread dimensions listed in Table 3. With increasing air temperature, the range of the high concentration region near the source decreases, and the cloud becomes less buoyant. The length and detachment distance of the cloud are increased by 7.81% and 51.23%, respectively, when increasing the air temperature from 253 K to 308 K. A reduction of 31.72% in cloud height is also observed. The air density decreases with increasing air temperature, and more rapid evaporation of liquid hydrogen under warmer atmospheric environment leads to more rapid cooling of the hydrogen vapor cloud. The lighter surrounding ambient air and heavier vapor cloud result in the restraining effect in cloud upward movement. The effects of ground air temperature on the dimensions of flammable vapor cloud with the given temperature lapse rate of 0.10 K/m are then analyzed. The dimensions and their variations relative to the case without inversion layer are listed in Table 4. With increasing ground air temperature, the detachment distance and its variation are increased. The
Fig. 13 e Location of the maximum vertical velocity region with different ground air temperatures.
result shows that the cloud will be less lifted in a hotter day, as listed in Table 3, and the presence of inversion layer worsens the situation due to the larger variation in detachment distance. Similarly, the height of the cloud also decreases with the ground air temperature. However, the height variation with the ground air temperature is not monotonous. The possible reason is that the locations of the high vertical velocity region with various ground air temperatures are different, as illustrated in Fig. 13. When the air temperature is 253 K, the region is close to the ground and the source, and the presence of inversion layer has less influence on the region location and the subsequent height variation of the cloud. For the air temperature of 273 K, the maximum vertical velocity region is higher than that of 308 K, and the variation in cloud height is more obvious. Thus, the effect of inversion layer on the cloud height is more obvious if the high vertical velocity region is away from the source or the ground.
Conclusions The effects of the presence of inversion layer, the temperature lapse rate and the ground air temperature in the dispersion of hydrogen cloud are numerically analyzed. The main conclusions are: The inversion layer influences the cloud spread in the far field, which makes the cloud less lifted, and increases the ground-level hydrogen concentration. In the presence of inversion layer (dT/dz ¼ 0.10 K/m), the height of the flammable cloud reduces from 35.00 m to 30.50 m, with a reduction rate up to 12.86%, which is due to the restraining effect in the vertical airflow and the mixing of the cloud with air. By increasing the temperature lapse rate, the effects of inversion layer on cloud spread, vertical velocity and dilution time are strengthened. Compared with the case without inversion, the cloud heights are reduced by 5.71%, 10.49% and 12.86%, respectively, with the temperature lapse rates of 0.03, 0.06 and 0.10 K/m. The restraining effect in cloud dispersion is strengthened by increasing the ground air temperature. The effect of inversion layer on the cloud height is more obvious if the high vertical velocity region is away from the source or the ground.
Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004
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Acknowledgement [16]
This study is financially supported by the State Key Laboratory of Technologies in Space Cryogenic Propellants (SKLTSCP1911), and the Fundamental Research Funds for the Central Universities.
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Please cite this article as: Jin T et al., Numerical investigation on the dispersion of hydrogen vapor cloud with atmospheric inversion layer, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.004