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Numerical investigation on the difference of dispersion behavior between cryogenic liquid hydrogen and methane
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 ) 2 2 3 6 8 e2 2 3 7 9
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Numerical investigation on the difference of dispersion behavior between cryogenic liquid hydrogen and methane Liang Pu a,b,*, Xin Tang a,b,**, Xiangyu Shao b, Gang Lei a, Yanzhong Li a,b a b
State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing 100028, China School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
highlights
graphical abstract
A mixture four-phase flow model is developed. Multicomponent phase transitions model have better agreements. Concentration dispersions
of
and
temperature
hydrogen
and
methane are compared. Hazard regions under different Froude number are investigated.
article info
abstract
Article history:
The potential hazard of cryogenic and combustible liquid propellants (hydrogen and
Received 8 March 2019
methane) leakage caused by spontaneous damage of tanks or rupture of pipelines is still a
Received in revised form
problem for both applications and human beings. Numerical simulations have been per-
25 May 2019
formed to predict the fuels’ leakage and dispersion behavior differences. Based on liquid
Accepted 28 May 2019
hydrogen release tests conducted by the Health & Safety Laboratory (HSL), a mixture four-
Available online 28 June 2019
phase flow model considering the liquid hydrogen and air phase transitions has been developed. The liquid phase movements in the near field, combustible clouds and cold
Keywords:
effect clouds movement in the far field were investigated. With Froude number increases
Liquid hydrogen and methane
from 0.47 to 3.72, liquid hydrogen represents a downward trend while liquid methane
leakage
shows a downwind trend. For combustible clouds, the movements of hydrogen are larger
Mixture four-phase model
than that of methane in both downwind and vertical direction on a quasi-stable state. For
Concentration and temperature
cold effect clouds, the dispersion of methane is greater than that of hydrogen in Froude
field comparison
number of 0.47, 0.93, 1.86, but then smaller in larger Froude number of 3.72.
Dispersion of dangerous propellants
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Safety
* Corresponding author. State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing 100028, China. ** Corresponding author. School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China. E-mail addresses: [email protected] (L. Pu), [email protected] (X. Tang). https://doi.org/10.1016/j.ijhydene.2019.05.219 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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 ) 2 2 3 6 8 e2 2 3 7 9
Introduction Chemical propellants remain the most feasible solution for space transportation fuels. There are three primary candidates [1]: nitrogen tetroxide and mono methyl hydrazine (NTO/MMH), liquid oxygen and liquid hydrogen (LOX/LH2) and liquid oxygen and liquid methane (LOX/LCH4). Nontoxic propellants (LOX/LH2/LCH4) are considered as sustainable and environmental-friendly fuels that minimize pollution with their exhausts. NASA concluded that LOX/LCH4 is the preferred propellant combination for human space transportation to Luna and Mars because of its easy production, and LH2 is also favored due to the high engine specific impulse [2]. Based on practical experience, liquid fuels are the most efficient and cost-effective means of transport and storage. However, once the combustible and cryogenic liquid propellants leak and evaporate because of structural defects, material fatigue or cracking of welding seam especially in the process filling and transferring through pipelines, hydrogen and methane will burn in volume fractions of relatively 4e75% and 5e15% when mixed with ambient air. Beside explosion, possible harmful effects also include frostbite because of their low-temperature release conditions (the storage temperature of liquid hydrogen is around 20 K, and that of liquid methane is 111 K). Therefore, they have great threats to near-ground facilities and personnel. In order to predict the distribution of hazard areas of accidently leaked cryogenic liquids, there are plenty of experiments applied to figure out the leakage and dispersion characteristics of flammable and cold effect clouds. The National Aeronautics and Space Administration [3] (NASA, 1980), the Germany Federal Institute for Materials Research and Testing [4] (BAM, 1994), the Health & Safety Laboratory [5,6] (HSL, 2010), etc. were for liquid hydrogen. As for liquid methane, Maplin sands (1980), Burro (1980), Coyote (1981), Falcon (1987) [7], etc. were conducted. They got plenty of data that expected to be the most effective prediction of the hazard effects caused by these dangerous fuels. Nevertheless, the cost of an experiment is too high to conduct; alternative approaches such as computational fluid dynamics (CFD) become popular currently. There are many CFD software applied to simulate substances diffusion in the atmosphere, like ADREA-HF [8e11], ANSYS FLUENT [12e14], ANSYS CFX [15,16], FLACS [17,18], PHAST [19] etc. For liquid hydrogen release and dispersion, Statharas JC [4] used ADREAHF 3D-time dependent finite volume code for cloud dispersion basing on the BAM experiments that released LH2 between buildings. Middha et al. [20] utilized FLACS program to verify the feasibility of numerical simulation and simulated the lowvelocity flow in a garage situation. Jin et al. [13] and Shao et al. [14,21] researched the effects of ambient temperature, wind speed and atmospheric pressure on hydrogen diffusion with FLUENT. Giannissi et al. [22] studied the effects of environmental humidity and atmospheric stability on hydrogen dispersion. Jakel et al. [23] did a series of validations of a multiphase-multicomponent model for liquid and gaseous
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hydrogen release without phase change. For liquid methane, Cormier et al. [24] compared the leakage of LNG (liquid natural gas) on water surface and concrete surface by CFD simulation. Gavelli et al. [25e27] simulated the Falcon experiment with FLUENT to study the influence of obstacles on the diffusion of LNG gas cloud in complex geometric environment. Afterwards, they proposed a three-step model for analyzing LNG leakage into trenches: the first step was to analyze and solve the flow state of LNG, and next was to calculate the evaporation rate of channel direction. In the third step, the evaporation rate was used as the source term for CFD calculation. As for LCH4 and LH2 release and dispersion comparison, Li et al. [19] used some harm criteria (cold effects, thermal effects, overpressure and missile effects) to compare the harm effects of an accidental release of cryo-compressed hydrogen versus natural gas and liquid natural gas for automobile applications. The outcomes turned out that cryo-compressed hydrogen release could result in the longest lethal and harmful distances for a combustible scenario without ignitions. Sklavounos et al. [15] simulated the large-scale liquefied hydrogen and liquefied natural gas spill testes separately, which had a great agreement with concentration data against experimental records. Both gas cloud shapes were indicated that liquid natural gas and hydrogen release and dispersion as heavy gases rather than light gases on a low-temperature outlet condition. Verfondern et al. [28] compared the transient pool shape of a continuous and instantaneous release of natural gas and hydrogen. Venetsanos et al. [29] undertook hydrogen and natural gas releasing from compressed gaseous systems on commercial vehicles in urban and tunnel environments; different storage pressures were considered. These CFD simulations have been primarily conducted to validate models for liquid hydrogen or methane release and dispersion, and the comparison simulation did not consider the dispersion behavior between these two propellants after their leakage. Because the explosion and cold effects are related to gas cloud volume fraction and temperature respectively, this paper presents a detailed 3D transient CFD model for propellants release and dispersion to figure out the different concentration and temperature spill behaviors and hazard regions between hydrogen and methane.
The HSL's LH2 spill tests A series of hydrogen release tests were performed by the HSL in 2010, which determined to figure out dispersion behavior of hydrogen cloud in an open environment under different meteorological and outlet conditions. The experiments were carried out in a valley, with a concrete surface of 32 m in diameter. A schematic layout (not drawn to scale) is displayed in Fig. 1. Liquid hydrogen was piped from the tanker to the release point through a 26.3 mm diameter vacuum insulated vacuum insulated hose. Most of the releases were made from an absolute storage pressure of 0.2 MPa and absolute release pressure of 0.12 MPa that gave a release rate of 0.07 kg/s of
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because of velocity and density difference between the components. The number of Eulerian phase is four, and the primary phase is mixture of H2, O2 and N2, secondary phases are liquid hydrogen, liquid oxygen and liquid nitrogen. The continuity equation for the mixture is: v ðr Þ þ Vðrm ! vm Þ ¼ 0 vt m
(1)
.
where v m is the mass-averaged velocity, rm is the mixture density. The momentum equation for the mixture can be obtained by summing the individual momentum equations for all phases. It can be expressed as: Fig. 1 e HSL test layout (not drawn to scale).
liquid hydrogen. There were plenty of hydrogen concentration sensors placed in downwind direction of 1.5 m, 3 m, 4.5 m, 6 m, 7.5 m with a 0.25 m height and 0.25 m, 0.75 m, 1.25 m, 1.75 m, 2.25 m, 2.7 m in the vertical direction with 7.5 m downwind. The experiments also monitored the meteorological measurements (wind speed, wind direction, air temperature and humidity, at the 2.5 m height), the detailed data are reported in Table 1. The adiabatic mixing hypothesis approach was contributed to the hydrogen concentration values, which calculated from the cloud temperature because the accuracy of the concentration sensors were severely influenced by the condensed water in the low temperature. The releases were made onto or above a concrete surface. Three release scenarios were considered: a) horizontally along the ground, b) vertically downwards from 100 mm above the ground, c) horizontally at a height of 860 mm above the ground. In this paper, the model is verified by test 5, and the release and weather conditions are shown in Table 1. The more detailed experiment data can be referred to Refs. [5,6].
i h v T ðrm ! v m þ V! v m Þ þ V,ðrm ! v m! v m Þ ¼ Vr þ V, mm V! v m þ rm ! g vt n X ! ak rk ! v dr;k ! v dr;k þ F V, k¼1
(2) .
where n is the number of phases, F is a body force, and mm ¼ Pn ! ! ! k¼1 ak mk is the viscosity of the mixture, v dr;k ¼ v k v m is the drift velocity for secondary phase k. The energy equation for the mixture takes the following form: n v X ðak rk Ek Þ þ V,½ak ! v k ðrk Ek þ pÞ ¼ V, keff VT þ SE vt k¼1
where keff is the effective conductivity, SE includes any other volumetric heat sources. For a compressible phase, and Ek ¼ hk for an incompressible phase, where hk is the sensible enthalpy for phase k. For turbulence flow, the realizable k ε model with enhanced wall treatment and mixture drift force is utilized. The modeled transport equations for k and ε in the realizable k ε model are [31]: v v v ðrkÞ þ rkuj ¼ vt vxj vxj
m vk mþ t þ Gk þ Gb rε YM þ Sk sk vxj
Simulation approach
(4)
This work focuses on the numerical simulation of dispersion resulting from low-temperature fuels (hydrogen and methane) release in an open scenario like rupture of cryogenic propellant container tanks or the failure of transportation pipelines. It involved complexed heat and mass transfer process during the low-temperature fluid evaporate and disperse periods. The mixture model [30] can model n phases by solving the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary phases, and algebraic expressions for the relative velocities. In this case, slip velocity and implicit body force are considered
m vε ε2 pffiffiffiffiffi mþ t þ rC1 Sε rC2 sε vxj k þ vε ε þ C1ε C3ε Gb þ Sε k
v v v ðrεÞ þ rεuj ¼ vt vxj vxj
LH2
0.07
(5)
where h C1 ¼ max 0:43;
qffiffiffiffiffiffiffiffiffiffiffiffiffi h i k ; h ¼ S ; S ¼ 2Sij Sij hþ5 ε
(6)
In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, YM represents the contribution of the fluctuating dilatation in
Table 1 e Release and weather conditions of HSL test 5. Fuel Mass flow rate (kg/s)
(3)
Storage pressure (MPa)
Release pressure (MPa)
Source location
Source direction
Wind speed (m/s) (2.5 m height)
Ambient temperature (K) (2.5 m height)
0.20
0.12
Ground
Horizontal
2.67
283.56
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outflow. The ground is concrete in the bottom plane of which temperature is 280.56 K and thermal properties are considered as 2350 kg/m3, 0.97 kJ/(kg$K) and 1.28 W/(m$K), the wall thickness is 10 m [14]. The right surface of the tanks are set as liquid fuels mass-flow-inlet. All other areas are set as wall.
Fuel two-phase jet
Fig. 2 e Computational domain and boundary conditions. compressible turbulence to the overall dissipation rate, C2 and C1ε are constants. sk and sε are the turbulent Prandtl numbers for k and ε, respectively. Sk and Sε are user-defined source terms. In order to simulate the dispersion phenomenon, Species Transport model with inlet and energy source diffusion is adopted. In turbulent flows, ANSYS Fluent computes the mass diffusion in the following form: m VT ! J i ¼ rDi;m þ t VYi DT;i T Sct
(7)
.
where J i is the diffusion flux of species i, which arises due to gradients of concentration and temperature. Di;m is the mass diffusion coefficient for species I in the mixture, and DT;i is the thermal diffusion coefficient. Sct is the turbulent Schmidt number, The default Sct is 0.7.
Computational domain and boundary conditions In order to simulation LH2 with an effective physical model, the computational domain, boundary conditions and mesh are shown in Figs. 2and 3. x ¼ - 3 and x ¼ 30 planes are left and right, y ¼ 0 and y ¼ 10 planes are ground and top, z ¼ - 6 and z ¼ 6 are front and back, the central points of two different height liquid fuels spill tanks are located in (0, 0.0111, 0) and (0, 0.8711, 0), with a characteristic diameter of 0.0263 m. The back, front and top planes are all set as symmetry for the reason that these planes are way far from the flow region. The left plane is set as wind in velocity inlet and the right plane is
Fig. 3 e Grids of the domain and the locations of the fuel inlet.
Saturated cryogenic liquid hydrogen was stored in 0.2 MPa pressure and release in 0.12 MPa pressure, which caused flash vaporization because of reducing pressure when the fuel leaks. This phenomenon affects the release condition of different gas-liquid ratio. The following equation is used to calculate the vapor mass fraction and mixture density of hydrogen after evaporated: qv ¼
H1l H2l H2v H2l
(8)
1 qv ql ¼ þ rmix rv rl
(9)
H1l is liquid enthalpy before release, H2l is liquid enthalpy after release, H2v is gas enthalpy after release, rmix is density of mixture.
Multicomponent phase transitions The release temperature of liquid hydrogen is 20 K; it can cause condensation of the air component including nitrogen and oxygen. Lee model can be selected with the Eulerian multiphase model if one of the overall interfacial heat transfer coefficient models will be used. In this paper, Lee Model is adopted for phases change with a mechanism of evaporationcondensation from liquid phase to gas species and vice versa. Through several sets of simulation in different phase change coefficients, the evaporation and condensation frequency are set as 10 and 20, the saturation temperature is constant of 20.324 K under the ambient pressure. The liquid-vapor mass transfer (evaporation and condensation) is governed by the vapor transport equation: v ! ðat rv Þ þ V,ðav rv V v Þ ¼ m_ lv m_ vl vt
(10)
Based on the following temperature regimes, the mass transfer can be described as follows: If Tl > Tsat (evaporation)
Fig. 4 e Steady wind profile.
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Fig. 5 e Validation between experiment and simulation.
Solution method ðT1 Tsat Þ m_ lv ¼ coeff ,al rl Tsat
(11)
If Tv < Tsat (condensation): m_ vl ¼ coeff ,av rv
ðTsat T1 Þ Tsat
(12)
coeff is a coefficient that must be fine tuned and can be interpreted as a relaxation time. a and r are the phase volume fraction and density, respectively. The source term for the energy equation can be obtained by multiplying the rate of mass transfer by the latent heat.
Wind speed A vertical wind velocity profile distributing by logarithmic law is applied first before cryogenic liquid hydrogen release. The wind profile obeys the logarithmic law: u ¼ u*
lgH lgH0 lg10 lgH0
(13)
where the wind speed is 2.675 m/s at 2.5 m height and the terrain roughness H0 is equal to 0.03. The steady-state wind field is displayed in Fig. 4, then the hydrogen mass flow release condition based on time transition is calculated, which uses the steady-state data as the initial field.
The pressure-velocity coupling scheme is PISO with both skewness and neighbor correction are set as 1. The gradient spatial discretization method is Least Squares Cell Based and pressure is Body Force Weighted. QUICK scheme applies to volume fraction discretization and others are all set as second order upwind scheme. The transient formulation is used second order implicit. Under-relaxation factors are adapted to the scaled residuals. All convergence criterion set as 106 in the steady condition and 104 in the transient section. The step size is 0.001s with approximately 20 iterations per time step to reach the limited residuals.
Model validation Fig. 5 depicts the HSL experimental data, simulation with air phase change and without air phase change in the location of (4.5, 0.25, 0) and (7.5, 0.75, 0). It can be turned out that the simulation value of model without oxygen and nitrogen condensation is higher than the experimental average data, while the simulation with air phase transition gains a better agreement with the tests. Fig. 6 presents the cloud shape in simulation and experiment. The numerical results predict that the model is suitable for small mass flow rate of cryogenic liquid hydrogen in an open environment.
Fig. 6 e Hydrogen cloud shape in simulation and experiment.
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Table 2 e Release condition of cryogenic liquid hydrogen and methane. Fuels Mass flow rate (kg/s) H2 CH4
Gas mass fraction (%)
Liquid mass fraction (%)
4.9 4.9
95.1 95.1
0.07 0.16
19.9 34.1
Results and discussion
Fr ¼
Dispersion behaviors Properties of methane are different from hydrogen in density. In order to have a better comparison of the dispersing behavior between liquid hydrogen and methane, Froude number (Fr) which represents the ratio of momentum and buoyancy is adopted to set as the same outlet conditions. When Fr > 1, the flow is a jet that initial momentum plays a leading role in the flow or the near field, otherwise it's a buoyant plume dominated by buoyancy. The relative magnitude of the two forces can be expressed by the dimensionless density Froude number. Definition is showed in Eq. (14), the value of Froude number depends on the density and velocity of the mixture, the mixing speed relates to the area of the leakage outlet, mixture mass and density in Eq. (15). The mixture density lies on gas and liquid mass fraction as shown in Eq. (8). Therefore, the Froude number can be calculated by Eq. (16). When the mixture density is constant, Froude number is only a function of velocity. More specifically, if gas and liquid mass fraction keep unchanged, mixture mass flow rate is the only factor affecting the value of Froude number. um Fr ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rmix ra gb ra
(14)
mmix rmix A
(15)
um ¼
Release mixture density Release velocity (m/s) (kg/m3)
m qmix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rmix A rmixrara gb
7.1 9.5
Release temperature (K) 20 111
(16)
um is characteristic velocity of the jet, ra is ambient fluid density, g is the acceleration of gravity, b is Characteristic length of the jet. mmix is mass of the mixture, A is the area of the leakage outlet. The HSL scenario of a release rate of 0.071 kg/s, when the release condition with the same Froude number of 3.72 and a gas fraction of 4.9%, methane spill rate is 0.16 kg/s, the detailed release condition of these two fuels can be seen in Table 2 and these simulations were performed. Outlet height set as 0.86 m, and the release direction is horizontal. According to the European Industrial Gases Association [32], when the volume concentration of hydrogen is 4e75% and that of methane is 5e15% in the air, it is likely to explode. When the temperature is lower than 233.16 K, it can damage the external facilities or people in the low temperature. Therefore, the lower flammable limit (LFL) of 4% volume concentration of hydrogen and 5% volume concentration of methane are these two fuels’ combustible effect boundaries, and the cold effect limit (CEL) of 233.16 K temperature is the cold effect boundary.
Concentration distributions Fig. 7 (a) presents the farthest downwind, vertical distance of hydrogen and methane combustible clouds changing over flow time, the combustible clouds are continuously increased in both directions because of air entrainment. The clouds go further and further until they reached a quasi-stable state that is around 14 s for hydrogen and 6 s for methane, and then
Fig. 7 e (a) The LFL movements of hydrogen and methane clouds changes as time varies. (b) The maximum concentration value and location in the symmetrical plane on a quasi-stable state.
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Table 3 e Hydrogen and methane combustible cloud shapes in the symmetrical plane at 4 s, 10 s, 16 s. H2
CH4
4s
10s
16s
flammable cloud field remains unchanged. The LFL distances of hydrogen and methane are 19.2 m and 13.5 m in the downwind direction, and 3.8 m and 1.9 m in the vertical direction, respectively. Table 3 presents liquids hydrogen and methane combustible cloud shape changing in the symmetrical plane at flow time of 4 s, 10 s, 16 s, it can be clearly seen that the clouds show a downward trend at the near field. At the far field, when the density of the fuel clouds gradually become smaller than that of the surrounding air, the clouds subject to buoyancy and move upward.
The maximum concentration values and locations on a quasi-stable state in the symmetrical plane are displayed in Fig. 7(b). The location of the hydrogen combustible cloud centerline is lower than methane within 2.7 m in the downwind direction, while higher in the far field. The volume fraction of hydrogen is always higher than that of methane after the location is 0.5 m away from the outlet. The concentration of the gas phase increases first and then decreases close to zero, in which the maximum volume fraction of hydrogen is 68.4% at the location of (1.5, 0.63, 0) and that of methane is 48.0% at location of
Fig. 8 e (a) The CEL movements of hydrogen and methane clouds changes as time varies. (b) The minimum dimensionless temperature values and locations in the symmetrical plane on a quasi-stable state.
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Table 4 e The hydrogen and methane cold effect cloud shapes in the symmetrical plane at 1s, 4s, 7s. H2
CH4
1s
4s
7s
(0.5, 0.86, 0). The volume fraction depends on the liquid evaporation rate and cloud diffusion rate. At the near field, the evaporation rate is greater than cloud diffusion rate, so more gas produced and the concentration goes larger, then with liquid disappeared and cloud move further with more ambient air, the concentration becomes smaller.
Temperature distributions It is necessary to analyze the temperature field of cloud diffusion because of the low-temperature damage to the surrounding environment and human beings. However, the outlet temperature of hydrogen is 20 K and the outlet temperature of methane is 111 K. Thus, lead into the dimensionless temperature to compare the temperature diffusion field of the hydrogen and methane. The formula for calculation is as follows:
Fig. 9 e Evaporation and spill behaviors of cryogenic liquid hydrogen and methane after leaking from storage tanks or pipelines.
Td ¼
Ta T Ta Ts
(17)
Ta is ambient temperature, Ts is cryogenic liquid release temperature, T is the field temperature. It can be seen from Fig. 8 (a) that the temperature field will also reach a quasi-stable state after a certain time, but the time is relatively short with around 5 s for hydrogen and 2 s for methane. Table 4 compares the hydrogen and methane cold effect cloud shapes in the symmetrical plane at the flow time of 1 s, 4 s, 7 s. The CEL (dimensionless temperature of hydrogen is 0.8 and methane is 0.7) movements of hydrogen and methane cloud are 5.5 m and 5.4 m in the downwind direction and 1.8 m and 1 m in the vertical direction. When the gas cloud reaches a quasi-steady state, the minimum temperature locations in the symmetrical plane and the dimensionless temperatures corresponding to the minimum temperatures are shown in Fig. 8(b). It can be seen that the temperature location curves are similar with the concentration location curves; it means the minimum
Table 5 e The value of mass flows rates correspond to different Froude numbers. Fr ¼ 0.47
Fr ¼ 0.93
Fr ¼ 1.86
Fr ¼ 3.72
Mass flow H2 CH4 H2 CH4 H2 CH4 H2 CH4 rate(kg/s) 0.009 0.020 0.018 0.040 0.035 0.080 0.071 0.160
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Table 6 e Liquid hydrogen and methane shapes in the symmetrical plane of different Froude number. H2
CH4
Fr ¼ 0.47
Fr ¼ 0.93
Fr ¼ 1.86
Fr ¼ 3.72
Fig. 10 e The farthest distance in downwind and downward direction of liquid hydrogen and methane in the volume fraction of 0.01% of different Froude number on a quasi-stable state.
temperature locations are consistent with the maximum concentration positions, which is consistent with the conclusions of many experiments and scholars using adiabatic mixing principle [15] to build the relationship between temperature and concentration. From the diagram, the minimum dimensionless temperature of hydrogen and methane increases continuously in the downwind direction, and finally tends to the ambient temperature (the dimensionless temperature is 1). The dimensionless temperature of hydrogen is always higher than that of methane; it means hydrogen has a greater temperature diffusion due to the larger temperature difference between liquid hydrogen and ambient air. As the concentration and temperature field analyzed above, there are some common stages between cryogenic liquid hydrogen and methane release and dispersion. After their leakage from damaged transport container tanks or ruptured pipelines, the mixture tend to go downward because of the heavy density, and then the density would become smaller and smaller because the cloud temperature goes higher for transferring energy with ambient air, therefore, the cloud would subject to positive buoyancy and tend to an
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upward movement. These stages of movement can divide into: 1) near-field movement: heavy mixture. The average density is higher than ambient air density mainly due to the liquid phase. 2) far-field movement: light gas. The average density is lower than ambient air density. The movements present clearly in Fig. 9. The disperse behaviors between these two cryogenic liquid fuels need further research. The behaviors of the liquid in the near field and light gas in the far field influenced by the Froude number are discussed in the next sections.
afterwards. In the vertical direction, there is little downward change in methane, but hydrogen has an obvious downward trend. When Fr ¼ 0.47, the two fuels distance differences in downwind direction and downward direction are 0.50 m and 0.02 m. As Fr ¼ 3.72, the distance difference is 1.01 m and 0.41 m. Therefore, at the near field, the farthest distance in volume fraction of 0.01% of liquid methane is further than hydrogen in the downwind direction when Froude number change from 0.47 to 3.72, while hydrogen shows a tendency to move more downward.
Near-field liquid movement differences
Far-field gas movement differences
The density of the mixed flow is larger than that of air in the near field mainly because of liquid fluid. Therefore, the movement of liquid phase analyzed in detail at the near field. With unchangeable gas fraction, in other words, the constant density in the initial condition of the outlet fluid, different mass flows rate correspond to different Froude numbers. Froude number of the buoyant plume of 0.47, 0.93 and the jet flow of 1.86, 3.72 are investigated. Detailed mass flow rates are shown in Table 5. To describe the downward tendency of liquid hydrogen and methane movements, the lowest location in the vertical direction is taken into consideration. The shapes of two liquid flows in the symmetry plane on a quasi-stable state are compared in Table 6. With the same Froude number, the volume fraction of liquid methane is smaller than liquid hydrogen and the former moves further than the latter. With the increase of Froude number, the moving distance of liquid hydrogen and methane increase gradually in the downwind direction, the distances of liquid hydrogen and methane in the volume fraction of 0.01% on a quasi-stable state are displayed in Fig. 10. The movement of methane in the downwind direction is always larger than that of hydrogen, but the increased distance of methane becomes smaller and smaller as Froude number increased, while the hydrogen shows a linear increasing trend, therefore the distance difference between these two liquid become greater firstly and goes smaller
LFL movements
Fig. 11 e The LFL movements of hydrogen and methane clouds of different Froude number on a quasi-stable state.
Fig. 12 e The CEL movements of hydrogen and methane cold effect clouds of different Froude number on a quasistable state.
After the liquids heat exchange and evaporate, the gas clouds move further and further under the effects of self-diffusion and wind-transportation combined. The farthest downwind distances and altitudes of hydrogen and methane combustible clouds of different Froude number on a quasi-stable state present in Fig. 11. For explosion distances, methane cloud moves shorter than hydrogen in both directions as Froude number changes from 0.47 to 3.72. With the increase of Froude number, both combustible clouds disperse farther and farther, and the two clouds distance differences become larger and larger. When Fr ¼ 0.47, the two fuels’ distance differences in the downwind direction and vertical direction are 0.83 m and 0.20 m. When Fr ¼ 3.72, the distance differences are 7.12 m and 2.10 m.
CEL movements Fig. 12 represents the changes of the cold effect clouds movement in different Froude number. With the increase of Froude number, in downwind direction, the propagation of hydrogen cloud increases continuously, while the lowtemperature cloud of methane firstly increases and then decreases, hence the movement of methane is higher than that of hydrogen and then smaller. Hydrogen cloud continues to increase in the vertical direction, while the methane is almost unchanged; the distance difference becomes larger and larger
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as Froude number increase. When Fr ¼ 0.47, the methane cloud is 0.83 m farther than hydrogen cloud in downwind direction, and the vertical distance difference is almost equal to zero. However, when Fr ¼ 3.72, the hydrogen cloud is 0.22 m farther than methane cloud in the downwind and 0.76 m in the vertical direction.
Conclusions A 3D transient CFD model has been developed to investigate the difference of dispersion behaviors between cryogenic liquid hydrogen and methane leakage. Multicomponent (H2, O2, N2) phase transitions which use the Lee model are considered to make the simulation have better agreements with the HSL experimental data than scenario without air phase change. Froude number has been adopted to set as the same outlet conditions of two propellants. With the same Froude number of 3.72, the flammable and low-temperature hazards regions, the maximum concentration centerline and its location, the minimum dimensionless temperature centerline and location have been compared. The results show that fuels’ hazard cloud would reach a quasi-stable state after a certain time, and it take shorter time for cold effect clouds to attain an equilibrium than the combustible clouds do. Cryogenic liquid hydrogen and methane release as heavy mixture in the near field and disperse as light gas in the far field. When Froude number changed from the buoyant plume of 0.47, 0.93 to the jet flow of 1.86, 3.72. The differences of liquid movement in the near field, the harmful gas cloud movement in the far field have been discussed. At the near field, the farthest distance in volume fraction of 0.01% of liquid methane is further than hydrogen on a quasi-stable state, and liquid hydrogen moves more and more downward as Froude number increased. At the far field, for the combustible effect, the hydrogen clouds are always larger than methane clouds and the distance differences become greater in larger Froude number conditions. For the cold effect, the downwind distance of methane is higher than that of hydrogen in the Froude number of 0.47, 0.93 and 1.86, but then smaller than that of hydrogen in large Froude number of 3.72. The vertical distance difference is almost equal to zero in small Froude number of 0.47 and 0.93, then the hydrogen cold effect altitude become greater than methane and the difference goes larger and larger.
Acknowledgement This study is financially supported by the State Key Laboratory of Technologies in Space Cryogenic Propellants (SKLTSCP1809).
references
[1] Mills GA, et al. Propellant selection for the lunar lander ascent stage. 2000.
[2] Chen TT, et al. ISRU propellant selection for space Exploration vehicles. In: Aiaa/asme/sae/asee joint propulsion conference; 2013. [3] Chirivella J, et al. Experimental results from fast 1500-gallon LH2 spills. 1986. [4] Statharas JC, et al. Analysis of data from spilling experiments performed with liquid hydrogen. J Hazard Mater 2000;A77:57e75. [5] Hooker P, et al. Experimental releases of liquid hydrogen. In: Proc 4th Int Conf on Hydrogen Safety; 2011. [6] Health and Safety Executive. Ignited releases of liquid hydrogen. 2014. [7] Luketa-Hanlin A. A review of large-scale LNG spills: experiments and modeling. J Hazard Mater 2006;132:119e40. [8] Giannissi SG, et al. Numerical simulation of LNG dispersion under two-phase release conditions. J Loss Prev Process Ind 2013;26:245e54. [9] Giannissi SG, et al. CFD modeling of hydrogen dispersion under cryogenic release conditions. Int J Hydrogen Energy 2014;39:15851e63. [10] Venetsanos AG, et al. CFD modelling of large-scale LH2 spills in open environment. Int J Hydrogen Energy 2007;1:2171e7. [11] Venetsanos AG, et al. CFD modelling of hydrogen release, dispersion and combustion for automotive scenarios. J Loss Prev Process Ind 2008;21:162e84. [12] Sun B, et al. Computational fluid dynamics analysis of liquefied natural gas dispersion for risk assessment strategies. J Loss Prev Process Ind 2013;26:117e28. [13] Jin T, et al. CFD modeling and analysis of the influence factors of liquid hydrogen spills in open environment. Int J Hydrogen Energy 2017:732e9. [14] Shao X, et al. Numerical investigation of flammable cloud on liquid hydrogen spill under various weather conditions. Int J Hydrogen Energy 2018;43:5249e60. [15] Sklavounos S, et al. Fuel gas dispersion under cryogenic release conditions. Energy Fuels 2005;19:2535e44. [16] Qi R, et al. Numerical simulations of LNG vapor dispersion in brayton fire training field tests with ANSYS CFX. J Hazard Mater 2010;183:51e61. [17] Middha P, et al. Validation of CFD modelling of LH2 spread and evaporation against large-scale spill experiments. Int J Hydrogen Energy 2011;36:2620e7. [18] Ichard M, et al. CFD computations of liquid hydrogen releases. Int J Hydrogen Energy 2012;37:17380e9. [19] Li Z, et al. Comparison of the harm effects of accidental releases: cryo-compressed hydrogen versus natural gas. Int J Hydrogen Energy 2013;38:11174e80. [20] Middha P, et al. Validation of CFD-model for hydrogen dispersion. J Loss Prev Process Ind 2009;22:1034e8. [21] Pu L, et al. Plume dispersion behavior and hazard identification for large quantities of liquid hydrogen leakage. Asia Pac J Chem Eng MAR-APR 2019;14(2). https://doi.org/ 10.1002/apj.2299. UNSP e2299. [22] Giannissi SG, et al. CFD Modeling of LH2 dispersion using the ADREA-HF code. In: 4th International Conference on Hydrogen Safety; 2011. [23] Jaekel C, et al. Validation of a 3D multiphase-multicomponent CFD model for accidental liquid and gaseous hydrogen releases. Int J Hydrogen Energy 2019;44:8807e18. [24] Cormier BR, et al. Application of computational fluid dynamics for LNG vapor dispersion modeling: a study of key parameters. J Loss Prev Process Ind 2009;22:332e52. [25] Gavelli F, et al. Application of CFD (Fluent) to LNG spills into geometrically complex environments. J Hazard Mater 2008;159:158e68. [26] Gavelli F, et al. Quantification of source-level turbulence during LNG spills onto a water pond. J Loss Prev Process Ind 2009;22:809e19.
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[27] Gavelli F, et al. Modeling of LNG spills into trenches. J Hazard Mater 2010;180:332e9. [28] Verfondern K, et al. Pool spreading and vaporization of liquid hydrogen. Int J Hydrogen Energy 2007;32:2106e17. [29] Venetsanos AG, et al. CFD modelling of hydrogen release, dispersion and combustion for automotive scenarios. J Loss Prev Process Ind 2008;21:162e84.
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[30] Mikko M, et al. On the mixture model for multiphase flow Vtt Publications288; 1996. p. 1e67. [31] Choi J, et al. A CFD simulation of hydrogen dispersion for the hydrogen leakage from a fuel cell vehicle in an underground parking garage. Int J Hydrogen Energy 2013;38:8084e91. [32] 75/07/E/rev ID. Determination of safety distances. European Industrial Gases Association; 2009.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Numerical investigation on the difference of dispersion behavior between cryogenic liquid hydrogen and methane Liang Pu a,b,*, Xin Tang a,b,**, Xiangyu Shao b, Gang Lei a, Yanzhong Li a,b a b
State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing 100028, China School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
highlights
graphical abstract
A mixture four-phase flow model is developed. Multicomponent phase transitions model have better agreements. Concentration dispersions
of
and
temperature
hydrogen
and
methane are compared. Hazard regions under different Froude number are investigated.
article info
abstract
Article history:
The potential hazard of cryogenic and combustible liquid propellants (hydrogen and
Received 8 March 2019
methane) leakage caused by spontaneous damage of tanks or rupture of pipelines is still a
Received in revised form
problem for both applications and human beings. Numerical simulations have been per-
25 May 2019
formed to predict the fuels’ leakage and dispersion behavior differences. Based on liquid
Accepted 28 May 2019
hydrogen release tests conducted by the Health & Safety Laboratory (HSL), a mixture four-
Available online 28 June 2019
phase flow model considering the liquid hydrogen and air phase transitions has been developed. The liquid phase movements in the near field, combustible clouds and cold
Keywords:
effect clouds movement in the far field were investigated. With Froude number increases
Liquid hydrogen and methane
from 0.47 to 3.72, liquid hydrogen represents a downward trend while liquid methane
leakage
shows a downwind trend. For combustible clouds, the movements of hydrogen are larger
Mixture four-phase model
than that of methane in both downwind and vertical direction on a quasi-stable state. For
Concentration and temperature
cold effect clouds, the dispersion of methane is greater than that of hydrogen in Froude
field comparison
number of 0.47, 0.93, 1.86, but then smaller in larger Froude number of 3.72.
Dispersion of dangerous propellants
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Safety
* Corresponding author. State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing 100028, China. ** Corresponding author. School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China. E-mail addresses: [email protected] (L. Pu), [email protected] (X. Tang). https://doi.org/10.1016/j.ijhydene.2019.05.219 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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Introduction Chemical propellants remain the most feasible solution for space transportation fuels. There are three primary candidates [1]: nitrogen tetroxide and mono methyl hydrazine (NTO/MMH), liquid oxygen and liquid hydrogen (LOX/LH2) and liquid oxygen and liquid methane (LOX/LCH4). Nontoxic propellants (LOX/LH2/LCH4) are considered as sustainable and environmental-friendly fuels that minimize pollution with their exhausts. NASA concluded that LOX/LCH4 is the preferred propellant combination for human space transportation to Luna and Mars because of its easy production, and LH2 is also favored due to the high engine specific impulse [2]. Based on practical experience, liquid fuels are the most efficient and cost-effective means of transport and storage. However, once the combustible and cryogenic liquid propellants leak and evaporate because of structural defects, material fatigue or cracking of welding seam especially in the process filling and transferring through pipelines, hydrogen and methane will burn in volume fractions of relatively 4e75% and 5e15% when mixed with ambient air. Beside explosion, possible harmful effects also include frostbite because of their low-temperature release conditions (the storage temperature of liquid hydrogen is around 20 K, and that of liquid methane is 111 K). Therefore, they have great threats to near-ground facilities and personnel. In order to predict the distribution of hazard areas of accidently leaked cryogenic liquids, there are plenty of experiments applied to figure out the leakage and dispersion characteristics of flammable and cold effect clouds. The National Aeronautics and Space Administration [3] (NASA, 1980), the Germany Federal Institute for Materials Research and Testing [4] (BAM, 1994), the Health & Safety Laboratory [5,6] (HSL, 2010), etc. were for liquid hydrogen. As for liquid methane, Maplin sands (1980), Burro (1980), Coyote (1981), Falcon (1987) [7], etc. were conducted. They got plenty of data that expected to be the most effective prediction of the hazard effects caused by these dangerous fuels. Nevertheless, the cost of an experiment is too high to conduct; alternative approaches such as computational fluid dynamics (CFD) become popular currently. There are many CFD software applied to simulate substances diffusion in the atmosphere, like ADREA-HF [8e11], ANSYS FLUENT [12e14], ANSYS CFX [15,16], FLACS [17,18], PHAST [19] etc. For liquid hydrogen release and dispersion, Statharas JC [4] used ADREAHF 3D-time dependent finite volume code for cloud dispersion basing on the BAM experiments that released LH2 between buildings. Middha et al. [20] utilized FLACS program to verify the feasibility of numerical simulation and simulated the lowvelocity flow in a garage situation. Jin et al. [13] and Shao et al. [14,21] researched the effects of ambient temperature, wind speed and atmospheric pressure on hydrogen diffusion with FLUENT. Giannissi et al. [22] studied the effects of environmental humidity and atmospheric stability on hydrogen dispersion. Jakel et al. [23] did a series of validations of a multiphase-multicomponent model for liquid and gaseous
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hydrogen release without phase change. For liquid methane, Cormier et al. [24] compared the leakage of LNG (liquid natural gas) on water surface and concrete surface by CFD simulation. Gavelli et al. [25e27] simulated the Falcon experiment with FLUENT to study the influence of obstacles on the diffusion of LNG gas cloud in complex geometric environment. Afterwards, they proposed a three-step model for analyzing LNG leakage into trenches: the first step was to analyze and solve the flow state of LNG, and next was to calculate the evaporation rate of channel direction. In the third step, the evaporation rate was used as the source term for CFD calculation. As for LCH4 and LH2 release and dispersion comparison, Li et al. [19] used some harm criteria (cold effects, thermal effects, overpressure and missile effects) to compare the harm effects of an accidental release of cryo-compressed hydrogen versus natural gas and liquid natural gas for automobile applications. The outcomes turned out that cryo-compressed hydrogen release could result in the longest lethal and harmful distances for a combustible scenario without ignitions. Sklavounos et al. [15] simulated the large-scale liquefied hydrogen and liquefied natural gas spill testes separately, which had a great agreement with concentration data against experimental records. Both gas cloud shapes were indicated that liquid natural gas and hydrogen release and dispersion as heavy gases rather than light gases on a low-temperature outlet condition. Verfondern et al. [28] compared the transient pool shape of a continuous and instantaneous release of natural gas and hydrogen. Venetsanos et al. [29] undertook hydrogen and natural gas releasing from compressed gaseous systems on commercial vehicles in urban and tunnel environments; different storage pressures were considered. These CFD simulations have been primarily conducted to validate models for liquid hydrogen or methane release and dispersion, and the comparison simulation did not consider the dispersion behavior between these two propellants after their leakage. Because the explosion and cold effects are related to gas cloud volume fraction and temperature respectively, this paper presents a detailed 3D transient CFD model for propellants release and dispersion to figure out the different concentration and temperature spill behaviors and hazard regions between hydrogen and methane.
The HSL's LH2 spill tests A series of hydrogen release tests were performed by the HSL in 2010, which determined to figure out dispersion behavior of hydrogen cloud in an open environment under different meteorological and outlet conditions. The experiments were carried out in a valley, with a concrete surface of 32 m in diameter. A schematic layout (not drawn to scale) is displayed in Fig. 1. Liquid hydrogen was piped from the tanker to the release point through a 26.3 mm diameter vacuum insulated vacuum insulated hose. Most of the releases were made from an absolute storage pressure of 0.2 MPa and absolute release pressure of 0.12 MPa that gave a release rate of 0.07 kg/s of
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because of velocity and density difference between the components. The number of Eulerian phase is four, and the primary phase is mixture of H2, O2 and N2, secondary phases are liquid hydrogen, liquid oxygen and liquid nitrogen. The continuity equation for the mixture is: v ðr Þ þ Vðrm ! vm Þ ¼ 0 vt m
(1)
.
where v m is the mass-averaged velocity, rm is the mixture density. The momentum equation for the mixture can be obtained by summing the individual momentum equations for all phases. It can be expressed as: Fig. 1 e HSL test layout (not drawn to scale).
liquid hydrogen. There were plenty of hydrogen concentration sensors placed in downwind direction of 1.5 m, 3 m, 4.5 m, 6 m, 7.5 m with a 0.25 m height and 0.25 m, 0.75 m, 1.25 m, 1.75 m, 2.25 m, 2.7 m in the vertical direction with 7.5 m downwind. The experiments also monitored the meteorological measurements (wind speed, wind direction, air temperature and humidity, at the 2.5 m height), the detailed data are reported in Table 1. The adiabatic mixing hypothesis approach was contributed to the hydrogen concentration values, which calculated from the cloud temperature because the accuracy of the concentration sensors were severely influenced by the condensed water in the low temperature. The releases were made onto or above a concrete surface. Three release scenarios were considered: a) horizontally along the ground, b) vertically downwards from 100 mm above the ground, c) horizontally at a height of 860 mm above the ground. In this paper, the model is verified by test 5, and the release and weather conditions are shown in Table 1. The more detailed experiment data can be referred to Refs. [5,6].
i h v T ðrm ! v m þ V! v m Þ þ V,ðrm ! v m! v m Þ ¼ Vr þ V, mm V! v m þ rm ! g vt n X ! ak rk ! v dr;k ! v dr;k þ F V, k¼1
(2) .
where n is the number of phases, F is a body force, and mm ¼ Pn ! ! ! k¼1 ak mk is the viscosity of the mixture, v dr;k ¼ v k v m is the drift velocity for secondary phase k. The energy equation for the mixture takes the following form: n v X ðak rk Ek Þ þ V,½ak ! v k ðrk Ek þ pÞ ¼ V, keff VT þ SE vt k¼1
where keff is the effective conductivity, SE includes any other volumetric heat sources. For a compressible phase, and Ek ¼ hk for an incompressible phase, where hk is the sensible enthalpy for phase k. For turbulence flow, the realizable k ε model with enhanced wall treatment and mixture drift force is utilized. The modeled transport equations for k and ε in the realizable k ε model are [31]: v v v ðrkÞ þ rkuj ¼ vt vxj vxj
m vk mþ t þ Gk þ Gb rε YM þ Sk sk vxj
Simulation approach
(4)
This work focuses on the numerical simulation of dispersion resulting from low-temperature fuels (hydrogen and methane) release in an open scenario like rupture of cryogenic propellant container tanks or the failure of transportation pipelines. It involved complexed heat and mass transfer process during the low-temperature fluid evaporate and disperse periods. The mixture model [30] can model n phases by solving the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary phases, and algebraic expressions for the relative velocities. In this case, slip velocity and implicit body force are considered
m vε ε2 pffiffiffiffiffi mþ t þ rC1 Sε rC2 sε vxj k þ vε ε þ C1ε C3ε Gb þ Sε k
v v v ðrεÞ þ rεuj ¼ vt vxj vxj
LH2
0.07
(5)
where h C1 ¼ max 0:43;
qffiffiffiffiffiffiffiffiffiffiffiffiffi h i k ; h ¼ S ; S ¼ 2Sij Sij hþ5 ε
(6)
In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, YM represents the contribution of the fluctuating dilatation in
Table 1 e Release and weather conditions of HSL test 5. Fuel Mass flow rate (kg/s)
(3)
Storage pressure (MPa)
Release pressure (MPa)
Source location
Source direction
Wind speed (m/s) (2.5 m height)
Ambient temperature (K) (2.5 m height)
0.20
0.12
Ground
Horizontal
2.67
283.56
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outflow. The ground is concrete in the bottom plane of which temperature is 280.56 K and thermal properties are considered as 2350 kg/m3, 0.97 kJ/(kg$K) and 1.28 W/(m$K), the wall thickness is 10 m [14]. The right surface of the tanks are set as liquid fuels mass-flow-inlet. All other areas are set as wall.
Fuel two-phase jet
Fig. 2 e Computational domain and boundary conditions. compressible turbulence to the overall dissipation rate, C2 and C1ε are constants. sk and sε are the turbulent Prandtl numbers for k and ε, respectively. Sk and Sε are user-defined source terms. In order to simulate the dispersion phenomenon, Species Transport model with inlet and energy source diffusion is adopted. In turbulent flows, ANSYS Fluent computes the mass diffusion in the following form: m VT ! J i ¼ rDi;m þ t VYi DT;i T Sct
(7)
.
where J i is the diffusion flux of species i, which arises due to gradients of concentration and temperature. Di;m is the mass diffusion coefficient for species I in the mixture, and DT;i is the thermal diffusion coefficient. Sct is the turbulent Schmidt number, The default Sct is 0.7.
Computational domain and boundary conditions In order to simulation LH2 with an effective physical model, the computational domain, boundary conditions and mesh are shown in Figs. 2and 3. x ¼ - 3 and x ¼ 30 planes are left and right, y ¼ 0 and y ¼ 10 planes are ground and top, z ¼ - 6 and z ¼ 6 are front and back, the central points of two different height liquid fuels spill tanks are located in (0, 0.0111, 0) and (0, 0.8711, 0), with a characteristic diameter of 0.0263 m. The back, front and top planes are all set as symmetry for the reason that these planes are way far from the flow region. The left plane is set as wind in velocity inlet and the right plane is
Fig. 3 e Grids of the domain and the locations of the fuel inlet.
Saturated cryogenic liquid hydrogen was stored in 0.2 MPa pressure and release in 0.12 MPa pressure, which caused flash vaporization because of reducing pressure when the fuel leaks. This phenomenon affects the release condition of different gas-liquid ratio. The following equation is used to calculate the vapor mass fraction and mixture density of hydrogen after evaporated: qv ¼
H1l H2l H2v H2l
(8)
1 qv ql ¼ þ rmix rv rl
(9)
H1l is liquid enthalpy before release, H2l is liquid enthalpy after release, H2v is gas enthalpy after release, rmix is density of mixture.
Multicomponent phase transitions The release temperature of liquid hydrogen is 20 K; it can cause condensation of the air component including nitrogen and oxygen. Lee model can be selected with the Eulerian multiphase model if one of the overall interfacial heat transfer coefficient models will be used. In this paper, Lee Model is adopted for phases change with a mechanism of evaporationcondensation from liquid phase to gas species and vice versa. Through several sets of simulation in different phase change coefficients, the evaporation and condensation frequency are set as 10 and 20, the saturation temperature is constant of 20.324 K under the ambient pressure. The liquid-vapor mass transfer (evaporation and condensation) is governed by the vapor transport equation: v ! ðat rv Þ þ V,ðav rv V v Þ ¼ m_ lv m_ vl vt
(10)
Based on the following temperature regimes, the mass transfer can be described as follows: If Tl > Tsat (evaporation)
Fig. 4 e Steady wind profile.
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Fig. 5 e Validation between experiment and simulation.
Solution method ðT1 Tsat Þ m_ lv ¼ coeff ,al rl Tsat
(11)
If Tv < Tsat (condensation): m_ vl ¼ coeff ,av rv
ðTsat T1 Þ Tsat
(12)
coeff is a coefficient that must be fine tuned and can be interpreted as a relaxation time. a and r are the phase volume fraction and density, respectively. The source term for the energy equation can be obtained by multiplying the rate of mass transfer by the latent heat.
Wind speed A vertical wind velocity profile distributing by logarithmic law is applied first before cryogenic liquid hydrogen release. The wind profile obeys the logarithmic law: u ¼ u*
lgH lgH0 lg10 lgH0
(13)
where the wind speed is 2.675 m/s at 2.5 m height and the terrain roughness H0 is equal to 0.03. The steady-state wind field is displayed in Fig. 4, then the hydrogen mass flow release condition based on time transition is calculated, which uses the steady-state data as the initial field.
The pressure-velocity coupling scheme is PISO with both skewness and neighbor correction are set as 1. The gradient spatial discretization method is Least Squares Cell Based and pressure is Body Force Weighted. QUICK scheme applies to volume fraction discretization and others are all set as second order upwind scheme. The transient formulation is used second order implicit. Under-relaxation factors are adapted to the scaled residuals. All convergence criterion set as 106 in the steady condition and 104 in the transient section. The step size is 0.001s with approximately 20 iterations per time step to reach the limited residuals.
Model validation Fig. 5 depicts the HSL experimental data, simulation with air phase change and without air phase change in the location of (4.5, 0.25, 0) and (7.5, 0.75, 0). It can be turned out that the simulation value of model without oxygen and nitrogen condensation is higher than the experimental average data, while the simulation with air phase transition gains a better agreement with the tests. Fig. 6 presents the cloud shape in simulation and experiment. The numerical results predict that the model is suitable for small mass flow rate of cryogenic liquid hydrogen in an open environment.
Fig. 6 e Hydrogen cloud shape in simulation and experiment.
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Table 2 e Release condition of cryogenic liquid hydrogen and methane. Fuels Mass flow rate (kg/s) H2 CH4
Gas mass fraction (%)
Liquid mass fraction (%)
4.9 4.9
95.1 95.1
0.07 0.16
19.9 34.1
Results and discussion
Fr ¼
Dispersion behaviors Properties of methane are different from hydrogen in density. In order to have a better comparison of the dispersing behavior between liquid hydrogen and methane, Froude number (Fr) which represents the ratio of momentum and buoyancy is adopted to set as the same outlet conditions. When Fr > 1, the flow is a jet that initial momentum plays a leading role in the flow or the near field, otherwise it's a buoyant plume dominated by buoyancy. The relative magnitude of the two forces can be expressed by the dimensionless density Froude number. Definition is showed in Eq. (14), the value of Froude number depends on the density and velocity of the mixture, the mixing speed relates to the area of the leakage outlet, mixture mass and density in Eq. (15). The mixture density lies on gas and liquid mass fraction as shown in Eq. (8). Therefore, the Froude number can be calculated by Eq. (16). When the mixture density is constant, Froude number is only a function of velocity. More specifically, if gas and liquid mass fraction keep unchanged, mixture mass flow rate is the only factor affecting the value of Froude number. um Fr ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rmix ra gb ra
(14)
mmix rmix A
(15)
um ¼
Release mixture density Release velocity (m/s) (kg/m3)
m qmix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rmix A rmixrara gb
7.1 9.5
Release temperature (K) 20 111
(16)
um is characteristic velocity of the jet, ra is ambient fluid density, g is the acceleration of gravity, b is Characteristic length of the jet. mmix is mass of the mixture, A is the area of the leakage outlet. The HSL scenario of a release rate of 0.071 kg/s, when the release condition with the same Froude number of 3.72 and a gas fraction of 4.9%, methane spill rate is 0.16 kg/s, the detailed release condition of these two fuels can be seen in Table 2 and these simulations were performed. Outlet height set as 0.86 m, and the release direction is horizontal. According to the European Industrial Gases Association [32], when the volume concentration of hydrogen is 4e75% and that of methane is 5e15% in the air, it is likely to explode. When the temperature is lower than 233.16 K, it can damage the external facilities or people in the low temperature. Therefore, the lower flammable limit (LFL) of 4% volume concentration of hydrogen and 5% volume concentration of methane are these two fuels’ combustible effect boundaries, and the cold effect limit (CEL) of 233.16 K temperature is the cold effect boundary.
Concentration distributions Fig. 7 (a) presents the farthest downwind, vertical distance of hydrogen and methane combustible clouds changing over flow time, the combustible clouds are continuously increased in both directions because of air entrainment. The clouds go further and further until they reached a quasi-stable state that is around 14 s for hydrogen and 6 s for methane, and then
Fig. 7 e (a) The LFL movements of hydrogen and methane clouds changes as time varies. (b) The maximum concentration value and location in the symmetrical plane on a quasi-stable state.
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Table 3 e Hydrogen and methane combustible cloud shapes in the symmetrical plane at 4 s, 10 s, 16 s. H2
CH4
4s
10s
16s
flammable cloud field remains unchanged. The LFL distances of hydrogen and methane are 19.2 m and 13.5 m in the downwind direction, and 3.8 m and 1.9 m in the vertical direction, respectively. Table 3 presents liquids hydrogen and methane combustible cloud shape changing in the symmetrical plane at flow time of 4 s, 10 s, 16 s, it can be clearly seen that the clouds show a downward trend at the near field. At the far field, when the density of the fuel clouds gradually become smaller than that of the surrounding air, the clouds subject to buoyancy and move upward.
The maximum concentration values and locations on a quasi-stable state in the symmetrical plane are displayed in Fig. 7(b). The location of the hydrogen combustible cloud centerline is lower than methane within 2.7 m in the downwind direction, while higher in the far field. The volume fraction of hydrogen is always higher than that of methane after the location is 0.5 m away from the outlet. The concentration of the gas phase increases first and then decreases close to zero, in which the maximum volume fraction of hydrogen is 68.4% at the location of (1.5, 0.63, 0) and that of methane is 48.0% at location of
Fig. 8 e (a) The CEL movements of hydrogen and methane clouds changes as time varies. (b) The minimum dimensionless temperature values and locations in the symmetrical plane on a quasi-stable state.
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Table 4 e The hydrogen and methane cold effect cloud shapes in the symmetrical plane at 1s, 4s, 7s. H2
CH4
1s
4s
7s
(0.5, 0.86, 0). The volume fraction depends on the liquid evaporation rate and cloud diffusion rate. At the near field, the evaporation rate is greater than cloud diffusion rate, so more gas produced and the concentration goes larger, then with liquid disappeared and cloud move further with more ambient air, the concentration becomes smaller.
Temperature distributions It is necessary to analyze the temperature field of cloud diffusion because of the low-temperature damage to the surrounding environment and human beings. However, the outlet temperature of hydrogen is 20 K and the outlet temperature of methane is 111 K. Thus, lead into the dimensionless temperature to compare the temperature diffusion field of the hydrogen and methane. The formula for calculation is as follows:
Fig. 9 e Evaporation and spill behaviors of cryogenic liquid hydrogen and methane after leaking from storage tanks or pipelines.
Td ¼
Ta T Ta Ts
(17)
Ta is ambient temperature, Ts is cryogenic liquid release temperature, T is the field temperature. It can be seen from Fig. 8 (a) that the temperature field will also reach a quasi-stable state after a certain time, but the time is relatively short with around 5 s for hydrogen and 2 s for methane. Table 4 compares the hydrogen and methane cold effect cloud shapes in the symmetrical plane at the flow time of 1 s, 4 s, 7 s. The CEL (dimensionless temperature of hydrogen is 0.8 and methane is 0.7) movements of hydrogen and methane cloud are 5.5 m and 5.4 m in the downwind direction and 1.8 m and 1 m in the vertical direction. When the gas cloud reaches a quasi-steady state, the minimum temperature locations in the symmetrical plane and the dimensionless temperatures corresponding to the minimum temperatures are shown in Fig. 8(b). It can be seen that the temperature location curves are similar with the concentration location curves; it means the minimum
Table 5 e The value of mass flows rates correspond to different Froude numbers. Fr ¼ 0.47
Fr ¼ 0.93
Fr ¼ 1.86
Fr ¼ 3.72
Mass flow H2 CH4 H2 CH4 H2 CH4 H2 CH4 rate(kg/s) 0.009 0.020 0.018 0.040 0.035 0.080 0.071 0.160
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Table 6 e Liquid hydrogen and methane shapes in the symmetrical plane of different Froude number. H2
CH4
Fr ¼ 0.47
Fr ¼ 0.93
Fr ¼ 1.86
Fr ¼ 3.72
Fig. 10 e The farthest distance in downwind and downward direction of liquid hydrogen and methane in the volume fraction of 0.01% of different Froude number on a quasi-stable state.
temperature locations are consistent with the maximum concentration positions, which is consistent with the conclusions of many experiments and scholars using adiabatic mixing principle [15] to build the relationship between temperature and concentration. From the diagram, the minimum dimensionless temperature of hydrogen and methane increases continuously in the downwind direction, and finally tends to the ambient temperature (the dimensionless temperature is 1). The dimensionless temperature of hydrogen is always higher than that of methane; it means hydrogen has a greater temperature diffusion due to the larger temperature difference between liquid hydrogen and ambient air. As the concentration and temperature field analyzed above, there are some common stages between cryogenic liquid hydrogen and methane release and dispersion. After their leakage from damaged transport container tanks or ruptured pipelines, the mixture tend to go downward because of the heavy density, and then the density would become smaller and smaller because the cloud temperature goes higher for transferring energy with ambient air, therefore, the cloud would subject to positive buoyancy and tend to an
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upward movement. These stages of movement can divide into: 1) near-field movement: heavy mixture. The average density is higher than ambient air density mainly due to the liquid phase. 2) far-field movement: light gas. The average density is lower than ambient air density. The movements present clearly in Fig. 9. The disperse behaviors between these two cryogenic liquid fuels need further research. The behaviors of the liquid in the near field and light gas in the far field influenced by the Froude number are discussed in the next sections.
afterwards. In the vertical direction, there is little downward change in methane, but hydrogen has an obvious downward trend. When Fr ¼ 0.47, the two fuels distance differences in downwind direction and downward direction are 0.50 m and 0.02 m. As Fr ¼ 3.72, the distance difference is 1.01 m and 0.41 m. Therefore, at the near field, the farthest distance in volume fraction of 0.01% of liquid methane is further than hydrogen in the downwind direction when Froude number change from 0.47 to 3.72, while hydrogen shows a tendency to move more downward.
Near-field liquid movement differences
Far-field gas movement differences
The density of the mixed flow is larger than that of air in the near field mainly because of liquid fluid. Therefore, the movement of liquid phase analyzed in detail at the near field. With unchangeable gas fraction, in other words, the constant density in the initial condition of the outlet fluid, different mass flows rate correspond to different Froude numbers. Froude number of the buoyant plume of 0.47, 0.93 and the jet flow of 1.86, 3.72 are investigated. Detailed mass flow rates are shown in Table 5. To describe the downward tendency of liquid hydrogen and methane movements, the lowest location in the vertical direction is taken into consideration. The shapes of two liquid flows in the symmetry plane on a quasi-stable state are compared in Table 6. With the same Froude number, the volume fraction of liquid methane is smaller than liquid hydrogen and the former moves further than the latter. With the increase of Froude number, the moving distance of liquid hydrogen and methane increase gradually in the downwind direction, the distances of liquid hydrogen and methane in the volume fraction of 0.01% on a quasi-stable state are displayed in Fig. 10. The movement of methane in the downwind direction is always larger than that of hydrogen, but the increased distance of methane becomes smaller and smaller as Froude number increased, while the hydrogen shows a linear increasing trend, therefore the distance difference between these two liquid become greater firstly and goes smaller
LFL movements
Fig. 11 e The LFL movements of hydrogen and methane clouds of different Froude number on a quasi-stable state.
Fig. 12 e The CEL movements of hydrogen and methane cold effect clouds of different Froude number on a quasistable state.
After the liquids heat exchange and evaporate, the gas clouds move further and further under the effects of self-diffusion and wind-transportation combined. The farthest downwind distances and altitudes of hydrogen and methane combustible clouds of different Froude number on a quasi-stable state present in Fig. 11. For explosion distances, methane cloud moves shorter than hydrogen in both directions as Froude number changes from 0.47 to 3.72. With the increase of Froude number, both combustible clouds disperse farther and farther, and the two clouds distance differences become larger and larger. When Fr ¼ 0.47, the two fuels’ distance differences in the downwind direction and vertical direction are 0.83 m and 0.20 m. When Fr ¼ 3.72, the distance differences are 7.12 m and 2.10 m.
CEL movements Fig. 12 represents the changes of the cold effect clouds movement in different Froude number. With the increase of Froude number, in downwind direction, the propagation of hydrogen cloud increases continuously, while the lowtemperature cloud of methane firstly increases and then decreases, hence the movement of methane is higher than that of hydrogen and then smaller. Hydrogen cloud continues to increase in the vertical direction, while the methane is almost unchanged; the distance difference becomes larger and larger
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as Froude number increase. When Fr ¼ 0.47, the methane cloud is 0.83 m farther than hydrogen cloud in downwind direction, and the vertical distance difference is almost equal to zero. However, when Fr ¼ 3.72, the hydrogen cloud is 0.22 m farther than methane cloud in the downwind and 0.76 m in the vertical direction.
Conclusions A 3D transient CFD model has been developed to investigate the difference of dispersion behaviors between cryogenic liquid hydrogen and methane leakage. Multicomponent (H2, O2, N2) phase transitions which use the Lee model are considered to make the simulation have better agreements with the HSL experimental data than scenario without air phase change. Froude number has been adopted to set as the same outlet conditions of two propellants. With the same Froude number of 3.72, the flammable and low-temperature hazards regions, the maximum concentration centerline and its location, the minimum dimensionless temperature centerline and location have been compared. The results show that fuels’ hazard cloud would reach a quasi-stable state after a certain time, and it take shorter time for cold effect clouds to attain an equilibrium than the combustible clouds do. Cryogenic liquid hydrogen and methane release as heavy mixture in the near field and disperse as light gas in the far field. When Froude number changed from the buoyant plume of 0.47, 0.93 to the jet flow of 1.86, 3.72. The differences of liquid movement in the near field, the harmful gas cloud movement in the far field have been discussed. At the near field, the farthest distance in volume fraction of 0.01% of liquid methane is further than hydrogen on a quasi-stable state, and liquid hydrogen moves more and more downward as Froude number increased. At the far field, for the combustible effect, the hydrogen clouds are always larger than methane clouds and the distance differences become greater in larger Froude number conditions. For the cold effect, the downwind distance of methane is higher than that of hydrogen in the Froude number of 0.47, 0.93 and 1.86, but then smaller than that of hydrogen in large Froude number of 3.72. The vertical distance difference is almost equal to zero in small Froude number of 0.47 and 0.93, then the hydrogen cold effect altitude become greater than methane and the difference goes larger and larger.
Acknowledgement This study is financially supported by the State Key Laboratory of Technologies in Space Cryogenic Propellants (SKLTSCP1809).
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