Authors: Han Sun, Guogang Yang, Xiangkun Ma, Zhonghua Sheng, Shian Li, Ying Cui, Zhuangzhuang Xv, Xiaoxing Yang, Hao Wang, Baiyi Qi
Categories: Article
Source: ACS Omega
Size and Pressure on Hydrogen Explosion Dynamic Characteristics
Explosion venting is an effective method to reduce the explosion damage; in order to study the mechanism of an explosion venting process in internal and external space, this paper investigates the influence of vent parameters on hydrogen–air explosion in a rectangular duct through numerical simulation. The model including the internal and external space is first constructed, and then the explosion dynamic behaviors of the full flow field are analyzed under different vent pressures and sizes. The study aims to reveal the coupling effect of the flame, pressure, and flow field on hydrogen explosion venting. The results indicate that the explosion intensity increases with the growth of the vent pressure and the reduction of the vent size. The maximum external overpressure increases to 2.6 and 2.3 times as the vent pressure increased to 10 times or vent size reduced by 90%. The flame and combustible gas mixture evolve from a mushroom cloud into a jet form as the vent size decreases, and vortexes formed at the flame front suppress flame propagation. However, the flame speed increases significantly as the flame passes the vent under the impact of larger pressure gradient, which results in a more violent turbulence intensity and secondary external explosion.
Hydrogen is considered as a clean energy source that can address issues related to greenhouse gas emissions, air pollution, and energy scarcity. However, it is essential to note that hydrogen has a high leakage capacity, an extensive explosion range, and fast flame speed. It can generate high pressure during hydrogen explosion, leading to huge loss of both life and property.^1^ The flammable range of hydrogen is 7 times that of methane, while the minimum ignition energy of hydrogen is only 8.5% that of methane. The laminar combustion velocity of hydrogen is 7.8 times that of methane. However, hydrogen is only 12% as dense as methane. It can be seen that hydrogen has a higher risk of leakage and explosion than methane. Explosive venting is a significant method to prevent explosion damage and to protect equipment and buildings. The study of the mechanism of hydrogen explosion venting is the key to prevent explosions and minimize the accidents damage. Currently, the coupling influence of flame, pressure, and flow field on explosion venting has become an essential topic. Therefore, studying the kinetic behavior of a hydrogen venting explosion is crucial to the safety application of hydrogen energy engineering. This work provides substantial references for the structure safety design of ships and is significant for protecting people and property.
Combustion and explosion occur when a combustible
hydrogen–air
cloud forms in a venting space. Full-scale experiments are usually
difficult to conduct due to size limitations and safety concerns,
and numerical simulations have become the good methods to study hydrogen
explosion. Some researchers have compared various CFD codes and noted
that Fluent has good computer accuracy. Baraldi et al.^2^ used four CFD codes to predict the hydrogen venting explosion
in a 0.95 m^3^ cylindrical vessel under different vent sizes,
noting that the CFD code Fluent demonstrated good prediction accuracy.
Bauwens et al.^3^ used OpenFoam to better
predict explosion behaviors for different vent sizes and post ignition
conditions. However, the prediction accuracy was not good for preignition
conditions. Vyazmina et al.^4^ suggested
that the FLACS CFD tool should not be used to predict explosions under
the center ignition conditions for smaller vents. Several scholars
have researched the explosion pressure under different vent parameters
during the hydrogen venting explosion. Zhou et al.^5,6^ found
that the location and size of the vent significantly impact the pressure
venting. The best vent effect is achieved when the vent is located
near the ignition. Cao et al.^7^ found that
the influence of the vent pipe length can be ignored for hydrogen
explosions, as the vent pressure (Pbur) is higher than 0.35 MPa. Guo et al.^8^ analyzed the explosion behavior in a cylindrical vessel of 0.0123
m^3^ under different ignition positions, vent sizes, and
hydrogen concentrations. Chao,^9^ Cui,^10^ and Bao^11^ noted that
reducing vent sizes increased the explosion overpressure, and that
vent pressure had varying effects on overpressure and overpressure
rise rate in different locations. Lv et al.^12^ analyzed the explosion pressure and flame propagation process in
an open pipe with obstacles and pointed out that the combustion rate
increases when the flame passes through the obstacles, resulting in
a large increase in explosion pressure. Rocourt^13^ studied the impact of vent size in a confined space, noting
that ignition at the rear wall produced the highest overpressure.
Wan et al.^14^ and Ajrash et al.^15^ demonstrated the effectiveness of lateral vent
in mitigating the explosions intensity. Gong et al.^16^ found that a small vent opening ratio for high-pressure
hydrogen spontaneous combustion deflagration can cause the bursting
piece to fail to open completely when the high-pressure hydrogen is
released. According to Kuznetsov et al.,^17^ peak overpressure more than 100 mbar can only be achieved for mixtures
with a hydrogen concentration greater than 15% when venting sizes
are larger than 50 × 50 cm^2^ in a 1 m^3^ space.
Excessive opening pressure of the vent can lead to more considerable
negative pressure in the late explosion stage. Liang’s experiment^18^ demonstrated that the combustion overpressure
is small when the concentration decreases below 9 vol %, regardless
of the vent size. There may be multiple pressure peaks during explosion
venting due to the influence of various factors in the internal and
external space. Rui et al.^19^ noted that
the first peak overpressure increases with the growth of vent pressure.
Ma et al.^20^ conducted numerical calculations
on the explosion venting in 5 L and 64 m^3^ vessels. They
found that adding hydrogen gas shortened the explosion time. Guo et
al.^21^ performed a 3D dimensional simulation
noting that varying vent sizes result in distinct peak overpressure.
Sun et al.^22^ concluded that a double-peak
pressure curve occurs under small-diameter venting conditions, but
a single-peak overpressure curve occurs under large diameter venting
conditions, and the concentration mainly influences the second peak
overpressure. The above scholars mainly focused on the change of overpressure,
but the dynamic pressure can not be ignored in some vent conditions.
Zhang and Zhang^23^ studied the impact of
vent pipe size on internal vent explosion and pointed out that the
vent had a greater influence on explosion overpressure than indoor
explosion temperature, dynamic pressure, and wind speed. Zhang and
Ma^24^ evaluated the risk of explosions in
underground coal mines and highlighted that the dynamic pressure from
high speed gaseous combustion products also causes significant damage.
Current studies have mainly focused on the explosion pressure characteristics
in an internal space, with fewer studies on explosion in an external
space. Most studies have analyzed data from a single monitor point
and have yet to study in depth the evolution of pressure at various
locations in internal and external space.
The pressure dynamics is greatly affected by the flame propagation in the internal and external space, and the flame propagation during the explosion venting is significantly influenced by the vent parameters. Therefore, it is crucial to study the flame propagation evolution under different venting explosion conditions. Cao et al.^25,26^ analyzed the changes in explosion peak pressure and flame propagation under various vent pressures through numerical calculations and discussed the under expanded jet near the vent. Li et al.^27^ and Cao et al.^28^ investigated the changes in peak pressure in a slender pipe with different concentrations and number of vents, observed three stages of flame front morphology transition. Zhang et al.^29^ and Guo et al.^30−32^ investigated the effects of the vent pressure, hydrogen concentration, and a double vents condition of explosion pressure characteristics. They observed multiple pressure peaks at the outlet when the vent pressure is low. Using two vents with the same total vent size significantly reduced the external flame length. Previous studies on flame structure evolution in numerical simulations have primarily focused on the internal space, with less attention given to the evolution of the flame propagation structure in the external space.
When the flame propagates into the external space, it contacts the outer combustible gas mixture and generates a secondary explosion. However, there is a lack of research on secondary external explosion. Pang et al.^33^ analyzed the external disaster area caused by a high speed hydrogen explosion airflow in a 64 m^3^ space. The results indicate that the maximum dynamic pressure increases with the vent open time in a specific range near the vent. Tolias and Venetsanos^34^ indicated that the dramatic increase of external pressure is happened only after the flame entered the turbulent recirculation zone. Li and Hao^35^ presented a CFD modeling method using FLACS/Fluent to model the internal turbulent flame and calculate shock waves propagation in low turbulence intensity air. Bauwens’s^36^ analytical results indicate that peak pressures were influenced by the combination of the maximum flame surface, combustion speed, and explosion outside the combustion chamber. They analyzed the gas cloud and flame shape as well as the explosion kinetics of propane in both internal and external spaces for various vent sizes. It has been demonstrated that a small vent size can destroy the vortex bubble, forming a jet that entraps a significant amount of an external atmosphere. Wang et al.^37^ discovered that the internal explosion overpressure and the external dynamic pressure increased as the vent size decreased. Proust and Leprette^38^ observed the flame and unburned gas being ejected from the internal space, coiling and sucking up to form a mushroom cloud morphology. The maximum peak of external overpressure near the vent may be smaller than that in the downstream region, indicating that external explosion occurs away from the vent. Wang et al.^39^ conducted experiments and found that the intensity of the R–T instability and the Helmholtz oscillation increased with increasing vent size.
In summary, previous work has primarily focused on studying the pressure characteristics of a single monitoring point and flame form evolution within the duct. However, there has been insufficient research on the pressure characteristics of different locations, the flame propagation behavior, and the phenomenon of secondary explosions within both the internal and external spaces. The coupling influences of the flame, pressure, and flow field on the explosive venting behaviors in internal and external space need to be further studied. This paper studies hydrogen explosion venting under various vent pressures and vent sizes with numerical simulation methods. The research aims to investigate the coupling effect of pressure, flame, flow field, and vent parameters to reveal the dynamic behaviors of the hydrogen venting explosion.
The hydrogen venting explosion process can be described by the momentum, energy, and mass conservation equations, and these equations are also available in the literature^33,40^ as
where x is the Cartesian
coordinate, p is static pressure, t is time, u is velocity, ρ is density, and i and j are coordinate directions. Additionally, Qc represents the chemical reaction source term,
and hm and Jm are the specific enthalpy and diffusion
flux of component m, respectively. τij is the viscous stress tensor, as is
expressed as the flow δ~ij~ is the Kronecker number, and μt is the turbulent
viscosity coefficient.
In this study, the scale-adaptive turbulence model (SAS)^25,41^ has been employed, as shown as
where k is the turbulent
kinetic energy and μ is the molecular viscosity. Coefficient
α* suppresses turbulent viscosity and makes low Reynolds number
corrections. The value of a1 is 0.31,
σφ is 2/3, C is 2, and Cμ is 0.09 m^2^/s. Gk is the generation of turbulent kinetic energy. The length
scale of the simulated turbulence is denoted by L, and S represents the strain rate scalar. Lvk is a 3D generalization of the classical boundary-layer
definition. σ~k, σω~, and β are computed using the following
The combustion resolved by utilizing the average reaction process variable equation^42^
where c is the reaction
process variable. The
turbulent Schmidt number is denoted by Sct, which is equal to 0.7. The reaction process source term is defined
by Sc, and the specific heat capacity
of the mixture is represented by Cp. Sc is calculated using eq 13
where ρu represents
the density of unburnt mixture, Ut is
the turbulent flame velocity, which is
calculated by the Zimont model, as the following ^43^
where A = 0.52 is
the model constant, u′ is the turbulence intensity, Ul is the laminar flame propagation velocity, Xu is the thermal conductivity of the unburned
hydrogen–air
mixture, and lt is the turbulence length
scale.
A 3D model of hydrogen venting explosion is established, which includes the internal duct and external field, as shown in Figure 1. The duct size is 600 mm × 120 mm × 120 mm, the external space extends 5 times of the duct diameter in the radial direction and 6 times of the duct length in the axial direction. The adiabatic nonslip wall is used, and the boundary of the external space is set as a nonreflective pressure outlet. The duct contains stoichiometric hydrogen–air, while the external space contains only air. The ignition source is set to a sphere region with a radius of 2 mm and ignition is achieved by setting the reaction process variable to c = 1. The computational domain is discretized using the PISO algorithm. The pressure is discretized by the second scheme, and density, energy, turbulent kinetic energy are discretized by the second upwind scheme. Adaptive time steps are used to ensure computational stability with an initial time step of 1 × 10^–6^ s and a Courant number of 0.8. The residuals of the mass, turbulent kinetic energy, average mixture fraction, turbulence dissipation rate, and process variable equations are all less than 1 × 10^–3^. Additionally, energy equation residual is less than 1 × 10^–6^ in the simulation calculations.
Figure 1 Geometric and mesh model.
Numerical calculations were conducted to simulate the process of hydrogen explosion release, as described in the literature.^12^ A rectangular obstacle with a 50% obstruction rate is inserted into a 100 × 100 × 500 mm^3^ rectangular duct, located 200 mm away from the ignition end. The pipe is filled with a hydrogen–air mixture at an equivalent ratio. The ignition source and pressure monitor are positioned at the bottom of the duct. Numerical calculation is performed using four different grid sizes, as shown in Figure 2. It is observed that when the mesh size is less than 4 mm, the flame propagation is minimally affected. Finally, a 3 mm grid is selected for subsequent calculations to ensure accuracy while avoiding excessive computational resources.
Figure 2 Grid independence validation.
The flame structure evolution image of the numerical simulation and the high-speed camera are shown in Figure 3. The flame spreads in spherical and finger forms in an early stage. The flame morphology and propagation position at different moments are in good agreement with the experimental results. After passing through the obstacle, the flame is deformed, the surface gradually increases, so the combustion rate and overpressure are increased significantly, and the flame’s acceleration will be evident. The simulation result shows that the overpressure and flame speed are in good agreement with the experimental. The error is generated may be by not considering the pipeline wall heat transfer.
Figure 3 Flame shape, explosion overpressure, and flame speed.
Figure 4a shows that
after the vent is opened, the overpressure at the bottom end of the
duct increases until the energy generated by the explosion inside
the duct equals the energy released at the vent.^44^Figure 4b illustrates that the internal explosion overpressure decreases
as the distance from the vent increases under the same vent pressure
(Pbur). The blue area represents the internal
space of the duct, and the light yellow area represents the external
space in Figure 4b.
The x-coordinate represents the distance from ignition
along the axis. The black curve is the peak overpressure at different
positions under various vent opening pressure, and the red curve is
the time to reach the peak overpressure at various positions. The
explosion overpressure in the external space attenuates gradually
toward the far field, and the peak explosion overpressure occurs at
a certain distance from the vent. This is because the external explosion
mainly occurs in the center of the unburned gas mixture. The peak
explosion overpressure evolves along the axial direction in the same
manner for all three different Pbur. However,
the amplitude of the peak explosion overpressure undergoes significant
changes. The internal peak overpressure is primarily dependent on
the effect of the Pbur, the internal combustion
rate, and the vent flow rate under low Pbur conditions, resulting in a significant difference in peak overpressure
at different locations in the duct. For instance, under 10 kPa condition,
the peak explosion overpressure at ignition (0 mm) is 2.5 times than
that of 500 mm, while under 100 kPa condition, the peak explosion
overpressure at 0 mm is only 1.08 times than that of 500 mm. The pressure
in the duct continues to accumulate as the Pbur increases, and the vent factor plays a dominant role in
the development of overpressure, resulting in the production of a
higher internal peak overpressure. Figure 4a shows the peak explosion overpressure at
the ignition (0 mm) is 33, 87, and 110 kPa under the Pbur at 10, 60, and 100 kPa. The peak of explosion overpressure
at 0 mm under 100 kPa vent pressure is 3.33 times of that under 10
kPa vent pressure. Increasing the Pbur causes the flame and combustible gas mixture to be sprayed at higher
speeds onto the external field, which increases the degree of turbulence
in the external space and exacerbates the external explosion.^14^ When the Pbur is
increased from 10 to 100 kPa, the peak explosion overpressure in the
external space increases by 2.65 times.
Figure 4 Explosion pressure, max overpressure rise rate (dp/dt)
max, and explosion intensity index (Kg) at three Pbur.
Figure 4b shows
that the impact of the vent is more significant to the overpressure
of the location that is closer to the vent, and the time to reach
the peak explosion overpressure will be earlier. As the Pbur increases, the duct remains closed for a more extended
period of time, which causes the unburned gas mixture to be discharged
into the external space later, resulting in delayed peak explosion
overpressure in different locations within the internal space. The
internal space takes at least 4.56 ms to reach the peak explosion
overpressure when the vent opens at a pressure of 10 kPa. When the Pbur increases to 100 kPa, it takes at least
8.16 ms to reach the peak explosion overpressure in the internal space. Figure 4d shows that the
peak pressure rise growth rate is directly proportional to the Pbur. The explosion intensity index (Kg) is a crucial parameter for measuring explosion
intensity and designing safety measures for industrial processing
and production. It is calculated as . Kg grows from
3.89 to 6.15 under three Pbur, indicating
that the explosion risk also increases when the Pbur increases, which is not desirable for explosion venting.
The evolution of the explosion dynamic pressure differs from that
of overpressure, as illustrated in Figure 4c. Under the same Pbur condition, the peak dynamic pressure generated by explosion
first increases and then decreases along the axis from the ignition
end to the far field direction. The peak dynamic pressure is generated
in the space closer to the vent. This is because the fluid velocity
in the area near the vent changes more significant due to pressure
difference. When Pbur increases, the peak
dynamic pressure increases significantly. For instance, the peak dynamic
pressure at Pbur of 100 kPa is 2.93 times
higher than the peak dynamic pressure at Pbur of 10 kPa. The increase of Pbur causes
a delay in the ejection of fluid and flame from the duct. As a result,
the moment to reach peak dynamic pressure at the exact location in
the internal and external space is gradually delayed.
Reducing
the vent size results in a slower release of the explosion
overpressure into the external field, which causes an increase in
the peak overpressure at different locations in the duct. Nondimensional
vent coefficient Kv is defined as the
following Kv = V^2/3^/Av. V is the volume of the pipe and Av is
the size of the vent. When the Kv increases
from 2.9 to 29.2, the peak explosion overpressure at ignition (0 mm)
increases to 3.2 times in Figure 5a. The combustible gas mixture covers a larger area
in the outer space when the vent size is reduced, leading to external
explosions occurring even at a distance of 1000 mm from the ignition
source. However, the peak overpressure is not a gradual decrease along
the axial direction to the far field region as for Kv 5.8. Instead, it shows a change of first increasing
and then decreasing to the far field in Figure 5b. This change is related to the conditions
of the flame in the external flow field of the irregular development.^38,45^ As the Kv increases from 2.9 to 29.2,
the moment of reaching peak explosion overpressure is gradually delayed
at different locations. The Kg are 3.89,
4.6, and 6.7, which indicate that reducing the vent size increases
the explosion intensity. The external space far field region experienced
a more intense secondary explosion and faster gas flow velocity, resulting
in a significant increase in the dynamic pressure of the external
space. The Kv of 29.2 conditions results
in a peak dynamic pressure increase of 5.5 times compared to the vent
fully open conditions. Additionally, the time lag of flame ejection
from the duct leads to the time lag of the peak dynamic pressure at
different locations in the external space.
Figure 5 Explosion pressure, max overpressure rise rate, and explosion intensity index at three vent sizes.
The combustible gas enrolls on both sides of the axis and forms a
mushroom cloud gas after ejecting from the duct under condition of
vent fully opening, and the unburned gas volume expands continuously
with the push of the internal explosion. Different vent opening pressures
have no considerable impact on the morphology of external combustible
clouds in Figure 6.
When the Pbur is at low level, the flame
maintains a finger shape in the duct as it propagates toward the vent.
The flame has a slight tensile deformation when passing through the
vent, as shown in Figure 6(a(2)). As the Pbur increases,
pressure waves inhibiting the flame propagation are emitted from the
vent side,^47^ and the flame front gradually
compresses and deforms in Figure 6(b1). When the vent is opened, the effect of the pressure
gradient near the vent on the flame is more significant. When the Pbur reaches 100 kPa, the degree of compression
deformation of the flame front increases, which causes the flame to
lag in the propagation position in Figure 8a. In summary, when Pbur increases, the internal flame will be compressed and deformed
by the inhibition of the end wall. However, it is worth noting that
the higher the Pbur, the more distorted
the flame becomes as it passes through the port due to the pressure
gradient around the vent. As a result, the flame may be irregularly
ejected from the vent.^48^ The flame released
from the vent will propagate along the axis and perpendicular to the
axis direction and contact with the unburned gas mixture sprayed out
of the duct, which causes a second explosion, triggers the formation
of a mushroom-shaped flame cloud, and drives the flame and gas clouds
to propagate outward. The distance between the flame and the leading
unburned gas front gradually decreases during this process. The Pbur cannot significantly affect the flame shape
at the end of the external explosion, which typically takes on a mushroom
cloud shape, as shown in Figure 6.
Figure 6 Flame shape and combustible gas mixture profile under different vent pressure. (The yellow part is the flame front, and the blue part is the combustible gas.)
Figure 8 Position of flame front and unburned gas front under different vent pressures and vent size.
The flame first develops in a spherical shape after ignition. As the spherical flame comes into touch with the surrounding wall, the flame that touches the wall is extinguished, and it transforms into a finger flame and continue to propagate forward.^46^ The vent size has a significant impact on the evolution of the flame and unburned cloud compared to the vent pressure. As the vent size is reduced by 50%, the combustible gas continues to expand after ejecting from the duct, and its front forms a sphere-like shape in Figure 7(b(1)). The volume of combustible gas outside the duct increases gradually driven by the internal flame, and this change is more obvious in the axis direction. When the flame spreads near the vent, the flame is compressed due to the influence of the reflected waves from the end wall of the vent. Compared with the condition of the vent fully opened, the flame can only propagate the duct through a smaller vent, resulting in a more slender flame shape when the flame just ejects the duct in Figure 7(b(2)). With the continuous expansion of the flame in the external space and the increase in its propagation range, the enrolling effect of the vortex region formed by the flame and external atmosphere on the flame is enhanced, making the flame develop in all directions and eventually form a flame front with the mushroom cloud shape, as shown in Figure 7(b(3)). When the vent size is reduced by 90%, the suppression effect of the waves reflected from the vent side causes the flame front in the tube to become concave, which decreases the flame speed, as shown in Figure 7(a(1)). This phenomenon also results in the flame surface propagation position lagging behind the other two conditions for a while, as shown in Figure 8b. When the combustible gas is ejected from the duct through a smaller vent, a jet form is formed in the external space, and the propagation range on both sides of the axis is significantly reduced. The flame passes through the vent with a large tensile deformation and forms an elongated jet flame pattern in the external space, as shown in Figure 7(a(3)). Compared with the other two vent size conditions, the external flame range in the radial direction is significantly reduced. In addition, it takes longer for the external flame to catch up with the combustible gas front due to the late time of flame ejection from the duct.
Figure 7 Flame shape and combustible gas mixture profile under different vent sizes. (The yellow part is the flame front, and the blue part is the combustible gas.)
Progress variable c = 0.5 is taken
as the position
of flame front, and the flame propagation speed at different moments
is extracted for analysis. The flame speed in the duct increases when
it spreads at an early stage. However, when the vent is opened at
60 kPa, the flame propagation is inhibited due to the pressure waves
reflected from the duct end. As a result, the flame undergoes compression
and deformation, causing a decrease in surface area and a slower flame
propagation speed compared to the Pbur of 10 kPa. When the Pbur is increased
to 100 kPa, the end wall reflection wave inhibits flame propagation
for a more extended period time,^47^ which
decreases flame speed more in Figure 9a. The inhibition of reflected waves on the flame gradually
disappears after opening the vent. The pressure gradient near the
vent drives the flame forward, and the propagation speed is higher
passing the vent when the pressure gradient is more significant. The
peak flame propagation speeds under three Pbur are 607, 536, and 322 m/s. The flame spreads the outer space propagation
stage after ejecting the vent, and the flame cloud’s volume,
temperature, and speed during the propagation process decrease. As Pbur increases, the combustible gas is sprayed
into the external space with a delay. The volume of the combustible
gas above the flammable limit gradually decreases due to external
reactions, and its propagation speed first increases and then decreases.
The peak propagation speed of the gas cloud is more significant with
higher Pbur. Figure 9c,d shows the changes in flame front and
combustible gas mixture velocity over time at different Kv. The difference in flame front propagation velocity
under three Kv is relatively small in
2 ms after the vent is opened. When the flame propagates to the middle
and back sections of the duct, the suppression effect of the waves
from vent gradually increases. As a result, the flame speed reaches
its peak and then decreases when the Kv are 5.8 and 29.2. However, when passing through the vent the flame
and combustible gas mixture experience a more significant pressure
gradient, resulting in more significant tensile deformation and a
higher peak propagation velocity^49^ of 322,
669, and 913 m/s under three Kv.
Figure 9 Location and speed of flame and combustible gas mixture.
Figure 10 shows
the superposition of the flame and the streamlines for different Pbur conditions. The streamlines of the internal
flow field are parallel to the axis and point to the far field. As
the combustible mixture is released from the duct, it disrupts the
flow field in the surrounding area, creating a vortex region near
the vent. This vortex is formed as the unburned gas mixture coils
and draws in external space, as illustrated in Figure 10(a(1)). When the flame reaches the vent,
the vortex becomes more apparent on both sides of the axis near the
vent outside the duct, as shown in Figure 10(a(2)). Once the flame propagates outside
the duct, it forms a mushroom cloud around the vent due to the vortex
area. The flow field changes are similar inside and outside the duct
under different Pbur conditions, which
are presented that the streamlines are parallel to the axial direction
in the duct, the combustible gas mixtures, and the flame cloud outside
the duct swirl suction atmosphere to form the vortex area.
Figure 10 Streamline diagram at different vent pressures (the top image is a flame-streamline image of the internal space of the duct, and the bottom image is a flame-streamline image of the external space of the duct).
Figure 11 displays
the streamlines of the flow field for various Kv. The internal flow line is parallel to the axial direction
as the flame propagates inside the duct as the vent coefficient is
full opening. The combustible gas mixture is expelled from the duct
to form a vortex in the external space. The vortex area contains the
flame and combustible gas mixture, driven in the far field direction.
When the Kv is increased to 5.8, the streamlines
inside the size remain parallel to the axial direction in early explosion
stage. However, as the flame propagates outside the duct, the influence
of the pressure wave reflected from both ends and fluid backflow cause
the streamlines in the duct to develop in different directions in Figure 11(b(3)). When the
flame is expelled from the duct, new cyclonic flow zones emerge in
the external flame cloud, resulting in a more complex flow field distribution.
Increased Kv to 29.2 enhances the impact
of the reflected pressure waves, forming multiple swirl zones in the
duct. The swirl zone located at the front duct caused the flame front
to become concave. When the flame is ejected from the duct as a jet,
multiple swirl zones are formed in the outflow field in Figure 11c, which leads
to a more complex distribution of the flow field in the internal and
external spaces.
Figure 11 Streamline diagram at different vent coefficients (K
v) (the top image is a flame-streamline image of the internal space of the duct, and the bottom image is a flame-streamline image of the external space of the duct).
Turbulence intensity is a crucial parameter that
reflects the irregularity
and turbulence of the flow field. The streamline diagram analysis
shows that the internal space of the duct is associated with low turbulence
intensity, whereas the external flow field has a higher turbulence
intensity in the area surrounding the vent. The presence of airflow
vortices on both sides of the vent contributes to the flow field’s
increased turbulence. Figure 12a shows the cloud diagram of the moment of peak turbulence
intensity at different Pbur. The turbulence
increases gradually when the flame is expelled into the outer space.
When the Pbur are 10, 60, and 100 kPa,
and the peak turbulence intensities are 35, 51, and 63. The peak turbulence
intensity occurs when the flame is ejected from the duct. The airflow
velocity near the vent reaches its highest due to a significant pressure
gradient that accelerates the airflow. The pressure gradient increases
with the Pbur, which leads to a greater
degree of fluid acceleration, resulting in peak velocities of 420,
580, and 720 m/s under the three Pbur conditions,
respectively. Figure 12b shows the cloud diagram indicating the moment of peak turbulence
intensity for different Kv. The turbulence
intensity reaches its peak during the external explosion, which occurs
in the external space under different Kv. Reducing the venting height increases turbulence in the external
space. The peak turbulence intensity corresponds to the three Kv are 35, 68, and 136. The peak airflow speed
of the fluid also significantly increases with the reduction of vent
size, peak velocities in the three Kv are
420, 640, and 1069 m/s. Therefore, reducing the vent size results
in a more significant increase in the velocity amplitude and turbulence
intensity, which increases the external explosion risk. The peak volume
and mass flow rate depend on both the explosion venting release rate
and the expansion rate of the combustion, and it increases to peak
then decreases. The Pbur significantly
affects the peak vent flow rate and time to reach the peak vent flow
rate. Increasing the Pbur results in a
more significant peak mass and volume vent flow rate, the moment at
which the peak mass flow rate and volume flow rate are also reached
is delayed in Figure 12e. As Kv increases, the peak volume flow
rate and mass flow rate also decrease, and the delay in reaching the
peak flow rate indicates that reducing the vent size is not beneficial
for hydrogen explosion venting.
Figure 12 Turbulent intensity, velocity amplitude, and venting rate under different vent pressure (P
bur) and vent coefficients (Kv).
This research is funded by the National Key R&D Program of China, grant number 2023YFB4301701.
The original contributions presented in the study are included in the article.
The authors declare no competing financial interest.
The original contributions presented in the study are included in the article.