Analysis of the inhomogeneous LPG-air flow field in a tube containing mixed obstructions

Based on numerical simulation, this paper further investigates the flow field structure near the obstacle during the premixed gas deflagration. In the deflagration flow field, the pressure gradient variation and vortex structure intensity in the upper surface region of the obstacle are larger, indicating that the pressure gradient has a stronger effect on the vortex structure. The changes in density gradients and pressure gradients induced by the combined rectangular, flat barrier configuration will be more pronounced than in the model with only flat barriers. This change in turn acts back on the combustion field, which in turn has a strong perturbative effect on the flame.


Introduction
With the widespread use of liquefied petroleum gas (LPG) in various fields, the prevention of flammable and explosive gas explosion disasters is particularly important.In general, there are various obstacles of different shapes and sizes in the pipelines of mines and shafts [1] .When the flame bypasses such an obstacle, due to the interaction of the flame with the obstacle [2] , the shape of the flame, the speed of propagation, the rate of combustion of combustible gases, the explosion overpressure, and the flow field around the flame through the obstacle all show significant changes [3] .In particular, the presence of obstacles will change the complexity of the geometric layout of the explosion tube, which will largely disrupt the flow field after the explosion [4] .Distortion happens due to Rayleigh-Taylor instability of the flame propagating in a semi-closed barrier tube [5] .Similarly, the presence of the R-T instability causes a large change in the gradient of the flow field inside the tube, which in turn complicates the flow field characteristics.The Kelvin-Helmholtz instability from the relative velocity of the fluid has a more significant effect on the flame front.No matter what kind of instability is described, it can reflect the change of pressure and density gradient in the pipeline, resulting in significant changes in flow fields such as flow and combustion.It is also such gradient changes that eventually lead to the emergence of vortex structures of varying intensity in the tube [6] , and the intensity distribution of vortex structures in the tube and the obstruction rate of the obstacle show a positive correlation [7] , and eventually also change the flame structure [8] .At present, on the obstacles, flame, combustible gas combustion rate, and the interrelationship of explosion overpressure, people have conducted a lot of research.Although there is much research on the mechanism of non-uniform blasting at present, the specific problems such as nonuniform blasting flow in blocked pipelines are not studied deeply.To this end, this paper mainly studied the flow field structure and vortex near the obstacle in the process of premixed gas deflagration in the tube through numerical simulation.The results of the study of various types of pipe corridors and other narrow space gas explosion prevention and management provide a theoretical basis for the actual production and life of the LPG leak explosion accidents regarding the significance.

Numerical simulation
Guo et al. [9] analyzed the dynamic overpressure and the coupling relationship between flame structure, density, and flame propagation velocity, but details such as the explosion flow field of premixed gas in the pipe under non-uniformity have not been studied in depth.In this paper, the flow field structure and vortices near the obstacle during the premixed gas detonation in the tube are further studied by numerical simulation.

Figure 1. Schematic diagram of the explosion pipeline
We build the pipe model as shown in the figure, to meet the needs of the calculation.The software ANSYSICEM2021R2 was used to structure the meshing of the calculation area in 3 mm units.

Numerical details
The numerical simulation is carried out by Fluent software, the coupling calculation of pressure and velocity is realized by the SIMPLE method, and the flow field is discrete by the second-order upwind method and second-order central difference method [10] .Propane was used in the simulation.The viscosity is calculated by Sutherland's law [11] with the pipe outlet set as the pressure boundary condition.The initial temperature is 300 Kelvin, and everything else is 0. The patch function is used to ignite the detonation by setting a hemispherical area with a radius of 5 mm [12] in the center of the closed end on the right side of the pipe and setting the reaction process of the area to 1.In the process of solving, the time step is set to 1x10 -6 seconds [10] , and the maximum number of iterations of each step is set to 40 times to ensure its convergence.

The effect of density gradient and pressure gradient (oblique pressure effect) on the vortex volume
From Figure 2(a), it can be seen that at 20 ms, a vortex appears on the lower right side of the first obstacle, resulting in a "C-shaped" return flow above the first obstacle.Second, vortexes also appear above the three obstacles, which is because, in the process of deflagration, the flame will drive up the temperature resulting in high pressure, which generates vortexes.Unlike obstacle 0, the model with rectangular obstacles has a more pronounced change in density gradient and pressure gradient, which produces stronger vortex volumes.This phenomenon is most evident in Figure 2(b).As the flame passes through the rectangular barrier and the first flat barrier, it can be seen that the flow field near the second and third barriers is greatly disturbed.As the flame propagates, the abnormal disturbance of the entire model flow field due to the interference of the rectangular obstacle leads to a more fragmented flame.This is mainly due to the premixed gas forming a high-pressure region during the combustion process and coupling with the vortex structure [12] .Figure 2. Effect of density gradient and pressure gradient on vortex volume

Relationship between pressure field, velocity field, and flame propagation
Figure 3 shows the flow field diagram of the pressure field, velocity field, and flame front coupling after the explosion of premixed combustible gas.Due to the disturbance of the rectangular obstacle, the pressure at 24 ms in Figure 3(b) is much larger than that at the same moment in Figure 3(a), and the flame propagates faster and the vortex to the right of the obstacle is more turbulent, especially to the right of the second flat obstacle.At 24 ms in Figure 3(c), there is a distinct eddy between the rectangular obstacle and the second slab, but it is not observed in Figure 3(b).This is because the rectangular obstacle in Figure 3(b) is closer to the ignition source, the initial flame propagation is slower, and the vortex is not obvious.This is because the rectangular obstacle in Figure 3(b) is closer to the ignition source, the initial flame propagation is slower, and the vortex is not obvious.In Figure 3(d), it can be observed that a more pronounced vortex appears at both ends of the rectangular barrier at 24 ms.In summary, regardless of the model, it can be demonstrated that the presence of an obstacle is a necessary condition for the appearance of a vortex.

4.Conclusion
Through numerical calculation, the flow structure and vortex generation are analyzed in detail.Further, we reduce the impact of oil and gas explosions caused by barrier disturbances.Through the research, we come to the following conclusions: (1) In the combustion process, the generation and distribution of the vortex structure are closely related to the oblique pressure moment caused by the pressure gradient.In addition, we also find that the pressure gradient changes more significantly near the obstacle surface, and the strength of the vortex structure in this region is relatively high, indicating that the oblique pressure gradient has a greater influence on the vortex structure than the density gradient.
(2) Compared with the model with only flat obstacles, under mixed barrier conditions, the density and pressure gradient in the flow field will be more significant.In particular, the pressure gradient in obstacle # 1 (FIGURE 2(b)) has a smaller change, which in turn acts on the combustion field, thus generating a stronger disturbance to the propagating flame, and ultimately resulting in a more obvious distortion of the flame.