Turbulence influence factor estimation of gasoline-air explosion in multi-branch tubes

To estimate the turbulence influence of the branch tubes on the rising rate of gasoline-air mixture explosion overpressure, turbulence factor α was introduced to modify the formula of the peak rise rate of explosion overpressure. Then, the experimental data of peak explosion overpressure and overpressure rise rate under the different numbers of branches were obtained. Finally, the experimental data and laminar flame velocity were put into the overpressure rise rate correction formula, and the turbulence influence factors under different branches were calculated. The results show that increasing the number of branches will improve the turbulence degree of the explosion process. When the number of branching pipes is 1, the turbulence impact factor is about 2.0 times that in the case of no branch tube, while when the number of branch tubes is more than 1, the turbulence impact factor fluctuates about 3.5 times.


Introduction
A combustible gas explosion is one of the common safety accidents, especially in the petrochemical industry.All kinds of combustible gas explosions often cause heavy casualties and huge property losses, thus causing widespread concern in society.Maximum explosion pressure, maximum pressure rise rate, and gas deflagration index KG are several commonly used parameters to evaluate the damaging force of various primary space gases and to improve the design ability of explosion-proof vessels or vents.However, these parameters are strongly influenced by the initial conditions [1][2][3][4][5][6].Particularly, Tan et al. [7] and Zhai et al. [8] pointed out that the initial turbulence level is greatly affected by the size and shape of the container.
Underground oil caverns, oil pipelines, natural gas pipelines, etc., have multi-branch structures, increasing the turbulence of gas flow in pipes and increasing the explosion overpressure when a gas explosion occurs.Because when the pipeline area changes rapidly (becomes larger or smaller), additional turbulence will be generated, and the turbulence of downstream flame flow will increase.In the process of a gas explosion, the propagation speed of flame will also increase rapidly, and a shock wave will be induced.
Due to the measurement difficulty of the turbulence level, the conclusions on the relationship between the explosive overpressure characteristics and the turbulence level obtained in the above literature are all qualitative descriptions, limiting the conclusions' engineering application.Therefore, the estimation of the turbulence factor in this paper is meaningful.

Modification of the formula for calculating the maximum overpressure rise rate.
According to the research conclusions of F. Cammarota et al. [9], the formula for calculating the maximum overpressure rise rate of combustible gas in a vertical cylindrical vessel is： is the maximum flame front area;  is the volume of the explosive vessel;  is laminar flame velocity;  is peak explosion pressure;  is initial pressure;  is the adiabatic gas index; is the peak rise rate.Equation (1) shows that the maximum overpressure rise rate is related to the shape and size of the container (i.e., AV and V), the laminar flame velocity, the peak overpressure, and the initial pressure.However, equation (1) does not consider the influence of turbulence level on the rate of overpressure rise.Therefore, it is necessary to modify the equation based on considering the effect of turbulence.Based on this, the turbulence factor is introduced to modify equation ( 1): So In Equation ( 3), ,  ,  , and (  ⁄ ) can be determined by experimental data.At the same time, the maximum flame front area  , laminar flame velocity  and gas adiabatic index  can only be obtained by theoretical calculation.Therefore, through Equation ( 3), the influence factors of turbulence in the gasoline-air explosion process of tubes with different multi-branch structures can be calculated.The relationship between the influence factors of turbulence and parameters such as the number and length of branch tubes can be further discussed.
3. Experimental data of overpressure peak and overpressure rise rate.An experimental system was built to obtain the overpressure peak and rise rate.The test bench is a square steel tube with a cross-section size of 0.1 m×0.1 m and a wall thickness of 10 mm.It consists of 6 different forms and length specifications: a straight pipe with a length of 0.5 m, a straight pipe with a length of 1m, a 90° bend pipe with a length of 1m, a main pipe with a branch of 0.5 m, a three-way pipe with a branch of 0.5 m, and a four-way pipe with a two-way of 1M.According to the experiment's needs, the square pipe of different specifications can be combined to build the experimental bench with different branch pipe numbers.Various sensors can be installed according to the requirements of the experiment.During the experiment, the total length of the pipe was kept at 6 m, and the number of branch pipes was changed from 1, 2, 3, to 4, respectively, as shown in Figure 1.

Laminar flame velocity and adiabatic gas index
Metghalhi and Kech [10] provided an equation for calculating the laminar flame propagation velocity of a fuel-air mixture: In Equation ( 5), ∅ the equivalent chemical ratio of combustible gas and ∅ and C2 can be determined by the type of combustible gas, as shown in Table 2.In this paper, No. 92 gasoline was selected in the experiment, and the volume concentration of gasoline-air was 1.2%.In the actual calculation, No. 92 gasoline was replaced by isooctane.

Turbulence factor estimation and discussion
By substituting the experimental data and theoretical calculation data into equation ( 3), the turbulence factors in different conditions can be calculated, and the calculation results are shown in Table 3.The number of branches 0 represents the working condition of a straight pipeline.The data in Table 2 plot Figure 2, It can be seen from Figure 2, the increase in the number of branches will improve the degree of turbulence in the explosion process in the tube.When the number of branches is 1, the impact factor of turbulence is 2.0 times that of a straight pipe; when the number of branches is more than 2, the impact factor of turbulence is more than 3 times that of a straight pipe.When the number of branches increases from 0 to 3, the turbulence impact factor increases with the number of branches, while when the number of branches exceeds 3, the turbulence impact factor decreases.That means the increase of branch tunnel number does not always increase flame velocity.Flame velocity will decrease if the branch tunnel number exceeds a certain value.
From the fluid dynamics perspective, when the number of branches increases from 0 to 3, the increase of turbulent kinetic energy further increases the explosion overpressure.When the number of branches is more than 3, due to the expansion of the inner wall surface of the pipe, the heat loss effect of the cold wall will exceed the impact of turbulence, and the impact of turbulence on the explosion overpressure will be weaker than other factors.It is the main internal reason for the decrease of turbulence influence factor when the number of branches is 4 in Figure 2.

Conclusions
According to the experimental data and some parameters from the theoretical calculation, turbulent impact factors in the process of gasoline-air explosion in the multi-branch pipes are estimated.The results show that when the number of branch pipes increases from 0 to 4, the turbulence impact factor is 53.93-201.45,and the increase in branch number does not always improve the turbulence impact factor.When the number of branches increases from 0 to 3, the turbulence impact factor increases with the number of branches, while when the number of branches exceeds 3, the turbulence impact factor decreases.
It should be pointed out that the turbulence factors calculated in this paper just are approximate estimations for the explosion experiments of the multi-branch tube.In reality, the explosion overpressure of gasoline-air mixture in complex structure pipes is influenced by many factors, such as fire heat release rate, the solid boundary of heat loss rate, etc., and the multi-branch is just one of the factors for the turbulence degrees.However, the research method and conclusion presented in this paper still have a certain reference value for studying the overpressure characteristics of gas explosions in a closed container.

1 .
Experimental field diagram of different branch numbers With the help of the above experimental devices, experiments of gasoline-air explosion under different branch numbers were carried out.The characteristic pressure data obtained are shown in

Figure 2 .
Figure 2. Scatter diagrams of turbulence factors under different numbers of branches

Table 1
[9]Peak values of overpressure and rise rate under different branch numbers of the bench.The maximum flame front area According to Cammarota et al.[9], the maximum flame front area  can be determined by analysis of the flame shape of the early explosion stage and can be approximately determined by the area of the front of the flame is the largest when it just contacts the side wall.Therefore the  under the condition of the experiments in this paper is:

Table 2 .
Values of   ,  2 , ∅   of different combustible gases Combustible gas

Table 3 .
Turbulence factors under different conditions Branch number