Computational Fluid Dynamics Simulation for Combustion Gas Leak of Solid Propellant

FU Xiao-long, Andreas Kroll, XU Fei, ZHANG Guo-fang, SHAO Chong-bin, Johannes Rangel, FAN Xue-zhong

(1. Xi′an Modern Chemistry Research Institute, Xi′an 710065, China；2. University of Kassel, Kassel D-34125, Germany；3. School of Chemistry & Chemical Engineering, Shaanxi Normal University,Xi′an 710062, China )

Introduction

Computational fluid dynamics (CFD) calculations are being used more and more to perform quantitative risk assessments in recent years, especially in combustion and explosion[1-2]. These tools provide the possibility to directly model with the physics of phenomena that are relevant to process safety such as combustion gas and explosion[3].

Combustion gas leaks are serious threats to human safety and equipment reliability, therefore considerable effort has been invested over the last few decades in designing combustion gas leak detection techniques[4-5].

Generally, combustion gases which are produced by propellant and explosive are including methane, nitrogen oxides and carbon oxides, etc[6]. Among these chemicals, methane is a typical gas. And it is considered as the research object in this paper. The methane leak is simulated by CFD simulation at different parameters. The innovation point of this paper is that the idea of the design for the test bench is based on the results of the CFD simulation and the simulation can be also contrasted with the detection of the gas camera. Meanwhile, the results of the simulation can be used to design the test bench for the gas model of propellant combustion.

1　Computational model

The standard turbulence generation (k)- turbulence dissipation (ε) model is often used to calculate the viscosity of light gases (methane, hydrogen, etc). The model[7]is modified to include the effects of buoyancy and the stability condition of the atmosphere by means of Richardson number, the non-dimensional parameter characterizing the stability of the atmosphere in terms of temperature, defined as:

(1)

whereRiis Richardson number;gis the gravitational acceleration (9.8m/s2);Tis the temperature(K);θis the potential temperature (K);ρis the total mass density;Gis the turbulence production rate by shear.

The equations forkandεare given below:

(2)

whereσεis the dimensionless turbulence model constant;Kis the turbulent kinetic energy per unit mass (m2/s2);C1andC2is thek-εturbulence model constants;CSis the turbulence production factor.

The turbulent viscosity (νt) is given by:

νt=CEk2/ε

(3)

From equations (1) to (3), the turbulent viscosity can be calculated.

The classical Gaussian model plume is a steady-state model that requires a continuous release of contaminant[8]. The ensemble average (i.e. probabilistic) plume shape is approximated by time averages sufficient to smooth the effects of plume meandering[9]. The equation for the Gaussian plume is a function only of the mean wind speed (assumed constant) and the crosswind and vertical standard deviations (σy(x) andσz(x)). Source strength (Q) is the mass of released material per unit time. The time averaged wind speed,v, is uniform everywhere. The contaminant concentration[10],C(x,y,z), is given by:

(4)

whereσyis the standard deviation ofC(x,y,z) in the cross-wind direction andσzis the standard deviation ofCin the vertical direction. The z-dependent terms model the trapping effect of the ground by proposing a mirror source at distancehsbeneath the ground.

According to Eq. (4), the concentration of light gas can be calculated.

2　Geometry and release scenarios

2.1　Geometry

The geometry of the simulation is based on the real condition of test bench for 1.2m ×1.2m×1.2m (length×width×height ) as shown in Figure. 1 and Figure 2. Figure 2 shows that the coordinate of the section of the gas chamber which is the section for the middle of the gas chamber from the front view as shown in Figure 1. And the coordinate of central of wind-in is (0,0).

2.2　Mesh of the 2D and 3D model

The mesh of the gas box is shown in Fig.3.

3　Results and discussion

In order to design the test bench of the gas leak, the influences of different parameters for the gas chamber are studied by CFD simulation.

3.1　The suitable size of gas chamber

The different sizes of the gas chamber are studied by simulation, and the parameters of gas chamber are listed in Table 1.

Table 1　The parameters of the simulation at different sizes of gas chamber

The concentration of methane leak at different sizes of gas chamber is shown in Fig. 4, it can be seen that when the gas chamber is small than 300mm2, there will be existence the phenomenon of backflow. This will make the gas flow of methane distortion. The suitable size of the gas chamber should be bigger than 300mm2. However the suitable size also depends on the different conditions of the equipment inside the box. The simulation only discusses about the same parameters which is generally used in the calculation.

3.2　The influence of fan-sizing for gas leak

The influence of fan-sizing for gas leak is studied by simulation. The position of the fan is in the middle of the box, and the relevant parameters are listed in Table 2.The mass fraction of methane leak is shown in Figures 5, 6 and Table 3.

Table 2　The parameters of the simulation at different fan-sizing

Table 3　The mass fraction of methane leak at coordinate (0, 0.6) for fan-sizing

CoordinateMassfraction(CH4)/%50mm100mm300mm600mm(0，0．6)0．056530．031220．011220．00122

As shown in Figures. 5 and 6, the mass fraction of methane leak in the central of the chamber is lower when the fan sizing is larger. Because there will be more air blow in the chamber to make the gas thinner than that in the chamber with smaller fun sizing.

3.3　The influence of temperature

The influence of temperature of the gas is studied by simulation and relevant parameters are listed in Table 4.

Table 4　The parameters of the simulation at different temperature

Figures 7 and 8 show the mass fraction of methane leak at different temperatures.

The influence of temperature is not obvious during the simulation of the gas leak. The main influence of temperature for methane is that when the temperature increased, the density of methane will be changed. According to the equationpV=nRT, the density of methane is 0.71kg/m3at 0℃. And the density of methane is 0.69kg/m3at 10℃. The change in density is very small at different temperatures. On the other hand, the temperature of the atmosphere is 20℃. When the gas flows into the chamber, there will have heat exchange between the methane and the atmosphere. That means the temperature of methane will be the same with that of the atmosphere. For these reasons, the influence of temperature is not obvious.

3.4　The influence of the geometry of flow disturbance objects

The geometry of flow disturbance objects is a sphere and a cubic in the center of the box. The relevant parameters are listed in Table 5.

Table 5　The parameters of the simulation for 3D model of the gas leak

Figures 9 and 10 are the 3D models of methane leak with cubic and sphere disturbance object, respectively.

The gas shapes will be different because of the different geometries of flow disturbance objects. Under the disturbance object, the gas shape is almost the same of the two geometries. When the gas is blocked by different shape object, the gas will rise along the edge of the object. And the gas shape will be influenced obviously by the object.

3.5　The design of the test bench

According to the results of the simulation, the test bench is designed as Fig.11. The parameters of the test bench are listed in Table 6.

Table 6　The parameters of the test bench

Based on the simulation and design of the gas leak situation, the test bench can be built. The test bench can use different gas of the combustion gas products. And the combustion gas products can be tested by IR-remote detection instrument which will be introduced in details in next paper.

4　Conclusions

A number of CFD simulations of gas leaks were performed as predictions of experiments, and the experiments will be built by Department of Measurement and Control Engineering in University of Kassel. Based on the comparison between observations and predictions, the following conclusions can be made:

(1) The prediction of the situations of methane leaks can be used to design the test bench. The combustion gas products can be tested by IR-remote detection instrument in this test bench.

(2) According to the simulation results, the following conditions of the experiment are recommended. The suitable size of the gas chamber should be bigger than 2.7×105mm3. The gas velocity should be higher than 0.5m/s. The suitable wind speed should be 0.2m/s. The suitable nozzle diameter should be from 0.5mm to 1.0mm. The suitable sizing of fan is around 100mm. The position which is in the middle of the box is recommended.

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