Study on concentration and turbulence of solid-liquid FAE in dispersal process

Ji-chen Chen,Xin M,Qiu-ju M

aChina Zhongyuan Engineering Corporation,Beijing 100191,China

bChina Ordnance Society,Beijing 100089,China

cCollege of Resources&Safety Engineering,China University of Mining&Technology(Beijing),Beijing 100083,China

Keywords:Solid-liquid mixed fuel Concentration Turbulence intensity Numerical simulation

A B S T R A C T This paper describes numerical simulation on dispersion of the solid-liquid mixed fuel driven by explosion load.A model used in numerical calculation for dispersion of solid-liquid mixed fuel was established in this study.The concentration and turbulent intensity in the multiphase cloud of the solidliquid mixed fuel were obtained by numerical simulation.It was found that the fuel concentration tended to be 0.15 kg/m3,the turbulence intensity tended to be 7 in 90 ms.The numerical results agree with those measured in the experiment.

1.Introduction

The dispersion of fuel air explosive(FAE)is the premise condition of detonation.A mixture of solid and liquid fuel is impacted by explosion drive load,which depends on the concentration and the turbulent intensity of the solid-liquid mixed fuel and affects the detonation power directly.

There have been a lot of researches about the dispersion of FAE fuel and the regularity of cloud state at home and abroad[1-4].Zhang[5,6]got the dispersal range,movement and regularity of fuel using the high speed camera.Ding[7]analyzed the initial period of formation and the development process of the fuel air cloud,and the whole process of fuel dispersion is predicted by numerical simulation.The energy density of solid-liquid mixed fuel is high and it has an advantage on the power.The optimization of the dispersion process relies on the experiment at present.Compared with the numerical simulation,it costs much,has poor security,and is difficult to get cloud concentration distribution and turbulence intensity.Therefore,exploring the numerical methods to simulate the dispersion process of solid-liquid mixed fuel is of great significance for the new FAE weapons.

This article explores the numerical simulation of the solid-liquid mixed fuel dispersion based on experiments.The dispersion of solid-liquid mixed fuel numerical calculation model was established.The physical process of solid-liquid mixed fuel dispersion was simulated,and the concentration and the turbulent intensity of the solid-liquid mixed fuel were obtained.

2.Calculation model

2.1.Control equations of gas phase flow

Mass conservation equation:

Whereρmis the density of gas(kg/m3),vmis the velocity vector offluid,and▽is the Laplacian operator.

Momentum equation:

Where,n is the number of phase,F is the body force,μmis the mixed viscosity,and vdr，kis the drift velocity of k phase.

Energy conservation equation:

Where,keffis the effective thermal conductivity,SEcontains the whole volumetric heat source.

Second phase(epoxy propane gas)volume fraction equation:

2.2.Evaporation phase transformation model

2.3.Discrete phase(particle phase)control equation

Through discrete phase model and stokes tracking(random trajectory)trajectory model,the differential equation of the forces acted on particles was solved under the Lagrangian coordinates to obtain the particle track of the dust.In this two model,the particle for the generation or divergent of continuous phase turbulence have direct impact.Based on the classical Newton's second law,force equilibrium equation of dust particle phase is:

Where,mpis∑ the mass of particles(mg),upis the velocity of particles(m/s),F is the resultant force acted on particles(N),Fdis the resistance acted on particles(N),Fgis the gravity of particles(N),Ffis the buoyancy acted on particles(N),Fxis the other forces acted on particles,including additional weight force,Magnus lift,thermophoresis force,Saffman lift,brown force,etc.which were neglected in this work(N).

Where,Cdis the drag coefficient,Cφis the dynamic shape factor.According to the experiment data,it was taken as 1,Apis the windward area of particles.

Drag coefficient Cdis related to the Reynolds number of particles:

Where,Repis the Reynolds number,a1,a2,and a3are the constant in certain range of Reynolds numbers for spherical particle,and dpis the particle diameter.

Besides resistance,gravity and buoyancy,the track of particles is affected by turbulence.The interaction between turbulence and particles can be calculated using the random orbit model.The velocity u is equal to the sum of the average valueand the pulsating value u′（t）.

The pulsating velocity is expressed as following formula:

Whereξis a random number between-1 and 1,and particle trajectory in direction of x can be obtained:

2.4.Geometry

The FAE device is shown in Fig.1.1 is the shell,2 is the solidliquid mixed fuel and 3 is the center explosive charge.The mass of the mixed fuel is 13kg,the percentage between the mass of center explosive charge and those of mixed fuel is 2%and the thickness of upper and lower end cover of the shell is 10mm.The inlet boundary was set as pressure-inlet,and the outlet boundary is pressure-outlet(outlet pressure is 1 bar).Both the FAE device and the centerexplosive charge are column structures.The radius of the FAE device is 100 mm,and the height is 300 mm.The radius of the center explosive charge is 15mm.The center explosive charge is 2 m high from the ground.

The numerical simulation model is shown in Fig.2,and the model size is consistent with that in the experiment.All the computational domain yields 28238 grids with the minimum size of 5mm which can satisfy the requirement in calculation.

2.5.Parameters

The FAE fuel is mixed by aluminum powder and liquid epoxy propane.The density of aluminum particle and liquid epoxy propane are 2700 kg/m3and 830 kg/m3respectively,and the density of epoxy propane gas is 2.6kg/m3under the standard conditions.The boiling temperature of liquid epoxy propane is 307 k,and the evaporation enthalpy of liquid epoxy propane is 450 kJ/kg.The dispersion process of the solid-liquid mixed fuel was impacted by the explosion drive load and the gravity in open space.

3.Experiment

The FAE dispersion experiments under the action of center charge explosion were conducted in open space.To observe and analyze the process of fuel explosive dispersal,a high-speed motion analysis system was adopted.The development of the liquid-solid mixed cloud is shown in Fig.3.

In the experimental process of cloud detonation device scatters which was filmed by high-speed motion analysis system,it presents obvious radial motion and turbulence change in the fuel dispersal process.According to the phenomenon that the dispersal status of fuel changes with time in Fig.3,we can see the radius of fuel cloud increases monotonously with time and the radius of fuel cloud no longer has a significant growth after about 40 ms later,when the radial motion phase goes to the end.However,the turbulence is a process that the fuel does “local”rolling along the curve track,which makes the fuel disperse more uniform in vertical direction,and then the cloud has further extension.

4.Results and analysis

The dispersal process of solid-liquid fuels inside the detonation device in the open space were simulated using the numerical calculation method.By using the SIMPLE algorithm,the iterative time steps is 5×10-6s and the whole process of the dispersion continues 0.1s.The whole process of the dispersion of the solidliquid mixed fuel was obtained from numerical simulation,as shown in Fig.4.

From the results of numerical simulation,we can see that in thefirst 6 ms duration of action of the initial explosion driving pressure load,namely between 0 and 6 ms,the solid-liquid mixed fuel continues to accelerate diffusion,but in this phase,the realm of the solid-liquid mixed fuel cloud is small.Due to the constant air-drag force,the liquid epoxy propane fuel evaporated into gaseous epoxy propane,low-concentration epoxy propane gas always existed in outer fuel,and the solid aluminum powder particles begins to generate a phenomenon that the cyclic particles cloud spreads into dispersed particles micelle;After 6ms,under the combined action of gravity,inertia,and air resistance,the fuel dispersion rate reduces,and the solid particles began to sink into the liquid and gaseous epoxy propane,but in the meantime,the internal epoxy propane gas begins to intensify gasification,therefore in Fig.3,the internal liquid fuel concentrationwas lower than the concentration in the center.From 60 ms later,solid-liquid mixed fuel is basically uniform,ready for the secondary ignition.

6 points that are respectively 1,2,3,4,5,6 m away from the blasting source were selected to analyze the fuel concentration.Figs.5 and 6 respectively present the fuel concentration and the turbulent intensity versus time at different locations.Both the fuel concentration and the turbulent intensity experience an increase before a downward tendency.

As is seen in the curve chart of the concentration and the turbulent intensity,with the increasing of the distance from blasting source location,the peak value of the concentration and turbulent intensity decrease,and the farther the distance from the blasting source location,the longer time was needed to reach the peak of concentration and turbulence level.In the end,the fuel density tends to be 30 kg/m3,and the turbulence intensity tends to be 7.In 90 ms,the concentration of fuel in the six monitoring points are uniform on the whole,the turbulence intensity also tends to be stable,therefore,it is reasonable to choose 90 ms as the secondary ignition delay time in actual experiments.

From Figs.4 and 5,we can know that,in the place which is located 6 m from the blasting source,aluminum powder particles are very few,therefore,the concentration in 6m is low in Fig.5,which is less than 10 kg/m3,and is only effected by powder particles and air.Its turbulence intensity is also lower than the one in the solid-liquid mixed fuel.

5.Conclusions

The numerical calculation model of dispersal process of solidliquid mixed fuel is presented in this paper,the development of the solid-liquid mixed fuel,the radial velocity,the range of clouds and turbulent process are consistent with the experimental results,the concentration and turbulence intensity of the solid-liquid mixed fuel that we get from the numerical simulation,provided a theoretical basis for the secondary ignition.

Acknowledgments

This paper is supported by National Key R&D Program of China(No.2016YFC0801800)and the opening project of State Key Laboratory of Explosion Science and Technology(Beijing Institute ofTechnology)(No.KFJJ18-03M).