Calculation Of Gas Flow Pressure Loss Under Single Cycle Elementary Volume In Goaf And Fractal Law

The law of gas flow is critical for coal spontaneous combustion and inert gas fire-fighting.Therefore,the calculation of gas flow pressure loss in goaf is very important for fire prevention and control in goaf.However,On the one hand,the current research on the calculation of the pressure loss of the porous medium in the goaf relies on the numerical simulation which requires strong theoretical knowledge,and the engineering applicability is not strong,on the other hand,the existing traditional pressure drop calculation formula contains specific empirical coefficients,and the physical meaning is unclear and the universality is not strong.Therefore,this paper studies the law of gas flow pressure loss in the goaf in view of these two deficiencies.Firstly,in view of the complex spatial structure of the goaf,based on the sphere filling theory,a flow model of the porous medium in the goaf is established in this paper.There are eight large spheres with a diameter of d in the flow model,a small diameter sphere of(7)3-1(8)d diameter and six small diameter hemispheres of(7)3-1(8)d diameter are filled between the large spheres.According to the principle of single-period flow,the flow model of porous media in goaf is cut into single-cycle elementary volume.The Navier-Stocks equation is used to deduce the four-segment function expression of the pressure loss per unit length on the single-cycle elementary volume.Through the length ratio weighting method,the weighted summation of the four-segment function expression is used to obtain the pressure loss calculator on the single-cycle elementary volume in the goaf.The formula is a function of dynamic viscosity,density and initial velocity,and particle size.And the pressure loss is quadratic in relation to initial velocity.The results show that when the initial velocity is the same,the pressure loss per unit length decreases with the increase of aerodynamic viscosity,and the pressure loss decreases faster with the increase of the initial velocity.Further,in order to obtain a pressure loss calculation formula with clear physical meaning and strong universality,this paper abstracts the goaf into a capillary model and a fork bypass flow+pore-throat model to characterize the structural characteristics of the goaf.According to the transport theory of fractal porous media,the capillary model is used to calculate the viscous loss part,and the fork flow+pore throat model is used to calculate the inertial loss part,and the fractal analysis solution for the calculation of the pressure loss in the goaf is obtained.The fractal analysis of the pressure loss is not only related to the dynamic viscosity of the fluid,the density and the velocity of the fluid,but also the fractal dimension number D_fof pores,porosity,goaf pore size,fractal dimension number D_Tof flow tube bending degree,tortuosity.It is related to the internal structure parameters of the porous medium in the goaf,and each parameter has a clear physical meaning.The calculation formula reveals the influence mechanism of the pressure loss during the flow of the fluid in the goaf,and has wider applicability.Then,in order to improve the fractal analysis solution for the calculation of the pressure loss in the goaf,the flow resistance coefficient of the fluid passing through the pore throat model at low Reynolds number was simulated based on the FLUENT numerical simulation software.The simulation results show that the local resistance coefficient is affected by the Reynolds number and the sudden expansion ratio or the sudden contraction coefficient at low Reynolds number,and the local resistance coefficient is inversely proportional to the Reynolds number.Further,the correlation formula of the local resistance coefficient at low Reynolds number is obtained by data fitting.This paper provides a theoretical basis for the calculation of the fluid flow pressure loss in the goaf,which is of great significance to the fire prevention and control in the goaf.