Forward And Inverse Study Of Concealed Spontaneous Fire Position In Coal Mine

Coal mine spontaneous combustion is one of coal mine five nature disasters.The position determination of coal mine spontaneous combustion concealed fire is the key to combustion question. In view of the characteristics of coal mine concealed fire, sums up the determination question of fire position for determining the unknown source term of heat conductivity equation.Under the perfect condition, simplifies the three-dimensional model of coal mine heat conduction as the two-dimensional model, establishes the heat conductivity equation, the initial condition and the boundary condition. Supposes fire as line fire, uses the discrete regularization method to solve the inversion problem of determining the unknown source term in one-dimensional heat conductivity. Based on this, applies this method into the inversion of coal mine concealed fire.Result indicates: this method can inverse accurately the characteristic of fire, and along with the enhancement of discretization degree, the separate solution approaches the real solution gradually. Supposes fire as point source, applies the finite difference into one-dimensional and two-dimensional unsteady heat conduction of the model, has simulated the dynamic process of heat conduction in coal mine. Based on this, takes the temperature of part points when t=12d as the supplemental condition to inverse.Gives the supplemental condition different perturbation to conduct the research. In the invariablesituation of step of x direction, y direction and the time axis, increases the perturbation,when the perturbation is 5%, the distance between inversion fire position and actual fire position is 0.085m,this erroneous level can be accepted; When the perturbation is 10%, the error increases, the distance between inversion fire position and actual fire position is 0.199m, this erroneous level can be accepted reluctantly; When the perturbation is 20%, the error continues to increase, the distance between inversion fire position and actual fire position is 0.37m, this erroneous level cannot be accepted. This has explained that when disturb is smaller than or equal to 10% inversion result is accurate. Finally, carrying on the comparison of the discrete regularization method and the finite difference, result indicates: these two methods all can inverse fire, but use scope is different. The discrete regularization method is more accurate than the finite difference.But the discrete regularization method can be used only when analytic solution of heat conductivity equation is known.Moreover it is affected by the regular parameter.Therefore, the discrete regularization method only can be applied in the simple situation relatively. The finite difference method can be used conveniently in reality. But it is affected by separate degree and perturbation of supplemental condition.When the separate degree is higher, perturbation is smaller, the result is more precise. When perturbation is big, it is very difficult to obtain accurate result by applying finite difference. Therefore, when mine condition is complex, the perturbation is small, the finite difference method can be choosed. In a word, it is an efficient path to determine fire point position by inversing source of heat conduction.It has high theory and practical application value for the research of coal mine fire prevention and extinguishing.