Inverse Heat Conduction Problem Of Undetermined Boundary Position

The inverse heat conduction problem of undetermined boundary position is a type of research that cannot directly measure the shape of the boundary or internal defects due to objective reasons.The basic research method is indirectly calculated by combining other measurable information with known boundary conditions.Based on the prediction of ironmaking blast furnace hearth erosion,this paper explores a numerical solution to the inverse heat conduction inversion of the pending hearth boundary position from the measured temperature data of the hearth,which provides a reference for the safe operation of the hightemperature reaction furnace.Based on the basic law of heat conduction,the physical model of the inverse heat conduction problem of undetermined boundary position is established,and the mathematical model under steady state and unsteady heat conduction conditions is given.Under the assumption that the boundary shape is a known shape such as a sine curve,a single zigzag line,an ellipse,and based on the temperature measurement point simulation data generated by the solution of the positive problem,the Powell method is used to determine the boundary shape under steady and unsteady conditions.The inversion calculation was carried out,and the influences of temperature measurement error,temperature measurement point position,initial value,and number of temperature measurement points on the inversion results were obtained.Numerical inversion results show that Powell method has obvious advantages in terms of accuracy when processing measurement point information with a large amount of data.In view of the possible phase change of the hearth material during the hearth erosion process,a mathematical model of the inverse heat conduction problem of undetermined boundary position is established by using the enthalpy method which analyze the Stefan problem.And a finite volume method(FVM)is proposed.FVM is a solution algorithm that discretizes differential equations and definite solution conditions.this paper also uses the Powell method to inverse the boundary shape,and compiles a corresponding numerical solution program.The calculation results show that Powell method can obtain more accurate boundary position inversion results under heat conduction with phase change.In order to further verify the accuracy of the algorithm in the actual measurement environment,an experimental device for the inverse heat conduction problem of undetermined boundary position is designed and built.Refined paraffin is used to simulate furnace hearth materials.Embedded temperature sensors are used to perform multi-point simultaneous temperature measurement on the furnace wall.Heating and melting paraffin wax is used to simulate furnace hearth erosion.Based on the measured temperature data,the proposed algorithm is used to inverse the boundary position.Actual boundary positions are compared.The results show that under the experimental conditions,the calculation results are consistent with the actual position.