Thermal Conducting Geometric Inversion Method Based On The Third Boundary Condition

In engineering practice,sometimes,the shape of a boundary of a test piece or the shape of an internal defect cannot be measured by means of direct geometric measurement and needs to be obtained indirectly through other measurements.In this thesis,the heat transfer mechanism of the system is studied,the heat transfer differential equation is established and then boundary shape of the internal or invisible edge is calculated by the inverse problem calculation,which is a typical inverse problem of heat conduction.This disertition starts from the basic heat transfer mechanism and studies the mathematical model abstracted from practical problems for the steady-state heat transfer system under the third boundary conditions.In the study of positive problems,the finite volume method was chosen.According to the basic idea of the finite volume method,the thermal conduction differential equations in the three-dimensional Cartesian coordinate system are discretized,and the temperature is solved by using the linear chase algorithm.Through the calculation of a large number of transformation parameters,the influence of various factors on boundary recognition in practical engineering is studied.Based on the calculation results and mathematical models,an experimental platform was built.This paper studies the application of L-M algorithm and conjugate gradient method,which are commonly used in parameter optimization,in the inverse heat conduction problem of boundary shape.For the specific application scenario,the iterative formulas and search targets of the two algorithms are deduced.On the basis of the principle of L-M algorithm and conjugate gradient algorithm,the algorithm implementation flow is designed.According to the flow design program,the influence of different parameters on the two algorithms is calculated.For L-M algorithm,the influence of different parameters describing the boundary on the calculation accuracy of the algorithm is calculated.It is found that the algorithm has superior performance when the initial conditions are assumed containing some errors and the material thermal conductivity is relatively large.However,when the number of parameters describing the defect or boundary shape increases,the accuracy of the inversion calculation results will be greatly reduced.Therefore,the L-M algorithm is only suitable for the identification of simple boundary shapes.For the more versatile conjugate gradient method,various parameters are calculated.The results show that the conjugate gradient method can overcome the ill-posedness caused by the inverse problem and obtain a more accurate numerical solution.It is very sensitive to temperature measurement errors and requires the selection of suitable materials and temperature measuring instruments in practical engineering applications.For the experimental platform built in this paper,the temperature field was measured using an infrared camera.For this model,using the finite volume method,the positive problem is calculated under the experimentally given parameter conditions,and compared with the instrument measurement results to analyze the source of temperature error.Further,according to the temperature field measurement data and the positive problem calculation results,the back-calculation of the boundary shape is performed using the L-M algorithm respectively,and the practical significance of the algorithm is studied.The calculation results show that the results of the infrared camera measurement have a certain deviation from the calculation results.Using the inversion algorithm to calculate,we can effectively calculate the geometric boundary shape parameters,and prove the effectiveness of the L-M algorithm.