Study On The Reduced-Order Model And Parameters Identification For Transient Nonlinear Heat Conduction Problems Based On The Free Element Method

The design and optimization of thermal protection system(TPS)is a key science and technology to ensure the safety of the whole structure of aircraft and the normal operation of internal instruments.Therefore,fast and accurate acquisition of thermal parameters in extreme environments and development of efficient thermal parameter characterization or identification methods are important conditions to ensure the safe and stable flight of aircraft.At the same time,it is of great significance to the optimal design of thermal protection system.High temperature and high pressure environment will damage or fail most temperature sensors,in situ measurement is very difficult.In view of this,this thesis studies the parameter inversion problems based on the numerical calculation method,and uses the limited temperature measurement information in the low temperature region of the structure to identify the thermal parameters in the high temperature region.The solution scheme of heat transfer inverse problem based on gradient method is widely used and the theory is mature,but it is difficult to meet the requirement of real-time measurement due to the large amount of calculation and low efficiency,and it is limited to some extent in analysis.Therefore,in this thesis,a high-fidelity and high-efficiency low-dimensional data-driven thermal parameter identification method is developed by combining the surrogate model and order reduction idea.The feasibility of this idea is verified by theoretical analysis and numerical examples.In order to achieve rapid characterization of thermal parameters in extreme environments,three key technologies that need to be broken through are the numerical methods of nonlinear physical problems,forward efficient calculation of physical field and rapid identification of parameters.The research of this thesis is carried out from the following aspects:(1)Free element method for transient nonlinear heat transfer problems.The mathematical theoretical formula of the free element method for transient nonlinear heat transfer problem is derived and the implementation process is analyzed from the aspects of material nonlinearity,transient term,heat source term and anisotropy.In this process,a Cross-Line element collocation scheme is proposed to simplify the Lagrange element on the boundary.The Cross-Line element has fewer nodes,and it is proved theoretically that the calculation accuracy of the first derivative can be consistent with that of the Lagrange element.The accuracy and convergence of the free element method in solving this kind of problems and its adaptability to irregular mesh are demonstrated by a two-dimensional analytical solution,a three-dimensional engine model,and a three-dimensional turbine model.The free element method absorbs the advantages of the finite element method and the meshfree method at the same time and has the advantages of adopting the high-order scheme easily,applying the boundary conditions easily,and having small bandwidth coefficient matrix.Therefore,it has great potential in the field of solving heat transfer problems.(2)An efficient solution to transient heat conduction problems with obvious material nonlinear characteristics.On the basis of the steady-state problem,the mathematical implementation of the free element method for solving the transient nonlinear heat transfer problem is derived from the treatment of the temperature-dependent thermal properties,the discretization of the transient term,the treatment of the heat source term,and the treatment of the anisotropy.Introducing nonlinear iteration will reduce the computational efficiency.Therefore,a full-order model and reduced-order model alternating iteration strategy for solving nonlinear problems is proposed.The algorithm uses the technique of Proper orthogonal decomposition(POD)to establish the low-dimensional model and adds the results of the full-order model in the process of time advance,training and updating the new database and new POD bases,and retaining the calculation process of the reduced-order model at some times.It not only absorbs the advantages of the full-order model that can accurately obtain the physical field,but also combines the characteristics of the fast solution of the reduced-order model to make the calculation results accurate and efficient.Compared with the existing extrapolation method based on model reduction technology,the accuracy and efficiency of the proposed algorithm are proved,which is of great significance in engineering practice.(3)Study on the fast reconstruction and parameter identification of transient nonlinear physical fields.Considering the disadvantages of the full-order model,such as low computational efficiency and slow response,a physical field reconstruction surrogate model with equivalent accuracy and high computational efficiency was established.Firstly,the free element method is used to establish the parameter-space-time three-dimensional database offline.Then,the database is compressed in the time dimension to obtain the parameter-dependent bases.Finally,the bases are compressed again in the parameter space to obtain a group of bases containing the common information of parameters and time,so that only a set of basis vectors are needed to span the global physical field.Not only can the precision of physical field reconstruction be guaranteed,but the output efficiency is greatly improved,which is close to instantaneous output,and the nonlinear mapping between the parameters to be solved and the physical field in time domain is realized.On this basis,combined with the intelligent optimization algorithm,the thermal parameters in the extreme environment were quickly identified.The two-dimensional and three-dimensional numerical examples were used to identify the thermal conductivities and the convective heat transfer coefficient,respectively.The accuracy,stability,and efficiency of the method were proved.(4)Study on the problem of identification of flaws location and shape parameters of multi-layered thermal protection materials.Based on the fact that structural flaws will change the structure temperature transfer process,by measuring the temperature distribution of the boundary area can be reached and using the above parameters identification method,flaws location,length,angle of multi-layered materials in thermal environment can be identified.The characteristic and calculation precision of the radial basis function method and kriging method are discussed.At the end,taking the seven-layered thermal protection material AFRSI(Advanced flexible reusable surface insulation)as an example,the aerodynamic heating,radiation and convective heat transfer boundary conditions of the aircraft in the reentry process are considered.The modeling and calculation work were carried out to identify the interlayer flaws locations of the multi-layered thermal protection system.The accuracy and convergence of the two surrogate models are compared by precise measurement.It is found that the kriging method has faster convergence speed and better reconstruction accuracy when dealing with this kind of problems.