Research On Nonlinear Inverse Heat Transfer Problems For Reconstruction Of Thermal Parameters

In order to guarantee the security and stability of interplanetary re-entry vehicle in extreme thermal environment,it is of crucial importance to develop efficient and feasible thermal protection techniques.For the optimization and evaluation of the thermal protection system(TPS),it is necessary to characterise the thermal environment and establish the thermal response model of the structure.Hence,this subject introduces three important thermal parameters,namely,heat flux on the surface of a structure,reaction-heating source and interfacial heat transfer coefficient(including thermal contact conductance and Stefan-Boltzmann radiation coefficient),which can influence the heat transfer behaviour of the structure.Because these parameters are dependent on various material properties,and are vulnerable to external environment of TPS,it is rather difficult to measure them directly.However,it is feasible to determine them from limited number of temperature measurements by solving inverse heat transfer problems,which means the determination of causes from effects.However,the heat diffusion in high temperature condition is obviously a nonlinear process.Furthermore,the inverse problem is inherently ill-posed.Hence,this subject is devoted to investigating three types of nonlinear inverse heat transfer problem(inverse boundary value problem,inverse heat source problem and inverse problem for identification of interfacial heat transfer coefficient).Procedures for the estimation of thermal parameters are proved to be feasible mathematically and implemented by some effective algorithms.In addition,an experimental study is conducted for the measurement of heat flux.Firstly,the nonlinear inverse boundary value problem is investigated for the estimation of boundary heat flux from two temperature measurements inside a finite domain with temperature-dependent thermal properties.For direct problem,the heat equation is linearized by time rescaling method and the concept of optimal position is proposed to minimize the error in the direct solution.Afterwards,the analytical solution of temperature is obtained by the shifting function method.For inverse problem,the existence and uniqueness of the solution is proved based on the theory of Cauchy problem.A non-iterative method for the estimation of heat flux is also proposed based on sequential regularization.The results show the dependence on the regularization parameter can be reduced by decreasing the rescaled time step size.Moreover,the uncertainty fromthermal conductivity is dominant in the heat flux uncertainty in long-duration measurement.The research presented above provide an effective method for the measurement of a long-duration heat flux in extreme environment.Secondly,in order to reduce the uncertainty and improve the accuracy of estimation,a water-cooled heat flux sensor is designed and a method for the estimation of heat flux is developed based on the calibration of sensor's unit step response(USR).The advantage of the calibration-based technique is that the heat flux estimate is independent of thermal properties,thermocouple position,thermocouple time constant and surface emissivity,the only information needed is temperature measurements.The USR is calibrated by different sources(tungsten halogen lamp,air heater and laser system).Based on Duhamel's theorem,a convolution integral equation between heat flux and temperature is established.The equation is then solved by the sequential regularization method and the truncated singular value decomposition method combined with a digital filter.The device and the proposed method are validated experimentally in convection and radiation conditions.The results show the accuracy attained by the water-cooled sensor is higher than that by the sensor based on conventional inverse method.Meanwhile,the uncertainty analysis shows the uncertainty of heat flux can be reduced dramatically by slightly increase the regularization parameter.The research developed a method with high accuracy and low uncertainty for heat flux measurement of TPS.Thirdly,by incorporating a nonlinear reaction-heating source into a one-dimensional transient heat equation,an inverse problem is investigated to reconstruct both reaction coefficient and heat flux from two internal temperature measurements.The existence and uniqueness of time-dependent reaction coefficient are proved rigorously with some sufficient conditions based on Banach fixed point theorem.The inverse problems are solved numerically by conjugate gradient method(CGM).The convergence,accuracy and stability of inverse solutions are all discussed in numerical experiments,and the optimization of measurement positions is also presented.When the reaction coefficient is a spacewise and time dependent function,the Sobolev gradient is used to improve the CGM,and the effect of the number of measurement points on the accuracy is also discussed.Numerical results show that the computation efficiency for the inverse source problem is better than that for the inverse boundary value problem,but the attainable accuracy and stability of solution are both worse than that of the latter.Besides,the improvement of CGM can reduce the sensitivity to measurement noise and the dependence on initial guess of reconstruction.The research is valuable in the characterization of effects of reaction-heating source on heat diffusion.It also extends the theory and application of inverse source problems.Finally,a generalized inverse problem is investigated for the identification a heat transfer coefficient at the interface of a bi-material from temperature measurements on an accessible boundary.The problem involves multi-dimensional heat conduction and nonhomogeneous thermal properties.The existence and uniqueness of inverse solution holds as can be seen from the Holmgren theorem,which proves the feasibility of non-invasive measurement.A new preconditioner generated from an inner product of a Hilbert space is proposed for the improvement of CGM,to overcome the vanishing of the conventional gradient of objective function at final time.The numerical results in both one-and twodimensions illustrate that the preconditioned CGM achieves higher accuracy and stability than the conventional version,when the input data is contaminated with noise and when the initial guess is arbitrary.Furthermore,the robustness of the algorithm strengthens as the smoothing factor increases.This research paves a way for the characterization of heat transfer behaviour at the interfaces of composite structures and for the interfacial defect detection.