Identification of Functionally Graded Materials Thermophysical Properties by Means of Inverse Problems Method

Аuthors

, Netelev A. V.^*, Rudoy I. A.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: netelev@mai.ru

Abstract

Up to date, breaking-up polymeric materials are widely applied in the structures of heat-loaded elements in various fields of technology. These materials are indispensable while creating frontal braking screens of the devices entering the atmosphere with a second cosmic velocity such as “Hayabusa” and “Stardust”. The phenolcarbon composite was employed on these devices as a thermal protection material. The destructive process of in these materials is of a complex multi-stage nature. Chemical reactions between the decomposing material components and components of the incoming stream may progress in parallel with heat release and absorption. In engineering practice, when designing destructive thermal protection, applications of these models, with parallel multi-stage processes, can significantly complicate the process of optimal technical solution selection. In such situations, the one-stage Arrhenius equation does not exactly fit to describe the process of destruction. The mathematical model accuracy increasing is possible by introducing into its composition a component that accounts for the heating rate. This article is devoted to the development of an algorithm for computing the coefficients of the non-equilibrium thermo-chemical kinetics equation by the inverse problem method. The developed algorithm is based on solving the coefficient inverse problem by the iterative regularization method. The iterative regularization method application is stipulated by its good convergence and universality, which were confirmed in practice while solving similar problems. The universality of the iterative regularization method algorithm is stipulated by the similarity of the computing apparatus of the steps involved in it. The iterative regularization method is based on the procedure for minimizing the target residual functional of the experimentally measured and calculated temperature values at the temperature sensors installation points. As additional conditions restricting the search for solutions, the conditions for the heat transfer problem in the material and on its surface are introduced into the functional. Correspondingly, the non-equilibrium thermochemical kinetics equations are also included into minimized functional. Minimization of the functional is performed by first-order gradient methods. The key step in gradient methods of minimization is the calculation of the gradient of the target functional. To do this, a solution to the conjugated heat transfer problem is made at the each iteration. The next step in minimizing the functional consists in calculating the descent depth. It is necessary to determine the temperature increment to calculate the descent depth for each of the unknown characteristics. After calculating the new values of the coefficients, it is necessary to solve the direct heat-transfer problem by substituting the newly obtained characteristics as the initial data. The conjugate problem, the problem of temperature increment and the direct problem of heat transfer are formally identical from a mathematical point of view. This circumstance significantly simplifies computational procedures of this algorithm program implementation.

Keywords:

inverse heat transfer problems, materials destruction, spacecraft, thermal protection

References

1. Mishin V.P., Alifanov O.M. Inverse heat-transfer problems, domains of application in design and testing of technical objects. Journal of Engineering Physics, 1982, vol. 42, no. 2, pp.181-192.

2. Alifanov O.M., Budnik S.A., Nenarokomov A.V., Netelev A.V., Titov D.M. Destructive materials thermal properties determination with application for spacecraft structures testing. In Proc. of 61st International Astronautical Congress, 2010, pp. 8541-8548.

3. Tikhonov A.N, Arsenin V.Ya. Metody resheniya nekorrektnykh zadach [Methods for solving ill-posed problems]. Moscow, Nauka, 1986, 288 p. In Russ.

4. Alifanov O.M., Artyukhin E.A, Rumyantsev S.V. Ekstremal’nye metody resheniya nekorrektnykh zadach i ikh prilozheniya k obratnym zadacham teploobmena [Extreme methods for solving ill-posed problems and their applications to inverse heat transfer problems]. Moscow, Nauka, 1988, 288 p.

5. Alifanov O.M., Rumyantsev S.V. Formulas for the discrepancy gradient in the iterative solution of inverse heat-conduction problems. Ii. Determining the gradient in terms of a conjugate variable. Journal of Engineering Physics, 1987, vol. 52, no. 4, pp.489-495.

6. Alifanv O.M., Nenarokomov A.V., Nenarokomov K.A., Finchenko V.S., Titov D.M. Nerazrushayucshaya defektoskopiya materialov gibkoy teplovoy zaschiti metodami nelineinoy akustiki [Non-destructive flaw detection of materials of elastic thermal protection by methods of nonlinear acoustics]. Teplovye protsessy v tekhnike – Thermal processes in engineering, 2016, vol. 8, no. 8, pp. 368-377.