PARAMETRIC IDENTIFICATION OF THE HEAT CONDUCTIVITY TENSOR IN CYLINDRICAL COORDINATES
https://doi.org/10.26583/vestnik.2022.242
Abstract
When designing the thermal regime of composite structures and structures characterized by a mixed type of heat exchange due to its complex physico-chemical and geometric structure, it is often necessary to know its effective thermophysical characteristics. In this paper, we propose a method for restoring the effective thermal conductivity tensor as a function of temperature based on minimizing the root-mean-square error between the theoretical and experimental temperature field at the temperature sensor installation sites. This technique has been tested on the frame of the descent spacecraft "Eagle". Since these tasks are considered incorrect, it is necessary to apply regularization that mitigates the error of the input noisy data. The algorithm of conjugate gradients is chosen as the minimization method, as the most accurate method of the first order of convergence.
About the Author
N. O. Borshchev
Astrocosmic Center of the Federal State Institution of Science S.A. Lebedev Institute
Russian Federation
Russian Federation
References
1. Krein S.G., Prozorovskaya O.I. Analiticheskie polugruppy i nekorrektnye zadachi dlya evolyucionnyh uravnenij [Analytical semigroups and ill-posed problems for evolutionary equations] // Reports of the Academy of Sciences of the USSR. 1960. Vol. 133. № 2. Р. 277–280 (in Russian).
2. Bassistov Yu.A., Yanovsky Yu.G. Nekorretnye zadachi v mekhanike (reologii) vyazkouprugih sred i ih regulyarizaciya [Uncorrected problems in mechanics (rheology) of viscoelastic media and their regularization] // Mechanics of composite materials and structures. 2010. Vol. 16. № 1. Р. 117–143 (in Russian).
3. Bakushinsky A.B., Kokurin M.Yu., Kokurin M.M. Pryamye i obratnye teoremy dlya iteracionnyh metodov resheniya neregulyarnyh operatornyh uravnenij i raznostnyh metodov resheniya nekorrektnyh zadach Koshi [Direct and inverse theorems for iterative methods for solving irregular operator equations and difference methods for solving ill-posed Cauchy problems] // Journal of Computational Mathematics and Mathematical Physics. 2020. Vol. 60. № 6. Р. 939–962 (in Russian).
4. Vasin V.V. Modificirovannyj metod naiskorejshego spuska dlya nelinejnyh regulyarnyh operatornyh uravnenij [Modified steepest descent method for nonlinear regular operator equations] // Reports of the Academy of Sciences. 2015. Vol. 462. № 3. Р. 264 (in Russian).
5. Golichev I.I. Modificirovannyj gradientnyj metod naiskorejshego spuska resheniya neleniarizovannoj zadachi dlya nestacionarnyh uravnenij Nav'e-Stoksa [Modified gradient method of the steepest descent of the solution of the non-leniarized problem for non-stationary Navier-Stokes equations] // Ufa Mathematical Journal. 2013. Vol. 5. № 4. Р. 60–76 (in Russian).
6. Bloch A.G., Zhuravlev Yu.A., Ryzhkov L.N. Teploobmen izlucheniem [Heat exchange by radiation]. M.: Enegoatomizdat Publ., 1991.
7. Zaletaev V.M., Kapinos Yu.V., Surguchev O.V. Raschet teploobmena kosmicheskogo apparata [Calculation of heat exchange of the spacecraft]. M.: Mashinostroenie Publ., 1979.
8. Favorsky O.N., Kadaner Ya.S. Voprosy teploobmena v kosmose [Questions of heat exchange in space]. M.: Higher School Publ., 1967.
9. Karslow U., Jaeger D. Teploprovodnost' tverdyh tel [Thermal conductivity of solids]. M.: Nauka Publ., 1964. 487 p.
10. Alifanov O.M., Artyukhin E.A., Rumyan¬tsev S.V. Ekstremal'nye metody resheniya nekorrektnyh zadach [Extreme methods of solving incorrect problems]. M.: Nauka. Gl. ed. phys.-mat. lit Publ., 1988. 288 p.
11. Alifanov O.M. Obratnye zadachi teploobmena [Inverse problems of heat transfer]. M.: Mechanical Engineering Publ., 1988. 280 p.
Review
For citations:
Borshchev N.O. PARAMETRIC IDENTIFICATION OF THE HEAT CONDUCTIVITY TENSOR IN CYLINDRICAL COORDINATES. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2022;11(5):329-342. (In Russ.) https://doi.org/10.26583/vestnik.2022.242
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