Mean-integral heat transfer coefficient parametric identification in coaxial heat pipes

DOI: 10.34759/vst-2022-3-111-121

Аuthors

Borschev N. O.

Leading Engineer of the Astrospace Center S.A. Lebedeva, 53, Leninskii av., Moscow, 119991, Russia

e-mail: www.moriarty93@mail.ru

Abstract

The article proposes a method for reconstructing the average integral heat transfer coefficient as a function of temperature for axial heat pipes. This method is based on the studied parameter representation in the form of its parameterized value, multiplied by the corresponding basis function that describes its dependence on the temperature. Linear-continuous function was selected as the basis one. Further, with the selected initial approximation of the heat transfer coefficient parameter, the “direct” problem of the theoretical temperature field determining is being solved under known initial-boundary conditions and thermo-physical properties of the material. Based on the flight thermal elaboration of the axial tube, the root-mean-square deviation between the theoretical and experimental temperature field at the sites of temperature sensors installation is being composed. The obtained functional is being minimized by the conjugate directions method, with preliminary selection of the descent step. The descent step is being selected from the condition of the residual functional minimum at all iterations, starting from the second one. Likewise, one of the most important tasks prior to minimization is finding the gradient component of this functional. For this purpose, the statement of the “direct” problem of heating the pipe is being solved again with a preliminary differentiation of this statement of the problem by the parameterized value of the heat transfer coefficient. The sum of errors, namely systematic, statement of the research problem, rounding and the set problem solving method, was selected as the iteration process termination criterion. Reaching the termination criterion assumes that the searched for parameterized value is found, otherwise the above described routine should be repeated again. To check the adequacy of the developed method, the obtained result was compared to the method for the heat transfer coefficient determining from the thermal resistances analysis based on the experimental temperature field. Analysis of relative errors shows good convergence in the case of this coefficient averaging over time with its experimental counterpart, otherwise, a greater number of considered time blocks and a more accurate thermal model of an axial heat pipe are required.

Keywords:

axial heat pipe, spacecraft, natural convection, thermal mode systems, coefficient inverse problem, iterative regularization method

References

1. Maidanik Yu.F., Fershtater Yu.G. Theoretical Basis and Classification of Loop Heat Pipes and Capillary Pumped Loops. 10th International Heat Pipe Conference (21–25 September 1997; Stuttgart, Germany).

2. Kotlyarov E.Y., Serov G.P. Methods of Increase of the Evaporators Reliability for Loop Heat Pipes and Capillary Pumped Loops. 24th International Conference on Environmental Systems, Society of Automotive Engineers, 1994. Paper 941578.

3. Vershinin S.V., Maidanik Yu.F. Teplovye protsessy v tekhnike, 2012, no. 12, pp. 559–565.

4. Zalmanovich S, Goncharov K. Radiators with LHP. International conference “Heat Pipes for Space Application” (15–18 September 2009; Moscow).

5. Idel’chik I.E. Spravochnik po gidravlicheskim soprotivleniyam (Handbook of hydraulic resistances), 3rd ed., Moscow, Mashinostroenie, 1992, 671 p.

6. Al’tov V.V., Gulya V.M., Kopyatkevich R.M. et al. Kosmonavtika i raketostroenie, 2010, no. 3(60), pp. 33-41.

7. Panin Yu.V., Antonov V.A., Balykin M.A. Vestnik NPO im. S.A. Lavochkina, 2021, no. 4(54), pp. 31-38. DOI: 10.26162/LS.2021.54.4.005

8. Gakal P.G., Ruzaikin V.I., Turna R.Yu. et al. Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2011, no. 5(82), pp. 21-30.

9. Nikonov A.A., Gorbenko G.A., Blinkov V.N., Teploobmennye kontury s dvukhfaznym teplonositelem dlya sistem termoregulirovaniya kosmicheskikh apparatov (Heat exchange circuits with a two-phase coolant for spacecraft temperature-control systems), Moscow, Poisk. Series “Rocket and Space technology”, 1991, 302 p.

10. Volodin Yu.G., Fedorov K.S., Yakovlev M.V. Izvestiya vysshikh uchebnykh zavedenii. Mashinostroenie, 2007, no. 1, pp. 26-28.

11. Zudin Yu.B. Teploenergetika, 1998, no. 3, pp. 31-33.

12. Knyazev V.A., Nikulin K.S. Voprosy atomnoi nauki i tekhniki. Seriya: Fizika yadernykh reaktorov, 2016, no. 1, pp. 56-64.

13. Ignat’ev S.A. Problemy mashinostroeniya i avtomatizatsii, 2009, no. 2, pp. 27-30.

14. Minakov A.V., Guzei D.V., Zhigarev V.A. Uchenye zapiski Kazanskogo universiteta. Seriya: Fiziko-matematicheskie nauki, 2015, vol. 157, no. 3, pp. 85-96.

15. Aminov D.M., Khafizov F.M. Innovatsionnaya nauka, 2016, no. 8-2, pp. 16-18.

16. Alifanov O. M., Ivanov N. A., Kolesnikov V. A Methodology and algorithm determining the temperature dependence of thermal and physical characteristics for anisotropic materials basing on an inverse problem solution. Aerospace MAI Journal, 2012, vol. 19, no. 5, pp. 14-20.

17. Alifanov O.M. Issledovanie nestatsionarnogo konvektivnogo teplo- i massoobmena. Sbornik statei, Minsk, Nauka i tekhnika, 1971, pp. 322–333.

18. Carslaw H.S., Jaeger J.C. Conduction of heat in solids. 2nd Edition, Oxford University Press, 520 p.

19. 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 the inverse heat transfer problems), Moscow, Nauka, 1988, 285 p.

20. Alifanov O.M. Obratnye zadachi teploobmena (Inverse problems of heat transfer), Moscow, Mashinostroenie, 1988, 280 p.