The aircraft hydraulic system units and pipelines heat exchange parameters study
Автор: Nikolaev V.N.
Журнал: Siberian Aerospace Journal @vestnik-sibsau-en
Рубрика: Aviation and spacecraft engineering
Статья в выпуске: 1 vol.24, 2023 года.
Бесплатный доступ
The paper offers a method of mathematical modelling of aircraft hydraulic system thermal state. The given mathematical model presents a system of partial differential equations for carbon-fiber composite thermal insulation together with ordinary differential equations for hydraulic system components that describe their heat exchange with the ambient air and close-located surfaces. To solve the direct thermal state problem for hydraulic system components, i. e., to solve a stiff ordinary differential equation system, a Rosenbrock-type second order approximation numerical scheme for non-autonomous systems was applied. A solution of a partial differential equation system in Monte-Carlo method based on a probabilistic representation of the solution as a functional expectation of the diffusion process was also used. The inverse problem of the hydraulic system elements’ thermal state was solved applying a composition of the steepest descent method, Newton method and quasi-Newton method of Broydon-Fletcher-Goldfarb-Shanno. A mathematical model of the thermal state of a hydraulic system unit operating in an unpressurized aircraft compartment has been also developed, and the confidence intervals of each of the required model coefficients have been estimated using 2 1 α χ distribution at confidence probability = 0.95.
Mathematical model, differential equations, aircraft hydraulic system, parametric identification, confidence intervals of model coefficients
Короткий адрес: https://sciup.org/148329681
IDR: 148329681 | DOI: 10.31772/2712-8970-2023-24-1-136-143
Список литературы The aircraft hydraulic system units and pipelines heat exchange parameters study
- Voronin G. I. Sistemy kondichionirovaniya na letetelnych apparatach [Air-conditioning systems on board the aircrafts]. Moskow, Mashinostroenie Publ., 1973, 443 p.
- Dul'nev G. N., Tarnovskii N. N. Teplovie rezhimy electronnoy apparatury [Thermal modes of electronics]. Leningrad, Energiya Publ., 1971, 248 p.
- Dul'nev G. N., Pol'shchikov B. V., Potyagailo A. Yu. [Algorithms for hierarchical modeling of heat ex-change processes in complex radioelectronic systems]. Radioelektronika. 1979, No. 11, P. 49–54 (In Russ.).
- Nikolaev V. N., Gusev S. A., Makhotkin O. A. [Mathematical model of the convective radiant heat exchange of the vented heat-insulated unpressurized aircraft compartment]. A series of the air-craft strength. Strength calculation of aircraft structural components.1996, Iss. 1, P. 98–108 (In Russ.).
- Gusev S. A., Nikolayev V. N. [ Monte-Carlo Method for Estimation of Thermal Exchange in Honeycomb Thermoisolation Panels]. Journal of Siberian Federal University. Engineering & Tech-nologies. 2017, Vol 18, No. 4, P. 719–726 (In Russ.).
- Misnar A. Teploprovodnoct tverdich tel, zhidkostey, gazov i ich kompozichiy [Thermal conduc-tivity of solids, liquids, gases and their compositions]. Moscow, Mir Publ., 1968, 460 p.
- Artem'ev S. S., Demidov G. V., Novikov E. A. Minimizachiya ovrazhnich funkchiy chislennim metodom dlya resheniya zhestkich system uravneniy [Minimization of ravine functions by numerical method for rigid equation system solving]. Preprint no. 74. Data center of Siberian Department of the Academy of Sciences of the USSR. Novosibirsk, 1980. 13 p.
- Ladyzhenskaya O. A., Solonnikov V. A., Ural'tseva N. N. Lineynie i kvazilineynie uravneniya para- bolicheckogo tipa [Linear and quasilinear equations of parabolic type]. Moskow, Nauka Publ., 1967. 736 p.
- Sobolev S. L. Nekotorie primeneniya funkchionalnogo analiza v matematicheskoy fizike [Appli-cations of functional analysis in mathematical physics]. Moscow, Nauka Publ., 1988, 336 p.
- Gusev S. A. Application of SDEs to Estimating Solutions to Heat Conduction Equations with Discontinuous Coefficients. Numerical Analysis and Applications. 2015, Vol. 8, No. 2, P. 122–134.
- Himmelblau D. Process analysis by statistical methods. New York, Wiley, 1970, 463 p.
- Gill P., Murray E. Quasi-Newton methods for unconstrained optimization. Journal of the Insti-tute of Mathematics and its Applications. 1971, Vol. 9, No. 1, P. 91–108.
- Himmelblau D. Application Nonlinear Programming. Texas, McGraw-Hill Book Company, 1972, 534 p.
- Vladimir N. Nikolaev. Confidence Intervals for Identification Parameters of Heat Exchange Processes in Aircraft Instrument. Mathematical modeling of processes and systems. Compartments // Actual Problems Of Electronic Instrument Engineering: XV International Scientific and Technical Conference. (APEIE 2021). https://ieeexplore.ieee.org/xpl/conhome/9647431/proceeding Published in December 27, 2021. DOI: 10.1109/APEIE52976.2021.9647437. Novosibirsk State Technical Univer-sity, Russian Federation. P. 539–542.
- Vladimir N. Nikolaev. Optimal Planning of a Flight Experiment During Parametric Identifica-tion of Heat Transfer Processes of the On-board Aircraft Equipment // 2022 XIX Technical Scientific Conference on Aviation Dedicated to the Memory of N.E. Zhukovsky (TSCZh). (APEIE 2022). Pub-lished in 23 June 2022. ISBN Information: INSPEC Accession Number: 21818057. DOI: 10.1109/TSCZh55469.2022.9802493. Moscow, Russian Federation. P. 39–42.
