Development of a method for assessing ther-mal stresses in structural elements of aircraft

A 2D computational-theoretical technique (on a structured computational grid) has been de-veloped that makes it possible to find a solution to a system of equations of linear thermoe-lasticity with boundary conditions of a general form for key elements of an aircraft moving at supersonic and hypersonic speeds in the Earth's atmosphere. It is assumed in the work that the effect of coupling between the deformation and temperature fields is small.

mathematical modeling, thermal deformation, development of numerical methods, aircraft

Volume 24, issue 2, 2023 year

Разработка методики оценки термонапря-жений в элементах конструкции летательных аппаратов

Разработана 2D расчетно-теоретическая методика (для структурированной расчетной сетки), позволяющая находить решение системы уравнений линейной термоупругости с граничными условиями общего вида для ключевых элементов летательного аппарата, двигающегося со сверхзвуковой и гиперзвуковой скоростью в атмосфере Земли. В ра-боте принято, что эффект связанности полей деформации и температуры мал.

математическое моделирование, термическая деформация, разработка численных ме-тодов, летательный аппарат.

Volume 24, issue 2, 2023 year

1. Kartashov E.M. Analytical methods in the theory of thermal conductivity of solids. Ed. 3rd, revised. and additional M.: Higher school, 2001. 550 p.
2. V. E. Zaliznyak, Fundamentals of Computational Physics Part 1. Introduction to finite dif-ference methods. Technosphere, Moscow, 2008. 223 p.
3. Kovalenko A.D. Thermoelasticity. Tutorial. K.: Vishcha shkola, 1975. 215 p.
4. Landau L. D., Lifshits E. M. Theoretical physics: Proc. allowance: For universities. In 10 vols. T. VII. Theory of elasticity. - 5th ed., stereo. - M.: FIZMAT LIT, 2003. - 264 p. - ISBN 5-9221-0122-6 (Vol. VII).
5. Anderson D., Tannehill J., Pletcher R. Computational fluid mechanics and heat transfer: In 2 vols. T. 1: Per. from English. M.: Mir, 1990. 384 p.
6. Melan E., Parkus G. Thermoelastic stresses caused by stationary temperature fields. – M.: Fizmatgiz, 1958. – 167 p.
7. Samarsky A.A., Nikolaev E.S. Methods for solving grid equations. M.: Nauka, 1978. 590 p.
8. Alshina E.A., Boltnev A.A., Kacher O.A. Empirical improvement of the simplest gradient methods // Mathematical Modeling. 2005. V. 17, No. 6. S. 43-57.
9. Golovachev Yu.P. Numerical simulation of viscous gas flows in the shock layer. M.: Nau-ka, 1996. 376 p.
10. Grigoriev Yu.N., Vshivkov V.A., Fedoruk M.P. Numerical simulation by methods of parti-cles in cells Ros. acad. Sciences, Sib. department, In-t calc. technologies, Novosib. state un–t. Novosibirsk: Publishing House of SO RAN, 2004. 360 p.
11. Thompson J.F. Numerical Grid Generation. - Amsterdam, North-Holland: Elsevier Science, 1985. - ISBN 0-444-00985-X.
12. Vabishchevich P. N., Pulatov S. I. Computational algorithm for conformal mapping // Mathematical Modeling. - January 1989. - V. 1, No. 1. - C. 132–139.
13. Handbook of Grid Generation / Ed. by J. F. Thompson, B. K. Soni, N. P. Weatherill. - CRC Press LLC, 1999. - ISBN 0-8493-2687-7.
14. Methods of computational fluid dynamics for safety analysis of fuel and energy facilities. : T78 Proceedings of IBRAE RAN / ed. ed. Corresponding Member RAS L. A. Bolshova. - Issue. 3. - M. : Nauka, 2008. - 207 p. : ill. ISBN 978-5-02-036941-2
15. Golovanov N.N. Geometric Modeling Ed. Phys.-Math. lit., 2002. 472 p.
16. De Boron K. A practical guide to splines. / Per. from English. - M .: Radio and communica-tion, 1985. - 304 p.
17. Nakamura S. Noniterative grid generation using parabolic difference equations for fuse-lage-wing flow calculations. VIII Internat. Conf. Numer. Meth. in Fluid Dynamics. Aa-checn, Germany, June 1982
18. Eremin V.V., Mikhalin V.A. Construction of a computational grid for calculating the flow around bodies of complex geometric shape. Designing algorithms and solving problems of mathematical physics: Sat. scientific tr. / Ed. G.P. Voskresensky and A.V. Zabrodin. - M., IPM im. M.V. Keldysh RAN, 1991.
19. Mikhalin V.A. Modification of the parabolic grid generator. Question. nuclear science and technology. - Ser. Mat. physical modeling. processes. 1995. #1–2.
20. S. K. Godunov “Difference method for numerical calculation of discontinuous solutions of hydrodynamic equations”, Matem. Sb., 47(89):3 (1959), 271–306
21. V. M. Kovenya. D. V. Chirkov. Methods of finite differences and finite volumes for solving problems of mathematical physics. Novosibirsk: Novosibirsk State University Press, 2013. 86 p.
22. Kuzenov V.V., Ryzhkov S.V. Approximate calculation of convective heat transfer near hy-personic aircraft surface // Journal of Enhanced Heat Transfer. 2018. V. 25 (2). P. 181-193.
23. Kuzenov V.V., Ryzhkov S.V. Calculation of heat transfer and drag coefficients for aircraft geometric models // Applied Sciences. 2022. V. 12. P. 11011.
24. Kuzenov V.V., Ryzhkov S.V. Numerical Simulation of Pulsed Jets of a High-Current Pulsed Surface Discharge // Computational Thermal Sciences. 2021. V. 13. P. 45-56.
25. Kuzenov V.V., Ryzhkov S.V., Starostin A.V. Development of a Mathematical Model and the Numerical Solution Method in a Combined Impact Scheme for MIF Target // Russian Journal of Nonlinear Dynamics. 2020. V. 16. No. 2. P. 325-341.
26. Kotov M.A., Ruleva L.B., Solodovnikov S., Surzhikov S.T. Carrying out experiments on the flow around models in a hypersonic shock wind tunnel//Physico-chemical kinetics in gas dynamics. 2013. Vol. 14, no. 4.
27. Glushko G.S., Ivanov I.E., Kryukov I.A. Modeling of turbulence in supersonic jet flows // Physico-chemical kinetics in gas dynamics. 2010. Volume 9.