A method, an algorythm, and a software for the numerical simulation of heat state of heat-protective composite materials subjected to the aerodynamic heating

Аuthors

Formalev V. F.^*, Kuznetsova E. L.^**, Selin I. A.^***

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

*e-mail: formalev38@mail.ru
**e-mail: lareyna@mail.ru
***e-mail: i.selin@bk.ru

Abstract

A mathematical model, an algorithm, and a software for the numerical simulation of heat state of heat protective composites undergoing various physical and chemical transformations under high temperature aero and gas dynamic heating of hypersonic (M>5) flying vehicles’ structures. Several high-temperature physical and chemical processes are taken into account, the normal heating of composites up to 600K, the thermal destruction (pyrolysis) of binding agents with generation of porous residuals from thin-fiber reinforcements and pyrolysis gases filtering through porous structures to outer surfaces streamlined by hypersonic flows, and the injection of these gases into the hypersonic flow. At the temperature of phase transform reached by the heated porous residual the mass loss such as the flowing, the evaporation, and the sublimation effected by the friction in the hypersonic boundary layer begins. The existence of two transient interfaces of phase transform of the composite around the thin area of the pyrolysis and the multi-dimensional transient heat and mass transfer with nonlinear and anisotropic thermal and physical properties have to be taken into account.
The proposed model considers all the mentioned above specificities of the process and it is based on the new pyrolysis and nonlinear filtration laws.
A numerical simulation algorithm is based on the new absolutely stable method of variable directions with extrapolation designed for the solution of multi-dimensional transient problems of heat and mass transfer in anisotropic bodies such as composite materials. The used method is the most stable and has no known analogs for nonlinear problems with mixed differential operators.
A software complex based on the described mathematical model and numerical simulation algorithm is developed using the PASCAL language and the DELPHI programming system. The software complex is constructed as the managing program allowing one to analyze the input data and to construct the oriented graphs of program realization of subcases of the general mathematical model. The nodes of the graph are the program modules, and the graph edges are the functional links between these modules. The proposed structure allows one to solve more than a hundred of various problems of heat and mass transfer for thermal protective composite materials heated by aero and gas dynamic flows.
Some different numerical simulations of various multi-dimensional thermal fields in heat protective composites subjected to the aero and gas dynamic heating and undergoing the phase transitions are performed using the developed software. Some results are presented in this article.

Keywords:

composite materials, heat and mass transfer, typersonic flying vehicles, heat protection, aero and gas dynamic heating, algorithm, software complex

References

1. Formalev V. F., Kuznetsova E. L. Teplomassoperenos v anizotropnykh telakh pri aerogazodinamicheskom nagreve (Heat Transfer in Anisotropic Bodies under Aero and Gas Dynamic Heating), Moscow, MAI-PRINT, 2011, 300 p.
2. Mugalev V. P. Izvestiya AN SSSR. Ser. Mekhanika I Mashinostroenie, 1965, no. 1, pp.16-25.
3. Kuznetsova E. L. Matematicheskoe modelirovanie teplomassoperenosa v komposicionnyh materialah pri vysokotemperaturnom nagreve v elementah raketno-kosmicheskoi tekhniki (Mathematical Modeling of Heat and Mass Transfer in Composite Materials and Structural Elements of Aerospace Vehicles under High-Temperature Heating), Moscow, MAI-PRINT, 2010, 158 p.
4. Formalev V. F., Reviznikov D. L. Chislennye metody (Numerical Methods), Moscow, Physmatlit, 2004, 400 p.

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