Mathematical Modeling of Heat and Mass Transfer During Aerodynamic Heating of the Nose Parts of Hypersonic Aircraft

Abstract

The study focuses on heat and mass transfer on the side surfaces of blunt nose cones of hypersonic aircraft under aerodynamic heating conditions and formulates the problem of viscous flow and heat and mass transfer in dynamic, thermal, and diffusion boundary layers. After minor simplifications, we found approximate analytical solutions related to the gas-dynamic, thermal, and diffusion characteristics of the dissociating flow and obtained closed analytical expressions for the distribution of enthalpy and concentrations of the gas mixture components over the thickness of the boundary layers. Furthermore, by the derivatives of the enthalpies and concentrations distributions with respect to the vertical variable on the wall, we determined convective and diffusion heat fluxes to the aircraft surface. Using the balance between the supplied convective-diffusion heat fluxes and the fluxes removed due to radiation and heat elimination into the body, we obtained a nonlinear equation for the wall temperature, which is solved numerically. Numerical results are obtained and analyzed on convective-diffusion heat fluxes and wall temperatures of hypersonic aircraft, depending on the Mach number and flight altitude in a wide range of values, which make it possible to determine the boundaries of speeds and altitudes at which the mass of the heat-shielding coating is not removed. Finally, we investigated the influence of the catalytic properties of the aircraft surface on heat transfer in the same ranges of the Mach number and flight altitude

The work was done within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (no. FSFF-2020-0013)

Please cite this article in English as:

Formalev V.F., Kolesnik S.A., Garibyan B.A. Mathematical modeling of heat and mass transfer during aerodynamic heating of the nose parts of hypersonic aircraft. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2022, no. 1 (100), pp. 107--121 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2022-1-107-121

References

[1] Krasnov N.F. Aerodinamika tel vrashcheniya [Aerodynamics of rotary bodies]. Moscow, Mashinostroenie Publ., 1964.

[2] Dorrance W.H. Viscous hypersonic flow. McGraw-Hill, 1962.

[3] Avduevskiy V.S. Osnovy teploperedachi v aviatsionnoy i raketno-kosmicheskoy tekhnike [Fundamentals of heat transfer in aerotechnics and rocket and space equipment]. Moscow, Mashinostroenie Publ., 1992.

[4] Nikitin P.V., Sotnik E.V. Kataliz i izluchenie v sistemakh teplovoy zashchity kosmicheskikh apparatov [Catalysis and radiation in systems of spacecraft thermal protection]. Moscow, Yanus-K Publ., 2013.

[5] Formalev V.F., Kolesnik S.A. Matematicheskoe modelirovanie sopryazhennogo teploperenosa mezhdu vyazkimi gazodinamicheskimi techeniyami i anizotropnymi telami [Mathematical modelling of conjecture heat transfer among viscous gas flows and anisotropic bodies]. Moscow, Lenand Publ., 2019.

[6] Formalev V.F., Kolesnik S.A. Conjugate heat transfer between wall gasdynamic flows and anisotropic bodies. High Temp., 2007, vol. 45, no. 1, pp. 76--84. DOI: https://doi.org/10.1134/S0018151X07010105

[7] Formalev V.F., Kolesnik S.A., Garibyan B.A. Heat transfer with absorption in anisotropic thermal protection of high-temperature products. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, no. 5 (86), pp. 35--49 (in Russ.). DOI: http://doi.org/10.18698/1812-3368-2019-5-35-49

[8] Formalev V.F., Kolesnik S.A., Garibyan B.A. Analytical solution of the problem of conjugate heat transfer between a gasdynamic boundary layer and anisotropic strip. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2020, no. 5 (92), pp. 44--59 (in Russ.). DOI: http://doi.org/10.18698/1812-3368-2020-5-44-59

[9] Formalev V.F., Kolesnik S.A., Kuznetsova E.L. The effect of longitudinal nonisothermality on conjugate heat transfer between wall gasdynamic flows and blunt anisotropic bodies. High Temp., 2009, vol. 47, no. 2, pp. 228--234. DOI: https://doi.org/10.1134/S0018151X09020138

[10] Formalev V.F., Kolesnik S.A., Kuznetsova E.L. Effect of components of the thermal conductivity tensor of heat-protection material on the value of heat fluxes from the gasdynamic boundary layer. High Temp., 2019, vol. 57, no. 1, pp. 58--62. DOI: https://doi.org/10.1134/S0018151X19010085

[11] Formalev V.F., Kolesnik S.A., Kuznetsova E.L. Modeling of conjugate heat transfer in packets of small-size planar gasdynamic cooled nozzles. High Temp., 2015, vol. 53, no. 5, pp. 697--702. DOI: https://doi.org/10.1134/S0018151X15050119

[12] Schlichting H. Grenzschicht-Theorie. Braun G., 1951.

[13] Lunev V.V. Giperzvukovaya aerodinamika [Hypersonic aerodynamics]. Moscow, Mashinostroenie Publ., 1975.

[14] Arzhanikov N.S., Sadekova G.S. Aerodinamika bol’shikh skorostey [Aerodynamics of a high velocity]. Moscow, Vysshaya shkola Publ., 1965.

[15] Galitseyskiy B.M., ed. Teplovaya zashchita lopatok turbin [Thermal protection of blades]. Moscow, MAI Publ., 1996.