Approximate thermal analysis of heating and deformation of a C/C-SiC plate in a scramjet engine

The paper provides a brief overview of heat-resistant materials used by the United States, Germany and Australia the creation of high-speed aircraft. A simplified mathematical model of heating and deformation processes in a C/C-SiC plate based on thermoelasticity equations is formulated. The problem statement is as follows: for a composite plate lo-cated on the scramjet engine housing, under given thermal effects and properties of the construction materials, the fields of temperatures, displacements, components of stress and strain tensors are determined. The heating and deformation values in the C/C-SiC plate are estimated.

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

Volume 24, issue 2, 2023 year

Приближенный термический анализ нагрева и деформации пластины C/C-SiC в двигателе ГПВРД

В работе приведен краткий обзор основных конструкционных материалов приме-няемых США, Германией и Австралией при создании высокоскоростных летатель-ных аппаратов (ВЛА). Сформулирована упрощенная математическая модель про-цессов нагрева и деформации в пластине C/C-SiC, основанная на уравнениях тер-моупругости. Постановка задачи выглядит следующим образом: для композитной пластины, располагающейся на корпусе гиперзвукового прямоточного воздушно-реактивного двигателя (ГПВРД), при заданных тепловых воздействиях и свойствах материалов конструкции определяются поля температур, перемещений, компонент тензоров напряжений и деформаций. Выполнена оценка величины нагрева и де-формации в пластине C/C-SiC.

математическое моделирование, термическая деформация, разработка численных методов, летательный аппарат

Volume 24, issue 2, 2023 year

1. Lunev V.V. The flow of real gases at high speeds. M.: FIZMATLIT, 2007. 760 p. [in Rus-sian].
2. Kuzenov V. V., Dikalyuk A. S. Implementation of an approximate method for calculating convective heat transfer near the surface of the GLA of a complex geometric shape, Physical Chemical Kinetics in Gas Dynamics, 2017. V.18, issue. 2. [in Russian].
3. Surzhikov S.T., Yatsukhno D.S. Analysis of the Flight Data on Convective and Radiative Heating of the Surface of Martian Schiaparelli Descent Space Vehicle, Fluid Dynamics, 2022. No. 6. S. 74-85.
4. Surzhikov S.T. Aerophysics of flow past a blunt wedge of finite dimensions, Fluid Dynam-ics, 2021. No. 5. S. 89-102.
5. Surzhikov S.T. Numerical Analysis of Shock Layer Ionization during the Entry of the Schia-parelli Spacecraft into the Martian Atmosphere, Fluid Dynamics, 2020. No. 3. S. 80-92.
6. Surzhikov S. T. Radiation-convective heating of the Martian apparatus EDL MSL at an an-gle of attack , Physical Chemical Kinetics in Gas Dynamics, 2015. V.16, issue. 2.[in Russian].
7. Surzhikov S. T., Shuvalov M. P. Analysis of radiation-convective heating of four types of descent spacecraft, Physical Chemical Kinetics in Gas Dynamics, 2014. V.15, issue. 4.[in Russian].
8. Surzhikov S. T. Radiation heating of the surface of superorbital descent spacecraft with al-lowance for atomic lines, Physical Chemical Kinetics in Gas Dynamics, 2014. V.15, issue. 4.[in Russian].
9. Surzhikov S. T. Modeling of radiation-convective heating of model chambers of ramjet en-gines on hydrogen and hydrocarbon fuels, Physical Chemical Kinetics in Gas Dynamics, 2014. V.15, issue. 3.[in Russian].
10. Seleznev R.K., Surzhikov S.T., Shang J.S. A review of the scramjet experimental data base // Prog. Aerosp. sci. Elsevier Ltd, 2019. Vol. 106, No. February. P. 43–70.
11. Nelson H.F. Radiative heating in scramjet combustors // J. Thermophys. heat transfer. 1997 Vol. 11, No. 1. P. 59–64.
12. Bouchez M. et al. Combustor and material integration for high speed aircraft in the European research program ATTLAS2 // AIAA Aviat. 2014-19th AIAA Int. sp. Planes Hypersonic Syst. Technol. Conf. 2014. No. June. P. 1–17.
13. Tenney D.R., Lisagor W.B., Dixon S.C. Materials and structures for hypersonic vehicles // J. Aircr. 1989 Vol. 26, No. 11. P. 953–970.
14. Steelant J. ATTLAS: Aero-Thermal loaded material investigations for high-speed vehicles // 15th AIAA Int. sp. Planes Hypersonic Syst. Technol. Conf. 2008. No. May. P. 1–11.
15. Choubey G., Suneetha L., Pandey K.M. Composite materials used in Scramjet-A Review // Mater. Today Proc. Elsevier Ltd, 2018. Vol. 5, No. 1. P. 1321-1326.
16. [Electronic resource].
17. [Electronic resource]. 2009 Vol. 58, no. 3.
18. Balat-Pichelin M. et al. Emissivity at high temperature of Ni-based superalloys for the design of solar receivers for future tower power plants // Sol. energy mater. Sol. Cells. 2021 Vol. 227, No. April.
19. [Electronic resource].
20. [Electronic resource] // Haynes Inter-national. 1997 Vol. 06002, no. 2. URL:
21. [Electronic resource].
22. [Electronic resource].
23. // Alloy Dig. 2021 Vol. 70, no. 8.
24. [Electronic resource].
25. Li L. et al. Study of Ti-6Al-4V alloy spectral emissivity characteristics during thermal oxida-tion process // Int. J. Heat Mass Transf. Elsevier Ltd, 2016. Vol. 101. P. 699–706.
26. Zhang W.J., Reddy B.V., Deevi S.C. Physical properties of TiAl-base alloys // Scr. mater. 2001 Vol. 45, No. 6. P. 645–651.
27. Eswara Prasad N., Gokhale A.A., Wanhill R.J.H. Aluminum–Lithium Alloys // Aerospace Materials and Material Technologies. 2017 Vol. 76, No. 2. P. 53–72.
28. [Electronic resource].
29. [Electronic resource].
30. Lanc Z. et al. Emissivity of aluminum alloy using infrared thermography technique // Mater. Tehnol. 2018 Vol. 52, No. 3. P. 323-327.
31. [Electronic resource].
32. Darolia R., Walston W.S., Nathal M.V. Nial Alloys for Turbine Airfoils. 2012. P. 561–570.
33. [Electronic resource].
34. WANG C. et al. Elastic and thermodynamic properties of NIAL and NI3AL from first-principles calculations // Int. J. Mod. Phys. B. 2011. Vol. 25, № 27. P. 3623–3631.
35. Semboshi S. et al. Thermal conductivity of Ni3V-Ni3Al pseudo-binary alloys // Intermetal-lics. 2015. Vol. 59. P. 1–7.
36. [Electronic resource].
37. Piatkowski J., Przeliorz R., Jabłońska M. The specific heat capacity and oxidation kinetics of NiAl, FeAl and TiAl alloys // Solid State Phenom. 2013. Vol. 203–204, № May 2014. P. 431–434.
38. [Electronic resource].
39. [Electronic resource].
40. Mironov R.A. et al. Spectral and Total Emissivity of the Reaction Bonded Silicon Nitride // Refract. Ind. Ceram. 2017. Vol. 58, № 4. P. 434–438.
41. [Electronic resource].
42. Ganiev I.N. et al. Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey) alumi-num conductor alloy doped with gallium // Mod. Electron. Mater. 2020. Vol. 6, № 1. P. 25–30.
43. [Electronic resource].
44. Van Der Meer P.L.A.C.M., Giling L.J., Kroon S.G. The emission coefficient of silicon coat-ed with Si3N4 or SiO2 layers // J. Appl. Phys. 1976. Vol. 47, № 2. P. 652–655.
45. [Electronic resource].
46. Demirbas M.D., Apalak M.K. Thermal stress analysis of one- and two-dimensional function-ally graded plates subjected to in-plane heat fluxes // Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl. 2019. Vol. 233, № 4. P. 546–562.
47. V. E. Zinoviev. Thermophysical properties of metals at high temperatures. [in Russian].
48. Chirkin V. S. Thermophysical properties of nuclear engineering materials. M.: Atomiz-dat, 1967. - 474 p. [in Russian].
49. Anuryev V. I. Handbook of the designer-machine builder in 3 volumes. T. 1/V. I. Anuriev; 8th ed., revised and additional. Ed. I. N. Zhestkovoy. - M .: Mashinostroenie, 2001. - P. 34. [in Russian]. ISBN 5-217-02963-3.
50. Shu S. et al. Study of the normal spectral emissivity of tungsten between 170 and 500 °C by a single-wavelength infrared thermometer // Fusion Eng. Des. Elsevier B.V., 2021. Vol. 173, № August. P. 112848.
51. Glass D.E. et al. Testing of refractory composites for scramjet combustors // J. Propuls. Pow-er. 2016. Vol. 32, № 6. P. 1550–1556.
52. [Elec-tronic resource].
53. Scarponi C. Carbon–carbon composites in aerospace engineering // Advanced Composite Materials for Aerospace Engineering. Elsevier, 2016. P. 385–412.
54. [Electronic resource].
55. Ohlhorst C.W. et al. Development of X-43A Mach 10 Leading Edges // 56th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. Vol. 8. P. 5290–5298.
56. Kolesnikov A. F., Sakharov V. I. Gas-dynamic aspects of the experiment on heat transfer of the surface of ultra-high-temperature ceramics in an underexpanded jet of dissociated , Phys-ical Chemical Kinetics in Gas Dynamics, 2022. V.23, issue. 6. [in Russian].
57. Hank J., Murphy J., Mutzman R. The X-51A Scramjet Engine Flight Demonstration Program // 15th AIAA International Space Planes and Hypersonic Systems and Technologies Confer-ence. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. No. May. P. 1–13.
58. 5Glass D.E. et al. Testing of DLR C/C-SiC and C/C for HIFiRE 8 scramjet combustor // AI-AA Aviat. 2014-19th AIAA Int. sp. Planes Hypersonic Syst. Technol. Conf. 2014. No. Jan-uary.
59. Guy, R. W., Rogers, R. C., Puster, R. L., Rock, K. E., and Diskin, G. S., “TheNASALang-ley ScramjetTest Complex,” 32ndAIAA, ASME, SAE, and ASEE, Joint Propulsion Confer-ence and Exhibit, AIAA Paper 1996-3243, 1996.
60. Driest, E. Turbulent Boundary Layer in Compressible Fluids // J. Aeronaut. sci. 1951 Vol. 18, no. 3.
61. 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). [in Russian].
62. Samarsky A. A., Gulin A. V. Numerical methods: Textbook, manual for universities, - M .: Nauka. Ch. ed. physics and mathematics lit., 1989.- 432 p.- ISBN 5-02-013996-3. [in Rus-sian].
63. Daryabeigi K., Cunnington G.R., Knutson J.R. Combined heat transfer in high-porosity high-temperature fibrous insulation: Theory and experimental validation // J. Thermophys. heat transfer. 2011 Vol. 25, No. 4. P. 536–546.