Turbulent Heat Exchange on the Surface of a Sharp Plate at a Supersonic Flow at M = 6 ÷ 8




The results of calculations of convective heating of a sharp plate during flow around it with a supersonic stream at a speed of M = 6 ÷ 8 are presented. For calculations, the author's computer code NERAT-2D was used, which implements the Reynolds-averaged Navier − Stokes equations, together with algebraic models of turbulence suggested by Baldwin − Lomax and Prandtl.
Good agreement is shown with experimental data for convective heating in a turbulent boundary layer.
The analysis of the distribution of gas-dynamic functions in different cross-sections of the streamlined plate is carried out.

convective heating, laminar-turbulent transition, flow around a plate, supersonic speed.


Volume 20, issue 4, 2019 year


Турбулентный теплообмен на поверхности острой пластины при сверхзвуковом обтекании при M = 6 ÷ 8

Представлены результаты расчетов конвективного нагрева острой пластины, при обтекании ее сверхзвуковым потоком со скоростью M = 6 ÷ 8. Для расчетов использовался авторский компьютерный код NERAT-2D, реализующий усредненные по Рейнольдсу уравнения Навье − Стокса, совместно с алгебраическими моделями турбулентности Болдуина − Ломакса и Прандтля.
Показано хорошее совпадение по конвективному нагреву в турбулентном пограничном слое с экспериментальными данными.
Выполнен анализ распределения газодинамических функций в разных поперечных сечениях обтекаемой пластины.

конвективный нагрев, ламинарно-турбулентный переход, обтекание пластины, сверхзвуковая скорость


Volume 20, issue 4, 2019 year



Chernyj G.G., Gazovaja dinamika (Gasdynamics), M.: Nauka, 1988, 424 p.
2. Agafonov V.P., Vertushkin V.K., Gladkov A.A., Poljakov O.Ju., Neravnovesnye fiziko-himicheskie processy v ajerodinamike (Non-equilibrium physical-chemical processes in aerodynamics), M.: Mashinostroenie, 1972, 226 p.
3. Zemljanskij B.A., Lunev V.V., Vlasov V.I., Konvektivnyj teploobmen letatel'nyh apparatov (Convective heat transfer of aircrafts), M.: Fizmatlit, 2014, 330 p.
4. Lojcjanskij L.G., Mehanika zhidkosti i gaza (Fluyid dynamics), M.: Drofa, 2003, 840 p.
5. Schlichting H., Boundary-Layer Theory, Springer-Verlag Berlin Heidelberg, 2017, 805 p.
6. Ginzburg I.P., Teorija soprotivlenija i teploperedachi (Theory of resistance and heat transfer), L.: Izd-vo Leningradskogo universiteta, 1979, 375 p.
7. Tugazakov R.Ja. Izv. RAN. MZhG, No. 5, 2019, pp.117−124.
8. Nikitin N.V., Pimanov V.O. Izv. RAN. MZhG, No.1, 2018, pp. 68−76.
9. Dilley A. D., “Evaluation of CFD Turbulent Prediction Techniques and Comparison with Hypersonic Experimental Data,” NASA/CR-2001-210837, March 2001, 26 p.
10. Bertram M. H., Cary Jr., A. M., Whitehead Jr. A. H. Experiments with Hypersonic Turbulent Boundary Layers on Flat Plate and Delta Wings. AGARD Specialists’ Meeting on Hypersonic Boundary Layers and Flow Fields. London, England, May 1968.
11. Bertram M. H., Neal Jr. L. Recent Experiments in Hypersonic Turbulent Boundary Layer. AGARD Specialists’ Meeting on Recent Developments in Boundary Layer Research. Italy, 1965.
12. Wallace J. E. Hypersonic Turbulent Boundary Layer Studies at Cold Wall Conditions. Proc. of the 1967 Heat Transfer and Fluid Mechanics Institute. Stanford University Press. 1967, pp. 427−451
13. Walters R.W., Reu T., McGrory W.D., Hicks J.W., “A Longitudinally Patched Approach with Application to High-Speed Flows,” AIAA Paper 88-0715, 1988, 13 p.
14. Baldwin B.S., Lomax H., “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper 78-0257, 1978, 8 p.
15. Surzhikov S.T., Teplofizika vysokih temperature, Vol. 51, No. 2, 2013, pp.261−276.
16. Surzhikov S.T., Komp'juternaja ajerofizika spuskaemyh kosmicheskih apparatov. Dvuhmernye modeli. (Computational models of reentry space crafts. Two-dimensional models), M.: Fizmatlit, 2018, 543 p.
17. Hayes, W., and Probstein, R., Hypersonic Flow Theory, Academic Press, New York, 1959, pp. 333−374.
18. Avduevskij V.S., Galicejskij B.M., Glebov G.A. Osnovy teploperedachi v aviacionnoj i raketno-kosmicheskoj tehnike (The basics of heat transfer in aviation and rocket and space technology), M: Mashinostroenie, 1975, 624 p.
19. Isaev S. I., Kozhinov I.A., Koranov V.I. Teorija teplomassoobmena (Heat transfer theory), M.: Vysshaja shkola, 1979, 495 p.
20. Bolgarskij A.V., Muhachev G.A., Shhukin V.K., Termodinamika i teploperedacha (Thermody-namics and heat transfer). Izd. 2-e, pererab. i dop., M: Vysshaja shkola, 1975, 496 p.
21. Tannehill J. C., Anderson D. A., Pletcher R. H., Computational Fluid Mechanics and Heat transfer, Taylor&Francis, 1997, 792 p.
22. Date A. W., Introduction to Computational Fluid Dynamics, Cambridge University Press, 2005, 377 p.
23. Cebeci T., Bradshaw P., Physical and Computational Aspects of Convective Heat Transfer, Springer- Verlag, 2012, 486 p.
24. Horstman C. C., “Prediction of Hypersonic Shock-Wave/Turbulent-Boundary-Layer Interaction Flows,” AIAA Paper 87-1367, 1987, 10 p.
25. Shirazi S. A., Truman C. R., “Comparison of Algebraic Turbulence Model for PNS Predictions of Supersonic Flow Past a Sphere-Cone,” AIAA Paper 87-0544, 1987, 12 p.
26. Shang J. S., Scherr S. J., “Navier − Stocks Solution for a Complete Re-Entry Configuration,” J. Aircraft, Vol. 23, No. 12, 1986, pp. 881−888.
27. Cheatwood F. M., Thompson R. A., “The addition of algebraic turbulence modeling to program LAURA,” NASA TM 107 758, 1993, 30 p.
28. Visbal M., Knight D., “The Baldwin − Lomax Turbulence Model for Two-Dimensional Shock-Wave/ Boundary-Layer Interaction,” AIAA Journal, Vol. 22, No. 7, 1984, pp. 921−928.
29. Surzhikov S.T., Physical-Chemical Kinetics in Gas Dynamics, Vol. 16, No. 2, 2015. http://chemphys.edu.ru/issues/2015-16-2/articles/604/
30. Surzhikov S.T., MZhG, No. 6, 2019, pp. 129–140.