ABOUT ONE MODEL FOR DESCRIBING TURBULENT FLOWS

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

Based on a simple kinetic model, which is used in the derivation of a quasi-gasdynamic system, additional equations for turbulent moments are obtained. The properties of the additional equations are demonstrated by the example of turbulent mixing layer simulation.

About the authors

B. N. Chetverushkin

Keldysh Institute of Applied Mathematics of RAS

Email: chetver@imamod.ru
Moscow, Russia

A. E. Lutsky

Keldysh Institute of Applied Mathematics of RAS

Email: allutsky@yandex.ru
Moscow, Russia

E. V. Shilnikov

Keldysh Institute of Applied Mathematics of RAS

Email: shilnikov@imamod.ru
Moscow, Russia

References

  1. Лойцянский, Л.Г. Механика жидкости и газа / Л.Г. Лойцянский. — М. : Дрофа, 2003. — 840 с.
  2. Loitsyanskii, L.G., Mechanics of Liquids and Gases, Oxford, 2014.
  3. Spalart, P.R. A one equation turbulence model for aerodynamic flows / P.R. Spalart, S.R. Allmaras // Recherche Aerospatiale. — 1994. — № 1. — P. 5–21.
  4. Spalart, P.R. and Allmaras, S.R., A one equation turbulence model for aerodynamic flows, Recherche Aerospatiale, 1994, no. 1, pp. 5–21.
  5. Comparative numerical testing of one and two equation turbulence models for flows with separation and reattachment / M. Shur, M. Strelets, L. Zaikov [et al.] // AIAA Paper. — 1995. — Art. 95–0863.
  6. Shur, M., Strelets, M., Zaikov, L. [et al.], Comparative numerical testing of one and two equation turbulence models for flows with separation and reattachment, AIAA Paper, 1995, art. 95–0863.
  7. Ивахненко, И.А. Квазигазодинамическая модель и мелкомасштабная турбулентность / И.А. Ивахненко, С.В. Поляков, Б.Н. Четверушкин // Мат. моделирование. — 2008. — Т. 20, № 2. — С. 13–20.
  8. Ivakhnenko, I.A., Polyakov, S.V., and Chetverushkin, B.N., Quasihydrodynamic model and small-scale turbulence, Math. Models Comput. Simul., 2009, vol. 1, pp. 44–50.
  9. Wilcox, D.E. Formulation of the K-omega turbulence model revisited / D.E. Wilcox // AIAA J. — 2008. — V. 46, № 11. — P. 2823–2838.
  10. Wilcox, D.E., Formulation of the K-omega turbulence model revisited, AIAA J., 2008, vol. 46, no. 11, pp. 2823–2838.
  11. Использование алгебраической модели турбулентности для расчёта нестационарных течений в окрестности выемок / И.В. Абалакин, А.Н. Антонов, И.А. Граур, Б.Н. Четверушкин // Мат. моделирование. — 2000. — Т. 12, № 1. — С. 45–56.
  12. Abalakin, I.V., Antonov, A.N., Graur, I.A., and Chetverushkin, B.N., Application of an algebraic turbulent model to unsteady flow simulation around a cavity, Mat. Model., 2000, vol. 12, no. 1, pp. 45–56.
  13. Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications / F.R. Menter // AIAA J. — 1994. — V. 32, № 8. — P. 1598–1605.
  14. Menter, F.R., Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J., 1994, vol. 32, no. 8, pp. 1598–1605.
  15. The k-e-Rt turbulence closure / V. Goldberg, O. Peroomain, P. Batten, S. Chakravarthy // Engineering Appl. of Comput. Fluid Mech. —2009. — V. 3, № 2. — P. 175–183.
  16. Goldberg, V., Peroomain, O., Batten, P., and Chakravarthy, S., The k-e-Rt turbulence closure, Engineering Appl. Comput. Fluid Mech., 2009, vol. 3, no. 2, pp. 175–183.
  17. Abdol-Hamid, K.S. Verification and validation of the K-KL turbulence model in FUN 3D and CFL 3D Codes / K.S. Abdol-Hamid, J.-R. Carlson, C.L. Rumsey // AIAA Paper. — 2016. — Art. 2016–3941.
  18. Abdol-Hamid, K.S., Carlson, J.-R., and Rumsey, C.L., Verification and validation of the K-KL turbulence model in FUN 3D and CFL 3D Codes, AIAA Paper, 2016, art. 2016–3941.
  19. Фриш, У. Турбулентность. Наследие А.Н. Колмогорова / У. Фриш. — М. : Физматлит, 1998. — 343 с.
  20. Frish, U., Turbulence: The Legacy of A.N. Kolmogorov, Cambridge: Cambridge University Press, 1995.
  21. Четверушкин, Б.Н. Кинетические схемы и квазигазодинамическая система уравнений / Б.Н. Четверушкин. — М. : Макс-Пресс, 2004. — 328 с.
  22. Chetverushkin, B.N., Kinetic Schemes and Quasi Gasdynamic System of Equations, Barcelona: CIMNE, 2008.
  23. Zlotnik, A.A. On a hyperbolic perturbation of a parabolic initial boundary value problem / A.A. Zlotnik, B.N. Chetverushkin // Appl. Math. Letters. — 2018. — V. 83. — P. 116–122.
  24. Zlotnik, A.A. and Chetverushkin, B.N., On a hyperbolic perturbation of a parabolic initial boundary value problem, Appl. Math. Letters, 2018, vol. 83, pp. 116–122.
  25. Злотник, А.А. О свойствах и погрешности параболического и гиперболического 2-го порядка возмущений гиперболической системы 1-го порядка / А.А. Злотник, Б.Н. Четверушкин // Мат. сб. — 2023. — Т. 214, № 4. — С. 3–37.
  26. Zlotnik, A.A. and Chetverushkin, B.N., Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system, Sb. Math., 2023, vol. 214, no. 4, pp. 444–478.
  27. Четверушкин, Б.Н. Кинетические алгоритмы расчёта течений электропроводящей жидкости на высокопроизводительных вычислительных системах / Б.Н. Четверушкин, В.И. Савельев, А.В. Савельев // Докл. РАН. — 2019. — Т. 489, № 6. — С. 552–557.
  28. Chetverushkin, B.N., Saveliev, A.V., and Saveliev, V.I., Kinetic algorithms for modeling conductive fluids flow on high-performance computing systems, Dokl. Math., 2019, vol. 100, pp. 577–581.
  29. Chetverushkin, B.N. Kinetic consistent MHD algorithme for imcompressible conductive fluids / B.N. Chetverushkin, A.V. Saveliev, V.I. Saveliev // Computer and Fluids. — 2023. — V. 255. — Art. 105724.
  30. Chetverushkin, B.N., Saveliev, A.V., and Saveliev, V.I., Kinetic consistent MHD algorithme for imcompressible conductive fluids, Computer and Fluids, 2023, vol. 255, art. 105724.
  31. Шлихтинг, Г. Теория пограничного слоя / Г. Шлихтинг ; пер. Г.А. Вольперта ; под ред. Л.Г. Лойцянского. — М. : Наука, 1974. — 711 с.
  32. Schlichting, H., Boundary-Layer Theory, Michigan: McGraw-Hill, 1979.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences