The influence of strongly turbulized liquid flow parameters on the near-wall transitional flows in the boundary layer

V.M. Zubarev

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia

E-mail: zubarev@ipmnet.ru

Received February 28, 2019

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DOI: 10.26907/2541-7746.2020.1.38-51

For citation: Zubarev V.M. The influence of strongly turbulized liquid flow parameters on the near-wall transitional flows in the boundary layer. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 1, pp. 38–51. doi: 10.26907/2541-7746.2020.1.38-51. (In Russian)

Abstract

The effect of the scale and the high intensity of incident-flow turbulence in a boundary layer on a smooth plane plate with rounded edge (experiment T3H) under a zero pressure gradient was analyzed. Using the well-known experimental and calculated data, the modeling problem of the initially laminar boundary layer transfer to the turbulent one was investigated by the numerical methods on the basis of the near-wall modified turbulence model with two additional transfer equations for the turbulent kinetic energy and the turbulence dissipation rate. Turbulent flows modeling near the flat surface with the high level of incident-flow turbulence is complicated by two general problems: the definition and description of the laminar-to-turbulent transfer along the surface and the viscous sublayer precise resolution under the developed turbulent mode. For the inviscid liquid flowing along the flat plate with the high turbulence degree of more than 1%, the turbulence scale and the incident-flow turbulence intensity joint influence on the flow dynamic and integral characteristics in the boundary layer and turbulence parameters was studied in detail.

Keywords: near-wall turbulent flows, mainstream turbulence parameters, turbulent k-ε model, boundary layer, numerical method, incompressible liquid

Acknowledgments. The study was performed as part of the state assignment (state registration no. AAAA-A20-120011690135-5).

Figure Captions

Fig. 1. The local friction coefficient Cf (Reξ ) (a) and shape factor H(Reξ ) (b) dependencies on the Reynolds number Reξ on longitudinal coordinate at the turbulence dissipation ε¯∞ different values in the external stream 1 –3: 5 is the laminar flow (the Blasius formula); 6 is the developed turbulent flow (Prandtl law); 4 are the experimental points [4].

Fig. 2. The Reynolds number Reθ (Reξ ) dependence by the momentum loss thickness on the Reynolds number Reξ on longitudinal coordinate at ε¯∞ = 1.84 (a); the local friction coefficient cf (Reθ ) dependence on the Reynolds number Reθ by the momentum loss thickness (b): solid line 1 is the calculation; curve 3 is the formula (8); curve 4 is the formula (9); 2 are the experimental points [4].

Fig. 3. The local friction coefficient Cf (Reξ ) dependence on the Reynolds number Reξ on longitudinal coordinate (a): solid line 1 is the approximation by the formula (10); curve 3 is the Blasius formula; curve 4 is the Prandtl formula; the local friction coefficient correlation Cf (Reθ ) on the Reynolds number Reθ by the momentum thickness (b): solid line 1 is the approximation by the formula (11); curve 3 is the laminar law, formula (8); curve 4 is the turbulence law, formula (9); 2 are the experimental points [4].

Fig. 4. The Reynolds number Reθ (Reξ ) (left) and the shape factor H(Reξ ) (right) dependencies (a): solid line 1 is the approximation by the formula (12); curve 3 is the approximation by the formula (13); 2, 4 are the experimental points [4]; the displacement thickness δ∗(ξ¯) (b): solid line 1 is formula [14]; dash curve 2 is formula from the study [16]; 3 are the experimental points [4].

Fig. 5. The longitudinal average velocity profiles u+(ζ+) distribution in wall law variables in the boundary layer sections ξ¯ = 0.2 (a), 0.3 (b): solid line 1 is the calculation; dotted line 3 is the linear wall law, u+ = ζ+ ; dash curve 4 is the logarithm profile (the Clauser formula) u+ = 2.5 ln ζ+ + 5.1 ; 2 are the experimental points [4].

Fig. 6. The kinetic energy intensity (2/3k)1/2/u and the longitudinal velocity measured mean-squared pulsations <u/2>1/2/u distribution across the boundary layer in sections ξ¯ = 0.2 (a), 0.3 (b): solid line 1 is the calculation; 2 are the experimental points [4].

References

  1. Taylor G.I. The statistical theory of isotropic turbulence. J. Aerosp. Sci., 1937, vol. 4, no. 8, pp. 311–315. doi: 10.2514/8.419.
  2. Dryden H.L. Transition from laminar to turbulent flow. In: Turbulent Flows and Heat Transfer. Lin Ch.-Ch. (Ed.). Princeton, Princeton Univ. Press, 1959, pp. 1–74. doi: 10.1515/9781400879410-003.
  3. Wilcox D.C. Turbulence Modeling for CFD. La Canada, California, DCW Industries Inc., 1994. XIX + 460 p.
  4. Epik E.Ya. Heat transfer effects in transitions. Turbulent Heat Transfer: Proc. Eng. Found. Conf. 1996 (New York; San Diego, California, March 10–15, 1996), 1996, pp. 1– 47.
  5. Zubarev V.M. Joint effect of free stream turbulence parameters on flow transition in a boundary layer. Tepl. Protsessy Tekh., 2016, vol. 8, no. 1, pp. 4–15. (In Russian)
  6. Myong H.K., Kasagi N. A new approach to the improvement of k-ε turbulence model for wall bounded shear flows. JSME Int. J., Ser. II, 1990, vol. 33, no. 1, pp. 63–72.
  7. Hirschel E.H., Kordulla W. Shear Flow in Surface-Oriented Coordinates (Notes on Numerical Fluid Mechanics, V. 4). Vieweg + Teubner Verlag, 1981. X, 266 p. doi: 10.1007/978-3-663-05276-0.
  8. McConnell A.J. Applications of Tensor Analysis. New York, Dover Publ., 1957. 318 p.
  9. Launder B.E., Spalding D.B. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng., 1974, vol. 3, no. 2, pp. 269–289. doi: 10.1016/0045-7825(74)90029-2.
  10. Patel V.P., Rodi W., Scheuerer G. Turbulence models for near-wall and low Reynolds number flows: A review. AIAA J., 1985, vol. 23, pp. 1308–1319. doi: 10.2514/3.9086.
  11. Schlichting H. Boundary-Layer Theory. New York, McGraw-Hill, 1979. 817 p.
  12. Kolmogorov A.N. Equations of motion of an incompressible turbulent fluid. Izv. Akad. Nauk SSSR Fiz., 1942, vol. 6, nos. 1–2, pp. 56–58. (In Russian)
  13. Prandtl L. U¨ ber ein neues Formelsystem fu¨r die ausgebildete Turbulenz. Nachr. Akad. Wiss. Goettingen, Math.-Phys. Kl. Göttingen, Vandenhoeck & Ruprecht, 1945. S. 6–19. (In German)
  14. Wang J.H., Jen H.F., Hartel E.O. Aerofoil heat transfer calculation using a low Reynolds number version of a two-equation turbulence model. Trans. ASME, J. Eng. Gas Turbines Power, 1985, vol. 107, no. 1, pp. 60–67. doi: 10.1115/1.3239698.
  15. Zubarev V.M. Numerical simulation of turbulent incompressible flow with increasing adverse pressure gradient. J. Eng. Phys. Thermophys., 2019, vol. 92, no. 3, pp. 631–639. doi: 10.1007/s10891-019-01972-0.
  16. Loitsyanskii L.G. Mekhanika zhidkosti i gaza [Mechanics of Liquids and Gases]. Moscow, Nauka, 1987. 824 p. (In Russian)

 

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