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Laminar Boundary Layer in Two-Dimensional Detached Flows

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Journal of Engineering Physics and Thermophysics Aims and scope

A new approach to the calculation of the laminar boundary layer in a two-dimensional detached fluid flow with the use of two or three integral relations representing the velocity profile of this flow in the form of a definite-degree polynomial is proposed. The initial problem on the indicated layer is defined by the system of two or three ordinary differential equations. The Howart, Tani, and Görtler flows with a decreasing velocity and the flows whose velocity initially increases and then decreases (the Curle flow, the transverse flow around a circular cylinder, and the flow around a sphere) were considered. A comparative analysis of the results of calculations of these flows has shown that the approach proposed allows one to practically exactly determine the point of separation of the boundary layer in them.

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References

  1. J. F. Wendt, Computational Fluid Dynamics. An Introduction, Springer, Berlin (2009).

  2. H. Schlichting and K. Gersten, Boundary-Layer Theory, Springer-Verlag, Berlin (2017).

    Book  Google Scholar 

  3. J. Katz, Low Speed Aerodynamic, Cambridge University Press, New York (2001).

    Book  Google Scholar 

  4. F. M. White, Viscous Fluid Flow, Vol. 1, McGraw-Hill (1974).

  5. V. N. Volkov, A refinement of the Karman–Pohlhausen integral method in boundary-layer theory, J. Eng. Phys. Thermophys., 9, No. 5, 371–374 (1965).

    Article  Google Scholar 

  6. V. A. Kot, Karman–Pohlhausen method: Critical analysis and new solutions for the boundary layer on a plane plate, J. Eng. Phys. Thermophys., 95, No. 4, 1063–1088 (2002).

    Article  Google Scholar 

  7. V. A. Kot, Polynomial approximation of the laminar boundary layer on a flat plate on the basis of the Karman momentum theory, J. Eng. Phys. Thermophys., 96, No. 2, 438–467 (2023).

    Article  Google Scholar 

  8. D. R. Hartree, A Solution of the Laminar Boundary-Layer Equation for Retarded Flow, British Aeronautical Research Council R&M 2426 (1939).

  9. L. Howart, On the solution of the laminar boundary layer equations, Proc. R. Soc. A: Math. Phys. Eng. Sci., 164, 547–579 (1938).

    Google Scholar 

  10. S. Goldstein, On laminar boundary layer flow near a position of separation, J. Mech. Appl. Math., 1, 43–69 (1947).

    Article  MathSciNet  Google Scholar 

  11. K. Stewartson, Is the singularity at separation removable? J. Fluid Mech., 44, 347–364 (1970).

    Article  Google Scholar 

  12. V. A. Wehrle, Determination of the separation point in laminar boundary-layer flows, AIAA J., 24, 1636–1641 (1986).

    Article  Google Scholar 

  13. H. Dumitrescu, V. Cardo, and N. Alexandrescu, Computation of separating laminar boundary-layer flows. Proc. Roman. Acad., Ser. A, 3, Article ID 312003 (2003).

  14. C. Bayeux, E. Radenac, and P. Villedieu, Theory and validation of a 2D finite-volume integral boundary layer method for icing applications, AIAA J., 57, No. 10, (2019); doi: https://doi.org/10.2514/1.J057461.

  15. A. Sunmonu, Development and separation of forced convective flow, Nonlinear Anal. Differ. Equ., 4, 751–778 (2016).

    Article  Google Scholar 

  16. E. A. Akinrelere, Forced convection near laminar separation, Aeronaut. Quart., 32, 212–227 (1981).

    Article  Google Scholar 

  17. V. A. Kot, New aspects in the theory of the laminar boundary layer, Proc. XVI Minsk Int. Forum on Heat and Mass Transfer, A. V. Luikov Institute of Heat and Mass Transfer, National Academy of Sciences of Belarus, Minsk (2022), pp. 140–145.

  18. T. C. Tai, An integral prediction method for three-dimensional flow separation, 22nd AIAA Aerospace Sci. Meeting (1984); doi:https://doi.org/10.2514/6.1984-14.

    Article  Google Scholar 

  19. I. Tani, On the solution of the laminar boundary layer equations, J. Phys. Soc. Jpn., 4, 149–154 (1949).

    Article  MathSciNet  Google Scholar 

  20. H. Gortler, Further development of a boundary-layer profile for a given pressure distribution, ZAMM, 19, 129–140 (1939).

    Google Scholar 

  21. C. Bayeux, Méthode Intégrale Pour la Couche Limite Tridimensionnelle, Université de Toulouse, Ph.D. Thesis (2017).

  22. M. Drela, Two-Dimensional Transonic Aerodynamic Design and Analysis Using the Euler Equations, Ph.D. Thesis, Massachusetts Inst. of Technology (1985).

  23. M. Drela and M. B. Giles, Two-dimensional transonic aerodynamics design method, Am. Inst. Aeronaut. Astronaut. J., 25, 1199–1206 (1987).

    Article  Google Scholar 

  24. B. Thwaites, Approximate calculation of the laminar boundary layer, Aeronaut. Quart., 1, No. 3, 245–280 (1949).

    Article  MathSciNet  Google Scholar 

  25. V. A. Wehrle, Determination of the separation point in laminar boundary-layer flows, AIAA J., 24, No. 10, 1636–1641 (1990).

    Article  Google Scholar 

  26. R. Timman, A one-parameter method for the calculation of laminar boundary layers, Rep. F.35, National Luchtvaartlaboratorium, Amsterdam, pp. 29–46 (1949).

  27. N. Curle, Accurate solutions of the laminar boundary-layer equations for flows having a stagnation point and separation, British Aeronaut. Res. Council R&M 3164 (1960).

  28. R. M. Terrill, Laminar boundary-layer flow near separation with and without suction, Philos. Trans. R. Soc. Lon., A, 253, 55–100 (1960).

  29. K. Hiemenz, Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Krieszylinder, Ph.D. Thesis, University of Göttingen (1911).

  30. N. Rott and L. F. Crabtree, Simplified laminar boundary-layer calculations for bodies of revolution and for yawed wings, J. Aeronaut. Sci., 8, 553–565 (1952).

    Article  Google Scholar 

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Correspondence to V. A. Kot.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 96, No. 6, pp. 1620–1640, November–December, 2023

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Kot, V.A. Laminar Boundary Layer in Two-Dimensional Detached Flows. J Eng Phys Thermophy 96, 1610–1630 (2023). https://doi.org/10.1007/s10891-023-02832-8

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