• Vitaliy Mamchuk National Aviation University
  • Ivan Lastivka National Aviation University
  • Oleksandr Bezverkhyi S. P. Timoshenko Institute of Mechanics



boundary layer, pressure gradient, turbulent viscosity, velocity profile, wall stream


Purpose: Mathematical modeling of complex turbulent near-wall flows, that occur during the flow of airfoils, is impossible without understanding the nature of the flow in boundary layer. From a mathematical point of view, the calculation of such flows, because in practical problems they regarded as turbulent, and the characteristics of turbulence are largely dependent on the geometry of the profile of the longitudinal component of the average velocity of the near-wall flow. Based on this, the purpose of this work is studying and mathematical modeling of turbulent near-wall flows in the interaction with the real streamlined surface, that has certain features, such as the curvature, roughness, etc., as well as the study and research of the influence of the pressure gradient on the empirical coefficients, parameters of the flow, velocity profiles and friction stress. Methods: We performed the calculations using numerical finite-difference marching method with algebraic model of turbulent viscosity coefficient. Results: In this paper we present some results of the numerical study of the effect of the positive pressure gradient on the empirical coefficients of the transition zone and the law of the near-wall and the outer-wall areas. Discussion: Comparison of the calculated results with the experimental data shows that the proposed approaches provide an opportunity to simulate the flow as close as possible to their physical properties. Presented mathematical model for the calculation of turbulent boundary layers and near-wall flows makes it possible to calculate such a complex and valuable from a practical point of view type of the flow as the aerodynamic trail behind the streamlined body.

Author Biographies

Vitaliy Mamchuk, National Aviation University

Ph.D., Associate Professor.

Higher and Computational Mathematics, Educational and Research Institute of Computer Information Technologies, National Aviation University, Kyiv, Ukraine.

Education: Ivan Franko National University of Lviv, Lviv, Ukraine (1973).

Research area: applied problems of mechanics

Ivan Lastivka, National Aviation University

Doctor of Technical Sciences, Professor.

Head of Department of Mathematics, Educational and Research Institute of Economics and Management, National Aviation University, Kyiv, Ukraine.

Education: Taras Shevchenko National University of Kyiv, Kyiv, Ukraine (1982).

Research area: models and methods to improve aerodynamic and aeroelastic performance of compressors of gas turbine engines.

Oleksandr Bezverkhyi, S. P. Timoshenko Institute of Mechanics

Doctor of physical and mathematical sciences, Professor.

Head of Department of electroelasticity of S.P.Timoshenko Institute of Mechanics, Kyiv, Ukraine

Education: Dnipropetrovsk State University, Dnipropetrovsk, Ukraine (1976).

Research area: hydroelectroelasticity


Ahlbery J. H. Theory of Splines and Their Applications / J. H. Ahlbery, E. N. Nilson, J.L. Walsh. – New York, 1967.

Computation of turbulent boundary layers. [Ed. S. J. Kline, E. A. Morcovin, G. Sovran, G.J. Cockrell]. 1968: AFOSRIPF Stanford Conference. – Stanford : University, 1969. Vol. 1, 590 p.

Fedyaevskyy K. K. Calculation of turbulent boundary layer of an incompressible fluid / K. K. Fedyaevskіy, A. S. Hynevskyy, A. V. Koles¬nikov. – St.P. : Sudostroenye, 1973, 256 p. (in Russian).

Kocheryzhnykov G. V. About experience of numerical integration of turbulent boundary layer. G. V. Kocheryzhnykov, S. K. Matveev Hydroaeromechanic and theory of elasticity. 1968, Vol. 13, P. 39–50. (in Russian).

Horstmen. Turbulence model for calculating nonequilibristic streams at positive pressure gradient / Horstmen // Rocket technics and spacecraft. – 1977, Vol. 15, № 2, P. 5–7. (in Russian).

Lapyn U. V. The problem of "merging" in theory nonequilibristic turbulent streams / U. V. Lapyn, A. L. Yarin // Mechanics of fluid and gas. – 1979, № 3, P. 33–41. (in Russian).

Mamchuk V. I. Mathematical modeling of turbulent near wall flaws on the oscillating bodies / V. I. Mamchuk // Bulletin of Lviv. Univ, Sir. glue. Math. and Information. 2002, Vol. 4, P. 131–136. (in Ukrainian).

Mamchuk V. I. Turbulence model and the results of calculations of plane turbulent near–wall steams / V. I. Mamchuk // Bulletin KIUCA. – K. : KIUCA. – 1998, № 1, P. 291–294. (in Ukrainian).

Novozhilov V. V. Theory flat turbulent boundary layer of an incompressible fluid / V. V. Novozhylov. St. P: Sudostroenye, 1977, 164 p. (in Russian).

Pletcher. Calculation of turbulent boundary layer at small Reynolds numbers. Rocket Technics and Space. 1976, Vol. 14, № 5, P. 181–183. (In Russian).

Sebesy. Kinematic turbulent viscosity at small Reynolds numbers. Rocket technics and spacecraft. – 1973, Vol. 11, № 1, P. 121–123. (in Russian).

Tulapurkara G. Interaction boundary layer with trace of bodies of different shapes / G. Tulapurkara, V. Ramzhy, R. Radzhasekar // Aerospace technic. – 1990, № 12, P. 3–10. (in Russian).

Hyntse Y. O. Turbulence. Moscow: Fyzmathyz, 1963, 680 p. (in Russian).

Yoon A. A. Theory and practice of modeling turbulent streams / A. A. Yoon. – Moscow: Book house "Liberkom", 2009, 272 p. (in Russian).

Mellor. Incomeresible turbulent boundary layer at arbitrary pressure gradient with parting transverse flow / Mellor // Rocket technics and spacecraft. – 1977, Vol. 5, № 9, P. 43–54. (in Russian).

Computation of turbulent boundary layers / Ed. P. E. Coles, E. A. Hirst. – 1968: AFOSR– IPF Stanford Conference. – Stanford : University, 1969, Vol. 2, 519 p.

Aerodynamic traces in the gas compressor turbine engines : Monograph / [Y. M. Tereshchenko, M. S. Kulik, I. O. Lastivka and others]; ed. Y. M. Tereshchenko. – K. : NAU-Druk, 2012, 232 p. (in Russian).

Lastivka I. O. The calculation of aerody¬namic trace parameters behind compressor grating blade / I. O. Lastivka // Eastern European Journal of advanced technologies. – Kharkiv: Technological Center, 2011, № 4/7 (52), P. 47–50. (in Ukrainian).



How to Cite

Mamchuk, V., Lastivka, I., & Bezverkhyi, O. (2016). RESEARCH AND MATHEMATICAL MODELING OF TURBULENT BOUNDARY LAYER AT POSITIVE PRESSURE GRADIENT. Proceedings of National Aviation University, 67(2), 37–43.