New approaches to calculation of the boundary layer by the Karman–Pohlhausen method

Abstract

Several efficient computational schemes, providing the attainment of minimum errors in determining the main parameters of a boundary layer, are presented. The new trinomial polynomial obtained for definition of the velocity profile in the boundary layer much exceeds in accuracy all the known analogous solutions. A scheme of finding a fairly exact solution in the form of the half-sum of the classical Pohlhausen polynomials of the third and fourth degrees is proposed. This solution possesses better approximation properties compared to those of the initial profiles. A high-accuracy solution has been obtained for the velocity profile in the form the velocity profile curve being almost coincident with the exact solution. The friction stress error is . This solution yields an almost exact value of friction stress with very small calculation errors of the displacement thickness (0.12 %) and the form parameter (0.12 %).