Calculation of the turbulent boundary layer of a flat plate

V. A. Pavlovsky ; S. A. Kabrits

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 4, pp. 370-380

Résumé

The calculation of the turbulent boundary layer is performed when a steady flow of a viscous fluid flows around a flat plate. The calculation is based on a system of equations of turbulent fluid motion, obtained by generalizing Newton’s formula for the tangential stress in a fluid by giving it a power-law form followed by writing the corresponding rheological relationship in tensor form and substituting it into the equation of motion of a continuous medium in stresses. The use of this system for the problem of longitudinal flow around a flat plate after estimates of the boundary layer form made it possible to write a system of equations describing a two-dimensional fluid flow in the boundary layer of a flat plate. This system is reduced to one ordinary third-order equation, similarly to how Blasius performed it for a laminar boundary layer. When solving this equation, the method of direct reduction of the boundary value problem to the Cauchy problem was used. The results of this solution made it possible to determine expressions for the thickness of the boundary layer, displacement and loss of momentum. These values are compared with the available experimental data.

Détail

Mots-clés : turbulence, drag coefficient
Keywords: differential equations of turbulent flow, flat plate, boundary layer, Reynolds number, boundary layer thickness, displacement thickness, momentum loss thickness.