Similarity Solutions of Two Dimensional Turbulent Boundary Layers by Prandtl Mixing Length Modelling

Bohua Sun

doi:10.20944/preprints202202.0008.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 31 January 2022 / Approved: 1 February 2022 / Online: 1 February 2022 (12:10:25 CET)

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no similarity solutions (special exact solutions) have ever been found. In the light of Blasius' pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. By author's Maple code, we numerically solve the ordinary differential equation and produce some useful quantities.

Turbulent boundary layers; laminar boundary layers; similarity transformation; similarity solution; Prandtl mixing length; Reynolds number

Physical Sciences, Fluids and Plasmas Physics

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Similarity Solutions of Two Dimensional Turbulent Boundary Layers by Prandtl Mixing Length Modelling

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