Author(s)

Luigi A. Antonialli, Aristeu Silveira-Neto

Faculdade de Engenharia Mecanica, Universidade Federal de Uberlandia, Uberlandia, Minas Gerais, Brazil.

This research used the common decomposition of the velocity and pressure in an average part and a fluctuating part, for high Reynolds number, of the Navier-Stokes equation, which leads to the classic problem of turbulent closure. The Prandtl’s mixing length model, based on the Boussinesq hypothesis and traditionally used for free shear flows, was chosen and adapted for internal flows to solve the closure problem. For channel flows, Johann Nikuradse proposed a model for the Prandtl mixing length. In the present paper, which has an academic character, the authors made a return to the model of the mixing length of Prandtl and the model of Nikuradse, to solve turbulent flows inside a plane channel. It was possible to develop an ordinary differential model for the velocity in the direction of the flow whose solution occurs computationally in a simple but extremely accurate way when compared with Direct Numerical Simulation databases. For the viscous stress on the wall, it was possible to determine the exact mathematical solution of the ordinary differential equation. It is a model of great academic value and even to be used as reference for verification of computational codes destined to the solution of complete numerical and computational models.

Mixing Length, Channel, Pipe, Turbulent Flow

Antonialli, L. and Silveira-Neto, A. (2018) Theoretical Study of Fully Developed Turbulent Flow in a Channel, Using Prandtl’s Mixing Length Model. Journal of Applied Mathematics and Physics, 6, 677-692. doi: 10.4236/jamp.2018.64061.