An algebraic-Q4 turbulent eddy viscosity model: Boundary layer flow over a flat plate and flow in a pipe

An algebraic turbulent eddy viscosity model is proposed based on a length scale model coupled with the turbulent viscosity expression of the renormalization group theory of turbulence. The eddy viscosity is presented as a solution of a quartic equation. The new length scale model is based on boundary layer characteristics (displacement thickness, shape factor). The model is applied to transitional boundary layer flow over a flat plate and to flow in a smooth pipe. Predictions for the laminar-turbulent transition, and integral characteristics, such as the total skin friction coefficient, mean velocity profile across the boundary layer, and the friction coefficient in a pipe, are found to be in good agreement with experimental data.