Two dimensional turbulent boundary layer with favorable pressure gradients: similarity type solution of momentum equation

The turbulent boundary layer momentum equation was solved by using similarity variables to transform the partial differential equation into a more manageable form. Contrary to the case for laminar boundary layers, this equation contained a term involving streamwise derivatives which was not negligible. Thus, a method to estimate the streamwise term was devised. A modification of an eddy viscosity distribution for pipe flow due to Gill and Sher was used to eliminate the Reynolds' shear stresses. The modified Gill and-Sher equation was used for the so-called inner region of the boundary layer while the eddy viscosity was assumed constant in the outer region. Although the eddy viscosity distribution was not representative of the flow for adverse pressure gradients, it was quite satisfactory for zero and favorable pressure gradients involving fully developed turbulent flow. As a consequence of the eddy viscosity distribution, unacceptable results were acquired for adverse pressure gradient cases. The present method was evaluated for zero and favorable pressure gradients by comparing the results with three different flows under various conditions. Good agreement was observed in all cases for the local and average skin friction coefficients and velocity profiles. Except for one boundary layer involving nonequilibrium flows, good results were obtained for the displacement and momentum thicknesses. One of the major advantages of the present method was that a minimum of input information was required. That is, for any given boundary layer, only the approach velocity and the streamwise pressure gradient were needed.