Drag reduction in a flat-plate boundary layer flow by polymer additives

This paper presents a theoretical study on the velocity distribution and the friction factor of boundary layer flows with polymer additives starting from the concept of “stress deficit.” A novel method of order of magnitude analysis is developed, which converts the governing equations of boundary layer flow into a solvable ordinary differential equation, thus the total shear stress distribution is obtained, then the formulas for the mean velocity profiles and the friction factor for a boundary layer flow are derived after introducing appropriate expressions for the “effective viscosity” and the thickness of viscous sublayer. The derived velocity equation is able to depict the velocity from a solid wall to the outer edge of boundary layer with or without polymer additives using only one fitted parameter D * that is a function of polymer species, its concentration, and Reynolds number. By integrating the velocity profiles, the friction factor and the thickness of boundary layer development are obtained. Experimental data agree well with the theoretical results.