Drag reduction in a flat-plate turbulent 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. Disciplines Engineering | Science and Technology Studies Publication Details Yang, S. & Dou, G. (2005). Drag reduction in a flat-plate turbulent boundary layer flow by polymer additives. Physics of Fluids, 17 (6), 065104-1-065104-13. This journal article is available at Research Online: http://ro.uow.edu.au/eispapers/2044 Drag reduction in a flat-plate boundary layer flow by polymer additives Shu-Qing Yang and G. Dou Division of Civil and Environmental System Engineering, Korea Maritime University, Busan 606791, Republic of Korea and Maritime Research Centre, Nanyang Technological University, Singapore 639798 sReceived 8 July 2004; accepted 7 April 2005; published online 26 May 2005d 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. © 2005 American Institute of Physics. fDOI: 10.1063/1.1924650g