Dilution of a Polymer Additive in a Turbulent Boundary Layer on a Body of Revolution.
Abstract
This paper treats the problem of calcuating wall concentration of a polymer additive injected into a turbulent boundary layer on a body of revolution. The theory requires specification of a similarity law for local concentration as well as a form for the time averaged velocity profile. The chosen concentration law is a generalized form of an empirical profile found valid for the flat plate case. solutions are presented for a 1/n power law profile (not deemed suitable for polymer seeded flows), and for a generalized logarithmic law of wall corrected by Coles' law of wake. the 1/n power law leads to a final solution for the boundary layer thickness (obtained from the momentum integral equation), which involves a straight-forward numerical quadrature dependent upon the geometry of the body. Assuming the generalized profile leads to a nonlinear differential equation for the shear velocity (related to the boundary layer thickness) requires a numerical solution. In nearly cylindrical regions, the solution of this equation simplifies to a quadrature dependent only on a boundary condition and on a polymer constant in the velocity profile. In each case, the dilution law, while appearing complicated, depends on a one-time evaluation of several special functions using values of the constants appearing in the assumed profiles. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 15, 1970
- Accession Number
- AD0874793
Entities
People
- R. C. Lessman
Organizations
- Naval Underwater Systems Center