Accession Number : AD0874793

Title :   Dilution of a Polymer Additive in a Turbulent Boundary Layer on a Body of Revolution.

Descriptive Note : Conditional rept.,

Corporate Author : NAVAL UNDERWATER SYSTEMS CENTER NEWPORT RI

Personal Author(s) : Lessman, R. C.

Report Date : 15 JUL 1970

Pagination or Media Count : 36

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)

Descriptors :   (*BODIES OF REVOLUTION, TURBULENT BOUNDARY LAYER), (*TURBULENT BOUNDARY LAYER, ADDITIVES), (*DRAG, POLYMERS), THICKNESS, REDUCTION, TORPEDOES, CONCENTRATION(CHEMISTRY), FLOW FIELDS, FLUID FLOW, NUMERICAL ANALYSIS, FLAT PLATE MODELS, VELOCITY, PROBLEM SOLVING, APPROXIMATION(MATHEMATICS), MOLECULAR WEIGHT, EJECTION, HYDRODYNAMICS.

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE