An Analysis of Uniform Injection of a Drag-Reducing Fluid into a Turbulent Boundary Layer

Abstract

The purpose of this analysis is to evaluate the mass flux requirements for drag reduction by uniform injection of a high molecular weight polymer solution into a turbulent boundary layer on a flat plate or slender body of revolution. This evaluation is necessary in order to determine the feasibility of using polymer solutions to reduce skin friction drag on marine vehicles. Uniform injection is chosen for analysis since it raises the additive concentration to the drag reducing level in the wall region only, where recent experiments have shown that it is needed. Calculations of skin friction reduction and mass flux required are plotted for conditions of interest for marine vehicles. Distributed injection is compared with slot injection and is found to require between 40 and 140 times less additive solution than does slot injection to maintain equivalent drag reduction. A “specific additive consumption” is defined and compared with specific fuel consumption of several underwater propulsion units. The comparison shows slot injection of a 1000 ppm solution to be of marginal value, while porous wall injection would give more performance increase than adding an equal amount of fuel. The point is made that there is considerably more performance advantage to be gained from a continuous ablating additive coating than from additional fuel, if it could be made to ablate at the optimum rate.