A note on the effects of polymer additives on the formation of Goertler vortices in an unsteady flow

Abstract

The addition of a polymer to a fluid has been observed to delay the transition to turbulence. The question then arises: Can the polymer delay the appearance of a hydrodynamic instability, such as the one that leads to Goertler vortices? The experimental technique was the same as that used in Maxworthy [Turbulence Measurements in Liquids (Univ. of Missouri—Rolla, Rolla, MO, 1971), pp. 32–38], where a cylindrical container of fluid in solid body rotation was suddenly brought to rest. The diffusing boundary layer on the curved side wall became unstable to a Goertler vortex pattern after a time that could be related to the initial rotation rate and the critical Goertler number (Gc). For small concentrations of polymer, the increase in Gc was linear in concentration for both Separan AP30 and polyethylene oxide. This number seemed to asymptote to a value of 9.5 for the Separan AP30 above a concentration of 0.10% by weight and to a value of 7.5 for the polyethylene oxide above a concentration of 0.07%. The wavelength of the instabilities increased due to the presence of the polymer; for a 0.1% concentration, the increase was 50% to 90%, depending on the initial rotation speed.