The influence of a drag-reducing surfactant on a turbulent velocity field

Abstract

A two-component laser-Doppler velocimeter, with high spatial and temporal resolution, was used to study how the introduction of a drag-reducing surfactant to water changes the fully-developed velocity field in an enclosed rectangular channel. Measurements were made for four different Reynolds numbers, Re = 13300; 19100; 32000, and 49100 (based on the bulk viscosity, the half-height of the channel, and the viscosity of water). For a fixed volumetric flow the pressure drop was reduced by 62 to 76% when compared to a Newtonian flow with an equal wall viscosity. Measurements were made of the mean streamwise velocity, the root mean square of two components of the fluctuating velocity, the Reynolds shear stress and the spectral density function of the fluctuating velocity in the streamwise direction. The Reynolds shear stress is found to be zero over the whole channel and the spectra of the streamwise velocity fluctuations show a sharp cutoff at a critical frequency, f_c. The ratio of the cutoff frequency to the root mean square of the streamwise velocity fluctuations is found to be approximately equal to 1 mm⁻¹. The observation of a zero Reynolds shear stress indicates the existence of additional mean shear stresses (or mean transfers of momentum) that are not seen with a Newtonian fluid. Furthermore, the presence of a random fluctuating velocity field suggests a production of turbulence by a mechanism other than that usually found for a fully developed flow. Possible explanations for this behaviour are presented.