A Study of Turbulence and Diffusion Using Tracers in a Water Tunnel

Abstract

A study of turbulence in a water tunnel was made by observing the motion of small liquid droplets having the same density as water. These tracers were injected into the flow and their trajectories were photographed with a fixed camera using a stroboscopic light. From measurements of the photographic plates it was possible to calculate instantaneous velocities, turbulence intensities and Lagrangian correlation coefficients. Runs were made both with and without a turbulence-producing grid; three geometrically similar grids were used. From 11 to 35 separate trajectories were measured for each run. Each point value of the turbulence characteristics is an ensemble average. The biggest limitation on the practical application of this method is the inevitable sampling error in the calculated intensities and correlations. These errors were large, even when 35 trajectories were measured; they can be reduced only by greatly increasing the number of trajectories analyzed. A satisfactory experimental technique for photographing and measuring the trajectories of the tracers was developed, but the computations are still very laborious. The results of the study showed that a large fraction of the turbulent energy of the field may be attributed to substantial differences between the mean velocities of different tracers over the 3-ft observation reach. The decay of turbulence energy with distance showed a linear relation between the reciprocal of the energy and the distance, as has been previously found, but a strong Reynolds number effect was observed. The correlation curves indicated that the time scale was fairly large, and it appeared that practically all the energy was associated with relatively low frequencies. Unfortunately, the data were not extensive enough to permit calculation of the diffusion coefficients from the Lagrangian correlations in accordance with Taylor's theory.