Coherent structures in uniformly sheared turbulent flow

Uniformly sheared turbulent flow has been generated in a water tunnel and its instantaneous structure has been examined using flow visualization and particle image velocimetry. The shear-rate parameter was approximately equal to 13 and the streamwise turbulence Reynolds number was approximately 150. The flow was found to consist of regions with nearly uniform velocity, which were separated by regions of high shear containing large vortices. The concentration of vortices and the distributions of their directions of rotation, strengths, sizes and shapes have been determined. These results demonstrate that horseshoe/hairpin-shaped vortices were prevalent, even though wall effects were negligible in this flow. Both ‘upright’ and ‘inverted’ vortices have been observed, in contrast to turbulent boundary layers, in which only ‘upright’ vortices can be found, suggesting that the presence of the wall may suppress the development of ‘inverted’ structures. Our observations demonstrate that the dominant coherent structures of fully developed uniformly sheared flow are very different from the structures observed in the flow exiting the shear-generating apparatus, which points to an insensitivity of the former to initial effect

Measurements of turbulent diffusion in uniformly sheared flow

The diffusion of a plume of dye in uniformly sheared turbulent flow in a water tunnel was investigated using simultaneous stereoscopic particle image velocimetry (SPIV) and planar laser-induced fluorescence (PLIF). Maps of the mean concentration and the turbulent concentration fluxes in planes normal to the plume axis were constructed, from which all components of the second-order turbulent diffusivity tensor were determined for the first time. Good agreement between the corresponding apparent and true diffusivities was observed. The turbulent diffusivity tensor was found to have strong off-diagonal components, whereas the streamwise component appeared to be counter-gradient. The different terms in the advection–diffusion equation were estimated from the measurements and their relative significance was discussed. All observed phenomena were explained by physical arguments and the results were compared to previous one

Relative dispersion of a passive scalar plume in turbulent shear flow

Relative dispersion of a passive scalar plume was investigated in uniformly sheared, nearly homogeneous, turbulent flow with Re??150 using planar laser-induced fluorescence. Mean concentration maps were determined both in the laboratory frame and in a frame attached to the instantaneous center of mass of the plume cross section. The distance-neighbor function had a shape that was compatible with Richardson's expression. The mean square particle separation, two estimates of which were found to be nearly identical, had a streamwise evolution that was consistent with Richardson-Obukhov scaling with a Richardson's constant of g=0.35. Batchelor scaling was also consistent with a wide range of the result

HANDS-ON EXPERIMENTATION IN THE FLUID MECHANICS CLASSROOM AS HOMEWORK WITH EFLUIDS.COM

ABSTRACT In an introductory fluid mechanics course, it is important for students to realize that the mathematical models they are deriving in class sometimes model the real world well and sometimes not so well. One way to demonstrate this is to have the students model a simple experiment and compare the results of the model to those of the experiment. This exercise teaches the importance of the model assumptions and the applicability of the model. It would be even more effective if the experiments were simple enough so that students could do them at home as a homework assignment, rather than restricting their experience to a "canned" two hour lab course. At eFluids.com, we are building a library of such experiments in an effort to build a community of educators that moves beyond the traditional mathematical exercises for homework. Here, we describe a number of these experiments and how they can be used in classes

On the accuracy of PLIF measurements in slender plumes

The purpose of this article was to assess the measurement uncertainty of the planar laser-induced fluorescence (PLIF) method and, as much as possible, to devise corrections for predictable biases. More specifically, we considered the measurement of concentration maps in cross sections parallel to and normal to the axis of a slender plume containing Rhodamine 6G as a passive scalar tracer and transported by a turbulent shear flow. In addition to previously examined sources of error related to PLIF, we also investigated several unexplored ones. First, we demonstrated that errors would arise if the laser sheet thickness was comparable to or larger than the thickness of the instantaneous plume. We then investigated the effect of secondary fluorescence, which was attributed to absorption and re-emission of primary fluorescence by dye both within and outside the laser sheet. We found that, if uncorrected, this effect would contaminate the calibration as well as the instantaneous concentration measurements of the plume, and proposed methods for the correction of these errors and for identifying the instantaneous boundaries of the in-sheet dye regions