Measuring Invariant (Frame Independent) Quantities Composed of Velocity Derivatives in Turbulent Flows

Abstract

This is a presentation of results of experiments on a turbulent grid flow and few results on measurements in the outer region of a boundary layer over a smooth plate. The air flow measurements included three velocity components and their nine gradients. This was achieved by a 12 hot-wire probe (3 arrays x 4 wires), produced for this purpose using specially made equipment (micromanipulators, etc.), calibration unit and calibration procedure. The probe has no common prongs and the calibration procedure was based on constructing a calibration function for each combination of three wires in each array (total 12) as a three-dimensional Chebishev polynomial of fourth order. A variety of checks were made in order to estimate the reliability of the results. Among the results the most prominent are the experimental confirmation of the strong tendency for alignment between vorticity and the intermediate eigenvector of the rate of strain tensor and the positiveness of the total enstrophy generating term even for rather short events. Emphasis is placed on the necessity to measure invariant quantities, i.e. independent of the choice of the system of reference, as the most appropriate to describe physical processes. From the methodical point of view the main result is that the multi-hotwire technique can be successfully used for measurements of all the nine velocity derivatives in turbulent flows, at least, at moderate Reynolds numbers.