The measurement of Reynolds stresses with a pulsed-wire anemometer

Abstract

An investigation of the errors arising in pulsed-wire anemometer measurements of the Reynolds stresses in turbulent flows is described. Attention is concentrated first on a theoretical approach, in which an idealized yaw response and an assumed form for the joint velocity probability-density distribution are used to determine the errors in measurements of, principally, $\overline{uv}$ and $\overline{v^2}$ when the probe is used like an ordinary single slanted hot wire. Actual pulsed-wire measurements in a range of turbulent shear flows are then compared with crossed-hot-wire results and with the theoretically simulated pulsed-wire response obtained from calculations and the crossed-wire data. It is shown that whilst pulsed-wire measurements of lateral intensity and shear stress are inevitably rather unsatisfactory in regions of low intensity (less than 10%, say) they agree reasonably well with crossed-wire measurements in flows where the intensities are higher, but do not exceed those for which sensible corrections to cross-wire data are possible (up to, say, 30%). In this medium-intensity range, however, the pulsed-wire errors are found to be critically dependent on the finite limit of the pulsed wire's yaw response; it seems that acceptable measurements can only be made if this exceeds about 75°. Beyond an intensity of about 30% the errors in $\overline{v^2} $ measurements (which are usually much higher than those for $\overline{uv}$) become less dependent on the exact nature of the yaw response and invariably decrease with increasing intensity. They can, with care, be made as low as 15%. It is concluded that pulsed-wire measurements of the Reynolds stresses can be made with an accuracy similar to that of crossed-wire measurements in medium-intensity flows. Such measurements are certainly adequate for many practical purposes in high-intensity flows where hot-wire techniques are useless.