Projected area of measurement volume in phase-Doppler anemometry and application for velocity bias correction and particle concentration estimation

The measurement volume in laser-Doppler anemometry is non-spherical, which leads to the fact that the projected area to the fluid flow varies with direction of the flow. The mathematical description of this direction-dependent projected area in the case of a 3-D phase-Doppler anemometer is developed. It is shown that depending on the angle between the 2-D and the 1-D probe the projected area variation with direction ranges from 40% for an orthogonal setup, to 275% when the angle is 30°. In the case of complex 3-D flows, as in agitated tanks, this projected area variation leads to a direction bias in determination of time averaged values of the flow. By using experimental data from an agitated suspension, it is shown that the bias effect on the mean velocity can be neglected for an orthogonal optical setup. However, at decreasing angle between the probes this effect may become important. In addition, it is also shown that in determination of particle concentrations in agitated tanks the variation in projected area must be accounted for.