Particle-sampling statistics in laser anemometers: sample-and-hold systems and saturable systems

Abstract

The output statistics of a laser anemometer operating in a low particle density are discussed. A rigorous derivation is given for the influence of two popular data-handling algorithms on these statistics. In particular it is shown that the measured statistics can differ from those of the flow statistics and from the particle-arrival statistics. The variables that control the statistical regime are derived and quantitative estimates are given for their ranges of influence.The first system discussed is a sample-and-hold system where the output is a piecewise-continuous signal obtained by holding the last processor measurement until a new one is obtained. The second system is one where an attempt is made to store all the measurements for processing, but which contains a rate-limiting device. Because of this device, some measurements may be lost when the particle rate is high. This system is referred to as a saturable system.In both cases it is found that the statistics of the output depend on the product of the mean particle rate and the flow correlation time as well as the flow statistics. The statistics of the saturable system also depend on the ratio of the mean particle rate to the maximum rate at which measurements can be accepted by the system. Because of this, the statistics of both systems depend on the particle density.Attainable conditions are demonstrated, where the output velocity measurement statistics are essentially identical with the flow statistics.