Measurement in Intermittent and Periodic Flow

Abstract

For the purpose of the present discussion, it may be taken for granted that the signals from the various individual probes (hot-wire, LDA, microphone) follow faithfully the physical variables at a given point, consequently the concern here is shifted to the signal processing techniques that enable the extraction of relevant information about the nature of the flow field.

The methods to be discussed here all deal with the full, essentially unfiltered, signals. On the other hand, sampling and averaging are performed subject to some criterion developed in real time. The earliest and also the most developed among the methods is conditional sampling in combination with ensemble averaging. Originally introduced by the author in the 1960’s with this method in an intermittent turbulent flow, one may obtain separate average values for the turbulent state and for the non-turbulent state. Further refinements include the introduction of the point average. In that case, samples are taken only at certain specific instants, subject to some well-defined criteria, such as the instant when the turbulent interface passes over the detector probe.

In the simplest case when the sampling criterion is obtained from a periodic signal, the above method is called periodic sampling. The applications are quite numerous. When studying the flow field in rotating machinery, the instantaneous position of the rotor blades may be used for a sampling criterion; then by averaging over a large number of periods the strictly periodic or “deterministic” portion of the phenomenon can be fully recovered.

The most advanced signal processing offered today is termed as “pattern recognition”. In its simplest form, this involves only rescaling typical events, both in amplitude and in time. The first events detected this way were the socalled “bursts” and “sweeps” observed near the wall in turbulent flows. As the use of large scale computers is advancing rapidly, this new method will be used more extensively to “recognize” the passage of typical large-scale coherent turbulent structures.

But, at this point, one must also give a word of caution. The conditional sampling and pattern recognition methods always give some spurious response when applied to a random signal. The only proper protection against such “false alarm” is to check-out the circuit, or the computer program, first on an artificial random signal, designed to possess the same overall statistical properties (spectra and probability density function) as the flow field and see how much “false alarm” will be detected by using the original criteria on this synthetic signal.