Estimation of cross-power spectra using sample-and-hold reconstruction of laser Doppler anemometry data

Abstract

Measurement of turbulent spatial and temporal length scales is an increasingly important aspect of analysis in fluid mechanics. This information is derived either from the cross correlation or the cross spectrum between two measurements. The use of a laser Doppler anemometer (LDA) further complicates the determination of these properties because of the random data acquisition associated with LDA measurements. The calculation of the cross spectrum obtained for LDA data with equispaced data from a conventional instrument such as a hot wire anemometer (HWA) and for two LDA systems is considered. For each case, sample-and-hold reconstruction of the LDA data is used. The errors in cross spectrum estimates together with coherence function calculations (i.e. frequency domain cross covariance) are derived and procedures for correcting the cross spectrum and, hence, the phase and the coherence, are proposed. The results from numerical simulations with prescribed coherence and phase are shown to produce good results up to and beyond the equivalent Nyquist frequency based on the mean LDA data rate. Finally, the procedures are applied to two point LDA measurements in a jet and the results, using the proposed procedures, are shown to compare favourably with those obtained from the correlation slotting method.