Spectral analysis of individual realization LDA data

Abstract

The estimation of the autocorrelation function (act) or the spectral density function (sdt) from LDA data poses unique data-processing problems. The random sampling times in LDA preclude the use of the spectral methods for equi-spaced samples. As a consequence, special data-processing algorithms are used to process the LDA data. However, the random sampling causes an additional statistical variability of the spectral estimates that obscures the behaviour of the sdf in the high frequency range. The maximum frequency at which reliable estimates can be made is usually less than the mean data rate. For LDA measurements in gas flows the mean data rate is often small compared to the highest frequencies of the velocity fluctuations. As a consequence, the small scales of the turbulent fluctuations cannot be studied from the estimated sdf's with the presently available data-processing methods. It is the objective of the present study to modify an existing data-processing method such that information on the spectral density can be revealed at much higher frequencies. The modification consists of two elements. First, a locally sealed autocorrelation function is computed. This modification of the conventional slotting technique results in a much lower statistical variance at small lag times. Next, the locally scaled acf is cosine-transformed using a lag window whose width is varied with frequency. The modified estimator is applied to two types of stimulated data to illustrate its performance. It is shown that the modified slotting technique in conjunction with a variable window forms a powerful spectral estimator for low data density flows.Aerospace Engineerin