Assessment of turbulent spectral bias in laser doppler velocimetry

Abstract

A critical evaluation is made of the spectral bias which occurs in the use of a laser Doppler velocimeter (LDV). In order to accommodate the randomly sampled LDV data, a doubly stochastic Poisson process is generated, which includes the intensity function of the velocity field. Assessment is performed for varying data densities (0.05 $\leq$ d.d. $\leq$ 5.0) and turbulence levels (t.i.=0.3, 1.0). In the first, one- and two-dimensional flow fields are examined. Systematical spectral evaluations are made by employing the three-processing algorithms, which are the sample and hold method (SH), the modified Shannon sampling technique (SR), and the direct transform (RG). The effects of the values of the Reynolds stress coefficients and of the transversal standard deviation on the spectral bias are dealt with in the present study. As an improved version of spectral estimator for the high data density flow, POCS (the projection onto convex sets) is developed and estimated. Next, a full three-dimensional treatment of the statistical bias is also considered. Toward this end, a promising autoregressive vector model is proposed and applied. In addition to the above three estimators, i.e., SH, SR and RG, the capability of the transit time weighting method (TW) for the low data density flow is investigated systematically. In order to move closer to realistic experimental conditions, the influences of the ratio of the minimum number of zero-crossings to the maximum fringe number (Q=0.57), and the relative velocity by frequency shifting (R=5.0) on spectral distortion are examined. Furthermore, the effect of the Reynolds stress coefficients on spectral bias is scrutinized. For the reduction of high variabilities by aforestated random sampling methods, an automatic smoothing technique is developed. The spectral compensation for SH and the exponential hold method (EH) is tested. This algorithm is found to be useful for the recovery of SH estimates, when the data density is low.