In Situ Calibration of Hot-Film Probes Using a Collocated Sonic Anemometer: Angular Probability Distribution Properties

In a recent paper by Kit et al., a novel algorithm for the calibration of hot-film probes using a collocated sonic anemometer combined with the neural network approach is described. An important step in the algorithm is the generation of a calibration dataset by an appropriate low-pass filtering of the voltage and velocity time series obtained from hot-film probes and a sonic anemometer, correspondingly. Kit et al. report that a polynomial least squares fit that was used to approximate the relations of these voltage–velocity data from the dataset failed while a neural network approach worked satisfactorily. The same polynomial fit worked successfully with a calibration dataset obtained using a standard calibration unit that enables one to generate calibration data at evenly distributed yaw angles, varying in a wide range (−30°, 30°). In the current study, an attempt is made to uncover the reason for the failure of the polynomial fit algorithm with a sonic anemometer–based calibration dataset (SBS-PF). The probability densities of the velocity angles for the calibration dataset, as well as for a full velocity dataset obtained using the neural network approach, are computed. Also developed are theoretical expressions for the same angular density probability distributions based on the following assumptions: (i) an axisymmetric turbulent velocity field, (ii) Gaussian density probability distribution for velocity components, and (iii) weak correlations between the velocity components (i.e., the probability density distribution of the entire velocity vector is a product of probabilities of its components). The agreement between measured and theoretical angular probability distributions is good. The results herein indicate that the angular density probability of the low-pass-filtered calibration dataset is twice as narrow as that of the full velocity time series. This result can explain the failure of the polynomial fit to reconstruct the full velocity time series satisfactorily as resulting from the intrinsic property of this algorithm to ascribe a large weight to the highly concentrated points and a light weight to the thinly concentrated points while performing fitting.