A Note on the Response Equations for Hot-Wire Anemometry

Abstract

The various heat transfer laws describing the response of the hot-wire to the velocity normal to its axis have been evaluated on a common basis to judge their effectiveness in representing the raw calibration data. The models compared were the King’s law, the exponent power-law, the extended power-law and the polynomial heat transfer law. These models were compared in the high and low velocity ranges of 0–100 m/s and 0–35 m/s, respectively. The criteria chosen for comparison were the minimum sum of the errors squared in the velocity and the estimated uncertainties in the calibration constants evaluated. The results indicate that the differences in the various models based on the sum of the errors in velocity, are not significant. However, when an uncertainty analysis for the constants are included in the study, the extended power-law proves to be robust in both the velocity ranges besides yielding a low error in the velocity. The fourth order polynomial law produces the lowest error in velocity, but the uncertainty in the constants evaluated are considerable. The nonlinear method of calibration together with the crierion of minimizing the errors in velocity offers no significant improvement in a statistical sense as compared to the linear method and the criterion of minimizing the errors in E2 .