A study of the three-term hot-wire system equation and analog linearization based on it

Abstract

The three-term hot-wire system equation of the form E 2=a 0+a 1 U 1 2 +a 2U , where E is the anemometer voltage and U is the effective cooling velocity normal to the hot-wire sensor, is considered as the basis for the analog linearization of the voltage signal from a constant-temperature hot-wire anemometer. The accuracy of the three-term system equation in the deduction of the mean and fluctuating fluid velocity components is considered and discussed. In particular, the accurate determination of small velocity fluctuations is considered by comparing the sensitivity coefficients determined from the static three-term calibration to the sensitivity coefficients determined by the dynamic calibration procedure. In many unsteady fluid investigations, large velocity fluctuations, greater than 10–15% of the mean velocity, are encountered. The accurate measurement of the time-dependent velocity in these cases requires hot-wire signal linearization (analog or digital) or the movement of the hot-wire probe at a large bias velocity. In this paper, the details of a simply constructed and accurate hot-wire analog linearization circuit are described. The complete hot-wire/linearizer system performance is evaluated by vibrating the hot-wire probe in the main stream direction, similar to the dynamic calibration technique. This forced probe oscillation results in velocity oscillations relative to the frame of reference fixed on the hot-wire probe. The measurement of these velocity oscillations with the hot-wire/linearizer system is compared to the vibration velocity measured with a miniature accelerometer.