Frequency Response of a Constant-Temperature Hot-Wire to Temperature Fluctuations

A temperature-sensitive hot-wire under constant-temperature operation is analyzed to predict its frequency response to temperature fluctuations of the fluid. Effects of the finite Wollaston length, the over-heat ratio and the transconductance of the amplifier are taken into account, and a precise expression for the transfer function is derived. Various probes with different geometries are dynamically calibrated using the new developed procedure, in which a linear temperature distribution or a thermal wake just behind parallel line-sources is utilized to generate prescribed temperature fluctuations over a wider range of frequencies. Good agreement is obtained between the predictions and the experimental results on the gain of the sensitivity. The gain increases slightly as the over-heat ratio increases, and is least affected by the transconductance. Owing to the moderate thermal inertia of the Wollaston portion, the attenuation in the gain sometimes appears in the range of energy-containing eddies