Dynamic response of constant temperature hot-wire system in turbulence velocity measurements

Analytical solutions have been derived for the first time for temperature fluctuations along a hot wire when it is exposed to turbulent velocity fluctuations of different frequencies and wave numbers. The solutions are used to analyse the dynamic response of the hot wire alone first. The results show that attenuation to the velocity fluctuations exists at high frequencies and depends on the relative end-conduction heat loss from the hot wire to its supports. A simplified circuit for a hot-wire anemometer is then used to analyse the frequency response of the combined hot wire and its anemometer. It is found that even though the frequency response of the anemometer (as that determined from a square wave test) can be very high, the cut-off frequency of the combined system is low, depending on the hot-wire length to diameter ratio, Reynolds numbers, overheat ratio and the hot-wire material used. A preliminary investigation of the spatial resolution of the hot wire to the velocity fluctuations at different wave numbers is also presented.