Dynamic response of constant temperature hot-wire systems under various perturbations

Differential equations of constant temperature hot-wire systems are solved numerically under various perturbation methods. The results show that cut-off frequencies determined from traditional square wave tests are inconsistent with those from velocity impulses at hot wires, with the latter being the proper method for dynamic systems such as hot-wire anemometers. It is also found that normalized energy spectral densities of responses of hot-wire systems to various perturbations can be used to determine the frequency responses and cut-off frequencies of the systems. Based on this finding, a new procedure is proposed to experimentally determine the frequency response and approximately estimate the cut-off frequency of the hot-wire systems. The frequency responses of hot-wire systems determined from square wave perturbations show the hot-wire attenuation below the cut-off frequency. This offers opportunities of possible experimental determination of this attenuation, which so far has been out of reach and denied the possibility of correcting its effects in turbulence measurements. The effects of this attenuation on the experimental results of small-scale turbulence could be large.