Effect of the spatial filtering and alignment error of hot-wire probes in a wall-bounded turbulent flow

The effort to describe velocity fluctuation distributions in wall-bounded turbulent flows has raised different questions concerning the accuracy of hot-wire measurement techniques close to the wall and more specifically the effect of spatial averaging resulting from the finite size of the wire. Here, an analytical model which describes the effect of the spatial filtering and misalignment of hot-wire probes on the main statistical moments in turbulent wall-bounded flows is presented. The model, which is based on the two-point velocity correlation function, shows that the filtering is directly related to the transverse Taylor micro-scale. By means of turbulent channel flow DNS data, the capacity of the model to accurately describe the probe response is established. At the same time, the filtering effect is appraised for different wire lengths and for a range of misalignment angles which can be expected from good experimental practice. Effects of the second-order terms in the model equations are also taken into account and discussed. In order to use the model in a practical situation, the Taylor micro-scale distribution at least should be provided. A simple scaling law based on classic turbulence theory is therefore introduced and finally employed to estimate the filtering effect for different wire lengths.