On the accuracy of measurement of turbulent velocity gradient statistics with hot-wire probes

A very high resolution minimal channel flow direct numerical simulation was used to examine, virtually, the ability of various multi-sensor hot-wire probe configurations to measure the statistics of velocity gradient components. Various array and sensor configurations and the spatial resolution of probes with these configurations were studied, building on designs and investigations of various authors. In contrast to our previous studies, which focused on turbulent vorticity, vorticity-velocity correlations, dissipation and production rate, here the measurement accuracy of each component of the velocity vector gradient tensor is analyzed separately. The results of the study show that the virtual experiments compare well with a physical experiment, and that such virtual experiments are a powerful tool to examine the accuracy of velocity gradient measurements. The cross-stream gradients needed to determine the vorticity components can be measured with sufficient accuracy with most of the array and sensor configurations of vorticity probes used so far. A systematic error of some of the gradient measurements can appear due to the array or sensor configurations. None of the examined probe designs can measure, with sufficient accuracy, the streamwise velocity gradients, directly or indirectly, using the continuity equation