The influence of temperature fluctuations on hot-wire measurements in wall-bounded turbulence

There are no measurement techniques for turbulent flows capable of reaching the versatility of hot-wire probes and their frequency response. Nevertheless, the issue of their spatial resolution is still a matter of debate when it comes to high Reynolds number near-wall turbulence. Another, so far unattended, issue is the effect of temperature fluctuations—as they are, e.g. encountered in non-isothermal flows—on the low and higher-order moments in wall-bounded turbulent flows obtained through hot-wire anemometry. The present investigation is dedicated to document, understand, and ultimately correct these effects. For this purpose, the response of a hot-wire is simulated through the use of velocity and temperature data from a turbulent channel flow generated by means of direct numerical simulations. Results show that ignoring the effect of temperature fluctuations, caused by temperature gradients along the wall-normal direction, introduces—despite a local mean temperature compensation of the velocity reading—significant errors. The results serve as a note of caution for hot-wire measurements in wall-bounded turbulence, and also where temperature gradients are more prevalent, such as heat transfer measurements or high Mach number flows. A simple correction scheme involving only mean temperature quantities (besides the streamwise velocity information) is finally proposed that leads to a substantial bias error reduction.