Spatial averaging effects in adverse pressure gradient turbulent boundary layers

Abstract

Thermal anemometry sensors for time-resolved velocity measurements average the measured signal over the length of their sensor, thereby attenuating fluctuations stemming from scales smaller than the wire length. Several compensation methods have emerged for wall turbulence, the most prominent ones relying on the small-scale universality in canonical flows or on the reconstruction based on two attenuated variance profiles obtained with sensors of different length. To extend these methods to non-canonical flows, the present work considers various adverse-pressure gradient (APG) turbulent boundary layer (TBL) flows in order to explore how the small-scale energy is affected in the inner and outer layer and how the two prominent correction methods perform as function of wall-distance, wire length and flow condition. Our findings show that the increased levels of small-scale energy in the inner, but also outer layer associated with APG TBLs reduces the applicability of empirical methods based on the universality of small-scale energy. On the other hand, a correction based on the relationship between the spanwise Taylor microscale and the two-point streamwise velocity correlation function, is able to correct the attenuated profiles of non-canonical cases. Combining the strength of both methods, a composite profile for the spanwise Taylor microscale is suggested, which then is used for the correction of probe-length attenuation effects across a multitude of flow conditions.