Investigation of cold-wire spatial and temporal resolution issues in thermal turbulent boundary layers

Abstract

In this study, we use simulations and experiments to investigate spatial and temporal attenuation of cold-wire sensors. A direct numerical simulation (DNS) of a heated smooth-wall turbulent channel flow is used to simulate the sensor spatial filtering effect in the spanwise direction, with results confirming that the increasing wire length does not affect the mean temperature, but significantly attenuates the variance of temperature fluctuations, especially in the vicinity of the wall. With increasing viscous-scaled wire length, the peaks of the one- and two-dimensional energy spectrograms of temperature fluctuations are increasingly attenuated, but in a manner that is approximately predictable based on the sensor length. The temporal resolution of the cold-wire is analysed through experimental measurements in a wind-tunnel thermal boundary layer. The wire length-to-diameter aspect ratio (lw/dw) is varied by changing the wire diameter and keeping the wire length constant, such that the viscous-scaled wire length remains constant. The wire aspect ratio has no effect on the mean temperature profile (similar to the observations for viscous-scaled wire length). When the wire aspect ratio lw/dw approaches 1000, we observe no additional temporal attenuation of the temperature fluctuations beyond that attributed to the spatial resolution of the finite sensor size. However, as lw/dw is reduced below this value (<1000), we observe increasing temporal attenuation. The attenuation of temperature fluctuations due to insufficient wire aspect ratios is seen at almost all wall-normal distances and is broadband, affecting all energy scales in the boundary layer. In contrast, the spatial attenuation only influences small-scale energy on the order of the probe scale, which predominates in the near-wall region. For a given wire diameter of the cold-wire sensor, temperature fluctuations are better resolved by maintaining lw/dw≈1000 and sacrificing spatial resolution by increasing the viscous-scaled wire length. Smaller diameter wires must be employed to alleviate this compromise.