Analysis of wall-mounted hot-wire probes

Abstract: Flush-mounted cavity hot-wire probes have been around since two decades, but have typically not been applied as often compared to the traditional wall hot-wires mounted several wire diameters above the surface. While the latter suffer from heat conduction from the hot wire to the substrate in particular when used in air flows, the former is belived to significantly enhance the frequency response of the sensor. The recent work using a cavity hotwire by Gubian et al. (2019) came to the surprising conclusion that the magnitute of the fluctuating wall-shear stress τ+w,rms reaches an asymptotic value of 0.44 beyond the friction Reynolds number Re τ ∼ 600. In an effort to explain this result, which is at odds with the majority of the literature, the present work combines direct numerical simulations (DNS) of a turbulent channel flow with a cavity modelled using the immersed boundary method, as well as an experimental replication of the study of Gubian et al. in a turbulent boundary layer to explain how the contradicting results could have been obtained. It is shown that the measurements of the mentioned study can be replicated qualitatively as a result of measurement problems. We will present why cavity hot-wire probes should neither be used for quantitative nor qualitative measurements of wall-bounded flows, and that several experimental short-comings can interact to sometimes falsely yield seemingly correct results.