Hot-wire spatial resolution issues in wall-bounded turbulence

Abstract

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows

“…For the TBL, we resort to the hotwire measurements performed in the Melbourne wind tunnel as first reported in Hutchins et al (2009). This dataset encompasses 5 different Re τ ranging from 2800 to 19000 at various wall normal locations.…”

On the Formation Mechanisms of Artificially Generated High Reynolds Number Turbulent Boundary Layers

“…The body of a Dantec Dynamics 55P05 hot-wire probe is etched in-house using a d w = 5 µm Wollaston wire with a sensing length l w ≈ 1 mm in order to ensure l w /d w ≥ 200 as suggested by Comte-bellot (1976) or Hutchins et al (2009) amongst others. Voltage signals are recorded using a Dantec Streamline in constant temperature mode.…”

Probing high-Reynolds-number effects in numerical boundary layers

“…3(b) we consider the peak streamwise velocity variance as a function of Re τ . In this respect, Townsend's attached eddy hypothesis predicts a logarithmic increase, and correlations of low-speed experiments indicate 27 R + 11 2 pk = 4.837 + 0.469 log Re τ .…”