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On spatial resolution issues related to time-averaged quantities using hot-wire anemometry

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Abstract

The effect of spatial resolution on streamwise velocity measurements with single hot-wires is targeted in the present study, where efforts have been made to distinguish between spatial resolution and Reynolds number effects. The basis for measurements to accurately determine the mean velocity and higher order moments is that the probability density distribution is measured correctly. It is well known that the turbulence intensity is increasingly attenuated with increasing wire length. Here, it is also shown (probably for the first time) that besides the probability density distribution and hence the higher order moments, even the mean velocity is affected, albeit to subtle extent, but with important consequences in studies of concurrent wall-bounded turbulence.

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Notes

  1. Note, however, that their conclusions are partially biased, due to the fact that they obtained, estimated or calculated the viscous-scaled wire length an order of magnitude too small, at least for the experiments by Purtell et al. (1981), Andreopoulos et al. (1984), and Erm and Joubert (1991), on which their analysis on the rms, skewness and flatness factors in zero pressure-gradient (ZPG) turbulent boundary layer (TBL) flows are primarily based.

  2. For further information regarding the flow quality in the MTL wind tunnel, the interested reader is refered to Lindgren and Johansson (2002).

  3. The reason for the observed different rms values within the overlap region may be twofold, viz. a Reynolds number effect and it could be caused by the scaling with the friction velocity, which in the case of Smith (1994) and DeGraaff and Eaton (2000) was deduced from a fit to the log law with classical values. The latter is probable to give higher values of the friction velocity and hence shifts the profiles towards lower values of the normalised velocity (Karlsson 1980; Murlis et al. 1982).

  4. Note that the log law constants are extracted from a huge number of measurement sets and present an average value. This explains the observed small offset seen in such a sensitive quantity as Ψ, which is not recognisable in the conventional U + versus y + plot.

  5. Note that while the open circles were extracted from the original data base, the shown mean velocity profiles in the figure were re-evaluated in order to fit the data better to the shown log law in order to ease comparison. Hence, some of the open circles are extracted from the same profiles as those represented by the solid symbols.

  6. Utilising the modified Musker profile (Musker 1979) by Chauhan et al. (2009), which incorporates the overshoot over the log law, one can employ the same procedure used to generate the upper insert in Fig. 6. Doing so, it can be found that Ψ pp increases asymptotically to a value of 0.28 at the higher end of Reynolds numbers measured by Österlund et al. (2000), giving an approximate increase of around 0.1 u τ from his lowest Reynolds number on.

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Acknowledgements

Dr. Jens H. M. Fransson and Mr. Thomas Kurian are acknowledged for their help in setting up the experiment. The authors made use of experimental data of Drs. D. B. DeGraaf, J. Österlund and R. W. Smith and express their thanks for making these data sets available. Dr. P. Schlatter is acknowledged for providing his numerical ZPG TBL data that were used to calculate the Kolmogorov scale in Section 3. The support of the Swedish Research Council (VR) is also acknowledged.

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  1. Linné Flow Centre, KTH Mechanics, 100 44, Stockholm, Sweden

    Ramis Örlü & P. Henrik Alfredsson

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  1. Ramis Örlü
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  2. P. Henrik Alfredsson
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Correspondence to P. Henrik Alfredsson.

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Örlü, R., Alfredsson, P.H. On spatial resolution issues related to time-averaged quantities using hot-wire anemometry. Exp Fluids 49, 101–110 (2010). https://doi.org/10.1007/s00348-009-0808-1

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