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Hot-wire anemometry behaviour at very high frequencies

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1996 Meas. Sci. Technol. 7 1297

(http://iopscience.iop.org/0957-0233/7/10/002)

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Meas. Sci. Technol. 7 (1996) 1297–1300. Printed in the UK

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Hot-wire anemometry behaviour atvery high frequencies

Seyed G Saddoughi and Srinivas V Veeravalli †Center for Turbulence Research, Building 500, Stanford University, CA 94305, USAand NASA Ames Research Center, CA 94035, USA

Received 7 June 1996, accepted for publication 26 June 1996

Abstract. It is shown that most of the present-day hot-wire anemometers have alimitation at high frequencies: namely that the tail of the power spectrum of theanemometer output signal has a spurious rise with frequency. This rise, which isproportional to the square of frequency (f 2), is of great concern when one dealswith small-scale measurements in high-Reynolds-number flows.

1. Introduction

In this paper we report on some of the difficulties thatwere encountered with hot-wire anemometry during oursmall-scale measurements in the 80 foot by 120 footfull-scale aerodynamics facility at NASA Ames ResearchCenter. The aim of those experiments (Saddoughi andVeeravalli 1994) was to test the local-isotropy predictions ofKolmogorov’s (1941) universal equilibrium theory in shearflows. This hypothesis, which states that, at sufficientlyhigh Reynolds numbers, the small-scale structures ofturbulent motions are independent of large-scale structuresand mean deformations, greatly simplifies the problem ofturbulence. Hence, Kolmogorov’s hypothesis has beenused in theoretical studies of turbulence and computationalmethods like large-eddy simulation.

In an experiment to investigate the local-isotropyhypothesis, it is imperative that the Reynolds number ofthe flow be high enough to separate the dissipating eddiessufficiently from the energy-containing scales. Most ofthe previous laboratory experiments did not satisfy thisrequirement. Also, spatial-resolution problems, whicharise because hot wires can resolve only those eddiesthat have length scales the same or larger than the hot-wire length, have affected most of the previous studies.Therefore, the only practical option is to use large facilitiesin which (i) high Reynolds numbers can be achievedand (ii) Kolmogorov length scales can be resolved bystandard hot wires. Note that, since the high-Reynolds-number requirement is an intrinsic part of the local-isotropyhypothesis, experiments should be conducted not only atlarge facilities, but also at high flow velocities.

Kolmogorov’s hypothesis is valid in the inertial sub-range and the dissipation range. This implies that we

† Present address: Department of Applied Mechanics, Indian Institute ofTechnology, New Delhi 110016, India.

need to concentrate on the high-wavenumber (or high-frequency) range of the power spectrum of the fluctuatingvelocity signals. Also, since, at a fixed position in theflow, the Kolmogorov frequency is a function of theflow velocity, the frequency-resolution requirement of hot-wire anemometry increases with flow velocity. In ourexperiments, in which acquisition of reliable data for thesmall-scale eddies was of prime concern, we were facedwith the limitation of hot-wire anemometry in resolvingthe high-frequency range of the power spectrum at highvelocities. This dictated our measurement strategy.

The aim of the present report is only to illustrate the factthat most of the present-day hot-wire anemometers have thislimitation. We offer no solution to this problem; however,we will highlight briefly the method by which we couldavoid this phenomenon.

2. Results and discussion

In figure 1 we show a longitudinal power spectrum (fullline) obtained in the boundary layer on the test-sectionceiling of the 80 foot by 120 foot wind tunnel at NASAAmes. The boundary-layer thickness,δ, was approximatelyequal to 1 m and the above spectrum was measured aty/δ ≈ 1.4 at a nominal free-stream velocity of 40 m s−1.The data recording equipment and a small wind tunnelused for calibrating the hot wires were installed in the atticabove the test-section ceiling. This spectrum was takenwith a Dantec model 55P51 crossed-wire probe, modifiedto support 2.5 µm platinum-plated tungsten wires with anetched length of approximately 0.5 mm, in conjunction withTSI model 1050 hot-wire bridges and model 1052 signalconditioners. The hot-wire output voltages were digitizedon a microcomputer equipped with Adtek AD830 12-bit,sample-and-hold, analogue-to-digital converters. The low-pass-filter cut-off was set at 100 kHz and 400 records of

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Figure 1. Longitudinal power spectra measured at a free-stream velocity of 40 m s−1 using different anemometers atdifferent laboratories: (——), TSI 1050 anemometers at y/δ ≈ 1.4 in the 80 foot by 120 foot wind tunnel at NASA Ames; andTSI IFA-100 in the calibration tunnel free stream at (· · · · · ·) NASA Ames and (- - - -) Stanford University respectively.

4096 samples each were recorded at a sampling frequencyof 330 kHz in order to avoid aliasing errors. Thespectral density was computed by a fast-Fourier-transformalgorithm. Note that, in this spectrum, apart from high-frequency spikes, a rise with frequency (f ) in the tail ofthe spectrum occurred before the final roll-off due to thelow-pass filter. This rise, which was proportional to thesquare of frequency (f 2), was of great concern since itoccurred at the expected Kolmogorov frequency for thatspeed. Therefore, no definite statement could be madeconcerning the behaviour of the dissipating eddies. In orderto resolve this issue, we conducted extensive tests, whichare presented here.

Figure 1 also shows the spectra taken both in the atticof the 80 foot by 120 foot wind tunnel (dotted line) andat the Stanford University laboratory (broken line) in thefree stream of our calibration wind tunnel. These datawere measured at the same flow velocity and low-pass-filter cut-off frequency as before, but the anemometersused were TSI IFA-100 model 150 bridges and model 157signal conditioners. These measurements were conductedto ensure that this problem (that is, a rise proportional tof 2 in the tail of the spectrum) was not peculiar to theflow inside the 80 foot by 120 foot wind tunnel. It canbe seen clearly that the same problem is present in both theexperimental facilities.

Furthermore, to isolate the source of this problem, thespectra were measured in the free stream of the calibrationwind tunnel at the Stanford University laboratory using hot-wire bridges manufactured by different companies: (i) aTSI IFA-100 bridge, (ii) a Dantec 56C17 bridge and (iii) abridge designed by Jon Watmuff of the Fluid MechanicsLaboratory at NASA Ames Laboratory. These spectra,which are shown in figure 2, were measured with a Dantecmodel 55P01 single hot-wire probe (2.5 µm tungsten wire).The high-frequency spikes are not present, but again itappears that, insofar as thef 2 phenomenon is concerned,the responses of all three bridges are similar. Note that,similar to our earlier data (figure 1) the low-pass-filtercut-off for these measurements was also set at 100 kHz.However, it can be seen in figure 2 that, unlike the otherspectra, the roll-off of the tail of the spectrum measured bythe Dantec bridge occurred at approximately 30 kHz. This

is because, although the square-wave responses of the TSIIFA-100 and Watmuff bridges were better than 100 kHz, forthe Dantec bridge the response was limited to only 20 kHz.

Finally, with a TSI IFA-100 bridge, spectra were takenin still air with 2.5 µm tungsten wires and also with astandard fuse wire. These data are compared in figure 3, inwhich the same trend at high frequencies is clearly present.These last measurements were conducted to show that thef 2 noise was neither induced by the flow nor generatedby the hot-wire element. Also, it is very important to notethat we did measure the noise spectra of the analogue-to-digital converter board (not shown) and that this spuriousphenomenon was not present in those measurements.

Therefore, it was clear that, under all these differentexperimental conditions, thef 2 behaviour was present inall the spectra and the only source of this phenomenon wasthe anemometers. The conclusion drawn from these testswas that, when the turbulent energy of the flow was verysmall, the performances of all the hot-wire bridges at highfrequencies were limited by thisf 2 noise.

In order to overcome this problem, our small-scaleexperiments were therefore divided into two sets. These,as well as our measurement strategy and procedure, weredescribed in detail by Saddoughi and Veeravalli (1994).However, a very brief description is also presented here.First, to obtain the maximum Reynolds number possible,measurements were taken at 50 m s−1, nearly the highestfree-stream velocity of the 80 foot by 120 foot wind tunnel.At this speed we had a fairly well-defined inertial sub-range,but, due to the above hot-wire anemometry limitation, itwas not possible to resolve the dissipation range. Ourfeasibility studies had also shown that, at this high free-stream velocity, spatial resolution in the dissipation rangewas a problem. Second, to allow accurate measurementof the dissipation range, measurements were taken at alower free-stream velocity, 10 m s−1, at which the expectedKolmogorov frequency was of the order of 5 kHz. Thef 2

noise was thus avoided and very good spatial resolution wasobtained without a large sacrifice in microscale Reynoldsnumber, but with a shorter inertial range than that obtainedat 50 m s−1.

To conduct these experiments, we acquired the latestinstruments, which had low background noise. In addition,

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Figure 2. Noise spectra measured in the calibration tunnel free stream at Stanford University with different hot-wireanemometer bridges: (· · · · · ·), TSI IFA 100; (- - - -), Watmuff; and (——), Dantec.

Figure 3. Noise spectra measured in still air with TSI IFA 100 hot-wire anemometers using different wires: (· · · · · ·), 2.5 µmtungsten wire at Stanford University; (- - - -), 2.5 µm tungsten wire at NASA Ames; and (——), standard fuse at StanfordUniversity.

all of our electronic equipment was connected to an OneacPower Conditioner (CB 1115) and Uninterruptible PowerSystem (UPS Clary PC 1.25K), which supplied clean powerand prevented loss of data due to power failure. All themeasurements were taken by TSI IFA-100 hot-wire bridges.The high-pass and low-pass filters used were FrequencyDevices model 9016 (Butterworth, 48 dB per octave). Toimprove the bandwidth of the spectra at low frequencies,the data were obtained in three spectral bands.

Figure 4 showsE11(f ) for both free-stream velocities.The Kolmogorov frequencies calculated by using theisotropic relation were about 69 and 4.5 kHz for the high-and low-speed measurements respectively. Because of thef 2 behaviour of the tail of the spectrum and also due to lackof sufficient spatial resolution, only frequencies up to about30 kHz could be resolved for the high-speed experiments.However, for the low-speed measurements, five decadesof frequency were obtained with no contamination fromelectronics noise and with good spatial resolution.

3. Conclusions

We have shown that most of the present-day hot-wireanemometers have a limitation at high frequencies: the tailof the power spectrum of the anemometer output signalhas a spurious rise with frequency. This rise, which is

proportional to the square of frequency (f 2), is of greatconcern when one deals with small-scale measurementsin high-Reynolds-number flows. Also, we have shownthat, by devising an alternative measurement strategy, wewere able somehow to overcome this problem in our high-Reynolds-number experiments (Saddoughi and Veeravalli1994). However, since reliable small-scale data in very-high Reynolds-number flows are of great interest, it isimperative that the hot-wire anemometer design be modifiedto eliminate this problem.

4. Epilogue

An important point was raised by one of the referees. ‘Whyhas this(f 2) effect never been recognised before? Thefrequency at which the odd behaviour begins is already 1or 2 kHz and there are numerous examples of publishedspectra above these limits, which do not show this effect’.

Firstly, the reason for this effect not being observedbefore at 1 or 2 kHz frequencies is that thef 2 noise can beobserved at such low frequencies only when the turbulentenergy of the flow is negligible. This can be seen veryclearly in figure 1. Note that, in the calibration tunnel,where the energy content in the tail of the spectrum is verysmall, thef 2 effect starts at a frequency of about 2 kHz.However, as this energy content increases in the spectrum

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Figure 4. Longitudinal power spectra measured around y/δ ≈ 0.5 of the boundary layer of the 80 foot by 120 foot windtunnel at two different free-stream velocities.

taken inside the 80 foot by 120 foot wind tunnel, thefrequency at which this phenomenon starts also increasesby about a decade to 20 kHz.

Secondly, there are two other possible reasons forthis phenomenon not having been recognized before. (i)Researchers not interested in the details of the dissipationrange have been in the habit of ‘chopping’ the spectrumwhenever they saw an inflection point in the monotonicallydecaying tail of the spectrum. (ii) As mentioned insection 1 we had the unique opportunity to conductfundamental experiments in the world’s largest wind tunnel,whereas those who have tried to analyse the dissipationranges of the spectra obtained in small-scale facilities havealways encountered hot-wire spatial resolution problems,before reaching the start of thef 2 phenomenon. Very

interestingly, these two points were also recognized byanother referee.

We would like to thank Professors P Bradshaw,W K George, A E Perry, J K Eaton and Dr J H Watmuff,with whom we discussed these and other hot-wireanemometry problems.

References

Kolmogorov A N 1941 The local structure of turbulence inincompressible viscous fluid for very large ReynoldsnumbersC. R. Acad. Sci URSS30 301

Saddoughi S G and Veeravalli S V 1994 Local isotropy inturbulent boundary layers at high Reynolds numberJ. FluidMech.268 333–72

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