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Hot-wire spatial resolution issues in wall-bounded turbulence. (English) Zbl 1183.76025
Summary: 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 \((Re_{\tau } = 18830)\). 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 \(k_{x}^{-1}\) scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the \(k_{x}^{-1}\) 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.

MSC:
76-05 Experimental work for problems pertaining to fluid mechanics
76F40 Turbulent boundary layers
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References:
[1] DOI: 10.1063/1.1589014 · Zbl 1186.76353
[2] Marusic, Proceedings of the the Sixth International Symposium on Turbulence and Shear Flow Phenomena (2009)
[3] DOI: 10.1007/BF00187234
[4] DOI: 10.1088/0950-7671/30/1/307
[5] DOI: 10.1088/0022-3735/22/6/013
[6] DOI: 10.1017/S002211206700196X
[7] DOI: 10.1017/S0022112084001026
[8] DOI: 10.1017/S0022112082002286
[9] DOI: 10.1007/BF00264405
[10] DOI: 10.1063/1.861765
[11] DOI: 10.1115/1.1538622
[12] DOI: 10.1088/0957-0233/15/5/003
[13] DOI: 10.1017/S0022112075000201
[14] Balint, J. Fluid Mech. 228 pp 53– (1991)
[15] DOI: 10.1088/0957-0233/15/9/022
[16] Townsend, The Structure of Turbulent Shear Flow. (1956) · Zbl 0070.43002
[17] DOI: 10.1017/S0022112008003492 · Zbl 1175.76003
[18] DOI: 10.1017/S0022112005007780
[19] DOI: 10.1017/S0022112003005251 · Zbl 1063.76514
[20] DOI: 10.1007/BF00266313
[21] DOI: 10.1017/S0022112090002889
[22] DOI: 10.1016/j.euromechflu.2003.08.005 · Zbl 1058.76520
[23] DOI: 10.1017/S002211200300733X · Zbl 1059.76031
[24] DOI: 10.1063/1.869889 · Zbl 1147.76430
[25] DOI: 10.1088/0957-0233/7/10/002
[26] DOI: 10.1115/1.1789528
[27] DOI: 10.1088/0957-0233/10/3/009
[28] DOI: 10.1017/S0022112094001370
[29] DOI: 10.1063/1.863452
[30] Kasagi, Second International Symposium on Seawater Drag Reduction. (2005)
[31] DOI: 10.1088/0957-0233/7/10/008
[32] DOI: 10.1017/S002211200200825X · Zbl 1049.76032
[33] DOI: 10.1017/S0022112083002487
[34] DOI: 10.1017/S0022112095003351 · Zbl 0849.76030
[35] DOI: 10.1016/S0142-727X(02)00164-9
[36] DOI: 10.1017/S0022112082001311 · Zbl 0517.76057
[37] DOI: 10.1098/rsta.2006.1942 · Zbl 1152.76421
[38] DOI: 10.1017/S0022112006003946 · Zbl 1113.76004
[39] DOI: 10.1017/S002211209800158X · Zbl 0948.76514
[40] Hutchins, Proceedings of the 15th Australasian Fluid Mechanics Conference (2004)
[41] DOI: 10.1098/rsta.2006.1950 · Zbl 1152.76414
[42] DOI: 10.1103/PhysRevLett.95.074501
[43] DOI: 10.1017/S0022112089001941
[44] DOI: 10.1017/S0022112004001788 · Zbl 1068.76040
[45] DOI: 10.1017/S0022112006008871 · Zbl 1156.76316
[46] DOI: 10.1007/BF00975261
[47] DOI: 10.1063/1.3006423 · Zbl 1182.76550
[48] DOI: 10.1017/S0022112006009244 · Zbl 1093.76510
[49] DOI: 10.1088/0022-3735/10/7/013
[50] DOI: 10.1063/1.869966 · Zbl 1147.76463
[51] DOI: 10.1088/0022-3735/10/7/012
[52] DOI: 10.1017/S0022112004008985 · Zbl 1060.76508
[53] DOI: 10.1017/S0022112097008513 · Zbl 0922.76020
[54] DOI: 10.1088/0957-0233/14/3/302
[55] DOI: 10.1063/1.868516
[56] DOI: 10.1017/S002211200700777X · Zbl 1141.76316
[57] DOI: 10.1017/S0022112091000691
[58] DOI: 10.1088/0957-0233/7/10/021
[59] DOI: 10.1007/BF00191694
[60] DOI: 10.1115/1.2820690
[61] DOI: 10.1063/1.1368852 · Zbl 1184.76365
[62] DOI: 10.1017/S0022112000001713 · Zbl 0958.76509
[63] DOI: 10.1063/1.1344894 · Zbl 1184.76364
[64] DOI: 10.1146/annurev.fl.08.010176.001233
[65] DOI: 10.1098/rsta.2006.1945 · Zbl 1152.76409
[66] DOI: 10.1017/S0022112009006946 · Zbl 1181.76008
[67] DOI: 10.1088/0022-3735/1/11/310
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