TY - JOUR
T1 - Direct numerical simulation of a 30R long turbulent pipe flow at R + = 685
T2 - Large-and very large-scale motions
AU - Wu, Xiaohua
AU - Baltzer, J. R.
AU - Adrian, Ronald
N1 - Funding Information:
The computer program used in this study was developed by the late Dr Charles D. Pierce of the Center for Turbulence Research at Stanford. X.W. was supported by the NSERC Discovery Grant and the Canada Research Chair Program (CRC) in Aeronautical Fluid Mechanics. The calculations were performed at the High Performance Computing Virtual Laboratory (HPCVL). Additional computations were performed using the Arizona State University Advanced Computing Center facilities. R.J.A. and J.R.B. gratefully acknowledge the support of the National Science Foundation with Award CBET-0933848. We gratefully acknowledge the experimental spectra provided by M. Hultmark and A. Smits, and those provided by H. Ng and J. Monty. We also wish to acknowledge J.-C. del Álamo, J. Jiménez, P. S. Zandonade, and R. D. Moser for making two-dimensional energy spectra for channel DNS available, and acknowledge C. Chin for pipe DNS spectra.
PY - 2012/5/10
Y1 - 2012/5/10
N2 - Fully developed incompressible turbulent pipe flow at Reynolds number ReD = 24 580 (based on bulk velocity) and Kàrmàn number R+ = 684. 8 is simulated in a periodic domain with a length of 30 pipe radii R. While single-point statistics match closely with experimental measurements, questions have been raised of whether streamwise energy spectra calculated from spatial data agree with the well-known bimodal spectrum shape in premultiplied spectra produced by experiments using Taylor's hypothesis. The simulation supports the importance of large-and very large-scale motions (VLSMs, with streamwise wavelengths exceeding 3R). Wavenumber spectral analysis shows evidence of a weak peak or flat region associated with VLSMs, independent of Taylor's hypothesis, and comparisons with experimental spectra are consistent with recent findings (del Álamo & Jiménez, J. Fluid Mech., vol. 640, 2009, pp. 5-26) that the long-wavelength streamwise velocity energy peak is overestimated when Taylor's hypothesis is used. Yet, the spectrum behaviour retains otherwise similar properties to those documented based on experiment. The spectra also reveal the importance of motions of long streamwise length to the uu energy and uv Reynolds stress and support the general conclusions regarding these quantities formed using experimental measurements. Space-time correlations demonstrate that low-level correlations involving very large scales persist over 40R/Ubulk in time and indicate that these motions convect at approximately the bulk velocity, including within the region approaching the wall. These very large streamwise motions are also observed to accelerate the flow near the wall based on force spectra, whereas smaller scales tend to decelerate the mean streamwise flow profile, in accordance with the behaviour observed in net force spectra of prior experiments. Net force spectra are resolved for the first time in the buffer layer and reveal an unexpectedly complex structure.
AB - Fully developed incompressible turbulent pipe flow at Reynolds number ReD = 24 580 (based on bulk velocity) and Kàrmàn number R+ = 684. 8 is simulated in a periodic domain with a length of 30 pipe radii R. While single-point statistics match closely with experimental measurements, questions have been raised of whether streamwise energy spectra calculated from spatial data agree with the well-known bimodal spectrum shape in premultiplied spectra produced by experiments using Taylor's hypothesis. The simulation supports the importance of large-and very large-scale motions (VLSMs, with streamwise wavelengths exceeding 3R). Wavenumber spectral analysis shows evidence of a weak peak or flat region associated with VLSMs, independent of Taylor's hypothesis, and comparisons with experimental spectra are consistent with recent findings (del Álamo & Jiménez, J. Fluid Mech., vol. 640, 2009, pp. 5-26) that the long-wavelength streamwise velocity energy peak is overestimated when Taylor's hypothesis is used. Yet, the spectrum behaviour retains otherwise similar properties to those documented based on experiment. The spectra also reveal the importance of motions of long streamwise length to the uu energy and uv Reynolds stress and support the general conclusions regarding these quantities formed using experimental measurements. Space-time correlations demonstrate that low-level correlations involving very large scales persist over 40R/Ubulk in time and indicate that these motions convect at approximately the bulk velocity, including within the region approaching the wall. These very large streamwise motions are also observed to accelerate the flow near the wall based on force spectra, whereas smaller scales tend to decelerate the mean streamwise flow profile, in accordance with the behaviour observed in net force spectra of prior experiments. Net force spectra are resolved for the first time in the buffer layer and reveal an unexpectedly complex structure.
KW - pipe flow boundary layer
KW - turbulent boundary layers
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U2 - 10.1017/jfm.2012.81
DO - 10.1017/jfm.2012.81
M3 - Article
AN - SCOPUS:84859965707
SN - 0022-1120
VL - 698
SP - 235
EP - 281
JO - journal of fluid mechanics
JF - journal of fluid mechanics
ER -