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Turbulent boundary layers and channels at moderate Reynolds numbers

Published online by Cambridge University Press:  02 June 2010

JAVIER JIMÉNEZ ,
SERGIO HOYAS ,
MARK P. SIMENS  and
YOSHINORI MIZUNO
JAVIER JIMÉNEZ*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
SERGIO HOYAS
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain CMT Motores Térmicos, Universidad Politécnica de Valencia, 46022 Valencia, Spain
MARK P. SIMENS
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
YOSHINORI MIZUNO
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
*
†Email address for correspondence: [email protected]
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Abstract

The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/δ = 0.3–0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reθ ≈ 2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010 , pp. 335 - 360
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of short laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of very large anisotropic scales in turbulent channels. Phys. Fluids 15, L41–L44.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor's approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the logarithmic region. J. Fluid Mech. 561, 329–358.CrossRefGoogle Scholar
Antonia, R. A., Teittel, M., Kim, J. & Browne, L. W. B. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579–605.CrossRefGoogle Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence, pp. 45–47. Cambridge University Press.Google Scholar
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.CrossRefGoogle Scholar
Buschmann, M. H., Kempe, T., Indinger, T. & Gad-el-Hak, M. 2009 Normal and crossflow Reynolds stresses differences between confined and semi-confined flows. In Turbulence, Heat and Mass Transfer 6 (ed. Hanjalić, K., Nagano, Y. & Jakirlić, S.), pp. 1–7. Begell House.Google Scholar
Chong, M. S., Soria, J., Perry, A. E., Chacin, J., Cantwell, B. J. & Na, Y. 1998 Turbulent structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225–247.CrossRefGoogle Scholar
Corrsin, S. & Kistler, A. L. 1955 Free-stream boundaries of turbulent flows. Tech. Rep. 1244. NACA.Google Scholar
Erm, L. P. & Joubert, P. N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 1–44.CrossRefGoogle Scholar
Farabee, T. M. & Casarella, M. J. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A 3, 2410–2420.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2005 Reynolds number effect on drag reduction in a microbubble-laden spatially developing turbulent boundary layer. J. Fluid Mech. 543, 93–106.CrossRefGoogle Scholar
Fiedler, H. E. & Head, M. R. 1966 Intermittency measurements in the turbulent boundary layer. J. Fluid Mech. 25, 719–735.CrossRefGoogle Scholar
Flores, O., Jiménez, J. & del Álamo, J. C. 2007 Vorticity organization in the outer layer of turbulent channels with disturbed walls. J. Fluid Mech. 591, 145–154.CrossRefGoogle Scholar
de Graaff, D. B. & Eaton, J. K. 2000 Reynolds number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Harris, F. J. 1978 On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66, 51–83.CrossRefGoogle Scholar
Hedley, T. B. & Keffer, J. F. 1974 Some turbulent/non-turbulent properties of the outer intermittent region of a boundary layer. J. Fluid Mech. 64, 645–678.CrossRefGoogle Scholar
Hinze, J. 1975 Turbulence, 2nd edn, pp. 61–68. McGraw-Hill.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re τ = 2003. Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.CrossRefGoogle Scholar
Hu, Z., Morley, C. & Sandham, N. 2006 Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 44, 1541–1549.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2009 Comparison of turbulent boundary layers and channels from direct numerical simulation. In Sixth International Symposium on Turbulence and Shear Flow Phenomena (ed. Sung, H. J. & Choi, H.), pp. 289–294.Google Scholar
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.CrossRefGoogle Scholar
Khujadze, G. & Oberlack, M. 2004 DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow. Theor. Comput. Fluid Dyn. 18, 391–441.CrossRefGoogle Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 239, 157–194.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kovasznay, L., Kibens, V. & Blackwelder, R. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283–325.CrossRefGoogle Scholar
Lee, S.-H. & Sung, H. J. 2007 Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125–146.CrossRefGoogle Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233–258.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong., M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong., M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156.CrossRefGoogle Scholar
Murlis, J., Tsai, H. & Bradshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.CrossRefGoogle Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191, 329–419.CrossRefGoogle Scholar
Nakagawa, H. & Nezu, I. 1977 Prediction of the contributions to the Reynolds stress from bursting events in open channel flow. J. Fluid Mech. 80, 99–128.CrossRefGoogle Scholar
Nikitin, N. 2007 Spatial periodicity of spatially evolving turbulent flow caused by inflow boundary condition. Phys. Fluids 19, 091703.CrossRefGoogle Scholar
Perot, J. B. 1993 An analysis of the fractional step method. J. Comput. Phys. 108, 51–58.CrossRefGoogle Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press, pp. 506–515.CrossRefGoogle Scholar
Schewe, G. 1983 On the structure and resolution of wall pressure fluctuations associated with turbulent boundary layer flow. J. Fluid Mech. 134, 311–328.CrossRefGoogle Scholar
Schlatter, P., Örlü, R., Li, Q., Fransson, J., Johansson, A., Alfredsson, P. H. & Henningson, D. S. 2009 Turbulent boundary layers up to Re θ = 2500 through simulation and experiments. Phys. Fluids 21, 05702.CrossRefGoogle Scholar
Simens, M. P. 2008 The study and control of wall-bounded flows. PhD thesis, Aeronautics, Universidad Politécnica, Madrid, Spain, http://oa.upm.es/1047/.Google Scholar
Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228, 4218–4231.CrossRefGoogle Scholar
Skote, M., Haritonides, J. & Henningson, D. 2002 Varicose instabilities in turbulent boundary layers. Phys. Fluids 14, 2309–2323.CrossRefGoogle Scholar
Skote, M. & Henningson, D. S. 2002 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 471, 107–136.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re θ = 1410. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Spalart, P. R., Coleman, G. N. & Johnstone, R. 2009 Retraction: direct numerical simulation of the Ekman layer: a step in Reynolds number, and cautious support for a log law with a shifted origin. Phys. Fluids 21, 109901.CrossRefGoogle Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral method for the Navier–Stokes equations with one infinite and two periodic dimensions. J. Comput. Phys. 96, 297–324.CrossRefGoogle Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.CrossRefGoogle Scholar
Tanahashi, M., Kang, S.-J., Miyamoto, T., Shiokawa, S. & Miyauchi, T. 2004 Scaling law of fine scale eddies in turbulent channel flow at to Re τ = 800. Intl J. Heat Fluid Flow 25, 331–340.CrossRefGoogle Scholar
Tsuji, Y., Fransson, J. H. M., Alfredsson, P. H. & Johansson, A. V. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 1–40.CrossRefGoogle Scholar
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 64, 39–48.CrossRefGoogle Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar
Wygnanski, I. J. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327–361.CrossRefGoogle Scholar