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Mean dynamics of transitional channel flow

Published online by Cambridge University Press:  03 May 2011

J. ELSNAB ,
J. KLEWICKI ,
D. MAYNES  and
T. AMEEL
J. ELSNAB
Affiliation:
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA
J. KLEWICKI*
Affiliation:
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA Department of Mechanical Engineering, University of Melbourne, Melbourne, VIC 3010, Australia
D. MAYNES
Affiliation:
Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA
T. AMEEL
Affiliation:
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA
*
†Email address for correspondence: [email protected]
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Abstract

The redistribution of mean momentum and vorticity, along with the mechanisms underlying these redistribution processes, is explored for post-laminar flow in fully developed, pressure driven, channel flow. These flows, generically referred to as transitional, include an instability stage and a nonlinear development stage. The central focus is on the nonlinear development stage. The present analyses use existing direct numerical simulation data sets, as well as recently reported high-resolution molecular tagging velocimetry measurements. Primary considerations stem from the emergence of the effects of turbulent inertia as represented by the Reynolds stress gradient in the mean differential statement of dynamics. The results describe the flow evolution following the formation of a non-zero Reynolds stress peak that is known to first arise near the critical layer of the most unstable disturbance. The positive and negative peaks in the Reynolds stress gradient profile are observed to undergo a relative movement toward both the wall and centreline for subsequent increases in Reynolds number. The Reynolds stress profiles are shown to almost immediately exhibit the same sequence of curvatures that exists in the fully turbulent regime. In the transitional regime, the outer inflection point in this profile physically indicates a localized zone within which the mean dynamics are dominated by inertia. These observations connect to recent theoretical findings for the fully turbulent regime, e.g. as described by Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst., vol. 24, 2009, p. 781) and Klewicki, Fife & Wei (J. Fluid Mech., vol. 638, 2009, p. 73). In accord with momentum equation analyses at higher Reynolds number, the present observations provide evidence that a logarithmic mean velocity profile is most rapidly approximated on a sub-domain located between the zero in the Reynolds stress gradient (maximum in the Reynolds stress) and the outer region location of the maximal Reynolds stress gradient (inflection point in the Reynolds stress profile). Overall, the present findings provide evidence that the dynamical processes during the post-laminar regime and those operative in the high Reynolds number regime are connected and describable within a single theoretical framework.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent transition
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 451 - 481
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Boiko, A., Grek, G., Dovgal, A. & Kozlov, V. 2002 The Origin of Turbulence in Near-Wall Flows. Springer.CrossRefGoogle Scholar
Criminale, W., Jackson, T. & Joslin, R. 2003 Theory and Computation in Hydrodynamic Stability. Cambridge University Press.CrossRefGoogle Scholar
Dean, R. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. J. Fluids Engng 100, 215–223.CrossRefGoogle Scholar
Elsnab, J. 2008 Mean velocity profiles in a high aspect ratio microchannel. PhD dissertation, University of Utah, Salt Lake City.Google Scholar
Elsnab, J., Maynes, D., Klewicki, J. & Ameel, T. 2010 Mean flow structure in high aspect ratio microchannel flows. Exp. Therm. Fluid Sci. 34, 1077–1088.CrossRefGoogle Scholar
Eyink, G. 2008 Turbulent flow in pipes and channels as cross-stream ‘inverse cascades’ of vorticity. Phys. Fluids 20, 125101.CrossRefGoogle Scholar
Fife, P., Wei, T., Klewicki, J. & McMurtry, P. 2005 a Stress gradient balance layers and scale hierarchies in wall bounded turbulent flows. J. Fluid Mech. 532, 165–189.CrossRefGoogle Scholar
Fife, P., Klewicki, J., McMurtry, P. & Wei, T. 2005 b Multiscaling in the presence of indeterminacy: Wall-induced turbulence. Multiscale Model. Simul. 4, 936–959.CrossRefGoogle Scholar
Fife, P., Klewicki, & Wei, T. 2009 Time averaging in turbulence settings may reveal an infinite hierarchy of length scales. J. Discrete Continuous Dyn. Syst. 24, 781–807.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, l73–l76.CrossRefGoogle Scholar
Hill, R. & Klewicki, J. 1996 Data reduction methods for flow tagging velocity measurements. Exp. Fluids 20, 142–152.CrossRefGoogle Scholar
Hoyas, S. & Jimenez, J. 2006 Scaling the velocity fluctuations in turbulent channels up to Re τ = 2003. Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Jordinson, R. 1970 The flat plate boundary layer. Part 1. Numerical integration of the Orr-Sommerfeld equation. J. Fluid Mech. 43, 801–811.CrossRefGoogle Scholar
Klewicki, J., Fife, P., Wei, T. & McMurtry, P. 2007 A physical model of the turbulent boundary layer consonant with mean momentum balance structure. Phil. Trans. R. Soc. A 365, 823–839.CrossRefGoogle ScholarPubMed
Klewicki, J., Fife, P. & Wei, T. 2009 On the logarithmic mean profile. J. Fluid Mech. 638, 73–93.CrossRefGoogle Scholar
Klewicki, J. 2010 Reynolds number dependence, scaling, and dynamics of turbulent boundary layers. J. Fluids Engng 132, 091202.CrossRefGoogle Scholar
Koochesfahani, M. & Nocera, D. 2007 Handbook of Experimental Fluid Dynamics, chap. 5.4, Molecular Tagging Velocimetry. Spring.Google Scholar
Kuroda, A., Kasagi, N. & Hirata, M. 1989 A direct numerical simulation of the fully developed turbulent channel flow. In Proceedings of the International Symposium on Computational Fluid Dynamics, Nagoya, pp. 1174–1179.Google Scholar
Laadhari, F. 2002 On the evolution of maximum turbulent kinetic energy production in a channel flow. Phys. Fluids 14, L65–L68.CrossRefGoogle Scholar
Maynes, D. & Webb, A. 2002 Velocity profile characterization in sub-millimeter diameter tubes using molecular tagging velocimetry. Exp. Fluids 32, 3–15.CrossRefGoogle Scholar
Metzger, M., Adams, P. & Fife, P. 2008 Mean momentum balance in moderately favourable pressure gradient turbulent boundary layers. J. Fluid Mech. 617, 107–140.CrossRefGoogle Scholar
Moffat, R. 1988 Describing the uncertainties in experimental results. Exp. Therm. Fluid Sci. 1, 3–17.CrossRefGoogle Scholar
Moser, R., Kim, J. & Mansour, N. 1999 Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11, 943–945.CrossRefGoogle Scholar
Nagib, H. & Chauhan, K. 2008 Variation of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.CrossRefGoogle Scholar
Natrajan, V. & Christensen, K. 2007 Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries. Exp. Fluids 43 (1), 1–16.CrossRefGoogle Scholar
Natrajan, V. & Christensen, K. 2009 Structural characteristics of transition to turbulence in microscale capillaries. Phys. Fluids 21, 034104.CrossRefGoogle Scholar
Orszag, S. & Kells, L. 1980 Transition to turbulence in plane Poiseuille flow and plane Couette flow. J. Fluid Mech. 96, 159–205.CrossRefGoogle Scholar
Orszag, S. & Patera, A. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.CrossRefGoogle Scholar
Ponce, A., Wong, P., Way, J. & Nocera, D. 1993 Intense phosphorescence triggered by alcohols upon formation of a cyclodextrin ternary complex. J. Phys. Chem. 97, 11137–11142.CrossRefGoogle Scholar
Shah, R. & London, A. 1978 Laminar Flow Forced Convection in Ducts. Academic.Google Scholar
Sherman, F. 1990 Viscous Flow. McGraw-Hill.Google Scholar
Smits, A., McKeon, B. & Marusic, I. 2011 High Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Sreenivasan, K. 1989 The turbulent boundary layer. In Frontiers in Experimental Fluid Mechanics (ed. Gad-el-Hak, M.), pp. 159–209. Springer.CrossRefGoogle Scholar
Sreenivasan, K. & Sahay, A. 1997 The persistence of viscous effects in the overlap region and the mean velocity in turbulent pipe and channel flows. In Self-Sustaining Mechanisms of Wall Turbulence (ed. Panton, R.), pp. 253–272. Computational Mechanics.Google Scholar
Thurlow, E. & Klewicki, J. 2000 Experimental study of turbulent Poiseuille-Couette flow. Phys. Fluids. 12, 865–875.CrossRefGoogle Scholar
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 a Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303–327.CrossRefGoogle Scholar
Wei, T., McMurtry, P., Klewicki, J. & Fife, P. 2005 b Meso scaling of the Reynolds shear stress in turbulent channel and pipe flows. AIAA J. 43, 2350–2353.CrossRefGoogle Scholar
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 c Scaling heat transfer in fully developed turbulent channel flow. Intl J. Heat Mass Transfer 48, 5284–5296.CrossRefGoogle Scholar
Wei, T., Fife, P. & Klewicki, J. 2007 On scaling the mean momentum balance and its solutions in turbulent Couette-Poiseuille flow. J. Fluid Mech. 573, 371–398.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.CrossRefGoogle Scholar