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Geometrical structure analysis of a zero-pressure-gradient turbulent boundary layer

Published online by Cambridge University Press:  04 May 2018

Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window]  and
Lipo Wang Open the ORCID record for Lipo Wang [Opens in a new window]
Weipeng Li
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
Lipo Wang*
Affiliation:
UM–SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The present work focuses on the geometrical features of a zero-pressure-gradient turbulent boundary layer based on vectorline segment analysis. In a turbulent vector field, tracing from any non-singular point, along either the vector or the inverse direction, one will reach a local extremum of the vector magnitude. The vectorline between the two local extrema is defined as the vectorline segment corresponding to the given spatial point. Specifically the vectorline segment can be the streamline segment for the velocity vector case, or the vorticity line segment for the vorticity vector case. Such a quantitatively defined and space-filling vectorline segment structure reflects the natural vectorial topology. Because of inhomogeneity in the wall-normal direction, vectorline segments corresponding to the grid points at specified wall-normal distances are sampled for statistics. For streamline segments, the probability density function (p.d.f.) of the normalized segment length in different flow regions matches a model solution, and for vorticity line segments such a p.d.f. in the log-law region and beyond matches the same model solution, which indicates some universality of different flow regions and different vector field structures. Typically the joint p.d.f. of the characteristic parameters of streamline segments presents clear asymmetry, which is closely related to the skewness of the velocity derivative. Moreover, the orientation statistics of vectorline segments, characterized by the coordinate difference between the segment starting point and ending point, have been provided to quantify the flow anisotropy.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 318 - 340
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Copyright
© 2018 Cambridge University Press 

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References

Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Re 𝜏 = 640. J. Fluids Engng 126 (5), 835–843.Google Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–53.Google Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Antonia, R. A. 1981 Conditional sampling in turbulence measurement. Annu. Rev. Fluid Mech. 13 (1), 131–156.Google Scholar
Boschung, J., Schaefer, P., Peters, N. & Meneveau, C. 2014 The local topology of stream- and vortex lines in turbulent flows. Phys. Fluids 26 (4), 045107.Google Scholar
Brandt, L., Henningson, D. S. & Ponziani, D. 2002 Weakly nonlinear analysis of boundary layer receptivity to free-stream disturbances. Phys. Fluids 14 (4), 1426–1441.CrossRefGoogle Scholar
Chen, J., Hussain, F., Pei, J. & She, Z. S. 2014 Velocity–vorticity correlation structure in turbulent channel flow. J. Fluid Mech. 742, 291–307.Google Scholar
Deguchi, K. & Hall, P. 2014 Canonical exact coherent structures embedded in high Reynolds number flows. Proc. R. Soc. Lond. A 372 (2020), 20130352.Google Scholar
Eckelmanns, H., Nychas, S. G., Brodkey, R. S. & Wallace, J. M. 1977 Vorticity and turbulence production in pattern recognized turbulent flow structures. Phys. Fluids 20 (20), S225–S231.CrossRefGoogle Scholar
Gampert, M., Goebbert, J. H., Schaefer, P., Gauding, M., Peters, N., Aldudak, F. & Oberlack, M. 2011 Extensive strain along gradient trajectories in the turbulent kinetic energy field. New J. Phys. 13 (4), 043012.Google Scholar
Gampert, M., Schaefer, P. & Peters, N. 2013 Experimental investigation of dissipation-element statistics in scalar fields of a jet flow. J. Fluid Mech. 724, 337–366.Google Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2006 Large-scale motions in a supersonic turbulent boundary layer. J. Fluid Mech. 556, 271–282.Google Scholar
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137–162.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 197–337.Google Scholar
Jimenez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.Google Scholar
Kang, Y. D., Choi, K. S. & Chun, H. H. 2008 Direct intervention of hairpin structures for turbulent boundary-layer control. Phys. Fluids 20 (10), 101517.Google Scholar
Karhunen, K. 1946 Uber lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann. Acad. Sci. Fenn., Ser. A1, Math. Phys. 37, 3–79.Google Scholar
Kawai, S.2016 Direct numerical simulation of transcritical turbulent boundary layers at supercritical pressures with strong real fluid effects. AIAAA Paper 2016-1934.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.Google Scholar
Li, W., Nonomura, T. & Fujii, K. 2013a Mechanism of controlling supersonic cavity oscillations using upstream mass injection. Phys. Fluids 25 (8), 086101.Google Scholar
Li, W., Nonomura, T. & Fujii, K. 2013b On the feedback mechanism in supersonic cavity flows. Phys. Fluids 25 (5), 056101.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 (2), 233–258.Google Scholar
Marusic, I. & Hutchins, N. 2008 Study of the log-layer structure in wall turbulence over a very large range of Reynolds number. Flow Turbul. Combust. 81, 115–130.Google Scholar
Monin, A. S. & Yaglom, A. M. 2007 Statistical Fluid Mechanics, vol. II. Dover.Google 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
Morgan, B., Larsson, J., Kawai, S. & Lele, S. K. 2011 Improving low-frequency characteristics of recycling/rescaling inflow turbulence generation. AIAA J. 49 (3), 582–597.Google Scholar
Mouri, H. 2017 Two-point correlation in wall turbulence according to the attached-eddy hypothesis. J. Fluid Mech. 821, 343–357.CrossRefGoogle Scholar
Nishida, H. & Nonomura, T. 2009 ADI-SGS scheme on ideal magnetohydrodynamics. J. Comput. Phys. 228 (9), 3182–3188.Google Scholar
Nonomura, T. & Fujii, K. 2011 Overexpansion effects on characteristics of Mach waves from a supersonic cold jet. AIAA J. 49 (10), 2282–2294.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205–231.Google Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2010 Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation. J. Fluid Mech. 657, 361–393.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary-layer. Annu. Rev. Fluid Mech. 23, 601–639.Google Scholar
Sagaut, P., Garnier, E., Tromeur, E., Larcheveque, L. & Labourasse, E. 2012 Turbulent inflow conditions for large-eddy-simulation of compressible wall-bounded flows. AIAA J. 42 (3), 469–477.Google Scholar
Sandham, N. D., Yao, Y. F. & Lawal, A. A. 2003 Large-eddy simulation of transonic turbulent flow over a bump. Intl J. Heat Fluid Flow 24 (4), 584–595.Google Scholar
Schaefer, P., Gampert, M. & Peters, N. 2013 A model equation for the joint distribution of the length and velocity difference of streamline segments in turbulent flows. Phys. Fluids 25 (11), 115107.Google Scholar
Schlueter-Kuck, K. L. & Dabiri, J. O. 2017 Coherent structure coloring: identification of coherent structures from sparse data using graph theory. J. Fluid Mech. 811, 468–486.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.Google Scholar
Skufca, J. D., Yorke, J. A. & Eckhardt, B. 2006 Edge of chaos in a parallel shear flow. Phys. Rev. Lett. 96, 174101.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re 𝜃 = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalart, P. R. & Allmaras, S. R.1992 A one equation turbulence model for aerodinamic flows. AIAA Paper 1992-0439.Google Scholar
Taylor, G. I. 1938 Production and dissipation of vorticity in a turbulent fluid. Proc. R. Soc. Lond. A 164, 15–23.Google Scholar
Visbal, M. R. & Gaitonde, D. V. 2002 On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181 (1), 155–185.Google Scholar
Vreman, A. W. & Kuerten, J. G. M. 2014 Statistics of spatial derivatives of velocity and pressure in turbulent channel flow. Phys. Fluids 26, 085103.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.CrossRefGoogle Scholar
Wallace, J. M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131–158.Google Scholar
Wang, L. 2010 On properties of fluid turbulence along streamlines. J. Fluid Mech. 648, 183–203.CrossRefGoogle Scholar
Wang, L. 2012 Structures of the vorticity tube segment in turbulence. Phys. Fluids 24, 045101.CrossRefGoogle Scholar
Wang, L. 2014 Analysis of the Lagrangian path structures in fluid turbulence. Phys. Fluids 26, 045014.Google Scholar
Wang, L., Chakraborty, N. & Zhang, J. 2013 Streamline segment analysis of turbulent premixed flames. Proc. Combust. Inst. 34, 1401–1409.Google Scholar
Wang, L. & Peters, N. 2006 The length-scale distribution function of the distance between extremal points in passive scalar turbulence. J. Fluid Mech. 554, 457–475.Google Scholar
Wang, L. & Peters, N. 2008 Length-scale distribution functions and conditional means for various fields in turbulence. J. Fluid Mech. 608, 113–138.Google Scholar
Wu, X. & Moin, P. 2009 Forest of hairpins in a low-Reynolds-number zero-pressure-gradient flat-plate boundary layer. Phys. Fluids 21 (9), 091106.CrossRefGoogle Scholar
Yang, Y. & Pullin, D. 2011 Evolution of vortex-surface fields in viscous Taylor–Green and Kida–Pelz flows. J. Fluid Mech. 685, 146–164.Google Scholar
Zhao, Y., Yang, Y. & Chen, S. 2016 Vortex reconnection in the late transition in channel flow. J. Fluid Mech. 802, R4.Google Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.Google Scholar