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Establishing the generality of three phenomena using a boundary layer with free-stream passing wakes

Published online by Cambridge University Press:  15 October 2010

XIAOHUA WU
XIAOHUA WU*
Affiliation:
Department of Mechanical Engineering, Royal Military College of Canada, Kingston, Ontario, CanadaK7K 7B4
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulation was performed on an incompressible, smooth flat-plate boundary layer at unit molecular Prandtl number and constant surface temperature under free-stream periodically passing turbulent planar wakes over the momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 1850. This inhomogeneous free-stream wake perturbation source with mean deficit differs markedly from the isotropic turbulent patch used in the previous studies of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5; Phys. Fluids, vol. 22, 2010, 085105). Preponderance of hairpin vortices is observed in both the transitional and turbulent regions of the boundary layer. In particular, the internal structure of merged turbulent spots is a hairpin forest; the internal structure of infant turbulent spots is a hairpin packet. Although more chaotic in the turbulent region, numerous hairpin vortices are readily detected in both the near-wall and outer regions of the boundary layer up to Reθ = 1850. This suggests that the hairpin vortices in the higher-Reynolds-number region are not simply the aged hairpin forests convected from the upstream transitional region. Temperature iso-surfaces in the companion thermal boundary layer are found to be a useful tracer in identifying boundary-layer hairpin vortex structures. Total shear stress overshoots wall shear stress in the transitional region and the excess relaxes gradually in the downstream turbulent region. This overshoot is shown to be associated with a localized streamwise acceleration of the streamwise velocity component. Breakdown of the wake-perturbed laminar boundary layer is closely related to the formation of hairpin packets out of quasi-streamwise vortices. Mean and second-order statistics are in good agreement with previous data on the standard turbulent boundary layer. Downstream of transition, normalized root-mean-square (r.m.s.) wall-shear-stress intensity shows almost no variation with Reθ, whereas normalized r.m.s. wall-pressure intensity increases slightly. Taken together with the previous results of Wu & Moin, the generality of the following three phenomena in quasi-standard boundary layers can be reasonably established, namely, preponderance of hairpin vortices in the transitional as well as in the turbulent regions up to Reθ = 1850, transitional total shear stress overshoot, and a laminar-layer breakdown process closely tied to the formation of hairpin packets.

JFM classification

Boundary Layers: Boundary Layers Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 193 - 219
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
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, 1–54.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Castillo, L., Araya, J. G., Meneveau, C. & Jansen, K. 2009 DNS of turbulent boundary layers with/without external pressure gradient based on a multi-scale, dynamic recycle inflow condition approach. Bull. Am. Phys. Soc. 54 (19), 60.Google Scholar
Chen, C. P. & Blackwelder, R. F. 1978 Large-scale motion in a turbulent boundary layer: a study using temperature contamination. J. Fluid Mech. 89, 1–31.CrossRefGoogle Scholar
Chow, Y. C., Uzol, O. & Katz, J. 2002 Flow non-uniformities and turbulent ‘hot spots’ due to wake–blade and wake–wake interactions in a multistage turbomachine. Trans. ASME: J. Turbomach. 124, 553–563.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Durbin, P. A. & Wu, X. 2007 Transition beneath vortical disturbances. Annu. Rev. Fluid Mech. 39, 107–128.CrossRefGoogle Scholar
Gad-el-Hak, M., Blackwelder, R. F. & Riley, J. J. 1981 On the growth of turbulent regions in laminar boundary layers. J. Fluid Mech. 110, 73–95.CrossRefGoogle Scholar
Gravante, S. P., Naguib, A. M., Wark, C. E. & Nagib, H. M. 1998 Characterization of the pressure fluctuations under a fully developed turbulent boundary layer. AIAA J. 36, 1808–1816.CrossRefGoogle Scholar
Henningson, D., Lundbladh, A. & Johansson, A. 1993 A mechanism for bypass transition from localized disturbances in wall-bounded shear flows. J. Fluid Mech. 250, 169–207.CrossRefGoogle Scholar
Henningson, D., Spalart, P. & Kim, J. 1987 Numerical simulations of turbulent spots in plane Poiseuille and boundary layer flow. Phys. Fluids 30, 2914–2917.CrossRefGoogle Scholar
Hunt, J. C. R. & Durbin, P. A. 1999 Perturbed shear layers and shear sheltering. Fluid Dyn. Res. 24, 375–404.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 1998 Shear sheltering and the continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10, 2006–2011.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulation of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jocksch, A. & Kleiser, L. 2008 Growth of turbulent spots in high-speed boundary layers on a flat plate. Intl J. Heat Fluid Flow 29, 1543–1557.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, 391441.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1986 The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339.CrossRefGoogle Scholar
Krishnan, L. & Sandham, N. D. 2006 On the merging of turbulent spots in a supersonic boundary layer flow. Intl J. Heat Fluid Flow 27, 542–550.CrossRefGoogle Scholar
Lee, J. H. & Sung, H. J. 2009 Hairpin packet structure of a turbulent boundary layer in inclined wall-normal/spanwise planes. Bull. Am. Phys. Soc. 54 (19), 100.Google Scholar
Li, Q., Schlatter, P., Brandt, L. & Henningson, D. S. 2009 Direct numerical simulation of a spatially developing turbulent boundary layer with passive scalar transport. Intl J. Heat Fluid Flow 30, 916–929.CrossRefGoogle Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulation J. Comp. Phys. 140, 233–258.CrossRefGoogle Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids. 13, 735–743.CrossRefGoogle Scholar
Marusic, I. 2009 Unravelling the mechanisms of wall turbulence. J. Fluid Mech. 629, 1–4.CrossRefGoogle Scholar
Marusic, I. & Perry, A. E. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389–407.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations. J. Fluid Mech. 155, 441–464.CrossRefGoogle Scholar
Murlis, J., Tsai, H. M. & Bradshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.CrossRefGoogle Scholar
Osterlund, J. M. 1999 Experimental studies of zero-pressure-gradient turbulent boundary layer flow. PhD thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
Ovchinnikov, V., Choudhari, M. M. & Piomelli, U. 2008 Numerical simulations of boundary-layer bypass transition due to high-amplitude free-stream turbulence. J. Fluid Mech. 613, 135–169.CrossRefGoogle Scholar
Perry, A. E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361–388.CrossRefGoogle Scholar
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low Reynolds number. Phys. Fluids 24, 802–811.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., Orlu, R., Li, Q., Brethouwer, G., Fransson, J. H. M., Johansson, A. V., Alfredsson, P. H. & Henningson, D. S. 2009 Turbulent boundary layers up to Re θ = 2500 studied through simulation and experiment. Phys. Fluids, 21, 051702.CrossRefGoogle Scholar
Schubauer, G. B. & Skramstad, H. K. 1947 Laminar boundary layer oscillations and stability of laminar flow. J. Aeronaut. Sci. 14, 69–78.CrossRefGoogle Scholar
Simens, M. P., Jimenez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comp. Phys. 228, 4218–4231.CrossRefGoogle Scholar
Soranna, F., Chow, Y. C., Uzol, O. & Katz, J. 2006 The effect of Inlet Guide Vanes on the flow structure and turbulence around a rotor blade. Trans. ASME: J. Turbomach. 128, 82–95.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R θ = 1410. J. Fluid Mech. 187, 61–98.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
Uzol, O., Chow, Y. C., Katz, J. & Meneveau, C. 2003 Average passage flow field and deterministic stresses in the tip and hub regions of a multi-stage turbomachine. Trans. ASME: J. Turbomach. 125, 714–725.Google Scholar
Van Atta, C. W. & Helland, K. N. 1980 Exploratory temperature-tagging measurements of turbulent spots in a heated laminar boundary layer. J. Fluid Mech. 100, 243–255.CrossRefGoogle Scholar
Wallace, J. M. 2009 Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: what have we learned about turbulence? Phys. Fluids 21, 021301.CrossRefGoogle Scholar
Wu, X. & Durbin, P. A. 2000 Numerical simulation of heat transfer in a transitional boundary layer with passing wakes. Trans. ASME J. Heat Transfer 122, 248–257.CrossRefGoogle Scholar
Wu, X., Jacobs, R., Hunt, J. C. R. & Durbin, P. A. 1999 Simulation of boundary layer transition induced by periodically passing wakes. J. Fluid Mech. 398, 109–153.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
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
Wu, X. & Moin, P. 2010 Transitional and turbulent boundary layer with heat transfer. Phys. Fluids 22 (8), 085105.CrossRefGoogle 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.CrossRefGoogle Scholar