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On the identification of well-behaved turbulent boundary layers

  • C. Sanmiguel Vila (a1), R. Vinuesa (a2), S. Discetti (a1), A. Ianiro (a1), P. Schlatter (a2) and R. Örlü (a2)...
Abstract

This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.

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Email address for correspondence: ramis@mech.kth.se
References
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Alfredsson, P. H. & Örlü, R. 2010 The diagnostic plot – a litmus test for wall bounded turbulence data. Eur. J. Mech. (B/Fluids) 29, 403406.
Alfredsson, P. H., Örlü, R. & Segalini, A. 2012 A new formulation for the streamwise turbulence intensity distribution in wall-bounded turbulent flows. Eur. J. Mech. (B/Fluids) 36, 167175.
Alfredsson, P. H., Segalini, A. & Örlü, R. 2011 A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the ‘outer’ peak. Phys. Fluids 23, 041702.
Bailey, S. C. C., Hultmark, M., Monty, J. P., Alfredsson, P. H., Chong, M. S., Duncan, R. D., Fransson, J. H. M., Hutchins, N., Marusic, I., McKeon, B. J. et al. 2013 Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes. J. Fluid Mech. 715, 642670.
Bobke, A., Vinuesa, R., Örlü, R. & Schlatter, P. 2017 History effects and near-equilibrium in adverse-pressure-gradient turbulent boundary layers. J. Fluid Mech. 820, 667692.
Castillo, L. & Johansson, T. G. 2002 The effects of the upstream conditions on a low Reynolds number turbulent boundary layer with zero pressure gradient. J. Turbul. 3, 119.
Castro, I. A. 2015 Turbulence intensity in wall-bounded and wall-free flows. J. Fluid Mech. 770, 289304.
Castro, I. A., Segalini, A. & Alfredsson, P. H. 2013 Outer-layer turbulence intensities in smooth- and rough-wall boundary layers. J. Fluid Mech. 727, 119131.
Chauhan, K. A., Monkewitz, P. A. & Nagib, H. M. 2009 Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn. Res. 41, 021404.
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191226.
Coles, D. E.1962 The turbulent boundary layer in a compressible fluid. Rand. Rep. R-403-PR.
Coles, D. E. 1968 The young person’s guide to the data. In AFOSR-IFP-Stanford Conference on Computation of Turbulent Boundary Layers (ed. Coles, D. E. & Hirst, E. A.), pp. 145. Thermosciences Division, Stanford University.
Drózdz, A., Elsner, W. & Drobniak, S. 2015 Scaling of streamwise Reynolds stress for turbulent boundary layers with pressure gradient. Eur. J. Mech. (B/Fluids) 49, 137145.
Eitel-Amor, G., Örlü, R. & Schlatter, P. 2014 Simulation and validation of a spatially evolving turbulent boundary layer up to Re 𝜃 = 8300. Intl J. Heat Fluid Flow 47, 5769.
Erm, L. P. & Joubert, P. N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 144.
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32, 245311.
Hosseini, S. M., Vinuesa, R., Schlatter, P., Hanifi, A. & Henningson, D. S. 2016 Direct numerical simulation of the flow around a wing section at moderate Reynolds number. Intl J. Heat Fluid Flow 61, 117128.
Hultmark, M, Bailey, S. C. C. & Smits, A. J. 2010 Scaling of near-wall turbulence in pipe flow. J. Fluid Mech. 649, 103113.
Hutchins, N. 2012 Caution: tripping hazards. J. Fluid Mech. 710, 14.
Hutchins, N., Monty, J. P., Hultmark, M. & Smits, A. J. 2015 A direct measure of the frequency response of hot-wire anemometers: temporal resolution issues in wall-bounded turbulence. Exp. Fluids 56, 18.
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335360.
Khujadze, G. & Oberlack, M. 2004 DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow. Theor. Comput. Fluid Dyn. 18, 391411.
Klebanoff, P. S. & Diehl, W. S.1954 Some features of artificially thickened fully developed turbulent boundary layers with zero pressure gradient. NACA Tech. Rep. 1110.
Kozul, M., Chung, D. & Monty, J. P. 2016 Direct numerical simulation of the incompressible temporally developing turbulent boundary layer. J. Fluid Mech. 796, 437472.
Lee, J. H., Kwon, Y. S., Monty, J. P. & Hutchins, N. 2014 Time-resolved PIV measurement of a developing zero pressure gradient turbulent boundary layer. In Proceedings of the 19th Australasian Fluid Mechanics Conference, 8–11 December 2014 (ed. Brandner, P. A. & Pearce, B. W.). Australasian Fluid Mechanics Society.
Lindgren, B. & Johansson, A. V.2002 Evaluation of the flow quality in the MTL wind-tunnel. Tech. Rep., Royal Institute of Technology (KTH), Stockholm, Sweden.
Lund, T., Wu, X. & Squires, K. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233258.
Marusic, I., Chauhan, K. A., Kulandaivelu, V. & Hutchins, N. 2015 Evolution of zero-pressure-gradient boundary layers from different tripping conditions. J. Fluid Mech. 783, 379411.
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.
Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M. 2007 Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101.
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Intl J. Heat Fluid Flow 32, 575585.
Morrison, J. F., McKeon, B. J., Jiang, W. & Smits, A. J. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99131.
Nagib, H. M., Chauhan, K. A. & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365, 755770.
Nickels, T. B. 2004 Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217239.
Örlü, R., Fransson, J. H. M. & Alfredsson, P. H. 2010 On near wall measurements of wall bounded flows – the necessity of an accurate determination of the wall position. Prog. Aerosp. Sci. 46, 353387.
Örlü, R. & Schlatter, P. 2013 Comparison of experiments and simulations for zero pressure gradient turbulent boundary layers at moderate Reynolds numbers. Exp. Fluids 54, 1547.
Örlü, R., Segalini, A., Klewicki, J. & Alfredsson, P. H. 2016 High-order generalisation of the diagnostic scaling for turbulent boundary layers. J. Turbul. 17, 664677.
Örlü, R. & Vinuesa, R. 2017 Thermal anemomentry. In Experimental Aerodynamics (ed. Discetti, S. & Ianiro, A.), pp. 257303. CRC Press.
Österlund, J. M.1999 Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, Royal Institute of Technology, Stockholm, Sweden.
Rodríguez-López, E., Bruce, P. J. K. & Buxton, O. R. H. 2015 A robust post-processing method to determine skin friction in turbulent boundary layers from the velocity profile. Exp. Fluids 56, 68.
Rodríguez-López, E., Bruce, P. J. K. & Buxton, O. R. H. 2016 On the formation mechanisms of artificially generated high Reynolds number turbulent boundary layers. Boundary-Layer Meteorol. 160, 201224.
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116126.
Schlatter, P. & Örlü, R. 2012 Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 534.
Sillero, J. A., Jiménez, J. & Moser, R. D 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≃ 2000. Phys. Fluids 25, 105102.
Simens, M., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228, 42184231.
Tang, Z., Jiang, N., Zheng, X. & Wu, Y. 2016 Bursting process of large- and small-scale structures in turbulent boundary layer perturbed by a cylinder roughness element. Exp. Fluids 57, 79.
Tani, I. 1969 Boundary-layer transition. Annu. Rev. Fluid Mech. 1, 169196.
Vincenti, P., Klewicki, J., Morrill-Winter, C., White, C. M. & Wosnik, M. 2013 Streamwise velocity statistics in turbulent boundary layers that spatially develop to high Reynolds number. Exp. Fluids 54, 1629.
Vinuesa, R., Bobke, A., Örlü, R. & Schlatter, P. 2016a On determining characteristic length scales in pressure-gradient turbulent boundary layers. Phys. Fluids 28, 055101.
Vinuesa, R., Duncan, R. D. & Nagib, H. M. 2016b Alternative interpretation of the Superpipe data and motivation for CICLoPE: the effect of a decreasing viscous length scale. Eur. J. Mech. (B/Fluids) 58, 109116.
Vinuesa, R. & Örlü, R. 2017 Measurement of wall shear stress. In Experimental Aerodynamics (ed. Discetti, S. & Ianiro, A.), pp. 393428. CRC Press.
Vinuesa, R., Rozier, P. H., Schlatter, P. & Nagib, H. M. 2014 Experiments and computations of localized pressure gradients with different history effects. AIAA J. 52, 368384.
Wu, X., Moin, P. & Hickey, J.-P. 2014 Boundary layer bypass transition. Phys. Fluids 26, 091104.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
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