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Transfer functions for flow predictions in wall-bounded turbulence

  • Kenzo Sasaki (a1) (a2) (a3), Ricardo Vinuesa (a2) (a3), André V. G. Cavalieri (a1), Philipp Schlatter (a2) (a3) and Dan S. Henningson (a1) (a2) (a3)...

Abstract

Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-thickness-based Reynolds number up to $Re_{\unicode[STIX]{x1D703}}\simeq 8200$ , using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45 % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case $Re_{\unicode[STIX]{x1D703}}=4430$ . These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single- and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20 % were also observed in the determination of the near-wall spectral peak, depending on the employed method.

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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: kenzo@ita.br

References

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Abreu, L. I., Cavalieri, A. V. & Wolf, W. 2017 Coherent hydrodynamic waves and trailing-edge noise. In 23rd AIAA/CEAS Aeroacoustics Conference, p. 3173. AIAA.
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.10.1017/S0022112006000607
Baars, W. J., Hutchins, N. & Marusic, I. 2016 Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner–outer interaction model. Phys. Rev. Fluids 1 (5), 054406.10.1103/PhysRevFluids.1.054406
Bendat, J. S. 1993 Spectral techniques for nonlinear system analysis and identification. Shock Vib. 1 (1), 2131.10.1155/1993/438416
Bendat, J. S. & Piersol, A. G. 2011 Random Data: Analysis and Measurement Procedures. vol. 729. Wiley.
Bernardini, M. & Pirozzoli, S. 2011 Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys. Fluids 23 (6), 061701.10.1063/1.3589345
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Time scales and correlations in a turbulent boundary layer. Phys. Fluids 15 (9), 15451554.10.1063/1.1694128
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243S252.10.1063/1.861737
Chevalier, M., Lundbladh, A. & Henningson, D. S.2007 Simson – a pseudo-spectral solver for incompressible boundary layer flow. Tech. Rep. TRITA-MEK, KTH Mechanics, Stockholm, Sweden.
Cossu, C., Pujals, G. & Depardon, S. 2009 Optimal transient growth and very large-scale structures in turbulent boundary layers. J. Fluid Mech. 619, 7994.10.1017/S0022112008004370
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77 (2), 387413.10.1017/S0022112076002176
Cuvier, C., Srinath, S., Stanislas, M., Foucaut, J. M., Laval, J. P., Kähler, C. J., Hain, R., Scharnowski, S., Schröder, A., Geisler, R., Agocs, J., Röse, A., Willert, C., Klinner, J., Amili, O., Atkinson, C. & Soria, J. 2017 Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology. J. Turbul. 18 (10), 929972.10.1080/14685248.2017.1342827
Dogan, E., Örlü, R., Gatti, D., Vinuesa, R. & Schlatter, P. 2019 Quantification of amplitude modulation in wall-bounded turbulence. Fluid Dyn. Res. 51 (1), 011408.10.1088/1873-7005/aaca81
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, 5769.10.1016/j.ijheatfluidflow.2014.02.006
Farrell, B. F. & Ioannou, P. J. 1996 Generalized stability theory. Part I. Autonomous operators. J. Atmos. Sci. 53 (14), 20252040.10.1175/1520-0469(1996)053<2025:GSTPIA>2.0.CO;2
Favre, A., Gaviglio, J. & Dumas, R. 1967 Structure of velocity space–time correlations in a boundary layer. Phys. Fluids 10 (9), S138S145.10.1063/1.1762432
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.10.1063/1.3464157
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.10.1017/S0022112006008871
Guillaume, P., Pintelon, R. & Schoukens, J. 1992 Nonparametric frequency response function estimators based on nonlinear averaging techniques. In Instrumentation and Measurement Technology Conference, 1992. IMTC’92, 9th IEEE, pp. 39. IEEE.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.10.1063/1.2162185
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.10.1017/S0022112006003946
Hwang, Y. & Cossu, C. 2010 Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664, 5173.10.1017/S0022112010003629
Illingworth, S. J., Monty, J. P. & Marusic, I. 2018 Estimating large-scale structures in wall turbulence using linear models. J. Fluid Mech. 842, 146162.10.1017/jfm.2018.129
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 2745.10.1146/annurev-fluid-120710-101039
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 101302.10.1063/1.4824988
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.10.1017/S0022112099005066
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.10.1063/1.869889
Komminaho, J., Lundbladh, A. & Johansson, A. V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259285.10.1017/S0022112096007537
Lang, Z. & Billings, S. A. 1996 Output frequency characteristics of nonlinear systems. Intl J. Control 64 (6), 10491067.10.1080/00207179608921674
Lundell, F. 2007 Reactive control of transition induced by free-stream turbulence: an experimental demonstration. J. Fluid Mech. 585, 4171.10.1017/S0022112007006490
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (11), 114504.10.1103/PhysRevLett.99.114504
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193196.10.1126/science.1188765
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311337.10.1017/S0022112009006946
Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537566.10.1017/jfm.2011.216
McKeon, B. J. 2017 The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech. 817, P1.10.1017/jfm.2017.115
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.10.1017/S002211201000176X
McKeon, B. J., Sharma, A. S. & Jacobi, I. 2013 Experimental manipulation of wall turbulence: a systems approach. Phys. Fluids 25 (3), 031301.10.1063/1.4793444
Moehlis, J., Faisst, H. & Eckhardt, B. 2004 A low-dimensional model for turbulent shear flows. New J. Phys. 6 (1), 56.10.1088/1367-2630/6/1/056
Naguib, A. M., Wark, C. E. & Juckenhöfel, O. 2001 Stochastic estimation and flow sources associated with surface pressure events in a turbulent boundary layer. Phys. Fluids 13 (9), 26112626.10.1063/1.1389284
Örlü, R. & Schlatter, P. 2011 On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows. Phys. Fluids 23 (2), 021704.10.1063/1.3555191
Panton, R. L. 2001 Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37 (4), 341383.10.1016/S0376-0421(01)00009-4
Peng, Z. K., Lang, Z. Q. & Billings, S. A. 2007 Crack detection using nonlinear output frequency response functions. J. Sound Vib. 301 (3–5), 777788.10.1016/j.jsv.2006.10.039
Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21 (1), 015109.10.1063/1.3068760
Rice, H. J. & Fitzpatrick, J. A. 1988 A generalised technique for spectral analysis of non-linear systems. Mech. Syst. Signal Process. 2 (2), 195207.10.1016/0888-3270(88)90043-X
Rice, H. J. & Fitzpatrick, J. A. 1991 A procedure for the identification of linear and non-linear multi-degree-of-freedom systems. J. Sound Vib. 149 (3), 397411.10.1016/0022-460X(91)90444-O
Rocklin, G. T., Crowley, J. & Vold, H. 1985 A comparison of H1 , H2 , and Hv frequency response functions. In Proceedings of the 3rd International Modal Analysis Conference, pp. 272278. Union College.
Sasaki, K., Morra, P., Fabbiane, N., Cavalieri, A. V. G., Hanifi, A. & Henningson, D. S. 2018a On the wave-cancelling nature of boundary layer flow control. Theor. Comput. Fluid Mech. 32 (5), 124.
Sasaki, K., Piantanida, S., Cavalieri, A. V. G. & Jordan, P. 2017 Real-time modelling of wavepackets in turbulent jets. J. Fluid Mech. 821, 458481.10.1017/jfm.2017.201
Sasaki, K., Tissot, G., Cavalieri, A. V. G., Silvestre, F. J., Jordan, P. & Biau, D. 2018b Closed-loop control of a free shear flow: a framework using the parabolized stability equations. Theoret. Comput. Fluid Dyn. 32 (6), 124.10.1007/s00162-018-0477-x
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116126.10.1017/S0022112010003113
Schlatter, P. & Örlü, R. 2012 Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 534.10.1017/jfm.2012.324
Schlatter, P., Örlü, 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 (5), 051702.10.1063/1.3139294
Schmid, P. J. & Henningson, D. S. 2012 Stability and Transition in Shear Flows. Springer Science & Business Media.
Schoukens, J., Rolain, Y. & Pintelon, R. 1997 Improved frequency response function measurements for random noise excitations. In Instrumentation and Measurement Technology Conference, pp. 749753. IEEE.
Schrauf, G. 2005 Status and perspectives of laminar flow. Aeronaut. J. 109 (1102), 639644.10.1017/S000192400000097X
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43 (1), 353375.10.1146/annurev-fluid-122109-160753
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821867.10.1017/jfm.2018.283
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578584.10.1126/science.261.5121.578
Vinuesa, R., Hites, M. H., Wark, C. E. & Nagib, H. M. 2015 Documentation of the role of large-scale structures in the bursting process in turbulent boundary layers. Phys. Fluids 27 (10), 105107.10.1063/1.4934625
Vinuesa, R. & Örlü, R. 2017 Measurement of wall shear stress. In Experimental Aerodynamics (ed. Discetti, S. & Ianiro, A.), pp. 393428. CRC Taylor Press.10.1201/9781315371733-12
Waleffe, F. 1995 Hydrodynamic stability and turbulence: beyond transients to a self-sustaining process. Stud. Appl. Math. 95 (3), 319343.10.1002/sapm1995953319
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883900.10.1063/1.869185
Wark, C. E. & Nagib, H. M. 1991 Experimental investigation of coherent structures in turbulent boundary layers. J. Fluid Mech. 230, 183208.10.1017/S0022112091000757
Welch, P. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 7073.10.1109/TAU.1967.1161901
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Transfer functions for flow predictions in wall-bounded turbulence

  • Kenzo Sasaki (a1) (a2) (a3), Ricardo Vinuesa (a2) (a3), André V. G. Cavalieri (a1), Philipp Schlatter (a2) (a3) and Dan S. Henningson (a1) (a2) (a3)...

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