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Prediction of near-wall turbulence using minimal flow unit

Published online by Cambridge University Press:  26 February 2018

Guang Yin ,
Wei-Xi Huang Open the ORCID record for Wei-Xi Huang [Opens in a new window]  and
Chun-Xiao Xu Open the ORCID record for Chun-Xiao Xu [Opens in a new window]
Guang Yin
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Wei-Xi Huang
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Chun-Xiao Xu*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
*
†Email address for correspondence: [email protected]
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Abstract

In the present study, direct numerical simulation (DNS) is carried out in a minimal channel at $Re_{\unicode[STIX]{x1D70F}}=2000$ to sustain healthy turbulence below $y^{+}=100$. Turbulence intensities are compared with those of the motions at the same scales as the minimal channel in the full-sized channel at $Re_{\unicode[STIX]{x1D70F}}=2003$ (Hoyas & Jiménez, Phys. Fluids, vol. 20 (10), 2008, article 101511). They show good agreement in $y^{+}<100$. The universal signals for the three velocity components similar to that in the predictive model of Marusic et al. (Science, vol. 329 (5988), 2010, pp. 193–196) are extracted from the DNS data of the full-sized channel. They correspond well to the near-wall velocity fluctuations in the minimal flow unit (MFU). The predictive models for the three components of near-wall velocity fluctuations are proposed based on the MFU data. The predicted turbulence intensities as well as the joint probability density functions of velocity fluctuations agree well with the DNS results of the full-sized channel turbulence.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 654 - 673
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Copyright
© 2018 Cambridge University Press 

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References

Agostini, L. & Leschziner, M. 2016a Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28 (1), 015107.Google Scholar
Agostini, L. & Leschziner, M. 2016b On the validity of the quasi-steady-turbulence hypothesis in representing the effects of large scales on small scales in boundary layers. Phys. Fluids 28 (4), 045102.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. A. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.Google Scholar
Agostini, L., Leschziner, M. & Gaitonde, D. 2016 Skewness-induced asymmetric modulation of small-scale turbulence by large-scale structures. Phys. Fluids 28 (1), 015110.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41.Google Scholar
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.CrossRefGoogle Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365 (1852), 665–681.Google ScholarPubMed
Chernyshenko, S. I., Marusic, I. & Mathis, R.2012 Quasi-steady description of modulation effects in wall turbulence. arXiv:1203.Google Scholar
Deng, B. Q. & Xu, C. X. 2012 Influence of active control on STG-based generation of streamwise vortices in near-wall turbulence. J. Fluid Mech. 710, 234–259.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.Google Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.Google Scholar
Garcia-Mayoral, R., Pierce, B. & Wallace, J. M. 2013 Off-wall boundary conditions for turbulent simulations from minimal flow units in transitional boundary layers. In TSFP Digital Library Online. Begel House.Google Scholar
de Giovanetti, M., Hwang, Y. & Choi, H. 2016 Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech. 808, 511–538.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20 (10), 101511.Google Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.Google Scholar
Hwang, J., Lee, J., Sung, H. J. & Zaki, T. A. 2016 Inner–outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128–157.CrossRefGoogle Scholar
Hwang, Y. 2013 Near-wall turbulent fluctuations in the absence of wide outer motions. J. Fluid Mech. 723, 264–288.Google Scholar
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254–289.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 044505.Google Scholar
Hwang, Y. & Cossu, C. 2011 Self-sustained processes in the logarithmic layer of turbulent channel flows. Phys. Fluids 23 (6), 061702.Google Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.Google Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97 (2), 414–443.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 (2), 417–422.CrossRefGoogle Scholar
Marusic, I., Baars, W. J. & Hutchins, N. 2015 An extended view of the inner–outer interaction model for wall-bounded turbulence using spectral linear stochastic estimation. Procedia Engng. 126, 24–28.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.CrossRefGoogle ScholarPubMed
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2011a A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.Google Scholar
Mathis, R., Marusic, I., Chernyshenko, S. I. & Hutchins, N. 2013 Estimating wall-shear-stress fluctuations given an outer region input. J. Fluid Mech. 715, 163.Google Scholar
Mathis, R., Marusic, I., Hutchins, N. & Sreenivasan, K. R. 2011b The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys. Fluids 23 (12), 121702.Google Scholar
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429–455.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.CrossRefGoogle Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 26 (10), 105109.CrossRefGoogle Scholar
Squire, D. T., Baars, W. J., Hutchins, N. & Marusic, I. 2016 Inner–outer interactions in rough-wall turbulence. J. Turbulence 17 (12), 1159–1178.Google Scholar
Talluru, K. M., Baidya, R., Hutchins, N. & Marusic, I. 2014 Amplitude modulation of all three velocity components in turbulent boundary layers. J. Fluid Mech. 746, R1.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tuerke, F. & Jiménez, J. 2013 Simulations of turbulent channels with prescribed velocity profiles. J. Fluid Mech. 723, 587–603.CrossRefGoogle Scholar
Woodcock, J. D. & Marusic, I. 2015 The statistical behaviour of attached eddies. Phys. Fluids 27 (1), 015104.Google Scholar
Yin, G., Huang, W. X. & Xu, C. X. 2017 On near-wall turbulence in minimal flow units. Intl J. Heat Fluid Flow 65, 192–199.Google Scholar
Yoon, M., Hwang, J., Lee, J., Sung, H. J. & Kim, J. 2016 Large-scale motions in a turbulent channel flow with the slip boundary condition. Intl J. Heat Fluid Flow 61, 96–107.Google Scholar
Zhang, C. & Chernyshenko, S. I. 2016 Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence. Phys. Rev. Fluids 1 (1), 014401.Google Scholar