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Influence of outer large-scale motions on near-wall structures in compressible turbulent channel flows

Published online by Cambridge University Press:  18 September 2024

Zisong Zhou Open the ORCID record for Zisong Zhou [Opens in a new window] ,
Yixiao Wang Open the ORCID record for Yixiao Wang [Opens in a new window] ,
Shuohan Zhang Open the ORCID record for Shuohan Zhang [Opens in a new window] ,
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]
Zisong Zhou
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Yixiao Wang
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Shuohan Zhang
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Wei-Xi Huang
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Chun-Xiao Xu*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: xucx@mail.tsinghua.edu.cn
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Abstract

The influence of outer large-scale motions (LSMs) on near-wall structures in compressible turbulent channel flows is investigated. To separate the compressibility effects, velocity fluctuations are decomposed into solenoidal and dilatational components using the Helmholtz decomposition method. Solenoidal velocity fluctuations manifest as near-wall streaks and outer large-scale structures. The spanwise drifting of near-wall solenoidal streaks is found to be driven by the outer LSMs, while LSMs have a trivial influence on the spanwise density of solenoidal streaks, consistent with the outer LSM impacts found in incompressible flows (Zhou et al., J. Fluid Mech., vol. 940, 2022, p. A23). Dilatational motions are characterized by the near-wall small-scale travelling-wave packets and the large-scale parts in the outer region. The streamwise advection velocity of the near-wall structures remains at $16 \sim 18u_{\tau }$, hardly influenced by Mach numbers, Reynolds numbers and wall temperatures. The spanwise drifting of near-wall dilatational structures, quantified by the particle image velocimetry method, follows a mechanism distinct from solenoidal streaks. This drifting velocity is notably larger than those of the solenoidal streaks, and the influence of outer LSMs is not the primary trigger for this drifting.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 994 , 10 September 2024 , A14
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Abe, H., Antonia, R. & Toh, S. 2018 Large-scale structures in a turbulent channel flow with a minimal streamwise flow unit. J. Fluid Mech. 850, 733–768.CrossRefGoogle Scholar
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 $Re_\tau =640$. Trans. ASME J. Fluids Engng 126 (5), 835–843.CrossRefGoogle Scholar
Adrian, R.J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Agostini, L.M., Leschziner, M., Poggie, J., Bisek, N.J. & Gaitonde, D.V. 2016 Causal relationship between large outer structures and small-scale near-wall turbulence in a compressible boundary layer at ${\rm Mach}= 2.3$. In 54th AIAA Aerospace Sciences Meeting, p. 0335. AIAA.CrossRefGoogle Scholar
Agostini, L.M., Leschziner, M., Poggie, J., Bisek, N.J. & Gaitonde, D.V. 2017 Multi-scale interactions in a compressible boundary layer. J. Turbul. 18 (8), 760–780.CrossRefGoogle Scholar
del Álamo, J.C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.CrossRefGoogle Scholar
del Álamo, J.C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
del Álamo, J.C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor's approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
del Álamo, J.C., Jiménez, J., Zandonade, P. & Moser, R.D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.CrossRefGoogle Scholar
Alizard, F., Pirozzoli, S., Bernardini, M. & Grasso, F. 2015 Optimal transient growth in compressible turbulent boundary layers. J. Fluid Mech. 770, 124–155.CrossRefGoogle 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. A Math. Phys. Engng Sci. 365 (1852), 665–681.CrossRefGoogle ScholarPubMed
Bendat, J.S. & Piersol, A.G. 2011 Random Data: Analysis and Measurement Procedures. John Wiley & Sons.Google Scholar
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.CrossRefGoogle Scholar
Bross, M., Scharnowski, S. & Kähler, C.J. 2021 Large-scale coherent structures in compressible turbulent boundary layers. J. Fluid Mech. 911, A2.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.CrossRefGoogle 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.CrossRefGoogle Scholar
Guala, M., Hommema, S.E. & Adrian, R.J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Hamilton, J., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Helm, C. & Martin, P. 2013 Predictive inner-outer model for turbulent boundary layers applied to hypersonic DNS data. In 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p. 265. AIAA.CrossRefGoogle Scholar
Hirasaki, G.J. & Hellums, J.D. 1970 Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Q. Appl. Maths 28 (2), 293–296.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re_\tau =2003$. Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A Math. Phys. Engng Sci. 365 (1852), 647–664.CrossRefGoogle ScholarPubMed
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Jiménez, J. 1998 The largest scales of turbulence. In CTR Annual Research Briefs, pp. 137–154. Stanford University.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids A: Fluid Dyn. 5 (3), 695–706.CrossRefGoogle 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.CrossRefGoogle Scholar
Kim, K.C. & Adrian, R.J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Li, X.-L., Fu, D.-X., Ma, Y.-W. & Liang, X. 2010 Direct numerical simulation of compressible turbulent flows. Acta Mechanica Sin. 26 (6), 795–806.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 a High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31 (3), 418–428.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 b 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.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.CrossRefGoogle Scholar
Monty, J.P., Hutchins, N., Ng, H.C.H., Marusic, I. & Chong, M.S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Pei, J., Chen, J., Fazle, H. & She, Z.S. 2013 New scaling for compressible wall turbulence. Sci. China Phys. Mech. Astron. 56, 1770–1781.CrossRefGoogle Scholar
Pei, J., Chen, J., She, Z.S. & Hussain, F. 2012 Model for propagation speed in turbulent channel flows. Phys. Rev. E 86 (4), 046307.CrossRefGoogle ScholarPubMed
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2013 Probing high-Reynolds-number effects in numerical boundary layers. Phys. Fluids 25 (2), 021704.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2010 On the dynamical relevance of coherent vortical structures in turbulent boundary layers. J. Fluid Mech. 648, 325–349.CrossRefGoogle Scholar
Ringuette, M.J., Wu, M. & Martin, M.P. 2008 Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3. J. Fluid Mech. 594, 59–69.CrossRefGoogle Scholar
Robinson, S.K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics, vol. 10. Springer.CrossRefGoogle Scholar
Samtaney, R., Pullin, D.I. & Kosović, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13 (5), 1415–1430.CrossRefGoogle Scholar
Taylor, G.I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 164 (919), 476–490.Google Scholar
Toh, S. & Itano, T. 2005 Interaction between a large-scale structure and near-wall structures in channel flow. J. Fluid Mech. 524, 249–262.CrossRefGoogle Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017 Spectra and statistics in compressible isotropic turbulence. Phys. Rev. Fluids 2 (1), 013403.CrossRefGoogle Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X.T. & Chen, S. 2012 a Scaling and statistics in three-dimensional compressible turbulence. Phys. Rev. Lett. 108 (21), 214505.CrossRefGoogle ScholarPubMed
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X.T. & Chen, S. 2012 b Effect of compressibility on the small-scale structures in isotropic turbulence. J. Fluid Mech. 713, 588–631.CrossRefGoogle Scholar
Yu, M., Liu, P.X., Fu, Y.L., Tang, Z.G. & Yuan, X.X. 2022 Wall shear stress, pressure and heat flux fluctuations in compressible wall-bounded turbulence. II. Spectra, correlation and nonlinear interactions. Phys. Fluids 34 (6), 065140.CrossRefGoogle Scholar
Yu, M. & Xu, C.-X. 2021 Compressibility effects on hypersonic turbulent channel flow with cold walls. Phys. Fluids 33 (7), 075106.CrossRefGoogle Scholar
Yu, M. & Xu, C.-X. 2022 Predictive models for near-wall velocity and temperature fluctuations in supersonic wall-bounded turbulence. J. Fluid Mech. 937, A32.CrossRefGoogle Scholar
Yu, M., Xu, C.-X. & Pirozzoli, S. 2019 Genuine compressibility effects in wall-bounded turbulence. Phys. Rev. Fluids 4 (12), 123402.CrossRefGoogle Scholar
Yu, M., Zhou, Z.S., Dong, S.W., Yuan, X.X. & Xu, C.X. 2024 On the generation of near-wall dilatational motions in hypersonic turbulent boundary layers. J. Fluid Mech. 984, A44.CrossRefGoogle Scholar
Zhou, Z., Xu, C.-X. & Jiménez, J. 2022 Interaction between near-wall streaks and large-scale motions in turbulent channel flows. J. Fluid Mech. 940, A23.CrossRefGoogle Scholar