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Predictive models for near-wall velocity and temperature fluctuations in supersonic wall-bounded turbulence

Published online by Cambridge University Press:  02 March 2022

Ming Yu Open the ORCID record for Ming Yu [Opens in a new window]  and
Chunxiao Xu Open the ORCID record for Chunxiao Xu [Opens in a new window]
Ming Yu
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics R&D Center, Mianyang 621000, PR China Key Laboratory of Applied Mechanics, Ministry of Education, Institute of Fluid Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Chunxiao Xu*
Affiliation:
Key Laboratory of Applied Mechanics, Ministry of Education, Institute of Fluid Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: xucx@tsinghua.edu.cn
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Abstract

Predictive models for near-wall velocity and temperature fluctuations in compressible wall-bounded turbulence are developed in the present study based on the model proposed by Marusic et al. (Science, vol. 329 (5988), 2010, pp. 193–196), which incorporates the superposition and amplitude modulation effects of the large-scale motions in the outer region on near-wall turbulence. The density variation is involved in the predictive model for velocity fluctuations to achieve Mach number independence. The predictive model for temperature fluctuations is derived to keep its consistency with the strong Reynolds analogy, in which the modulation effect is supposed to be cast as the quadratic function of the large-scale velocity fluctuations. An algebraic method is proposed to directly determine the modulation coefficients and extract the universal signals. A direct numerical simulation (DNS) of turbulent channel flow at the friction Reynolds number of $1170$ and bulk Mach number of $2.88$ is carried out for parameter calibration and validations. The variances and joint probability density functions of the predicted velocity and temperature fluctuations agree well with the DNS results.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Compressible boundary layers Turbulent Flows: Compressible turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 937 , 25 April 2022 , A32
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

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
Agostini, L. & Leschziner, M. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2016 a 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. 2016 b Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28 (1), 015107.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2019 On the departure of near-wall turbulence from the quasi-steady state. J. Fluid Mech. 871, R1.CrossRefGoogle 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
Baars, W., 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
Baars, W., Talluru, K., Hutchins, N & Marusic, I. 2015 Wavelet analysis of wall turbulence to study large-scale modulation of small scales. Exp. Fluids 56 (10), 1–15.CrossRefGoogle Scholar
Bandyopadhyay, P. & Hussain, A. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 2221–2228.CrossRefGoogle 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
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to $Re_\tau = 4000$. J. Fluid Mech. 742, 171–191.CrossRefGoogle Scholar
Bross, M., Scharnowski, S. & Kãďhler, C.J. 2021 Large-scale coherent structures in compressible turbulent boundary layers. J. Fluid Mech. 911, A2.CrossRefGoogle Scholar
Brown, G. & Thomas, A. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243–S252.CrossRefGoogle Scholar
Chernyshenko, S., Marusic, I. & Mathis, R. 2012 Quasi-steady description of modulation effects in wall turbulence. Preprint, arXiv:1203.3714.Google Scholar
Duan, L. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419–445.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N. & Dolling, D. 2006 Large-scale motions in a supersonic turbulent boundary layer. J. Fluid Mech. 556, 271–282.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.CrossRefGoogle Scholar
Gaviglio, J. 1987 Reynolds analogies and experimental study of heat transfer in the supersonic boundary layer. Intl J. Heat Mass Transfer 30, 911–926.CrossRefGoogle Scholar
Guala, M., Hommema, S. & Adrian, R. 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 (1), 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.Google Scholar
Helm, C. & Martin, P. 2014 Predictive wall model for temperature fluctuations in hypersonic turbulent boundary layers. In 32nd AIAA Applied Aerodynamics Conference, p. 3284.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re_\tau = 2003$. Phys. Fluids 18 (1), 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 365 (1852), 647–664.CrossRefGoogle ScholarPubMed
Hwang, Y. 2013 Near-wall turbulent fluctuations in the absence of wide outer motions. J. Fluid Mech. 723, 264–288.CrossRefGoogle Scholar
Hwang, J., Lee, J., Sung, H. & Zaki, T. 2016 Inner–outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128–157.CrossRefGoogle Scholar
Illingworth, S., Monty, J. & Marusic, I. 2018 Estimating large-scale structures in wall turbulence using linear models. J. Fluid Mech. 842, 146–162.CrossRefGoogle Scholar
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 101302.CrossRefGoogle Scholar
Jimenez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Jiménez, J., Kawahara, G., Simens, M., Nagata, M. & Shiba, M. 2005 Characterization of near-wall turbulence in terms of equilibrium and ‘bursting’ solutions. Phys. Fluids 17 (1), 015105.CrossRefGoogle 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, K. & Adrian, R. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Lagha, M., Kim, J., Eldredge, J. & Zhong, X. 2011 A numerical study of compressible turbulent boundary layers. Phys. Fluids 23 (1), 015106.CrossRefGoogle Scholar
Lee, M. & Moser, R. 2015 Direct numerical simulation of turbulent channel flow up to $Re_\tau \approx 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Li, X., Fu, D. & Ma, Y. 2010 Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack. Phys. Fluids 22 (2), 025105.CrossRefGoogle Scholar
Marusic, I., Baars, W. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner-outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.CrossRefGoogle 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 a 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
Mathis, R., Monty, J., Hutchins, N. & Marusic, I. 2009 b Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows. Phys. Fluids 21 (11), 111703.CrossRefGoogle Scholar
Modesti, D. & Pirozzoli, S. 2016 Reynolds and Mach number effects in compressible turbulent channel flow. Intl J. Heat Fluid Flow 59, 33–49.CrossRefGoogle Scholar
Monty, J., Hutchins, N., Ng, H., Marusic, I. & Chong, M. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Morkovin, M.V. 1962 Effects of compressibility on turbulent flows. Méc. Turbul. 367 (380), 26.Google Scholar
Patel, A., Boersma, B. & Pecnik, R. 2016 The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809, 793–820.CrossRefGoogle Scholar
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
Rao, K., Narasimha, R. & Narayanan, M. 1971 The ‘bursting’ phenomenon in a turbulent boundary layer. J. Fluid Mech. 48 (2), 339–352.CrossRefGoogle Scholar
Ringuette, M., Wu, M. & Pino, M. 2008 Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3. J. Fluid Mech. 594, 59–69.CrossRefGoogle Scholar
Smits, A., McKeon, B. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Talluru, K., 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
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
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28 (2), 026102.CrossRefGoogle Scholar
Van Driest, E. 1951 Turbulent boundary layer in compressible fluids. Intl J. Aeronaut. Space Sci. 18 (3), 145–160.CrossRefGoogle Scholar
Yao, Y., Huang, W. & Xu, C. 2018 Amplitude modulation and extreme events in turbulent channel flow. Acta Mechanica Sin. 34 (1), 1–9.CrossRefGoogle Scholar
Yin, G., Huang, W. & Xu, C. 2017 On near-wall turbulence in minimal flow units. Intl J. Heat Fluid Flow 65, 192–199.CrossRefGoogle Scholar
Yin, G., Huang, W. & Xu, C. 2018 Prediction of near-wall turbulence using minimal flow unit. J. Fluid Mech. 841, 654–673.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. & Pirozzoli, S. 2019 Genuine compressibility effects in wall-bounded turbulence. Phys. Rev. Fluids 4 (12), 123402.CrossRefGoogle Scholar
Zhang, Y., Bi, W., Hussain, F. & She, Z. 2014 A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech. 739, 392–420.CrossRefGoogle Scholar
Zhang, C. & Chernyshenko, S. 2016 Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence. Phys. Rev. Fluids 1 (1), 014401.CrossRefGoogle Scholar