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Small-scale turbulent characteristics in transcritical wall-bounded flows

Published online by Cambridge University Press:  10 May 2024

Fangbo Li Open the ORCID record for Fangbo Li [Opens in a new window] ,
Weiwei Zhang Open the ORCID record for Weiwei Zhang [Opens in a new window] ,
Bofeng Bai  and
Matthias Ihme Open the ORCID record for Matthias Ihme [Opens in a new window]
Fangbo Li*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
Weiwei Zhang
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
Bofeng Bai
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
Matthias Ihme*
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Department of Photon Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
*
†Email addresses for correspondence: fbli@nwpu.edu.cn, mihme@stanford.edu
†Email addresses for correspondence: fbli@nwpu.edu.cn, mihme@stanford.edu
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Abstract

Considerable efforts have been devoted to the understanding of the small-scale characteristics in turbulent flows. While the universality of small-scale quantities has been established for incompressible flows, their extension to high-pressure transcritical flows remains an open area of research. To address this question, we investigate the real-fluid thermodynamic effects on small-scale velocity statistics of high-pressure transcritical wall-bounded turbulence. We show that in the locally isotropic region for transcritical flows, low-order moments of small-scale statistics collapse for all cases and Kolmogorov's (1941) theory holds. However, real-fluid thermodynamic effects introduce deviations in the tails of the probability density function for the velocity derivative and, consequently, high-order moments of velocity gradients and dissipation rate in transcritical flows cannot collapse in the locally isotropic region. Analysis of the intermittency shows that the low-order structure functions in transcritical flows follow extended self-similarity, while the dependence of the intermittency factor on real-fluid effects is observed for high-order structure functions. The real-fluid effects on intermittency are explained by turbulent structures related to rare events. Additionally, the dissipation rate moments for transcritical flows follow a universal scaling with Reynolds number, and the scaling exponents are different from those of incompressible flows. These results extend the small-scale universality in incompressible flows (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965) to realistic flows with significant changes in thermodynamic properties, and provide a physical underpinning of the scaling laws of small-scale statistics at transcritical conditions.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 986 , 10 May 2024 , A36
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Abe, H., Antonia, R. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.10.1017/S0022112008005569CrossRefGoogle Scholar
Antonia, R.A., Djenidi, L., Danaila, L. & Tang, S.L. 2017 Small scale turbulence and the finite Reynolds number effect. Phys. Fluids 29, 020715.10.1063/1.4974323CrossRefGoogle Scholar
Antonia, R.A., Kim, J. & Browne, L.W.B. 1991 Some characteristics of small-scale turbulence in a turbulent duct flow. J. Fluid Mech. 233, 369–388.10.1017/S0022112091000526CrossRefGoogle Scholar
Antonia, R.A., Tang, S.L., Djenidi, L. & Danaila, L. 2015 Boundedness of the velocity gradient skewness in various turbulent flows. J. Fluid Mech. 781, 727–744.CrossRefGoogle Scholar
Belin, F., Maurer, P.T. & Willaime, H. 1997 Velocity gradient distributions in fully developed turbulence: an experimental study. Phys. Fluids 9, 3843–3850.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48, 29–32.10.1103/PhysRevE.48.R29CrossRefGoogle ScholarPubMed
Bolmatov, D., Brazhkin, V. & Trachenko, K. 2013 Thermodynamic behavior of supercritical matter. Nat. Commun. 4, 2331.CrossRefGoogle ScholarPubMed
Boschung, J., Hennig, F., Gauding, M., Pitsch, H. & Peters, N. 2016 Generalized higher-order Kolmogorov scales. J. Fluid Mech. 794, 233–251.CrossRefGoogle Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–52.CrossRefGoogle Scholar
Chung, T.H., Ajlan, M., Lee, L.L. & Starling, K.E. 1988 Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Ind. Engng Chem. Res. 27, 671–679.10.1021/ie00076a024CrossRefGoogle Scholar
Chung, W.T., Jung, K.S., Chen, J.H. & Ihme, M. 2022 BLASTNet: a call for community-involved big data in combustion machine learning. Appl. Energy Combust. Sci. 12, 100087.Google Scholar
Coleman, G.N., Kim, J. & Moser, R.D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.10.1017/S0022112095004587CrossRefGoogle Scholar
Congiunti, A., Bruno, C. & Giacomazzi, E. 2003 Supercritical combustion properties. AIAA Paper 2003-478.CrossRefGoogle Scholar
Djenidi, L., Antonia, R., Talluru, M. & Abe, H. 2017 Skewness and flatness factors of the longitudinal velocity gradient in wall-bounded flows. Phys. Rev. Fluids 2, 064608.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M.P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.CrossRefGoogle Scholar
Elsing, G.E. & Marusic, I. 2010 Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.CrossRefGoogle Scholar
Garcia, C.M., Jackson, P.R. & Garcia, M.H. 2005 Confidence intervals in the determination of turbulence parameters. Exp. Fluids 40, 514–522.CrossRefGoogle Scholar
Guo, J., Yang, X.I.A. & Ihme, M. 2022 Structure of the thermal boundary layer in turbulent channel flows at transcritical conditions. J. Fluid Mech. 934, A45.CrossRefGoogle Scholar
Hamlington, P.E., Krasnov, D., Boeck, T. & Schumacher, J. 2012 Local dissipation scales and energy dissipation-rate moments in channel flow. J. Fluid Mech. 701, 419–429.CrossRefGoogle Scholar
Hickey, J.-P., Ma, P.C., Ihme, M. & Thakur, S. 2013 Large eddy simulation of shear coaxial rocket injector: real fluid effects. AIAA Paper 2013-4071.CrossRefGoogle Scholar
Hirai, R., Pecnik, R. & Kawai, S. 2021 Effects of the semi-local Reynolds number in scaling turbulent statistics for wall heated/cooled supersonic turbulent boundary layers. Phys. Rev. Fluids 6, 124603.CrossRefGoogle Scholar
Huang, P.G., Coleman, G.N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–221.CrossRefGoogle Scholar
Jiang, H.Y., Hu, X.Y., Cheng, L. & Zhou, T.M. 2022 Direct numerical simulation of the turbulent kinetic energy and energy dissipation rate in a cylinder wake. J. Fluid Mech. 946, A11.CrossRefGoogle Scholar
Kawai, S. 2019 Heated transcritical and unheated non-transcritical turbulent boundary layers at supercritical pressures. J. Fluid Mech. 865, 563–601.CrossRefGoogle Scholar
Kerr, R.M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.CrossRefGoogle Scholar
Kim, J. & Antonia, R.A. 1993 Isotropy of the small scales of turbulence at low Reynolds number. J. Fluid Mech. 251, 219–238.CrossRefGoogle Scholar
Kim, K., Hickey, J.-P. & Scalo, C. 2019 Pseudophase change effects in turbulent channel flow under transcritical temperature conditions. J. Fluid Mech. 871, 52–91.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kolmogorov, A.N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85.CrossRefGoogle Scholar
Lepore, J. & Mydlarski, L. 2012 Finite-Peclet-number effects on the scaling exponents of high-order passive scalar structure functions. J. Fluid Mech. 713, 453–481.CrossRefGoogle Scholar
Li, F.B., Guo, J., Bai, B.F. & Ihme, M. 2023 Analysis of real-fluid thermodynamic effects on turbulent statistics in transcritical channel flows. Phys. Rev. Fluids 8, 024605.CrossRefGoogle Scholar
Lumley, J.L. & Newman, G.R. 1977 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161–178.CrossRefGoogle Scholar
Ma, P.C., Yang, X.I.A. & Ihme, M. 2018 Structure of wall-bounded flows at transcritical conditions. Phys. Rev. Fluids 3, 034609.CrossRefGoogle Scholar
Mestayer, P. 1982 Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 125, 475–503.CrossRefGoogle Scholar
Miller, R.S., Harstad, K.G. & Bellan, J. 2001 Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen. J. Fluid Mech. 436, 1–39.CrossRefGoogle Scholar
Obukhov, A.M. 1962 Some specific features of atmospherical turbulence. J. Fluid Mech. 125, 475–503.Google Scholar
Patel, A., Peeters, J.W.R., Boersma, B.J. & Pecnik, R. 2015 Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27, 095101.CrossRefGoogle Scholar
Peng, D.-Y. & Robinson, D. B. 1976 A new two-constant equation of state. Ind. Engng Chem. Fundam. 15, 59–64.CrossRefGoogle Scholar
Poling, B.E., Prausnitz, J.M. & O'Connell, J.P. 2001 The Properties of Gases and Liquids. McGraw-Hill.Google Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pumir, A., Xu, H.T. & Siggia, E.D. 2016 Small-scale anisotropy in turbulent boundary layers. J. Fluid Mech. 804, 5–23.CrossRefGoogle Scholar
Schumacher, J. 2001 Derivative moments in stationary homogeneous shear turbulence. J. Fluid Mech. 441, 109–118.CrossRefGoogle Scholar
Schumacher, J. 2007 Sub-Kolmogorov scale fluctuations in fluid turbulence. Europhys. Lett. 80, 54001.CrossRefGoogle Scholar
Schumacher, J., Scheel, J.D., Krasnov, D., Donzis, D.A., Yakhot, V. & Sreenivasan, K.R. 2014 Small-scale universality in fluid turbulence. Proc. Natl Acad. Sci. USA 111, 10961–10965.CrossRefGoogle ScholarPubMed
Sciacovelli, L., Cinnella, P. & Grasso, F. 2017 Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech. 825, 515–549.CrossRefGoogle Scholar
Sengupta, U., Nemati, H., Boersma, B.J. & Pecnik, R. 2017 Fully compressible low-Mach number simulations of carbon-dioxide at supercritical pressures and trans-critical temperatures. Flow Turbul. Combust. 99 (3–4), 909–931.CrossRefGoogle ScholarPubMed
She, Z.S. & Leveque, E. 1994 Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72 (3), 336–339.CrossRefGoogle ScholarPubMed
Simeoni, G., Bryk, T., Gorelli, F., Krisch, M., Ruocco, G., Santoro, M. & Scopigno, T. 2010 The widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids. Nat. Phys. 6, 503–507.CrossRefGoogle Scholar
Simeski, F. & Ihme, M. 2023 Supercritical fluids behave as complex networks. Nat. Commun. 14, 1996.CrossRefGoogle ScholarPubMed
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
Tang, S., Antonia, L., A, R., Djenidi, L., Abe, H., Zhou, T., Danaila, L. & Zhou, Y. 2015 Transport equation for the mean turbulent energy dissipation rate on the centerline of a fully developed channel flow. J. Fluid Mech. 777, 151–177.CrossRefGoogle Scholar
Tang, S.L., Antonia, R.A., Djenidi, L. & Zhou, Y. 2019 Can small-scale turbulence approach a quasi-universal state. Phys. Rev. Fluids 4, 024607.CrossRefGoogle Scholar
Taylor, G.I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A: Math. Phys. Engng Sci. 151, 421–444.CrossRefGoogle Scholar
Toki, T., Teramoto, S. & Okamoto, K. 2020 Velocity and temperature profiles in turbulent channel flow at supercritical pressure. J. Propul. Power 36, 3–13.CrossRefGoogle Scholar
Van Atta, C.W. & Antonia, R.A. 1980 Reynolds number dependence of skewness and flatness factors of turbulent velocity gradients. Phys. Fluids 23, 252–257.CrossRefGoogle Scholar
Vreman, A.W. & Kuerten, J.G.M. 2014 Comparison of direct numerical simulation databases of turbulent channel flow. Phys. Fluids 26, 015102.CrossRefGoogle Scholar
van de Water, W. & Herweijer, J.A. 1999 High-order structure functions of turbulence. J. Fluid Mech. 387, 3–37.CrossRefGoogle Scholar
Xu, G., Antonia, R.A. & Rajagopalan, S. 2001 Sweeping decorrelation hypothesis in a turbulent round jet. Fluid Dyn. Res. 28, 311–321.CrossRefGoogle Scholar
Yakhot, V. 2006 Probabilities in strong turbulence. Physica D 215, 166–174.CrossRefGoogle Scholar
Yakhot, V. & Sreenivasan, K.R. 2005 Anomalous scaling of structure functions and dynamic constraints on turbulence simulations. J. Stat. Phys. 121, 823–884.CrossRefGoogle Scholar
Zhang, P.J.Y., Wan, Z.H., Liu, N.S., Sun, D.J. & Lu, X.Y. 2022 Wall-cooling effects on pressure fluctuations in compressible turbulent boundary layers from subsonic to hypersonic regimes. J. Fluid Mech. 946, A14.CrossRefGoogle Scholar
Zhang, Y.S., Bi, W.T., Hussain, S., Li, X.L. & She, Z.S. 2012 Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers. Phys. Rev. Lett. 109, 054502.CrossRefGoogle ScholarPubMed