Hostname: page-component-5b777bbd6c-2c8nx Total loading time: 0 Render date: 2025-06-18T16:25:15.655Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent/non-turbulent interface in polymer-laden jets

Published online by Cambridge University Press:  19 May 2025

Sheng-Hong Peng ,
Xi-Ran Liu ,
Yi-Bao Zhang Open the ORCID record for Yi-Bao Zhang [Opens in a new window]  and
Heng-Dong Xi Open the ORCID record for Heng-Dong Xi [Opens in a new window]
Sheng-Hong Peng
Affiliation:
Institute of Extreme Mechanics and School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, PR China BYD Auto Company Limited, Xi’an 710072, PR China
Xi-Ran Liu
Affiliation:
Institute of Extreme Mechanics and School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, PR China
Yi-Bao Zhang*
Affiliation:
Institute of Extreme Mechanics and School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, PR China Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, PR China
Heng-Dong Xi*
Affiliation:
Institute of Extreme Mechanics and School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, PR China
*
Corresponding authors: Yi-Bao Zhang, zhangyibao@mail.tsinghua.edu.cn; Heng-Dong Xi, hengdongxi@nwpu.edu.cn
Corresponding authors: Yi-Bao Zhang, zhangyibao@mail.tsinghua.edu.cn; Heng-Dong Xi, hengdongxi@nwpu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an experimental study on the effects of polymer additives on the turbulent/non-turbulent interface (TNTI) in a fully developed round water jet. The Reynolds number based on the jet diameter is fixed at $Re=7075$. The Weissenberg number $Wi$ ranges from 24 to 86. We employ time-resolved simultaneous particle image velocimetry and laser-induced fluorescence measurements to investigate the local entrainment and engulfment process along the TNTI in two regimes: entrainment transition and enhancement regimes. In polymer-laden jets, the TNTI fluctuates more intermittently in the radial direction and more ambient fluid can be engulfed into the turbulent region due to the augmented large scale motion. Though the contribution of engulfment to the total flux increases with $Wi$, engulfment is still not the major contribution to the entrainment in polymer-laden jets. We further show that the local entrainment velocity is increased in both regimes compared with the pure water jet, due to two contributions: polymer elastic stress and the more intermittent character of the TNTI. In the entrainment transition regime, we observe smaller fractal dimension and shorter length of TNTI compared with the Newtonian case, consistent with previous numerical simulations (Abreu et al. J. Fluid Mech. vol. 934, 2022, A36); whereas those in the enhancement regime remain largely unchanged. The difference between the two regimes results from the fact that the jet flow decays in the streamwise direction. In the entrainment transition regime, turbulence intensity is strong enough to significantly stretch the polymers, resulting in a smoother TNTI in the inertial range. However, in the entrainment enhancement regime, the polymer’s feedback is not strong enough to alter the fractal dimension due to the low elasticity. The above mentioned differences of entrainment velocity and TNTI in the entrainment reduction/transition and enhancement regimes also explain the reduced and enhanced spreading rate of the viscoelastic jet observed in previous numerical simulations and experiments (Guimarães et al. J. Fluid Mech. 2020,vol. 899, A11; Peng et al. Phys. Fluids, 2023, vol. 35, 045110).

JFM classification

Flow Control: Mixing enhancement Wakes/Jets: Jets Non-Newtonian Flows: Polymers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1010 , 10 May 2025 , A25
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abreu, H., Pinho, F.T. & da Silva, C.B. 2022 Turbulent entrainment in viscoelastic fluids. J. Fluid Mech. 934, A36.CrossRefGoogle Scholar
Bailey, F.E. & Koleske, J.V. 1976 Poly (ethylene oxide). Academic Press.CrossRefGoogle Scholar
Baj, P., Bruce, P.J.K. & Buxton, O.R.H. 2016 On a PLIF quantification methodology in a nonlinear dye response regime. Exp. Fluids 57 (6), 1–19.CrossRefGoogle Scholar
Balamurugan, G., Rodda, A., Philip, J. & Mandal, A.C. 2020 Characteristics of the turbulent non-turbulent interface in a spatially evolving turbulent mixing layer. J. Fluid Mech. 894, A4.CrossRefGoogle Scholar
Boffetta, G., Mazzino, A. & Musacchio, S. 2011 Effects of polymer additives on Rayleigh–Taylor turbulence. Phys. Rev. E 83 (5), 056318.CrossRefGoogle ScholarPubMed
Boffetta, G., Mazzino, A., Musacchio, S. & Vozella, L. 2010 Polymer heat transport enhancement in thermal convection: the case of Rayleigh–Taylor turbulence. Phys. Rev. Lett. 104 (18), 184501.CrossRefGoogle ScholarPubMed
Boulafentis, T., Lacassagne, T., Cagney, N. & Balabani, S. 2024 Coherent structures of elastoinertial instabilities in Taylor–Couette flows. J. Fluid Mech. 986, A27.CrossRefGoogle Scholar
Cai, W.-H., Li, F.-C. & Zhang, H.-N. 2010 Dns study of decaying homogeneous isotropic turbulence with polymer additives. J. Fluid Mech. 665, 334–356.CrossRefGoogle Scholar
Cocconi, G., De Angelis, E., Frohnapfel, B., Baevsky, M. & Liberzon, A. 2017 Small scale dynamics of a shearless turbulent/non-turbulent interface in dilute polymer solutions. Phys. Fluids 29 (7), 075102.CrossRefGoogle Scholar
Crimaldi, J.P. 2008 Planar laser induced fluorescence in aqueous flows. Exp. Fluids 44 (6), 851–863.CrossRefGoogle Scholar
Deblais, A., Herrada, M.A., Eggers, J. & Bonn, D. 2020 Self-similarity in the breakup of very dilute viscoelastic solutions. J. Fluid Mech. 904, R2.CrossRefGoogle Scholar
Guimarães, M.C., Pimentel, N., Pinho, F.T. & da Silva, C.B. 2020 Direct numerical simulations of turbulent viscoelastic jets. J. Fluid Mech. 899, A11.CrossRefGoogle Scholar
Guimarães, M.C., Pinho, F.T. & da Silva, C.B. 2022 Turbulent planar wakes of viscoelastic fluids analysed by direct numerical simulations. J. Fluid Mech. 946, A26.CrossRefGoogle Scholar
Guimarães, M.C., Pinho, F.T. & da Silva, C.B. 2023 Viscoelastic jet instabilities studied by direct numerical simulations. Phys. Rev. Fluids 8 (10), 103301.CrossRefGoogle Scholar
Guimarães, M.C., Pinho, F.T. & da Silva, C.B. 2024 The similarity theory of free turbulent shear flows of viscoelastic fluids. J. Non-Newtonian Fluid Mech. 323, 105148.CrossRefGoogle Scholar
Guimarães, M.C., Pinho, F.T. & da Silva, C.B. 2025 Mixing of passive scalars in viscoelastic turbulent jets and wakes. Phys. Rev. Fluids 10 (2), 023303.CrossRefGoogle Scholar
Gupta, V.K., Sureshkumar, R. & Khomami, B. 2005 Passive scalar transport in polymer drag-reduced turbulent channel flow. AIChE J. 51 (7), 1938–1950.CrossRefGoogle Scholar
Holzner, M., Liberzon, A., Nikitin, N., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2008 A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation. J. Fluid Mech. 598, 465–475.CrossRefGoogle Scholar
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106 (13), 134503.CrossRefGoogle ScholarPubMed
Jahanbakhshi, R. & Madnia, C.K. 2016 Entrainment in a compressible turbulent shear layer. J. Fluid Mech. 797, 564–603.CrossRefGoogle Scholar
Kankanwadi, K.S. & Buxton, O.R.H. 2020 Turbulent entrainment into a cylinder wake from a turbulent background. J. Fluid Mech. 905, A35.CrossRefGoogle Scholar
Kohan, K.F. & Gaskin, S. 2020 The effect of the geometric features of the turbulent/non-turbulent interface on the entrainment of a passive scalar into a jet. Phys. Fluids 32 (9), 095114.CrossRefGoogle Scholar
Krug, D., Holzner, M., Lüthi, B., Wolf, M., Kinzelbach, W. & Tsinober, A. 2015 The turbulent/non-turbulent interface in an inclined dense gravity current. J. Fluid Mech. 765, 303–324.CrossRefGoogle Scholar
Lavoie, P., Avallone, G., De Gregorio, F., Romano, G.P. & Antonia, R.A. 2007 Spatial resolution of piv for the measurement of turbulence. Exp. Fluids 43 (1), 39–51.CrossRefGoogle Scholar
Liberzon, A., Holzner, M., Lüthi, B., Guala, M. & Kinzelbach, W. 2009 On turbulent entrainment and dissipation in dilute polymer solutions. Phys. Fluids 21 (3), 035107.CrossRefGoogle Scholar
Long, Y.G., Wang, J.J. & Pan, C. 2022 Universal modulations of large-scale motions on entrainment of turbulent boundary layers. J. Fluid Mech. 941, A68.CrossRefGoogle Scholar
Mathew, J. & Basu, A.J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14 (7), 2065–2072.CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K.R. 1990 Interface dimension in intermittent turbulence. Phys. Rev. A 41 (4), 2246–2248.CrossRefGoogle ScholarPubMed
Mistry, D., Philip, J. & Dawson, J.R. 2019 Kinematics of local entrainment and detrainment in a turbulent jet. J. Fluid Mech. 871, 896–924.CrossRefGoogle Scholar
Mistry, D., Philip, J., Dawson, J.R. & Marusic, I. 2016 Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J. Fluid Mech. 802, 690–725.CrossRefGoogle Scholar
Moazzen, M., Lacassagne, T., Thomy, V. & Bahrani, S.A. 2023 Friction dynamics of elasto-inertial turbulence in Taylor–Couette flow of viscoelastic fluids. Phil. Trans. R. Soc. Lond. A 381 (2246), 20220300.Google ScholarPubMed
Morton, B.R., Taylor, G.I. & Turner, J.S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 1–23.Google Scholar
Nie, S., Chiu, D.T. & Zare, R.N. 1994 Probing individual molecules with confocal fluorescence microscopy. Science 266 (5187), 1018–1021.CrossRefGoogle ScholarPubMed
Ouellette, N.T., Xu, H.-T. & Bodenschatz, E. 2009 Bulk turbulence in dilute polymer solutions. J. Fluid Mech. 629, 375–385.CrossRefGoogle Scholar
Oxlade, A.R., Valente, P.C., Ganapathisubramani, B. & Morrison, J.F. 2012 Denoising of time-resolved PIV for accurate measurement of turbulence spectra and reduced error in derivatives. Exp. Fluids 53 (5), 1561–1575.CrossRefGoogle Scholar
Parker, D.A., Burridge, H.C., Partridge, J.L. & Linden, P.F. 2020 A comparison of entrainment in turbulent line plumes adjacent to and distant from a vertical wall. J. Fluid Mech. 882, A4.CrossRefGoogle Scholar
Peng, S.-H., Zhang, Y.-B. & Xi, H.-D. 2023 Effects of polymer additives on the entrainment of turbulent water jet. Phys. Fluids 35 (4), 045110.Google Scholar
Philip, J., Meneveau, C., de Silva, C.M. & Marusic, I. 2014 Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers. Phys. Fluids 26 (1), 015105.CrossRefGoogle Scholar
Polmar, N. & Moore, K.J. 2004 Cold War Submarines: the Design and Construction of US and Soviet Submarines. Potomac Books, Inc.Google Scholar
Prasad, R.R. & Sreenivasan, K.R. 1989 Scalar interfaces in digital images of turbulent flows. Exp. Fluids 7 (4), 259–264.CrossRefGoogle Scholar
Ray, P.K. & Zaki, T.A. 2014 Absolute instability in viscoelastic mixing layers. Phys. Fluids 26 (1), 014103.CrossRefGoogle Scholar
Ray, P.K. & Zaki, T.A. 2015 Absolute/convective instability of planar viscoelastic jets. Phys. Fluids 27 (1), 014110.CrossRefGoogle Scholar
ur Rehman, S., Lee, J. & Lee, C. 2022 Effect of Weissenberg number on polymer-laden turbulence. Phys. Rev. Fluids 7 (6), 064303.CrossRefGoogle Scholar
Roshko, A. 1976 Structure of turbulent shear flows: a new look. AIAA J. 14 (10), 1349–1357.CrossRefGoogle Scholar
Rosti, M.E., Perlekar, P. & Mitra, D. 2023 Large is different: nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers. Sci. Adv. 9 (11), eadd3831.CrossRefGoogle Scholar
da Silva, C.B., Hunt, J.C.R., Eames, I. & Westerweel, J. 2014 a Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46 (1), 567–590.CrossRefGoogle Scholar
da Silva, C.B. & Taveira, R.R. 2010 The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer. Phys. Fluids 22 (12), 121702.CrossRefGoogle Scholar
da Silva, C.B., Taveira, R.R. & Borrell, G. 2014 b Characteristics of the turbulent/nonturbulent interface in boundary layers, jets and shear-free turbulence. Journal of Physics: Conference Series, vol. 506, pp. 012015. IOP Publishing.CrossRefGoogle Scholar
de Silva, C.M., Philip, J., Chauhan, K., Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers. Phys. Rev. Lett. 111 (4), 044501.CrossRefGoogle ScholarPubMed
Soligo, G. & Rosti, M.E. 2023 Non-Newtonian turbulent jets at low-Reynolds number. Intl J. Multiphase Flow 167, 104546.CrossRefGoogle Scholar
Vaithianathan, T., Robert, A., Brasseur, J.G. & Collins, L.R. 2007 Polymer mixing in shear-driven turbulence. J. Fluid Mech. 585, 487–497.CrossRefGoogle Scholar
Valente, P.C., da Silva, C.B. & Pinho, F.T. 2014 The effect of viscoelasticity on the turbulent kinetic energy cascade. J. Fluid Mech. 760, 39–62.CrossRefGoogle Scholar
Valente, P.C., da Silva, C.B. & Pinho, F.T. 2016 Energy spectra in elasto-inertial turbulence. Phys. Fluids 28 (7), 075108.CrossRefGoogle Scholar
Vonlanthen, R. & Monkewitz, P.A. 2013 Grid turbulence in dilute polymer solutions: PEO in water. J. Fluid Mech. 730, 76–98.CrossRefGoogle Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014 Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys. Fluids 26 (10), 105103.CrossRefGoogle Scholar
Watanabe, T., Zhang, X. & Nagata, K. 2018 Turbulent/non-turbulent interfaces detected in dns of incompressible turbulent boundary layers. Phys. Fluids 30 (3), 035102.CrossRefGoogle Scholar
Wei, M.-H., Li, B., David, R.L.A., Jones, S.C., Sarohia, V., Schmitigal, J.A. & Kornfield, J.A. 2015 Megasupramolecules for safer, cleaner fuel by end association of long telechelic polymers. Science 350 (6256), 72–75.CrossRefGoogle ScholarPubMed
Westerweel, J., Fukushima, C., Pedersen, J.M. & Hunt, J.C.R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230.CrossRefGoogle Scholar
White, C.M. & Mungal, M.G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40 (1), 235–256.CrossRefGoogle Scholar
Wolf, M., Lüthi, B., Holzner, M., Krug, D., Kinzelbach, W. & Tsinober, A. 2012 Investigations on the local entrainment velocity in a turbulent jet. Phys. Fluids 24 (10), 105110.CrossRefGoogle Scholar
Xi, H.-D., Bodenschatz, E. & Xu, H.T. 2013 Elastic energy flux by flexible polymers in fluid turbulence. Phys. Rev. Lett. 111 (2), 024501.CrossRefGoogle ScholarPubMed
Xi, L. 2019 Turbulent drag reduction by polymer additives: fundamentals and recent advances. Phys. Fluids 31 (12), 121302.CrossRefGoogle Scholar
Xu, C.Y., Long, Y.G. & Wang, J.J. 2023 Entrainment mechanism of turbulent synthetic jet flow. J. Fluid Mech. 958, A31.CrossRefGoogle Scholar
Xu, D. & Chen, J. 2013 Accurate estimate of turbulent dissipation rate using PIV data. Exp. Therm. Fluid Sci. 44, 662–672.CrossRefGoogle Scholar
Yamani, S., Keshavarz, B., Raj, Y., Zaki, T.A., McKinley, G.H. & Bischofberger, I. 2021 Spectral universality of elastoinertial turbulence. Phys. Rev. Lett. 127 (7), 074501.CrossRefGoogle ScholarPubMed
Yamani, S., Raj, Y., Zaki, T.A., McKinley, G.H. & Bischofberger, I. 2023 Spatiotemporal signatures of elastoinertial turbulence in viscoelastic planar jets. Phys. Rev. Fluids 8 (6), 064610.CrossRefGoogle Scholar
Zhang, Y.-B., Bodenschatz, E., Xu, H. & Xi, H.-D. 2021 Experimental observation of the elastic range scaling in turbulent flow with polymer additives. Sci. Adv. 7 (14), eabd3525.CrossRefGoogle ScholarPubMed
Zhang, Y.-B. & Xi, H.-D. 2022 Measured energy injection, transfer, and dissipation rates in the bulk of dilute polymeric turbulent flow: the concentration and Weissenberg number effects. Phys. Fluids 34 (7), 075114.CrossRefGoogle Scholar