Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T06:08:44.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent entrainment in viscoelastic fluids

Published online by Cambridge University Press:  19 January 2022

Hugo Abreu Open the ORCID record for Hugo Abreu [Opens in a new window] ,
Fernando T. Pinho Open the ORCID record for Fernando T. Pinho [Opens in a new window]  and
Carlos B. da Silva Open the ORCID record for Carlos B. da Silva [Opens in a new window]
Hugo Abreu
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
Fernando T. Pinho
Affiliation:
CEFT, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal
Carlos B. da Silva*
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) of turbulent fronts spreading into an irrotational flow region are used to analyse the turbulent entrainment mechanism for viscoelastic fluids. The simulations use the FENE-P fluid model and are initiated from DNS of isotropic turbulence with Weissenberg and turbulence Reynolds numbers varying in the ranges $1.30 \le Wi \le 3.46$ and $206 \le Re_{\lambda }^{0} \le 404$, respectively. The enstrophy dynamics near the turbulent/non-turbulent interface (TNTI) layer, that separates regions of turbulent and irrotational flow, includes a new mechanism – the viscoelastic production – caused by the interaction between the vorticity field and the polymer stresses. This term can be a sink or a source of enstrophy in the turbulent core region of the flow, depending on the Weissenberg number, and contributes to the initial growth of the enstrophy in the viscous superlayer, together with the viscous diffusion, which is the only mechanism present for Newtonian fluids. For low and moderate Weissenberg numbers the scaling of the TNTI layer is similar to the scaling of TNTI layers for Newtonian fluids, but this is no longer the case at high Weissenberg numbers where the enstrophy tends to be concentrated into thin vortex sheets instead of vortex tubes. Finally, it is shown that the substantial decrease of the entrainment rates observed in turbulent flows of viscoelastic fluids, compared with Newtonian fluids, is caused by a reduction of the surface area and fractal dimension of the irrotational boundary, originated by the depletion of ‘active’ scales of motion in the fluid solvent caused by the viscoelasticity.

JFM classification

Non-Newtonian Flows: Viscoelasticity Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A36
Copyright
© The Author(s), 2022. 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.)

References

REFERENCES

Alvelius, K. 1999 Random forcing of three-dimensional homogeneous turbulence. Phys. Fluids 11 (7), 1880–1889.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
Bird, R.B., Curtiss, C.F., Armstrong, R.C. & Hassager, O. 1987 Dynamics of polymeric liquids. Volume 2: Kinetic Theory. John Wiley & Sons.Google Scholar
Bird, R.B., Dotson, P.J. & Johnson, N.L. 1980 Polymer solution rheology based on a finitely extensible bead-spring chain model. J. Non-Newtonian Fluid Mech. 7, 213–235.CrossRefGoogle Scholar
Bisset, D.K., Hunt, J.C.R. & Rogers, M.M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.CrossRefGoogle Scholar
Cai, W., Li, D. & Zhang, H. 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
Corrsin, S. & Kistler, A.L. 1955 Free-stream boundaries of turbulent flows. Tech. Rep. TN-1244. NACA.Google Scholar
De Angelis, E., Casciola, C.M., Benzi, R. & Piva, R. 2005 Homogeneous isotropic turbulence in dilute polymers. J. Fluid Mech. 531, 1–10.CrossRefGoogle Scholar
Ferreira, P.O., Pinho, F.T. & da Silva, C.B. 2017 Large-eddy simulations of forced isotropic turbulence with viscoelastic fluids described by the fene-p model. Phys. Fluids 28, 125104.CrossRefGoogle Scholar
Graham, M.D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26 (10), 101301.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, 11–37.CrossRefGoogle Scholar
Holzner, M., Liberzon, A., Nikitin, N., Kinzelbach, W. & Tsinober, A. 2007 Small-scale aspects of flows in proximity of the turbulent/non-turbulent interface. Phys. Fluids 19, 071702.CrossRefGoogle Scholar
Holzner, M. & Luthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106, 134503.CrossRefGoogle ScholarPubMed
Krug, D., Holzner, M., Marusic, I. & Reeuwijk, M. 2017 Fractal scaling of the turbulence interface ingravity currents. J. Fluid Mech. 820, R3.CrossRefGoogle Scholar
Li, F.-C., Cai, W.-H., Zhang, H.-N. & Wang, Y. 2012 Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations. Chin. Phys. B 21 (11), 114701.CrossRefGoogle Scholar
Li, W. & Graham, M.D. 2007 Polymer induced drag reduction in exact coherent structures of plane poiseuille flow. Phys. Fluids 19, 083101.CrossRefGoogle Scholar
Liberzon, A., Holzner, M., Luthi, B., Guala, M. & Kinzelbach, W. 2009 On turbulent entrainment and dissipation in dilute polymer solutions. Phys. Fluids 21, 035107.CrossRefGoogle Scholar
Lumley, J.L. 1973 Drag reduction in turbulent flow by polymer additives. J. Polym. Sci. 7 (1), 263–290.Google Scholar
Mistry, D., Philip, J., Dawson, J.R. & Marusic, I. 2017 Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet. J. Fluid Mech. 802, 690–725.CrossRefGoogle Scholar
Ouellette, N.T., Xu, H. & Bodenschatz, E. 2009 Bulk turbulence in dilute polymer solutions. J. Fluid Mech. 629, 375–385.CrossRefGoogle Scholar
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199–227.CrossRefGoogle Scholar
Reeuwijk, M., Krug, D. & Holzner, M. 2018 Small-scale entrainment in inclined gravity currents. Environ. Fluid Mech. 18, 225–239.CrossRefGoogle ScholarPubMed
da Silva, C.B., Hunt, J.C.R., Eames, I. & Westerweel, J. 2014 a Interfacial layers between regions of different turbulent intensity. Annu. Rev. Fluid Mech. 46, 567–590.CrossRefGoogle Scholar
da Silva, C.B. & Pereira, J.C.F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/non-turbulent interface in jets. Phys. Fluids 20, 055101.CrossRefGoogle Scholar
da Silva, C.B. & Pereira, J.C.F. 2009 Erratum: “Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/non-turbulent interface in jets” [Phys. Fluids, 20, 055101, 2008]. Phys. Fluids 21, 019902.CrossRefGoogle Scholar
da Silva, C.B., dos Reis, R.J.N. & Pereira, J.C.F. 2011 The intense vorticity structures near the turbulent/non-turbulent interface a jet. J. Fluid Mech. 685, 165–190.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. J. Phys. 506, 012015.Google 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, 044501.CrossRefGoogle ScholarPubMed
Silva, T.S., Zecchetto, M. & da Silva, C.B. 2018 The scaling of the turbulent/non-turbulent interface at high Reynolds numbers. J. Fluid Mech. 843, 156–179.CrossRefGoogle Scholar
Sreenivasan, K.R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23, 539–600.CrossRefGoogle Scholar
Taveira, R.R., Diogo, J.S., Lopes, D.C. & da Silva, C.B. 2013 Lagrangian statistics across the turbulent/non-turbulent interface in a turbulent plane jet. Phys. Rev. E 88, 043001.CrossRefGoogle Scholar
Taveira, R.R. & da Silva, C.B. 2014 Characteristics of the viscous superlayer in free shear turbulence and in planar turbulent jets. Phys. Fluids 26, 021702.CrossRefGoogle Scholar
Teixeira, M.A.C. & da Silva, C.B. 2012 Turbulence dynamics near a turbulent/non-turbulent interface. J. Fluid Mech. 695, 257–287.CrossRefGoogle Scholar
Toms, B.A. 1948 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proc. Int. Congress of Rheology, Holland, North-Holland, Amsterdam (ed. J.M. Burgers), vol. Section II, pp. 135–141. North-Holland.Google Scholar
Townsend, A.A. 1948 Local isotropy in the turbulent wake of a cylinder. Aust. J. Sci. Res. A 1 (2), 161–174.Google Scholar
Townsend, A.A. 1966 The mechanism of entrainment in free turbulent flows. J. Fluid Mech. 26, 689–715.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Vaithianathan, T., Robert, A., Brasseur, J.G. & Collins, L.R. 2006 An improved algorithm for simulating three-dimensional, viscoelastic turbulence. J. Non-Newtonian Fluid Mech. 140 (1), 3–22.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, 075108.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, 105103.CrossRefGoogle Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2015 Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers. Phys. Fluids 27, 085109.CrossRefGoogle Scholar
Watanabe, T., da Silva, C.B. & Nagata, K. 2019 Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence. J. Fluid Mech. 875, 321–344.CrossRefGoogle Scholar
Westerweel, J., Fukushima, C., Pedersen, J.M. & Hunt, J.C.R. 2005 Mechanics of the turbulent/non-turbulent interface of a jet. Phys. Rev. Lett. 95, 174501.CrossRefGoogle Scholar
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, 235–256.CrossRefGoogle Scholar
Wolf, M., Luthi, B., Holzner, M., Krug, D. & Kinzelbach, W. 2012 Investigations on the local entrainment velocity in a turbulent jet. Phys. Fluids 24, 105110.CrossRefGoogle Scholar
Zecchetto, M. & da Silva, C.B. 2021 Universality of small-scale motions within the turbulent/non- turbulent interface layer. J. Fluid Mech. 916, A9.CrossRefGoogle Scholar