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Turbulent planar wakes of viscoelastic fluids analysed by direct numerical simulations

Published online by Cambridge University Press:  08 August 2022

Mateus C. Guimarães Open the ORCID record for Mateus C. Guimarães [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]
Mateus C. Guimarães
Affiliation:
IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Fernando T. Pinho
Affiliation:
CEFT, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal ALiCE, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal
Carlos B. da Silva*
Affiliation:
IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
*
†Email address for correspondence: carlos.silva@tecnico.ulisboa.pt
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Abstract

Direct numerical simulations employing the finitely extensible nonlinear elastic constitutive model closed with Peterlin's approximation (FENE-P) are used to investigate the far-field region of turbulent planar wakes of viscoelastic fluids and to develop the theory describing these flows. The theoretical results display excellent agreement with the simulations and provide new scaling laws for the evolution of the shear layer thickness $\delta (x) \sim x^{1/2}$, mean velocity deficit ${\rm \Delta} U(x) \sim x^{-1/2}$ and, for very high Deborah numbers, of the maximum polymer shear stresses $\sigma ^{[p]}_c(x) \sim x^{-2}$ and averaged polymer chain extension $\textrm {tr}(\bar {C}(x) - \boldsymbol{\mathsf{I}}) \sim x^{-2}$, where $x$ is the streamwise distance from the solid body generating the wake. The theory is able to show the existence of self-similarity for the profiles of mean velocity, mean polymer shear stress, averaged polymer chain extension and the conditions for similarity of the turbulent shear stress, and is very well supported by the numerical simulations. Similarly to the case of viscoelastic turbulent planar jets (Guimarães et al., J. Fluid Mech., vol. 899, 2020, p. A11), when the inlet Weissenberg and Deborah numbers are sufficiently large, turbulent viscoelastic wakes exhibit a considerable reduction of the spreading rate and of the normalised Reynolds stresses. However, for very large downstream locations the turbulent viscoelastic wake recovers the classical evolution laws observed for Newtonian turbulent planar wakes.

JFM classification

Non-Newtonian Flows: Viscoelasticity Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A26
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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