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Direct numerical simulations of turbulent viscoelastic jets

Published online by Cambridge University Press:  20 July 2020

Mateus C. Guimarães Open the ORCID record for Mateus C. Guimarães [Opens in a new window] ,
Nuno Pimentel ,
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, 1049-001Lisboa, Portugal
Nuno Pimentel
Affiliation:
IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001Lisboa, Portugal
Fernando T. Pinho
Affiliation:
CEFT, Faculdade de Engenharia, Universidade do Porto, 4200-465Porto, Portugal
Carlos B. da Silva*
Affiliation:
IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001Lisboa, Portugal
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations (DNS) of spatially evolving turbulent planar jets of viscoelastic fluids described by the FENE-P model, such as those consisting of a Newtonian fluid solvent carrying long chain polymer molecules, are carried out in order to develop a theory for the far field of turbulent jets of viscoelastic fluids. New evolution relations for the jet shear-layer thickness $\unicode[STIX]{x1D6FF}(x)$, centreline velocity $U_{c}(x)$ and maximum polymer stresses $\unicode[STIX]{x1D70E}_{c}^{[p]}(x)$ are derived and validated by the new DNS data, yielding $\unicode[STIX]{x1D6FF}(x)\sim x$, $U_{c}(x)\sim x^{-1/2}$, and $\unicode[STIX]{x1D70E}_{c}^{[p]}(x)\sim x^{-5/2}$, respectively, where $x$ is the coordinate in the streamwise direction. It is shown that, compared with a classical (Newtonian) turbulent jet, the effect of the polymers is to reduce the spreading rate, centreline velocity decay, Reynolds stresses and viscous dissipation rate. The self-preserving character of the flow is analysed and it is shown that profiles of mean velocity, Reynolds stresses and polymer stresses are self-similar provided the proper scales are used in the normalisation of these quantities. A fundamental difference from the Newtonian jet in this regard is the necessity for two, instead of only one, different velocity and length scales to properly characterise the evolution of the turbulent flow. These extra velocity and length scales are directly related to a time scale associated with the characteristic fading memory property of viscoelastic fluids.

JFM classification

Wakes/Jets: Jets Non-Newtonian Flows: Viscoelasticity Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A11
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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