Direct numerical simulations of turbulent viscoelastic jets

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.