A Reynolds stress model for turbulent flows of viscoelastic fluids

Abstract

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic – Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.

Keywords:

• turbulence model
• drag reduction
• polymer solutions
• second-order closure

Acknowledgements

The authors would like to acknowledge funding of FEDER via grants POCI/56342/EQU/2004 and POCI/59338/EME/2004 of Fundação para a Ciência e Tecnologia (FCT). P.R. Resende wishes also to acknowledge FCT for personal funding via SFRH/BD/18475/2004.