A Reynolds stress model for turbulent flows of viscoelastic fluids

Abstract

A second-order closure is developed for predicting turbulent flows of viscoelastic fluidsdescribed by a modified generalised Newtonian fluid model incorporating a nonlinearviscosity that depends on a strain-hardening Trouton ratio as a means to handle someof the effects of viscoelasticity upon turbulent flows. Its performance is assessed bycomparing its predictions for fully developed turbulent pipe flow with experimental datafor four different dilute polymeric solutions and also with two sets of direct numericalsimulation data for fluids theoretically described by the finitely extensible nonlinearelastic - Peterlin model. The model is based on a Newtonian Reynolds stress closureto predict Newtonian fluid flows, which incorporates low Reynolds number dampingfunctions to properly deal with wall effects and to provide the capability to handlefluid viscoelasticity more effectively. This new turbulence model was able to capturewell the drag reduction of various viscoelastic fluids over a wide range of Reynoldsnumbers and performed better than previously developed models for the same typeof constitutive equation, even if the streamwise and wall-normal turbulence intensitieswere underpredicted.