Added stresses because of the presence of FENE-P bead–spring chains in a random velocity field

Abstract

FENE-P bead-spring chains unravel in the presence of large enough velocity gradients. In a turbulent flow, this can result in intermittent added stresses and exchanges of energy between the chains and the fluid, whose magnitudes depend on the degree of unravelling and on the orientations of the bead-spring chains. These effects are studied by calculating the average behaviour at different times of an ensemble of chains, contained in a fluid particle that is moving around in a random velocity field obtained from direct numerical simulation of turbulent flow of a Newtonian fluid in a channel. The results are used to evaluate theoretical explanations of drag reduction observed in very dilute solutions of polymers.In regions of the flow in which the energy exchange with the fluid is positive, the possibility arises that turbulence can be produced by mechanisms other than the interaction of Reynolds stresses and the mean velocity gradient field. Of particular interest, from the viewpoint of understanding polymer drag reduction, is the finding that the exchange is negative in velocity fields representative of the wall vortices that are large producers of turbulence. One can, therefore, postulate that polymers cause drag reduction by selectively changing the structures of eddies that produce Reynolds stresses. The intermittent appearance of large added shear stresses is consistent with the experimental finding of a stress deficit, whereby the total local shear stress is greater than the sum of the Reynolds stress and the time-averaged shear stress calculated from the time-averaged velocity gradient and the viscosity of the solvent.

New Answers on the Interaction Between Polymers and Vortices in Turbulent Flows

“…Although we can only simulate MDR using a minimal channel flow, the fact that (i) turbulence is sustained in the reference case and (ii) f x = 0 leads to relaminarization indicates that the turbulence enhancing activity in the streamwise direction that we have isolated is the key of the selfsustained generation process of turbulence at MDR. This point was also inferred by [22] by using FENE-P bead-spring chain in turbulent flow.…”

“…By investigating the polymer body force, it is established that polymers reduce turbulence by opposing the downwash and upwash flows generated by near-wall vortices, while they enhance streamwise velocity fluctuations in the very near-wall region. The numerical experiments allow us to characterize the importance of each component of the polymer body force on the drag-reducing and turbulence-enhancing properties found or suggested in other publications [7,22,27]. The exact localization of polymer drag-reducing activity is now crucial for the development of a predictive model for polymer drag reduction.…”

Polymer dynamics in a model of the turbulent buffer layer

“…Later work by the same group found that the stresses introduced by the stretched polymers in a turbulent flow lead to added dissipations, both positive and negative. 36 The positive dissipations are associated with the streamwise vortices in the near-wall region and would decrease the production of Reynolds shear stress in these structures. A study of FENE dumbbells in steady, Gaussian ran- dom flows shows that stochastic flow fields can produce large conformation changes in the polymer.…”

Dynamics of dissolved polymer chains in isotropic turbulence

“…By comparing the performance of the various polymer models in the same flow field, we obtain a quantitative estimate of the error associated with the FENE-P model. Our approach is similar to the one taken by Zhou and Akhavan (2003) and others (Massah and Hanratty 1997, Massah et al 1993. However, those studies focused on inhomogeneous turbulent channel flow, where the statistics of the trajectory are a strong function of the initial condition.…”