E. De Angelis

DNS of wall turbulence: dilute polymers and self-sustaining mechanisms

Several studies, both numerical and experimental, have shown that the introduction of a small amount of long chain polymers in a turbulent flow alters dramatically the length and time scales which are typical of Newtonian fluids, even though turbulence self-sustaining mechanisms remain approximately the same. In such viscoelastic flows wall turbulence regeneration is still influenced by the mean shear and by the interaction of the coherent structures which still generate low and high speed streaks, but more ordered and larger with respect to Newtonian flows. In order to gain a deeper understanding of the regeneration mechanisms and the modifications induced by the presence of the polymers, we analyze the data obtained from direct numerical simulation with a micro-rheological model for the polymers. Thus, the velocity fields have been studied together with the coupling terms in the momentum equations, i.e. the divergence of the extra-stress terms due to the polymers. The analysis seems to suggest, as main effect of the viscoelastic reaction, a quite concentrated action on bursting phenomena and a stabilization of the streaks with a related decrease in the population of the wall-layer coherent structures. In addition the correlations between velocity fluctuations and viscoelastic responses have been considered with the aim to single out the passive or the active role of the polymers in different flow locations.

Homogeneous isotropic turbulence in dilute polymers

arm ´ an–Howarth equation, two kinds of energy fluxes exist, namely the classical transfer term and the coupling with the polymers. Depending on the Deborah number, the response of the flow may result either in a pure damping or in the depletion of the small scales accompanied by increased fluctuations at large scale. The latter behaviour corresponds to an overall reduction of the dissipation rate with respect to an equivalent Newtonian flow with identical fluctuation intensity. The relevance of the position of the crossover scale between the two components of the energy flux with respect to the Taylor microscale of the system is discussed.

Maximum drag reduction asymptotes and the cross-over to the Newtonian plug

We employ the full FEN E-P model of the hydrodynamics of a dilute polymer solution to derive a theoretical approach to drag reduction in wall-bounded turbulence. We recapture the results of a recent simplified theory which derived the universal maximum drag reduction (MDR) asymptote, and complement that theory with a discussion of the cross-over from the MDR to the Newtonian plug when the drag reduction saturates. The FENE-P model gives rise to a rather complex theory due to the interaction of the velocity field with the polymeric conformation tensor, making analytic estimates quite taxing. To overcome this we develop the theory in a computer-assisted manner, checking at each point the analytic estimates by direct numerical simulations (DNS) of viscoelastic turbulence in a channel.

Energy Transfer in turbulent polymer solutions

The paper addresses a set of new equations concerning the scale-by-scale balance of turbulent fluctuations in dilute polymer solutions. The main difficulty is the energy associated with the polymers, which is not of a quadratic form in terms of the traditional descriptor of the micro-structure. A different choice is however possible, which, at least for mild stretching of the polymeric chains, directly leads to an L 2 structure for the total free-energy density of the system thus allowing the extension of the classical method to polymeric fluids. On this basis, the energy budget in spectral space is discussed, providing the spectral decomposition of the energy of the system. New equations are also derived in physical space, to provide balance equations for the fluctuations in both the kinetic field and the micro-structure, thus extending, in a sense, the celebrated Karman Howarth and Kolmogorov equations of classical turbulence theory. The paper is limited to the context of homogeneous turbulence. However the necessary steps required to expand the treatment to wall-bounded flows of polymeric liquids are indicated in detail.

Microstructure and Turbulence in Dilute Polymer Solutions

An appropriate picture of the interaction of polymers chains and turbulence structure is crucial to grasp the drag-reducing mechanisms of dilute polymers solutions. In most models the physically small diffusion is normally neglected. However, in the presence of a continuous spectrum of length and time scales, like in turbulence, the introduction of a diffusion term, however small, is crucial to enforce a cutoff at large wave number. Such a term can also be regarded as a natural consequence of a detailed picture of the substructural interactions between the polymeric chains and the fluid. The results obtained through numerical simulations are used in the appropriate thermodynamic framework to extract valuable information concerning the interaction between turbulence and microstructure. A general multifield formulation is finally employed to explore possible additional interaction mechanisms between neighboring populations of polymers that may play a role in accounting for slightly nonlocal interactions between polymer macromolecules in the solvent.

Microcavity quantum superradiance

Two-dipole superradiance in a planar symmetrical microcavity has been investigated for the first time in the space-time domain by a controlled femtosecond excitation of two ensembles of molecules located at a mutual distance R on the plane parallel to the cavity mirrors. A significant enhancement of the time decay of the dipole excitation for a decreasing inter-dipole transverse distance R has been found. Furthermore, we have observed a striking transition from the classical to the quantum behaviour in the photon partition statistics of the emitted field for R ≤ lc, the transverse extension of the single allowed cavity mode.

Substructural interactions and transport in polymer flows

Abstract A model for semidilute polymer flows is developed within the setting of multifield theories describing material substructures. We associate a coarse grained order parameter to the family of polymer chains in each material element and account for substructural interactions which develop power in the rate of the order parameter and are balanced. A measure of substructural interactions occurring between neighboring families of polymeric chains is prescribed first; then we find the need of the existence of self-interactions in each family by means of a requirement of invariance of the power. We obtain balance equations that involve terms that stabilize numerical algorithms in turbulent regime. Versions of the standard dumbbell model, that fit experimental data, seem to fall within our modeling. Moreover, we obtain evolution equations which are sufficiently flexible to be applied to different (even non-standard) cases. In fact, we make distinction between the balance of (standard and substructural) interactions and their representation. Then, such a representation is a consequence of the prescription of two ingredients: the explicit form of the bulk free energy density and appropriate ‘viscous’ coefficients. The transport of polymer chains between neighboring material elements is also discussed.

Dynamics of Viscoelastic Wall Turbulence in Different Ranges of Scales

We address the dynamics of viscoelastic wall turbulence by means of a generalization of a scale-by-scale approach extended to both an inhomogeneous and viscoelastic case. Analysing the results obtained by a series of Direct Numerical Simulations of a dilute polymer solution in a plane channel, we focus our attention on the alteration of the inertial transfer across the scales and the polymer scaledependent term in the budget for the second order velocity structure function. We confirm that both these observables lead to a scenario were the main alteration of turbulence structure in a channel flow occurs in the buffer layer.

Budgets of polymer free energy in homogeneous turbulence

Turbulence in dilute polymer solutions has gained more and more interest over the last decades. Original studies were mainly oriented to drag reduction observed in wall bounded flows, however, recently studies have moved from applied problems to a more fundamental approach. In details a renewed interest has been devoted to problems different from bounded flows such as jets or basically homogeneous flows. On the other hand from a theoretical viewpoint some relevant development have appeared. In this contribution the analysis of spectral budgets of homogeneous and isotropic turbulence based on the set of equations derived in [1] is proposed. The study is performed on low-Reynolds number numerical results obtained for a dilute polymer solution in the mild stretch regime.

Scale by Scale Budget in Viscoelastic Wall Turbulence

Despite the growing interest on the subject, many of the efforts to the comprehension of practical aspects of turbulence in dilute polymer solutions, such as drag reduction, have proven inconclusive, suggesting that, even from the point of view of applications, a more fundamental approach is required. Recently the influence of polymers on the turbulent cascade has been studied in the contest of homogeneous and isotropic turbulence [2]. Those results allowed for the identification of a scale below which the flux towards polymers is larger than the nonlinear transfer. More relevant for the real problems is the study of wall turbulence where the alteration of the energy cascade might have a large effect. On the basis of the DNS data for the turbulent channel flow, an analysis of the interaction between polymers and turbulence at different distances from the wall is provided. A detailed balance of the scale by scale budget of the turbulent kinetic energy is shown.