Since the studies by Toms (1946), it is known that a small amount of polymers, few parts per million, drastically reduces the friction drag in turbulent pipes or boundary layers. However, there is still an open debate on the ways turbulence and polymers interact, especially when a significant drag reduction (DR) is achieved. The complexity arises from the coupled multi-scale dynamics of turbulence and polymer chains.
We propose an innovative micro-mechanical model for the interaction of the polymers with a background turbulent flow. The idea consists in considering a multi-mode Finite Extensible Non Linear Elastic (FENE) bead spring model to represent a single effective polymer chain that retains the relevant degrees of freedom (spatial and temporal scales). The population of millions of effective chains is followed in a Lagrangian way and momentum-coupled with the carrier flow exploiting the fact that each bead experiences a drag force when interacting with the solvent. The approach resolves the micro-structure of the suspension achieving momentum coupling at the level of each instantaneous configuration. This avoids infeasible assumptions (Gaussian distribution of the polymer configuration) that are made in pre-averaged models. The proposed approach is thus able to explore a range of parameters that is unreachable to standard methods given their intrinsic numerical instabilities and the relatively poor physical modelling.
The micro-structure of the polymers is actually resolved and needs the calculation of the momentum feedback of millions of beads. This requires specific techniques that have been developed by the research group for particle and bubble laden flows where the Exact Regularized Point Particle (ERPP) has been developed in its hybrid MPI/GPU implementation.
This research will account the feedback effects of each single polymer chain on wall turbulence in a context where the micro-structure of the chains are retained in all their relevant features.
The innovativeness of the present research consists in embedding in one physically consistent formulation the complex multi-scale interaction of polymers chains with a Newtonian solvent. From the momentum coupling between the polymers and carrier flow, the non-Newtonian response of the multi-phase flow follows.
Innovative features are present both at the level of physical modelling and at the level of computer science, when the physical model has to be implemented in codes that are able to exploit the next generation of Tier-0 supercomputers.
Under the physical point of view, we propose to overcome the behaviour of actual polymer chains modelled as a simple FENE dumbbells and the related difficulties of the pre-averaged models. In the present research, the polymer chains, even though modelled as effective Rouse chains, are described in terms of their Lagrangian instantaneous configuration that retains most of the spatial and temporal scales of their dynamics. This feature is crucial when the chains are momentum-coupled with the carrier phase given the multi-scale nature of turbulence and the non trivial interaction that consequently arises. Clearly, by retaining the instantaneous behaviour of the polymer chains, there is no need for pre-averaging approaches to grab the polymer extra stress on the fluid. In fact, by considering a multi-mode FENE bead spring model, every beads of the polymer chains experience a friction force with the fluid (Stoked drag). The friction force, with an opposite sign, is thus experienced by the fluid itself achieving on a physical ground the inter-phase momentum coupling.
This last aspect calls for innovative computational approaches that are highly efficient and can safely run on Tier-0 supercomputers both on CPUs and GPUs. In fact, once the micro-structure of the polymers is retained, it is necessary to compute the feedback effect of millions of polymer beads on the flow. The Exact Regularized Point Particle (ERPP) approach developed by the present research group, in the context of particle-laden and bubble-laden free shear and wall bounded flows represents the solution to this issue. The algorithm is suitable for its parallel implementation both on MPI based architectures and, most relevant for the present research, on GPUs based architectures. Indeed, from the implementation on GPUs, we expect the ``quantum leap'' of the present research. Actually, hundred of millions of polymer chain will be simulated by retaining their relevant degrees of freedom and no approximation induced by pre-averaging procedures is needed to achieve the momentum coupling of the polymers with the fluid. The proposed approach is able to capture the micro-structure of the suspension which is at the origin of its non Newtonian behaviour. Given this highly accurate physical-based description of the interaction between polymers and turbulence, the present research aims at a quantitative matching the polymer parameters in terms of concentration and Weissemberg number with actual experiments. Our ``numerical experiments'' will thus be able to address open issue in viscoelastic turbulence such the onset of the Drag Reduction and the Low Drag Reduction and High Drag reduction regimes which at the moment, can be only quantitatively captured by experimental investigations.
The present research can be also pushed to explore high concentrated polymer solutions embedded in a turbulent flow by including polymer-polymer chain interactions. This aspect will allow to study entanglement effects and the origin of polymer chains networks that are observed in turbulent flows.