Eajf Frank Peters

Instationary Eulerian viscoelastic flow simulations using time separable Rivlin-Sawyers constitutive equations

Abstract A time dependent method for solving integral constitutive equations of the Rivlin–Sawyers type is introduced. The deformation history is represented by a finite number of deformation fields. Using these fields the stress integral is approximated as a finite sum. When the flow evolves the deformation fields are convected and deformed. The approach presented in this paper is the first Eulerian method that can handle integral equations in a time dependent way. The method is validated by using the upper-convected Maxwell (UCM) benchmark of a sphere moving in a tube. We show that the method converges with mesh and time step refinement and that the results are accurate, comparable to the results obtained with the differential equivalent of the UCM model. To demonstrate that complicated linear spectra are easily incorporated, results of a Rouse model simulation of 100 modes are presented. We also compare results on a falling sphere problem to the results obtained by a Lagrangian method as reported by Rasmussen and Hassager [H.K. Rasmussen, O. Hassager, On the sedimentation velocity of spheres in a polymeric liquid, Chem. Eng. Sci. 51 (1996) 1431–1440]. The model being employed is the PSM model, for which no differential equivalent exists.

A new approach to the deformation fields method for solving complex flows using integral constitutive equations

Abstract In this paper, we present a new approach to the deformation fields method that has recently been introduced to solve integral type models in complex flows (E.A.J.F. Peters, M.A. Hulsen, B.H.A.A. van den Brule, J. Non-Newtonian Fluid Mechanics 89 (2000) 209–228). The new approach is based on a change of the reference time of the fields from an absolute time to a time relative to the current time. This basically removes most, if not all, stability and accuracy problems that exist in the original method compared to using differential models. Also the new implementation is much more flexible with respect to the time integral discretisation, opening the way to adaptive refinement. The new implementation has been tested for two problems: the standard 2:1 benchmark of a the flow around a sphere using a UCM model and the flow around a sphere in a different geometry using a PSM model.

Generalization of the deformation field method to simulate advanced reptation models in complex flow

In this paper we will show how the recently introduced deformation field method [Peters et al. (1999) and van Heel et al. (1999)] can be generalized to complex flow simulations of nontime–strain separable integral constitutive models. To illustrate this generalization we start with the time–strain separable Doi–Edwards model and we show how the approach can be generalized to nontime–strain separable models. As an example of such a model we consider the reptation model which was recently introduced by Mead et al. [Mead et al. (1998)]. In this reptation model also tube-stretch and convective constraint release are taken into account. We use both models to simulate startup of two-dimensional flow past a cylinder positioned between two parallel plates.

A generalized method for parameterization of dissipative particle dynamics for variable bead volumes

We present a generalized protocol to compute dissipative particle dynamics interaction parameters where beads may have variable (local) densities in the simulations. A generalized relationship for pair-wise interactions is derived and proof-of-concept simulations are performed. In this general relation, excess repulsions are related to the experimental Flory-Huggins parameters for any molar volume ratio of beads.

Rejection-free Monte Carlo sampling for general potentials

A Monte Carlo method to sample the classical configurational canonical ensemble is introduced. In contrast to the Metropolis algorithm, where trial moves can be rejected, in this approach collisions take place. The implementation is event-driven; i.e., at scheduled times the collisions occur. A unique feature of the new method is that smooth potentials (instead of only step-wise changing ones) can be used. In addition to an event-driven approach, where all particles move simultaneously, we introduce a straight event-chain implementation. As proof of principle, a system of Lennard-Jones particles is simulated.

Mesoscopic simulations for the molecular and network structure of a thermoset polymer

Meso-scale simulations are performed to obtain a fully cross-linked, equilibrated structure of an epoxy network. We derive and study the interactions giving rise to the final structure. Both equilibrium structures with no cross-links and fully cross-linked are examined. The simulations were performed using a recent dissipative particle dynamics parameterization method in which beads attain their pure volumes in the final structure. Preferential attractive and repulsive behavior of different chemical functional groups is revealed. When those are simulated as monomers, two phases form where intra-bead interactions are attractive and inter-bead interactions are repulsive. A homogeneous density distribution over the simulation box is noticed when simulated as chains. The network properties are characterized as well. The cross-link conversions are analyzed which show that the bead type consisting of initially primary amines have the highest value. Moreover, different cross-link formation rates for secondary amines are incorporated in the simulations and effects on the structure and conversion are discussed.

Viscoelastic flow simulations in model porous media

In this article, the extensional flow and viscosity and the converging-diverging geometry were examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model, which successfully describes shearthinning, elasticity and thixotropic time-dependency, was used for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm, originally proposed by Philippe Tardy, that employs this model to simulate steadystate time-dependent flow was implemented in a non-Newtonian flow simulation code using pore-scale modeling and the initial results were analyzed. The findings are encouraging for further future development.

Computational Fluid Dynamics–Discrete Element Method (CFD-DEM) Study of Mass-Transfer Mechanisms in Riser Flow

We report a computational fluid dynamics-discrete element method (CFD-DEM) simulation study on the interplay between mass transfer and a heterogeneous catalyzed chemical reaction in cocurrent gas-particle flows as encountered in risers. Slip velocity, axial gas dispersion, gas bypassing, and particle mixing phenomena have been evaluated under riser flow conditions to study the complex system behavior in detail. The most important factors are found to be directly related to particle cluster formation. Low air-to-solids flux ratios lead to more heterogeneous systems, where the cluster formation is more pronounced and mass transfer more influenced. Falling clusters can be partially circumvented by the gas phase, which therefore does not fully interact with the cluster particles, leading to poor gas-solid contact efficiencies. Cluster gas-solid contact efficiencies are quantified at several gas superficial velocities, reaction rates, and dilution factors in order to gain more insight regarding the influence of clustering phenomena on the performance of riser reactors.

Accurate method for the Brownian dynamics simulation of spherical particles with hard-body interactions

In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common “naive simulation method” accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at ...

Lane change in flows through pillared microchannels

It is known that viscoelastic fluids exhibit elastic instabilities in simple shear flow and flow with curved streamlines. During flow through a straight microchannel with pillars, we found strikingly strong hydrodynamic instabilities characterized by very large transversal excursions, even leading to a complete change in lanes, and the presence of fast and slow moving lanes. Particle image velocimetry measurements through a pillared microchannel provide experimental evidence of these instabilities at a very low Reynolds number (<0.01). The instability is characterized by a rapid increase in spatial and temporal fluctuations of velocity components and pressure at a critical Deborah number. We characterize under which conditions these strong instabilities arise.