Multiscale simulation of viscoelastic free surface flows

@article{citeulike:1244280, abstract = {A micro-macro approach based on combining the Brownian configuration fields (BCF) method [M.A. Hulsen, A.P.G. van Heel, B.H.A.A. van den Brule, Simulation of viscoelastic flow using Brownian configuration fields, J. Non-Newtonian Fluid Mech. 70 (1997) 79-101] with an Arbitrary Lagrangian-Eulerian (ALE) Galerkin finite element method, using elliptic mesh generation equations coupled with time-dependent conservation equations, is applied to study slot coating flows of polymer solutions. The polymer molecules are represented by dumbbells with both linear and non-linear springs; hydrodynamic interactions between beads are incorporated. Calculations with infinitely extensible (Hookean) and pre-averaged finitely extensible (FENE-P) dumbbell models are performed and compared with equivalent closed-form macroscopic models in a conformation tensor based formulation [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on the conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363-409]. The BCF equation for linear dumbbell models is solved using a fully implicit time integration scheme which is found to be more stable than the explicit Euler scheme used previously to compute complex flows. We find excellent agreement between the results of the BCF based formulation and the macroscopic conformation tensor based formulation. The computations using the BCF approach are stable at much higher Weissenberg numbers, (where [lambda] is the characteristic relaxation time of polymer, and is the characteristic rate of strain) compared to the purely macroscopic conformation tensor based approach, which fail beyond a maximum Wi. A novel computational algorithm is introduced to compute complex flows with non-linear microscopic constitutive models (i.e. non-linear FENE dumbbells and dumbbells with hydrodynamic interactions) for which no closed-form constitutive equations exist. This algorithm is fast and computationally efficient when compared to both an explicit scheme and a fully implicit scheme involving the solution of the non-linear equations with Newton's method for each configuration field.}, author = {Bajaj, Mohit and Bhat, Pradeep P. and Ravi and Pasquali, Matteo }, booktitle = {Special Issue on the XIVth International Workshop on Numerical Methods for Non-Newtonian Flows, Santa Fe, 2005, XIVth International Workshop on Numerical Methods for Non-Newtonian Flows, Santa Fe, 2005}, citeulike-article-id = {1244280}, journal = {Journal of Non-Newtonian Fluid Mechanics}, keywords = {multiscale}, month = {December}, number = {1-3}, pages = {87--107}, posted-at = {2007-04-23 06:03:10}, priority = {3}, title = {Multiscale simulation of viscoelastic free surface flows}, url = {http://www.sciencedirect.com/science/article/B6TGV-4K5RBJ5-3/2/62e5c45bc93b85fc1dedafa345da83d0}, volume = {140}, year = {2006} }

TY - JOUR ID - citeulike:1244280 L3 - citeulike-article-id:1244280 TI - Multiscale simulation of viscoelastic free surface flows T2 - Special Issue on the XIVth International Workshop on Numerical Methods for Non-Newtonian Flows, Santa Fe, 2005, XIVth International Workshop on Numerical Methods for Non-Newtonian Flows, Santa Fe, 2005 JF - Journal of Non-Newtonian Fluid Mechanics VL - 140 IS - 1-3 SP - 87 EP - 107 N2 - A micro-macro approach based on combining the Brownian configuration fields (BCF) method [M.A. Hulsen, A.P.G. van Heel, B.H.A.A. van den Brule, Simulation of viscoelastic flow using Brownian configuration fields, J. Non-Newtonian Fluid Mech. 70 (1997) 79-101] with an Arbitrary Lagrangian-Eulerian (ALE) Galerkin finite element method, using elliptic mesh generation equations coupled with time-dependent conservation equations, is applied to study slot coating flows of polymer solutions. The polymer molecules are represented by dumbbells with both linear and non-linear springs; hydrodynamic interactions between beads are incorporated. Calculations with infinitely extensible (Hookean) and pre-averaged finitely extensible (FENE-P) dumbbell models are performed and compared with equivalent closed-form macroscopic models in a conformation tensor based formulation [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on the conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363-409]. The BCF equation for linear dumbbell models is solved using a fully implicit time integration scheme which is found to be more stable than the explicit Euler scheme used previously to compute complex flows. We find excellent agreement between the results of the BCF based formulation and the macroscopic conformation tensor based formulation. The computations using the BCF approach are stable at much higher Weissenberg numbers, (where [lambda] is the characteristic relaxation time of polymer, and is the characteristic rate of strain) compared to the purely macroscopic conformation tensor based approach, which fail beyond a maximum Wi. A novel computational algorithm is introduced to compute complex flows with non-linear microscopic constitutive models (i.e. non-linear FENE dumbbells and dumbbells with hydrodynamic interactions) for which no closed-form constitutive equations exist. This algorithm is fast and computationally efficient when compared to both an explicit scheme and a fully implicit scheme involving the solution of the non-linear equations with Newton's method for each configuration field. KW - multiscale AU - Bajaj, Mohit AU - Bhat, Pradeep AU - Ravi AU - Pasquali, Matteo PY - 2006/12/30/ UR - http://www.sciencedirect.com/science/article/B6TGV-4K5RBJ5-3/2/62e5c45bc93b85fc1dedafa345da83d0 ER -