@article { ISI:000246532500010,
	title = {Simulation of viscoelastic flows of polymer solutions in abrupt contractions using an arbitrary lagrangian eulerian (ALE) based finite element method},
	journal = {Journal of Non-Newtonian Fluid Mechanics},
	volume = {143},
	number = {2-3},
	year = {2007},
	month = {MAY},
	pages = {157-169},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {<p>We present a method for simulation of viscoelastic flows using an Arbitrary Lagrangian Eulerian (ALE) technique based finite element formulation. The ALE technique provides advantages of both Lagrangian and Eulerian frameworks by allowing the computational mesh to move in an arbitrary manner, independent of the material motion. In the present method, a fractional step ALE technique is employed in which the Lagrangian phase of material motion and convection arising out of mesh motion are decoupled. In the first step the relevant flow and constitutive equations are solved in Lagrangian framework. The simpler representation of polymer constitutive equations in a Lagrangian framework avoids the difficulties associated with convective terms thereby resulting in a robust numerical formulation. In the second step the mesh is moved in ALE mode and the associated convection of the stress is performed using a Godunov type scheme. This ALE technique is easy to implement and can accurately simulate the complex viscoelastic behaviour of transient polymer flow through complex geometries. In the present study, steady flows through abrupt contractions of planar and axisymmetric geometries are studied by performing transient flow simulations until steady state is achieved. The proposed method is validated with previously published numerical and experimental studies for polymer solutions obeying the Oldroyd B and Phan Thien Tanner (PTT) models. The simulated corner and lip vortex enhancement mechanism and flow behavior are in good agreement with experimentally obtained flow visualization photographs. The strength of the proposed method lies in its ability to simulate free surface flows such as swell. (C) 2007 Elsevier B.V. All rights reserved.</p>},
	keywords = {abrupt contraction, Arbitrary Lagrangian Eulerian, finite element, simulations},
	issn = {0377-0257},
	doi = {10.1016/j.jnnfm.2007.02.009},
	author = {Ganvir, Vivek and Lele, Ashish K. and Thaokar, Rochish and Gautham, Basavarsu P.}
}
@article { ISI:000263008600003,
	title = {Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method},
	journal = {Journal of Non-Newtonian Fluid Mechanics},
	volume = {156},
	number = {1-2},
	year = {2009},
	month = {JAN},
	pages = {21-28},
	publisher = {ELSEVIER SCIENCE BV},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {<p>Accurate prediction of extrudate (die) swell in polymer melt extrusion is important as this helps in appropriate die design for profile extrusion applications. Extrudate swell prediction has shown significant difficulties due to two key reasons. The first is the appropriate representation of the constitutive behavior of the polymer melt. The second is regarding the simulation of the free surface, which requires special techniques in the traditionally used Eulerian framework. In this paper we propose a method for simulation of extrudate swell using an Arbitrary Lagrangian Eulerian (ALE) technique based finite element formulation. The ALE technique provides advantages of both Lagrangian and Eulerian frameworks by allowing the computational mesh to move in an arbitrary manner, independent of the material motion. In the present method, a fractional-step ALE technique is employed in which the Lagrangian phase of material motion and convection arising out of mesh motion are decoupled. In the first step, the relevant flow and constitutive equations are solved in Lagrangian framework. The simpler representation of polymer constitutive equations in a Lagrangian framework avoids the difficulties associated with convective terms thereby resulting in a robust numerical formulation besides allowing for natural evolution of the free surface with the flow. In the second step, mesh is moved in ALE mode and the associated convection of the variables due to relative motion of the mesh is performed using a Godunov type scheme. While the mesh is fixed in space in the die region, the nodal points of the mesh on the extrudate free surface are allowed to move normal to flow direction with special rules to facilitate the simulation of swell. A differential exponential Phan Thien Tanner (PTT) model is used to represent the constitutive behavior of the melt. Using this method we simulate extrudate swell in planar and axisymmetric extrusion with abrupt contraction ahead of the die exit. This geometry allows the extrudate to have significant memory for shorter die lengths and acts as a good test for swell predictions. We demonstrate that our predictions of extrudate swell match well with reported experimental and numerical simulations. (c) 2008 Elsevier BY. All rights reserved.</p>},
	keywords = {Arbitrary Lagrangian Eulerian, Extrudate (die) swell, Free surface simulations},
	issn = {0377-0257},
	doi = {10.1016/j.jnnfm.2008.06.006},
	author = {Ganvir, Vivek and Lele, Ashish K. and Thaokar, Rochish and Gautham, Basavarsu P.}
}
