Spectral/hp element methods for plane Newtonian extrudate swell. (English) Zbl 1390.76077
Summary: Spectral/hp element methods and an arbitrary Lagrangian-Eulerian (ALE) moving-boundary technique are used to investigate planar Newtonian extrudate swell. Newtonian extrudate swell arises when viscous liquids exit long die slits. The problem is characterised by a stress singularity at the end of the slit which is inherently difficult to capture and strongly influences the predicted swelling of the fluid. The impact of inertia (\(0 \leqslant \mathrm{Re} \leqslant 100\)) and slip along the die wall on the free surface profile and the velocity and pressure values in the domain and around the singularity are investigated. The high order method is shown to provide high resolution of the steep pressure profile at the singularity. The swelling ratio and exit pressure loss are compared with existing results in the literature and the ability of high-order methods to capture these values using significantly fewer degrees of freedom is demonstrated.
Software:
Nektar++References:
| [1] | Tanner, R., Engineering rheology, (2002), Oxford University Press Oxford · Zbl 1012.76002 |
| [2] | Russo G. Spectral element methods for predicting the die-swell of Newtonian and viscoelastic fluids. PhD thesis, School of Mathematics, Cardiff University, Wales (UK); 2009. |
| [3] | Mitsoulis, E.; Georgiou, G.; Kountouriotis, Z., A study of various factors affecting Newtonian extrudate swell, Comput Fluids, 57, 0, 195-207, (2012) · Zbl 1365.76124 |
| [4] | Salamon, T.; Bornside, D.; Armstrong, R.; Brown, R., The role of surface tension in the dominant balance in the die swell singularity, Phys Fluids, 7, 10, 2328-2344, (1995) · Zbl 1026.76514 |
| [5] | Georgiou, G.; Boudouvis, A., Converged solutions of the Newtonian extrudate-swell problem, Int J Numer Methods Fluids, 29, 3, 363-371, (1999) · Zbl 0947.76049 |
| [6] | Tanner R. Die-swell reconsidered: some numerical solutions using a finite element program. In: Appl Polym Symp, vol. 20; 1973. p. 201-8. |
| [7] | Nickell, R.; Tanner, R.; Caswell, B., The solution of viscous incompressible jet and free-surface flows using finite-element methods, J Fluid Mech, 65, 1, 189, (1974) · Zbl 0298.76022 |
| [8] | Crochet, M.; Keunings, R., Finite element analysis of die swell of a highly elastic fluid, J Non-Newton Fluid Mech, 10, 3, 339-356, (1982) · Zbl 0489.76004 |
| [9] | Reddy, K.; Tanner, R., Finite element solution of viscous jet flows with surface tension, Comput Fluids, 6, 2, 83-91, (1978) · Zbl 0382.76030 |
| [10] | Ho, L.; Rønquist, E., Spectral element solution of steady incompressible viscous free-surface flows, Finite Elem Anal Des, 16, 3-4, 207-227, (1994) · Zbl 0812.76064 |
| [11] | Donea, J.; Huerta, A.; Ponthot, J.; Rodríguez-Ferran, A., Arbitrary Lagrangian-Eulerian methods, Encyclopedia Compos Mech, (2004) |
| [12] | Scovazzi G, Hughes T. Lecture notes on continuum mechanics on arbitrary moving domains. Tech rep, Technical report SAND-2007-6312P, Sandia National Laboratories; 2007. |
| [13] | Pena G. Spectral element approximation of the incompressible Navier-Stokes equations in a moving domain and applications. PhD thesis, École Polytechnique Fédérale de Lausanne; 2009. |
| [14] | Nobile F. Numerical approximation of fluid-structure interaction problems with application to haemodynamics. PhD thesis, Ecole Polytechnique Féderale de Lausanne, Switzerland; 2001. |
| [15] | Robertson, I.; Sherwin, S.; Graham, J., Comparison of wall boundary conditions for numerical viscous free surface flow simulation, J Fluids Struct, 19, 4, 525-542, (2004) |
| [16] | Choi, Y.; Hulsen, M., Simulation of extrudate swell using an extended finite element method, Korea-Aust Rheol J, 23, 3, 147-154, (2011) |
| [17] | Deville, M.; Fischer, P.; Mund, E., High-order methods for incompressible fluid flow, vol. 9, (2002), Cambridge Univ. Pr. Cambridge · Zbl 1007.76001 |
| [18] | Kountouriotis, Z.; Georgiou, G.; Mitsoulis, E., On the combined effects of slip, compressibility, and inertia on the Newtonian extrudate-swell flow problem, Comput Fluids, 71, 297-305, (2013) |
| [19] | Cantwell, C.; Moxey, D.; Comerford, A.; Bolis, A.; Rocco, G.; Mengaldo, G., Nektar++: an open-source spectral/element framework, Comput Phys Commun, (2015) · Zbl 1380.65465 |
| [20] | Dubiner, M., Spectral methods on triangles and other domains, J Sci Comput, 6, 345-390, (1991) · Zbl 0742.76059 |
| [21] | Karniadakis, G. E.; Sherwin, S. J., Spectral/hp element methods for computational fluid dynamics, (2005), Oxford University Press Oxford · Zbl 1116.76002 |
| [22] | Brezzi, F., On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO Anal Numér, 8, 129-151, (1974) · Zbl 0338.90047 |
| [23] | Ainsworth, M.; Sherwin, S., Domain decomposition preconditioners for p and hp finite element approximation of stokes’ equations, Comput Methods Appl Mech Eng, 175, 3-4, 243-266, (1999) · Zbl 0934.76040 |
| [24] | Sherwin, S.; Ainsworth, M., Unsteady Navier-Stokes solvers using hybrid spectral/hp element methods, Appl Numer Math, 33, 1-4, 357-363, (2000) · Zbl 0995.76050 |
| [25] | Taliadorou, E.; Georgiou, G.; Mitsoulis, E., Numerical simulation of the extrusion of strongly compressible Newtonian liquids, Rheol Acta, 47, 1, 49-62, (2007) |
| [26] | Tillett, J., On the laminar flow in a free jet of liquid at high Reynolds numbers, J Fluid Mech, 32, 2, 273-292, (1968) · Zbl 0159.58203 |
| [27] | Mitsoulis, E.; Malamataris, N., Free (open) boundary condition: some experiences with viscous flow simulations, Int J Numer Methods Fluids, 68, 10, 1299-1323, (2011) · Zbl 1427.76137 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
