×

An arbitrary Lagrangian-Eulerian finite element approach to non-steady state turbulent fluid flow with application to mould filling in casting. (English) Zbl 0973.76044

Summary: This paper presents a two-dimensional Lagrangian-Eulerian finite element approach to non-steady state turbulent fluid flows with free surfaces. The proposed model is based on a velocity-pressure finite element Navier-Stokes solver, including an augmented Lagrangian technique and an iterative resolution of Uzawa type. Turbulent effects are taken into account with the \(k\)-\(\varepsilon\) two-equation statistical model. Mesh updating is carried out through an arbitrary Lagrangian-Eulerian method in order to describe properly the free surface evolution. Three comparisons between experimental and numerical results illustrate the efficiency of the method. The first one is turbulent flow in an academic geometry, the second one is a mould filling in effective casting conditions, and the third one is a precise confrontation to a water model.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76F60 \(k\)-\(\varepsilon\) modeling in turbulence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Finite element free surface flow analysis: a new tool for foundry engineers. In Proceedings of the 6th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, (eds). The Minerals, Metals and Materials Society: Warrendale, PA, 1993; 405-412.
[2] Predicting the mould filling time with Simulor. In Proceedings of the NUMIFORM’92 International Conference on Numerical Modelling of Forming Processes, (eds). Balkema: Rotterdam, 1992; 777-785.
[3] Codina, International Journal for Numerical Methods in Heat Fluid Flow 4 pp 291– (1994) · Zbl 0923.76116 · doi:10.1108/EUM0000000004108
[4] Lewis, Numerical Methods in Thermal Problems 7 pp 273– (1993)
[5] Lewis, International Journal for Numerical Methods in Fluids 20 pp 493– (1995) · Zbl 0845.76046 · doi:10.1002/fld.1650200606
[6] Simulation and experimental validation of mould filling. In Proceedings of the 7th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, (eds). The Minerals Metals and Materials Society: Warrendale, PA, 1995; 3-14.
[7] Médale, International Journal for Numerical Methods in Fluids 24 pp 615– (1997) · Zbl 0888.76043 · doi:10.1002/(SICI)1097-0363(19970330)24:6<615::AID-FLD514>3.0.CO;2-H
[8] Finite element free surface modeling. In Proceedings of the 6th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, (eds). The Minerals Metals and Materials Society: Warrendale, PA, 1993; 357-364.
[9] Computer simulation of fluid flow and heat transfer in partially reinforced casting. In Proceedings of the 7th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, (eds). The Minerals Metals and Materials Society: Warrendale, PA, 1995; 23-30.
[10] Hirt, Journal of Computational Physics 39 pp 201– (1981) · Zbl 0462.76020 · doi:10.1016/0021-9991(81)90145-5
[11] Thompson, International Journal for Numerical Methods in Fluids 6 pp 749– (1986) · doi:10.1002/fld.1650061005
[12] Harlow, Internal Physics of Fluids 8 pp 2182– (1965) · Zbl 1180.76043 · doi:10.1063/1.1761178
[13] Chen, Transactions of the Japanese Foundrymen’s Society 12 pp 94– (1993)
[14] Cheng, International Journal for Numerical Methods in Fluids 21 pp 15– (1995) · Zbl 0841.76063 · doi:10.1002/fld.1650210103
[15] Zaidi, Computing Methods and Applied Mechanics in Engineering 144 pp 227– (1997) · Zbl 0895.76048 · doi:10.1016/S0045-7825(96)01018-3
[16] Navti, Computing Methods and Applied Mechanics in Engineering 147 pp 41– (1997) · Zbl 0901.76034 · doi:10.1016/S0045-7825(97)00017-0
[17] Muttin, International Journal for Numerical Methods in Engineering 36 pp 2001– (1991) · Zbl 0774.76053 · doi:10.1002/nme.1620361204
[18] Hirt, Journal of Computational Physics 14 pp 227– (1974) · Zbl 0292.76018 · doi:10.1016/0021-9991(74)90051-5
[19] An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid structure interaction problems. Proceedings of the SMIRT-5 Conference, Berlin. 1979; 1-10.
[20] Liu, Computing Methods and Applied Mechanics in Engineering 58 pp 227– (1986) · Zbl 0585.73117 · doi:10.1016/0045-7825(86)90097-6
[21] Benson, Computing Methods and Applied Mechanics in Engineering 72 pp 305– (1989) · Zbl 0675.73037 · doi:10.1016/0045-7825(89)90003-0
[22] Schreurs, Computing Methods and Applied Mechanics in Engineering 58 pp 19– (1986) · Zbl 0595.73085 · doi:10.1016/0045-7825(86)90076-9
[23] Modélisation du remplissage des moules d’injection pour polymères thermoplastiques par une méthode eulérienne lagrangienne arbitraire (Modelling of the filling of injection moulds for thermoplastic polymers by an arbitrary Eulerian Lagrangian method). PhD thesis (in French), Ecole des Mines de Paris, 1994.
[24] Donéa, Computing Methods and Applied Mechanics in Engineering 95 pp 169– (1992) · Zbl 0772.76035 · doi:10.1016/0045-7825(92)90139-B
[25] Brooks, Computing Methods and Applied Mechanics in Engineering 32 pp 199– (1982) · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[26] Méthodes des Eléments Finis pour les Fluides (Finite Element Method for Fluid Flow) (in French). Masson: Paris, 1988.
[27] Ghosh, Computing Methods and Applied Mechanics in Engineering 86 pp 127– (1991) · Zbl 0825.73687 · doi:10.1016/0045-7825(91)90126-Q
[28] Lewis, International Journal for Numerical Methods in Fluids 25 pp 931– (1997) · Zbl 0902.76060 · doi:10.1002/(SICI)1097-0363(19971030)25:8<931::AID-FLD594>3.0.CO;2-1
[29] An arbitrary Lagrangian-Eulerian finite element approach to non steady state fluid flows. Application to mould filling. In Proceedings of the 7th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, (eds). The Minerals Metals and Materials Society: Warrendale, PA, 1995; 163-170.
[30] An arbitrary Lagrangian-Eulerian finite element approach to non steady state fluid flows. Application to mould filling. In Proceedings of the ECCOMAS’96, 2nd ECCOMAS (European Community on Computational Methods in Applied Sciences) Computational Fluid Dynamics Confrence, (eds). Wiley: Chichester, 1996; 973-979.
[31] Modélisation et Simulation des Ecoulements Turbulents (Modelling and Simulation of Turbulent Flows) (in French). Hermès: Paris, 1993.
[32] Lectures in Mathematical Models of Turbulence (3rd edn). Academic Press: London, 1979.
[33] Dynamique des Fluides (Fluid Dynamics) (in French) (2nd edn). Presses Polytechniques Universitaires Romandes: Lausanne, 1991.
[34] Simulation numérique d’coulements turbulents avec réactions chimiques (Numerical simulation of turbulent flows with chemical reactions). PhD thesis (in French), Ecole Polytechnique de Montréal, 1990.
[35] Simulation numérique par éléments finis bidimensionnels du remplissage de moules de fonderie et étude expérimentale sur maquette hydraulique (Bidimensional finite element numerical simulation of the filling of casting moulds and experimental study on a water model). PhD thesis (in French), Ecole des Mines de Paris, 1997.
[36] Algorithmes multigrilles et algorithmes implicites pour les écoulements compressibles turbulents (Multigrid algorithms and implicit algorithms for compressible turbulent flows). PhD thesis (in French), Université de Nice-Sophia-Antipolis, 1994.
[37] Fortin, Internatioanl Journal for Numerical Methods in Fluids 5 pp 911– (1985) · Zbl 0573.76032 · doi:10.1002/fld.1650051005
[38] Brezzi, RAIRO R2 pp 129– (1974)
[39] Méthodes de Lagrangien Augmenté (Augmented Lagrangian Methods) (in French). Collection Méthodes Mathématiques de l’Informatique: Dunod, 1982.
[40] Pelletier, ASME Advances in Finite Element Analysis in Fluid Dynamics 200 pp 59– (1994)
[41] Grandes déformations et remaillage automatique (Large deformations and automatic remeshing). PhD thesis (in French), Ecole des Mines de Paris, 1991.
[42] Glut, Journal of Material Processing Techniques 34 pp 69– (1992) · doi:10.1016/0924-0136(92)90091-6
[43] A new finite element method for the Navier-Stokes equations coupled with a temperature equation. In Proceedings of the 4th International Symposium on Finite Element in Flow Problem, (ed.). North-Holland: Amsterdam, 1982; 295-301.
[44] Experimental study of flow reattachment in a single-sided sudden expansion. NASA Contract Report 3765, 1984.
[45] Jaeger, International Journal for Numerical Methods in Fluids 14 pp 1325– (1992) · Zbl 0753.76096 · doi:10.1002/fld.1650141105
[46] Méthode directe de résolution d’coulements turbulents discrétisés par les éléments finis (Direct method of resolution of turbulent flows discretised by finite elements). PhD thesis (in French), Université catholique de Louvain, Louvain-la-Neuve, 1994.
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.