Numerical simulation of reactive flow in liquid composite molding using flux-corrected transport (FCT) based finite element/control volume (FE/CV) method

International Journal of Heat and Mass Transfer

Volumn 53, Issue 9-10, 2010, Pages 2256-2271

  Tan, Hua ^a   Pillai, Krishna M ^a  

^a University of Wisconsin Milwaukee   (United States)

Author keywords

Flux Corrected Transport (FCT); Liquid Composite Molding; Mold Filling; PORE FLOW; Streamline upwind Petrov Galerkin (SUPG)

Indexed keywords

COMPOSITES MANUFACTURING; CONTROL-VOLUME METHOD; CONVECTION-DOMINATED; CONVECTIVE TRANSPORT; EXCELLENT PERFORMANCE; FLOW STREAMLINES; FLUX-CORRECTED TRANSPORTS; GALERKIN FINITE ELEMENT METHODS; LIQUID COMPOSITE MOLDING; MOLD FILLING; MOLD-FILLING SIMULATION; MOVING BOUNDARIES; NONISOTHERMAL; NONISOTHERMAL FLOWS; NUMERICAL EXAMPLE; NUMERICAL INSTABILITY; NUMERICAL SIMULATION; REACTIVE FLOW; SHARP SOLUTIONS; SIMULATION CODE; SPURIOUS OSCILLATIONS; STABILIZATION TECHNIQUES; STABILIZED METHOD; STREAMLINE-UPWIND PETROV-GALERKIN;

BOUNDARY ELEMENT METHOD; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; FILLING; FINITE ELEMENT METHOD; GALERKIN METHODS; INDUSTRIAL APPLICATIONS; LIQUIDS; MOLDING; REACTIVE MOLDING; REQUIREMENTS ENGINEERING;

MOLDS;

EID: 76749135240     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2009.12.003     Document Type: Article

References (53)

1. Chan A.W., and Hwang S.T. Modeling nonisothermal impregnation of fibrous media with reactive polymer resin. Polym. Eng. Sci. 32 5 (1992) 310-318
2. Bruschke M.V., and Advani S.G. Numerical approach to model non-isothermal viscous flow through fibrous media with free surfaces. Int. J. Numer. Methods Fluids 19 7 (1994) 575-603
3. Young W.B. Three-dimensional nonisothermal mold filling simulations in resin transfer molding. Polym. Compos. 15 2 (1994) 118-127
4. Wang T.J., Lee L.J., and Young W.B. Control volume finite element method for mold filling simulation. Int. Polym. Proc. 10 1 (1995) 82-90
5. Voller V.R., Peng S., and Chen Y.F. Numerical solution of transient, free surface problems in porous media. Int. J. Numer. Methods Eng. 39 17 (1996) 2889-2906
6. Mohan R.V., Ngo N.D., and Tamma K.K. Three-dimensional resin transfer molding: isothermal process modeling and explicit tracking of moving fronts for thick geometrically complex composites manufacturing applications - part 1. Numer. Heat Transfer Part A 35 8 (1999) 815-838
7. Shojaei A., Ghaffarian S.R., and Karimian S.M.H. Numerical simulation of three-dimensional mold filling process in resin transfer molding using quasi-steady state and partial saturation formulations. Compos. Sci. Technol. 62 6 (2002) 861-879
8. Young W.B. Development of a helicopter landing gear prototype using resin infusion molding. J. Reinf. Plast. Compos. 28 7 (2009) 833-849
9. Trochu F., and Gauvin R. Limitations of a boundary-fitted finite difference method for the simulation of the resin transfer molding process. J. Reinf. Plast. Compos. 11 7 (1992) 772-786
10. Yoo Y.E., and Lee W.I. Numerical simulation of the resin transfer mold filling process using the boundary element method. Polym. Compos. 17 3 (1996) 368-374
11. Baliga B.R., and Patankar S.V. New finite-element formulation for convection-diffusion problems. Numer. Heat Transfer 3 4 (1980) 393-409
12. Phelan F.R.J.R. Simulation of the injection process in resin transfer molding. Polym. Compos. 18 4 (1997) 460-476
13. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 32 (1982) 199-259
14. Hughes T.J.R., Franca L.P., and Hulbert G.M. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput. Methods Appl. Mech. Eng. 73 2 (1989) 173-189
15. Donea J. A Taylor-Galerkin method for convective transport problems. Int. J. Numer. Methods Eng. 20 1 (1984) 101-119
16. Löhner R., Morgan K., and Zienkiewicz O.C. The solution of non-linear hyperbolic equation systems by the finite element method. Int. J. Numer. Methods Fluids 4 11 (1984) 1043-1063
17. Codina R. A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation. Comput. Methods Appl. Mech. Eng. 110 3-4 (1993) 325-342
18. Madden N., and Stynes M. Linear enhancements of the streamline diffusion method for convection-diffusion problems. Comput. Math. Appl. 32 10 (1996) 29-42
19. John V., and Knobloch P. On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: part I - a review. Comput. Methods Appl. Mech. Eng. 196 17-20 (2007) 2197-2215
20. Boris J.P., and Book D.L. Flux-corrected transport. I. Shasta, a fluid transport algorithm that works. J. Comput. Phys. 11 1 (1973) 38-69
21. Zalesak S.T. Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31 3 (1979) 335-362
22. Löhner R., Morgan K., Peraire J., et al. Finite element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations. Int. J. Numer. Methods Fluids 7 10 (1987) 1093-1109
23. Kuzmin D., and Turek S. Flux correction tools for finite elements. J. Comput. Phys. 175 2 (2002) 525-558
24. Kuzmin D., MÖLLER M., and Turek S. High-resolution FEM-FCT schemes for multidimensional conservation laws. Comput. Methods Appl. Mech. Eng. 193 45-47 (2004) 4915-4946
25. Kuzmin D. Explicit and implicit FEM-FCT algorithms with flux linearization. J. Comput. Phys. 228 7 (2009) 2517-2534
26. John v., and Schmeyer E. Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion. Comput. Methods Appl. Mech. Eng. 198 3-4 (2008) 475-494
27. Parnas R.S., and Phelan Jr. F.R. Effect of heterogeneous porous media on mold filling in resin transfer molding. SAMPE Quart. 22 2 (1991) 53-60
28. Pillai K.M., and Advani S.G. A model for unsaturated flow in woven fiber preforms during mold filling in resin transfer molding. J. Compos. Mater. 32 19 (1998) 1753-1783
29. Tan H., Roy T., and Pillai K.M. Variations in unsaturated flow with flow direction in resin transfer molding: an experimental investigation. Composites Part A 38 8 (2007) 1872-1892
30. Pillai K.M. Governing equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows. Composites Part A 33 7 (2002) 1007-1019
31. Pillai K.M., and Munagavalasa M.S. Governing equations for unsaturated flow through woven fiber mats. Part 2. Non-isothermal reactive flows. Composites Part A 35 4 (2004) 403-415
32. Whitaker S. Flow in porous media. I: a theoretical derivation of Darcy's law. Transp. Porous Med. 1 1 (1986) 3-25
33. Dessenberger R.B., and Tucker C.L. Thermal dispersion in resin transfer molding. Polym. Compos. 16 6 (1995) 495-506
34. Liu B., and Advani S.G. Operator splitting scheme for 3-D temperature solution based on 2-D flow approximation. Comput. Mech. 16 2 (1995) 74-82
35. Shojaei A., Ghaffarian S.R., and Karimian S.M.H. Simulation of the three-dimensional non-isothermal mold filling process in resin transfer molding. Compos. Sci. Technol. 63 13 (2003) 1931-1948
36. Young W.B. Thermal behaviors of the resin and mold in the process of resin transfer molding. J. Reinf. Plast. Compos. 14 4 (1995) 310
37. Lin R.J., Lee L.J., and Liou M.J. Mold filling and curing analysis liquid composite molding. Polym. Compos. 14 1 (1993) 71-81
38. Chiu H.T., Yu B., Chen S.C., et al. Heat transfer during flow and resin reaction through fiber reinforcement. Chem. Eng. Sci. 55 17 (2000) 3365-3376
39. Tucker C.L., and Dessenberger R.B. Governing equations for flow through stationary fiber beds. In: Advani S.G. (Ed). Flow and Rheology in Polymer Composites Manufacturing (1994), Elsevier, Amsterdam
40. Bear J. Dynamics of Fluids in Porous Media (1971), Elsevier, New York
41. Whitaker S. The Method of Volume Averaging. first ed. (1998), Springer, Berlin
42. Kaviany M. Principles of Heat Transfer in Porous Media. Mechanical Engineering Series. second ed. (1995), Springer, New York
43. Marcos P., and Marcelo L. Thermal dispersion in porous media as a function of the solid-fluid conductivity ratio. Int. J. Heat Mass Transfer 51 (2008) 5359-5367
44. Lee L.J., Young W.B., and Lin R.J. Mold filling and cure modeling of RTM and SRIM processes. Compos. Struct. 27 1-2 (1994) 109-120
45. Kim J.H., Ochoa-Tapia J.A., and Whitaker S. Diffusion in anisotropic porous media. Transp. Porous Med. 2 (1987) 327-356
46. Han N.W., Bhakta J., and Carbonell R.G. Longitudinal and lateral dispersion in packed beds: effect of column length and particle size distribution. AIChE J. 31 2 (1985) 277-288
47. Strong A.B. Plastics: Materials and Processing. third ed. (2006), Pearson Education
48. Kamal M.R., and Sourour S. Kinetics and thermal characterization of thermoset cure. Polym. Eng. Sci. 13 1 (1973) 59-64
49. Castro J.M., and Macosko C.W. Studies of mold filling and curing in the reaction injection molding process. AIChE J. 28 2 (1982) 250-260
50. Reddy J.N., and Gartling D.K. The finite element method in heat transfer and fluid dynamics (2000), CRC Press, New York
51. Hirt C.W., and Nichols B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 1 (1981) 201-225
52. Tan H., and Pillai K.M. Effect of fiber-mat anisotropy on 1D mold filling in LCM: a numerical investigation. Polym. Compos. 29 8 (2008) 869-882
53. Lundstrom T.S. Measurement of void collapse during resin transfer moulding. Composites Part A 28A (1997) 201-214