The main advances in the modeling and simulation of the filling phenomenon that takes place in dual-scale fibrous reinforcements used in liquid composites molding processes are grouped and classified in the present work. Special emphasis is done in the classification of the simulation methods according to the dimension of the mesh, the identification of the interface conditions porous medium-free fluid, the comparison between the most used fluid-front tracking techniques and the survey of researches dealing with the non-uniform filling of representative unitary cells, which in turn is responsible for the void formation at mesoscopic scale and the sink effect at macroscopic scale. As an original contribution to this field of study, a new methodology to quantify the sink effect in macroscopic fillings is presented and subsequently assessed by comparing the results of experimental radial injections with numerical results obtained by the dual reciprocity-boundary element method. The proposed methodology is physically consistent and leads to results that are closer to the experimental ones than the results obtained when the sink effect is neglected; however, the accuracy is liable to be improved.
ChanAWMorganRJ. Tow impregnation during Resin Transfer Moulding of bidireccional woven fabrics. Polym Compos1993; 14: 335–350.
2.
LekakouCJohariMNormanDet al.Measurement techniques and effects on in-plane permeability of woven cloths in resin transfer moulding. Compos Part A Appl Sci Manuf1996; 27: 401–408.
3.
GourichonBBinetruyCKrawczakP. Experimental investigation of high fiber tow count fabric unsaturation during RTM. Compos Sci Technol2006; 66: 976–982.
4.
JinlianHYiLXuemingS. Study on void formation in multi-layer woven fabrics. Compos Part A Appl Sci Manuf2004; 35: 595–603.
5.
KangKKoellingK. Void transport in resin transfer molding. Polym Compos2004; 25: 417–432.
6.
MunagavalasaMS. Theoretical modelling of unsaturated flow in fibrous dual scale porous media using volume averaging method, USA: PhD Dissertation, College Of Engineering and Applied Science, University of Wisconsin Milwaukee USA, 2006.
7.
PillaiKMMunagavalasaMS. Governing equations for unsaturated flow through woven fiber mats. Part 2. Non-isothermal reactive flows. Compos Part A Appl Sci Manuf2004; 35: 403–415.
8.
PillaiKM. Governing equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows. Compos Part A Appl Sci Manuf2002; 33: 1007–1019.
9.
LawrenceJMNeacsu VAdvaniSG. Modeling the impact of capillary pressure and air entrapment on fiber tow saturation during resin infusion in LCM. Compos Part A Appl Sci Manuf2009; 40: 1053–1064.
10.
SimacekPAdvaniSG. A numerical model to predict fiber tow saturation during liquid composite molding. Compos Sci Technol2003; 63: 1725–1736.
11.
TanHPillaiKM. Multiscale modeling of unsaturated flow in dual-scale fiber preforms of liquid composite molding I: Isothermal flows. Compos Part A Appl Sci Manuf2012; 43: 29–44.
12.
TanHPillaiKM. Multiscale modeling of unsaturated flow of dual-scale fiber preform in liquid composite molding II: non-isothermal flows. Compos Part A Appl Sci Manuf2012; 43: 14–28.
13.
KangMKLeeW IlHahnHT. Formation of microvoids during resin-transfer molding process. Compos Sci Technol2000; 60: 2427–2434.
14.
LeeGWLeeKJ. Mechanism of void formation in composite processing with woven fabrics. Polym Compos2003; 11: 563–572.
15.
PillaiKMAdvaniSG. A Model for unsaturated flow in woven fiber preforms during mold filling in resin transfer molding. J Compos Mater1998; 32: 1753–1783.
16.
TanHPillaiKM. Multiscale modeling of unsaturated flow in dual-scale fiber preforms of liquid composite molding III: reactive flows. Compos Part A Appl Sci Manuf2012; 43: 29–44.
17.
VanegasJDPatiñoIDVargasCA. Boundary element approaches for filling simulations of anisotropic reinforced preforms used in the resin transfer molding process. J Compos Mater2013; 48: 2603–2629.
18.
SaffmanPG. On the boundary condition at the surface of a porous medium. Stud Appl Math1971; L2: 93–101.
19.
BeaversGSSparrowEMMagnusonRA. Experiments on coupled parallel flows in a channel and a bounding porous medium. J Basic Eng1970; 92D: 843–848.
20.
BabuBZPillaiKM. Experimental investigation of the effect of fiber-mat architecture on the unsaturated flow in liquid composite molding. J Compos Mater2003; 38: 57–79.
21.
Babu BZ. The effect of fiber mat compression and architecture on the unsaturated flow in liquid composite molding – experimental study. MsC Thesis, College of Engineering and Applied Science, University of Wisconsin, Milwaukee, USA, 2002.
22.
WhitakerSBearJ. The method of volume averaging, 1st ed. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1999, pp. 207–207.
23.
CoulterJPGuceriSI. Resin impregnation during the manufacturing of composite materials subject to prescribed injection rate. J Reinf Plast Compos1988; 7: 200–219.
24.
MohanRNgoNTammaK. On a pure finite-element-based methodology for resin transfer mold filling simulations. Polym Eng Sci1999; 39: 26–43.
25.
ShojaeiAGhaffarianSRKarimianSMH. Numerical simulation of three-dimensional mold filling process in resin transfer molding using quasi-steady state and partial saturation formulations. Compos Sci Technol2002; 62: 861–879.
26.
ShojaeiAGhaffarianSRKarimianSMH. Modeling and simulation approaches in the resin transfer molding process: a review. Polym Compos2003; 24: 525–544.
27.
BruschkeMVAdvaniSG. A finite element/control volume approach to mold filling in anisotropic porous media. Polym Compos1990; 11: 398–405.
28.
Fracchia CA, Castro J and Tucker CL. A finite element/control volume simulation of resin transfer mold filling. In: Brown D (ed.) American society for composites fourth technical conference, Blacksburg, USA, 1989, pp.157–66.
29.
TuckerCLDessenbergerRBGoverning equations for flow through stationary fiber beds. In: AdvaniSG (ed). Flow and rheology in polymer composites manufacturing, 1st ed. Amsterdam, The Netherlands: Elsevier Publisher, 1994, pp. 257–323.
30.
TadmorZBroyerEGudfingeC. Flow analysis network (FAN) - a method for solving problems in polymer processing. Polym Eng Sci1974; 14: 660–665.
31.
SevostianovIVerijenkoVEvon KlempererCJ. Mathematical model of cavitation during resin film infusion process. Compos Struct2000; 48: 197–203.
32.
LiuX-L. Isothermal flow simulation of liquid composite molding. Compos Part A Appl Sci Manuf2000; 31: 1295–302.
33.
SouzaJARochaLAOAmicoSCet al.A numerical investigation of the resin flow front tracking applied to the RTM process. Mater Res2011; 14: 345–354.
34.
BruschkeMVAdvaniSG. RTM: filling simulation of complex three dimensional shell-like structures. Sampe Quartely1991; 23: 2–11.
35.
LiuBBickertonSAdvaniS. Modelling and simulation of RTM gate control, venting and dry spot prediction. Compos Part A1996; 27: 135–141.
36.
Cairns DS and Rossell SM. Fluid flow modeling of resin transfer molding for composite material wind turbine. Technical Report SAND2004-0076T. Montana State University, Bozeman, USA, 2004.
37.
TrochuFGauvinRGaoD-M. Numerical analysis of the resin transfer molding process by the finite element method. Adv Polym Technol1993; 12: 329–342.
38.
RuizEAchimVSoukaneSet al.Advanced numerical simulation of liquid composite molding for process analysis and optimization. Compos Part A Appl Sci Manuf2006; 37: 890–902.
39.
BréardJRemacleJFPhamXTet al.The effect of the pressure boundary condition on mold filling simulations in liquid composite molding. Trans Eng Sci1998; 21: 77–86.
40.
DialloMLGauvinRTrochuF. Experimental analysis and simulation of flow through multilayer fiber reinforcements in liquid composite molding. Polym Compos1998; 19: 246–256.
41.
RuizEAchimVSoukaneSet al.Optimization of injection flow rate to minimize micro/macro-voids formation in resin transfer molded composites. Compos Sci Technol2006; 66: 475–486.
42.
GantoisRCantarelADusserreGet al.Mold filling simulation of resin transfer molding combining BEM and level set method. Appl Mech Mater2011; 62: 57–65.
43.
SoukaneSTrochuF. Application of the level set method to the simulation of resin transfer molding. Compos Sci Technol2006; 66: 1067–1080.
44.
YooY-ELeeW Il. Numerical simulation of the resin transfer mold filling process using the boundary element method. Polym Compos1996; 17: 368–374.
45.
VollerVRPengS. An algorithm for analysis of polymer filling molds. Polym Eng Sci1995; 35: 1758–1765.
46.
UmM-KLeeW Il. A study on the mold filling process in resin transfer molding. Polym Eng Sci1991; 31: 765–771.
47.
VanegasJDPatiñoID. Filling simulation of the RTM process in isotropic homogeneous/non-homogeneous media using the boundary element method. Adv Compos Mater2015; 24: 113–139.
48.
ClementsDL. A boundary integral equation method for the numerical solution of a second order elliptic equation with variable coefficients. J Aust Math Soc1980; 22: 218–228.
49.
ClementsDL. Boundary value problems governed by second order elliptic systems, 1st ed. London, United Kingdom: Pitman Advanced Publishing Program, 1981, pp. 176–176.
50.
GantoisRCantarelACossonBet al.BEM-based models to simulate the resin flow at macroscale and microscale in LCM processes. Polym Compos2013; 34: 1235–1244.
51.
SkergetLJeclRBoundary element method for transport phenomena in porous medium. In: InghamDPopI (eds). Transport phenomena in porous media II, 1st ed. Oxford, United Kingdom: Pergamon, 2002, pp. 20–53.
52.
PartridgePWBrebbiaCAWrobelLC. The dual reciprocity boundary element method, 1st ed. Southampton, England: Computational Mechanics Publication, 1992, pp. 200–200.
53.
ŠarlerBPerkoJGobinDet al.Dual reciprocity boundary element method solution of natural convection in Darcy–Brinkman porous media. Eng Anal Bound Elem2004; 28: 23–41.
54.
LafeOELiggettJALiuPL. BIEM solutions to combinations of leaky, layered, confined, unconfined, nonisotropic aquifers. Water Resour Res1981; 17: 1431–1444.
55.
Lennon GP. Boundary element analysis of flow in heterogeneous porous media. In: ASCE/HYD Specialty Conference. Hydraulic Division, Cour d’Alene, USA, 1984 Aug, pp.177–179.
56.
RangogniR. Numerical solution of the generalized Laplace equation by coupling the boundary element method and the perturbation method. Appl Math Model1986; 10: 266–270.
57.
DivoEKassabA. A generalized boundary-element method for steady-state heat conduction in heterogeneous anisotropic media. Numer Heat Transf1997; 32: 37–61.
58.
KassabAJDivoE. A generalized boundary integral equation for isotropic heat conduction spatially varying thermal conductivity. Eng Anal Bound Elem1997; 18: 273–286.
59.
AngW-TClementsDLVahdatiN. A dual-reciprocity boundary element method for a class of elliptic boundary value problems for non-homogeneous anisotropic media. Eng Anal Bound Elem2003; 27: 49–55.
60.
TanakaMMatsumotoTSudaY. A dual reciprocity boundary element method applied to the steady-state heat conduction problem of functionally gradient materials. study on two-dimensional problems. Trans Japan Soc Mech Eng A2001; 67: 1589–1594.
61.
MartínezMACuetoEDoblareMet al.Natural element meshless simulation of flows involving short fiber suspensions. J Nonnewton Fluid Mech2003; 115: 51–78.
62.
GarcíaJAGascónLCuetoEet al.Meshless methods with application to liquid composite molding simulation. Comput Methods Appl Mech Eng2009; 198: 2700–2709.
63.
GonzálezDCuetoEChinestaFet al.A natural element updated Lagrangian strategy for free- surface fluid dynamics. J Comput Phys2007; 223: 127–150.
64.
HuangL-HChiangI-LSongC-H. A re-investigation of laminar channel flow passing over porous bed. J Chinese Inst Eng1997; 20: 435–441.
65.
LevyTSánchez PalenciaE. On boundary conditions for fluid flow in porous media. Int J Eng Sci1975; 13: 923–940.
66.
JägerWMikelićA. Modeling effective interface laws for transport phenomena between an unconfined fluid and a porous medium using homogenization. Transp Porous Media2009; 78: 489–508.
67.
CarraroTGollCMarciniak-CzochraAet al.Pressure jump interface law for the Stokes-Darcy coupling : Confirmation by direct numerical simulations. J Fluid Mech2013; 732: 510–536.
68.
OrmLA. VMS stabilization for Stokes-Darcy flow in porous media undergoing finite deformations: application to infusion composite processing, PhD Dissertation, Mécanique et Ingénierie, Nationale École Superiore des Mines Saint Étiennne: France, 2013.
69.
Blais M, Moulin N, Liotier P, et al. Resin-infusion based processes simulation : coupled Stokes-Darcy flows in orthotropic preforms undergoing finite strain. In: Conference on computational methods in manufacturing processes, Keiting, Taiwan, 2015 May, pp.1–3.
70.
Patiño ArcilaIDPowerHNieto LondoñoCet al.Boundary element simulation of void formation in fibrous reinforcements based on the Stokes–Darcy formulation. Comput Methods Appl Mech Eng2016; 304: 265–293.
71.
NealeGNaderW. Practical significance of Brinkman’s extension of Darcy’s law: coupled parallel flows within a channel and a bounding porous medium. Can J Chem Eng1974; 52: 475–478.
72.
RichardsonJPowerH. A BEM analysis of creeping flow past two porous bodies of arbitrary shape. Eng Anal Bound Elem1996; 17: 193–204.
73.
Ochoa-tapiaJAWhitakerS. Momentum transfer at the boundary between a porous medium and a homogeneous fluid I. Theoretical development. Int J Heat Mass Transf1995; 38: 2635–2646.
74.
Ochoa-tapiaJAWhitakerS. Momentum transfer at the boundary between a porous medium and a homogeneous fluid—II. Comparison with experiment. Int J Heat Mass Transf1995; 38: 2647–2655.
75.
Valdes-ParadaFJOchoa-tapiaAAlvarez-RamirezJ. On the effective viscosity for the Darcy–Brinkman equation. Phys A Stat Mech its Appl2007; 385: 69–79.
76.
HwangWRAdvaniSG. Numerical simulations of Stokes–Brinkman equations for permeability prediction of dual scale fibrous porous media. Phys Fluids2010; 22: 1–14.
77.
TanHPillaiKM. Finite element implementation of stress-jump and stress-continuity conditions at porous-medium, clear-fluid interface. Comput Fluids2009; 38: 1118–1131.
78.
PatiñoIDPowerHNieto-LondoñoCet al.Stokes–Brinkman formulation for prediction of void formation in dual-scale fibrous reinforcements: a BEM/DR-BEM simulation. Comput Mech2017; 59: 1–23.
79.
Patiño ID and Power H. Boundary Element method for filling of dual scale porous media used in the processing of composites materials. In: Harris P (ed.) 10th Conference on boundary integral methods, Brighton, United Kingdom, 2015 Jul, pp.1–12.
80.
SethianJA. Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 2nd ed. Cambridge, England: Cambridge University Press, 1999, pp. 363–363.
81.
JungYKimSJHanW-S. Numerical simulation of RTM process using the extended finite element method combined with the level set method. J Reinf Plast Compos2013; 32: 308–317.
82.
LundströmTFrishfeldsVJakovicsA. Bubble formation and motion in non-crimp fabrics with perturbed bundle geometry. Compos Part A Appl Sci Manuf2010; 41: 83–92.
83.
AdalsteinssonDSethianJA. The fast construction of extension velocities in level set methods. J Comput Phys1999; 148: 2–22.
84.
GremaudPAKusterCM. A study of numerical methods for the level set approach. Appl Numer Math2005; 57: 837–846.
85.
SethianJASmerekaP. Level set method for fluid interfaces. Annu Rev Mater Res2003; 35: 341–372.
86.
Thai M-Q, Schmidt F, Dusserre G, et al. BEM computation of 3D stokes flow including moving front. Int J Mater Form 2017; 10: 567–580.
87.
GarcíaJAGascónLChinestaF. A fixed mesh numerical method for modelling the flow in liquid composites moulding processes using a volume of fluid technique. Comput Methods Appl Mech Eng2003; 192: 877–893.
88.
YangJJiaYSunSet al.Mesoscopic simulation of the impregnating process of unidirectional fibrous preform in resin transfer molding. Mater Sci Eng A2006; 435–436: 515–520.
89.
DevalveCPitchumaniR. Simulation of void formation in liquid composite molding processes. Compos Part A Appl Sci Manuf2013; 51: 22–32.
90.
GarcíaJA. Gestión del frente de avance en la modelización numérica del conformado de Transferencia de Resina (RTM), PhD Dissertation, Department of Mechanical and Materials Engineering, Universitat Politècnica de València: Spain, 2000.
91.
Lebel F. Controle de la Fabrication des Composites par injection sur renforts. PhD. Dissertation, Département de Génie Méchanique, Université de Montréal, Canada, 2012.
92.
PatelNLeeLJ. Effects of fiber mat architecture on void formation and removal in liquid composite. Polym Compos1995; 16: 386–399.
93.
LeclercJSRuizE. Porosity reduction using optimized flow velocity in resin transfer molding. Compos Part A2008; 39: 1859–1868.
94.
ParkCHLebelASaouabAet al.Modeling and simulation of voids and saturation in liquid composite molding processes. Compos Part A Appl Sci Manuf2011; 42: 658–668.
95.
SchellJSUDelegliseMBinetruyCet al.Numerical prediction and experimental characterisation of meso-scale-voids in liquid composite moulding. Compos Part A Appl Sci Manuf2007; 38: 2460–2470.
96.
LeeDHLeeW IlKangMK. Analysis and minimization of void formation during resin transfer molding process. Compos Sci Technol2006; 66: 3281–3289.
97.
GourichonBBinetruyCKrawczakP. A new numerical procedure to predict dynamic void content in liquid composite molding. Compos Part A Appl Sci Manuf2006; 37: 1961–1969.
98.
GourichonBDelégliseMBinetruyCet al.Dynamic void content prediction during radial injection in liquid composite molding. Compos Part A Appl Sci Manuf2008; 39: 46–55.
99.
LundströmTS. Measurement of void collapse during resin transfer moulding. Compos Part A Appl Sci Manuf1997; 28: 201–214.
100.
FoleyMEGillespieJW. Modeling the effect of fiber diameter and fiber bundle count on tow impregnation during liquid molding processes. J Compos Mater2005; 39: 1045–1065.
101.
NeacsuV. Modeling and measurement of microflow of microflow in dual-scale porous media, PhD Dissertation, Department of Mechanical Engineering, University of Delaware USA, 2009.
102.
FrishfeldsVLundströmTSJakovicsA. Bubble motion through non-crimp fabrics during composites manufacturing. Compos Part A Appl Sci Manuf2008; 39: 243–251.
103.
BréardJHenzelYTrochuFet al.Analysis of dynamic flow through porous media. Polym Compos2003; 24: 390–408.
104.
ParkCHLeeW Il. Modeling void formation and unsaturated flow in liquid composite molding processes: a survey and review. J Reinf Plast Compos2011; 30: 957–977.
105.
GascónLGarcíaJALebelFet al.A two-phase flow model to simulate mold filling and saturation in resin transfer molding. Int J Mater Form2016; 9: 229–239.
106.
GascónLGarcíaJALeBelFet al.Numerical prediction of saturation in dual scale fibrous reinforcements during liquid composite molding. Compos Part A Appl Sci Manuf2015; 77: 275–284.
107.
LeBelFFanaeiAERuizEet al.Experimental characterization by fluorescence of capillary flows in the fiber tows of engineering fabrics. Open J Inorganis No-Metallic Mater2012; 2: 25–45.
108.
FrishfeldsVLundströmTSJakovicsA. Lattice-gas analysis of fluid front in non-crimp fabrics. In: 19th international symposium transport phenomena, Reykyjavik, Iceland, 2008Aug, pp. 1–9.
109.
GangloffJJHwangWRAdvaniSG. Characterization of bubble mobility in channel flow with fibrous porous media walls. Int J Multiph Flow2014; 60: 76–86.
110.
Di FrattaCKlunkerFTrochuFet al.Characterization of textile permeability as a function of fiber volume content with a single unidirectional injection experiment. Compos Part A Appl Sci Manuf2015; 77: 238–247.
111.
TahirMWHallströmSÅkermoM. Effect of dual scale porosity on the overall permeability of fibrous structures. Compos Sci Technol2014; 103: 56–62.
112.
CenderTASimacekPAdvaniSG. Resin film impregnation in fabric prepregs with dual length scale permeability. Compos Part A Appl Sci Manuf2013; 53: 118–128.
113.
HajiHSaouabANawabY. Simulation of coupling filtration and flow in a dual scale fibrous media. Compos Part A Appl Sci Manuf2015; 76: 272–280.
114.
ZhouFAlmsJAdvaniSG. A closed form solution for flow in dual scale fibrous porous media under constant injection pressure conditions. Compos Sci Technol2008; 68: 699–708.
115.
ZhouFKuentzerNSimacekPet al.Analytic characterization of the permeability of dual-scale fibrous porous media. Compos Sci Technol2006; 66: 2795–2803.
116.
ShouDYeLTangYet al.Longitudinal permeability determination of dual-scale fibrous materials. Compos Part A2015; 68: 42–46.
117.
ShouDYeLTangYet al.Transverse permeability determination of dual-scale fibrous materials. Int J Heat Mass Transf2013; 58: 532–539.
118.
AchesonJASimacekPAdvaniSG. The implications of fiber compaction and saturation on fully coupled VARTM simulation. Compos Part A Appl Sci Manuf2004; 35: 159–169.
119.
BayldonJMDanielIM. Flow modeling of the VARTM process including progressive saturation effects. Compos Part A Appl Sci Manuf2009; 40: 1044–1052.
120.
Tan H and Pillai KM. Modeling unsaturated flow in dual-scale fiber mats of liquid composite molding: some recent developments. In: The 10th international conference on flow processes in composite materials (FPCM10) (eds V Michaud and P Ermanni eds), Monte Verità, Switzerland, 2010, pp.1–5.
121.
WangYGroveSM. Modelling microscopic flow in woven fabric reinforcements and its application in dual-scale resin infusion modelling. Compos Part A Appl Sci Manuf2008; 39: 843–855.
122.
SimacekPAdvaniSG. Modeling resin flow and fiber tow saturation induced by distribution media collapse in VARTM. Compos Sci Technol2007; 67: 2757–2769.
123.
De ParsevalYPillaiKMAdvaniSG. A simple model for the variation of permeability due to partial saturation in dual scale porous media. Transp Porous Media1997; 27: 243–264.
124.
LundströmTSStenbergRBergströmRet al.In-plane permeability measurements: a nordic round-robin study. Compos Part A Appl Sci Manuf2000; 31: 29–43.
125.
ArbterRBeraudJMBinetruyCet al.Experimental determination of the permeability of textiles: a benchmark exercise. Compos Part A Appl Sci Manuf2011; 42: 1157–1168.
126.
PosrikidisC. A practical guide to boundary element methods, 1st ed. London, United Kingdom: Chapman & Hall/ CRC, 2002, pp. 418–418.
127.
KatsikadelisJT. Boundary elements: theory and applications, 1st ed. Oxford, England: Elsevier, 2002, pp. 278–278.
128.
PowerHWrobelLC. Boundary integral methods in fluid mechanics, 1st ed. Southhampton, United Kingdom: Computational Mechanics Publications, 1995, pp. 325–325.
129.
TellesJF. A self adaptative coordinate transformation for efficient numerical evaluation of general boundary element integrals. Int J Numer methods Eng1987; 24: 959–973.
130.
GebartBR. Permeability of unidirectional reinforcements for RTM. J Compos Mater1992; 26: 1100–1133.
