A closed form solution to the flow of resin in vacuum assisted resin transfer molding process (VARTM) has been derived. VARTM is used extensively for affordable manufacturing of large composite structures. During the VARTM process, a highly permeable distribution medium is incorporated into the preform as a surface layer. During infusion, the resin flows preferentially across the surface and simultaneously through the preform giving rise to a complex flow front. The analytical solution presented here provides insight into the scaling laws governing fill times and resin inlet placement as a function of the properties of the preform, distribution media and resin. The formulation assumes that the flow is fully developed and is divided into two regimes: a saturated region with no crossflow and a flow front region where the resin is infiltrating into the preform from the distribution medium. The flow front region moves with a uniform velocity. The law of conservation of mass and Darcy’s Law for flow through porous media are applied in each region. The resulting equations are nondimensionalized and are solved to yield the flow front shape and the development of the saturated region. It is found that the flow front is parabolic in shape and the length of the saturated region is proportional to the square root of the time elapsed. The results thus obtained are compared to data from full scale simulations and an error analysis of the solution was carried out. It was found that the time to fill is determined with a high degree of accuracy while the error in estimating the flow front length, d, increases with a dimensionless parameter ε=K2xxh22/K2yyd2. The solution allows greater insight into the process physics, enables parametric and optimization studies and can reduce the computational cost of full-scale 3-dimensional simulations. A parametric study is conducted to establish the sensitivity of flow front velocity to the distribution media/preform thickness ratio and permeabilities and preform porosity. The results provide insight into the scaling laws for manufacturing of large scale structures by VARTM. [S1087-1357(00)02002-5]

1.
Seeman II, W., 1990, “Plastic Transfer Molding Techniques for the Production of Fiber Reinforced Plastic Structures,” United States Patent 4,902,215, February.
2.
Bruschke
,
M. V.
, and
Advani
,
S. G.
,
1990
, “
A Finite Element/Control Volume Approach to Mold Filling in Anisotropic Porous Media
,”
Polym. Compos.
,
11
, pp.
398
405
.
3.
Bruschke
,
M. V.
, and
Advani
,
S. G.
,
1991
, “
A Numerical Approach to Model Non-Isothermal, Viscous Flow with Free Surfaces Through Fibrous Media
,”
Int. J. Numer. Methods Fluids
,
19
, pp.
575
603
.
4.
Liu
,
D.
,
Bickerton
,
S.
, and
Advani
,
S. G.
,
1996
, “
Modeling and Simulation of RTM: Gate Control, Venting and Dry Spot Prediction
,”
Composites Part A
,
27A
, pp.
135
141
.
5.
Mohan
,
R. V.
,
Ngo
,
N. D.
,
Tamma
,
K. K.
, and
Fickie
,
K. D.
,
1999
, “
On a Pure Finite Element Based Methodology for Resin Transfer Mold Filling Simulations
,”
Polym. Eng. Sci.
,
39
, No.
1
, pp.
26
43
.
6.
Bruschke
,
M. V.
, and
Advani
,
S. G.
,
1991
, “
RTM: Filling Simulation of Complex Three-Dimensional Shell-Like Structures
,”
SAMPE Q.
,
23
, No.
1
, pp.
2
11
.
7.
Trochu
,
F.
,
Gauvin
,
R.
,
Gao
,
D. M.
, and
Boudreault
,
J.-F.
,
1994
, “
RTMFLOT—An Integrated Software Environment for the Computer Simulation of the Resin Transfer Molding Process
,”
J. Reinf. Plast. Compos.
,
13
, No.
3
, pp.
262
270
.
8.
Lee
,
L. J.
,
Young
,
W. B.
, and
Lin
,
R. J.
,
1994
, “
Mold Filling and Cure Modeling of RTM and SRIM Processes
,”
Compos. Struct.
,
27
, Nos. 1–2.
9.
De Parseval
,
Y.
,
Pillai
,
K. M.
, and
Advani
,
S. G.
,
1997
, “
A Simple Model for the Variation of Permeability Due to Partial Saturation in Dual Scale Porous Media
,”
Transp. Porous Media
,
27
, pp.
243
264
.
10.
Bickerton
,
S.
, and
Advani
,
S. G.
,
1997
, “
Experimental Investigation and Flow Visualization of Resin Transfer Molding Process in a Non-Planar Geometry
,”
Compos. Sci. Technol.
,
57
, pp.
23
33
.
11.
Simacek
,
P.
,
Sozer
,
E. M.
, and
Advani
,
S. G.
,
1998
, User manual for DRAPE 1.1 and LIMS 4.0. Technical Report, Center for Composite Materials.
12.
Gallez, X. E., and Advani, S. G., 1996, “Numerical Simulations for Impregnation of Fiber Preforms in Composites Manufacturing,” in Proceedings of the Fourth International Conference on Flow Processes in Composite Materials, University of Wales, 1996.
13.
Scheidegger, Adrian E., 1974, The Physics of Flow Through Porous Media, University of Toronto Press.
14.
Bear, J., Flow Through Porous Media, American Elsevier, 1972.
15.
Adler, Pierre M., Porous Media: Geometry and Transports, Butterworth-Heinemann, 1992.
16.
Woerdeman
,
D. L.
,
Phelan
,
F. R.
, and
Parnas
,
R. S.
,
1996
, “
Interpretation of 3-D Permeability Measurements for RTM Modeling
,”
Polym. Compos.
,
16
, pp.
470
480
.
17.
Tari
,
M. J.
,
Imbert
,
J. P.
,
Lin
,
M. Y.
,
Lavine
,
A. S.
, and
Hahn
,
H. T.
,
1998
, “
Analysis of Resin Transfer Molding with High Permeability Layers
,”
J. Manuf. Sci. Eng.
,
120
, pp.
609
616
.
18.
Pillai
,
K. M.
, and
Advani
,
S. G.
,
1998
, “
Numerical Simulation of Unsaturated Flow in Woven or Stitched Fiber Mats in Resin Transfer Molding
,”
Polym. Compos.
,
19
, No.
1
,
71
80
.
19.
Murphy, G. M., Ordinary Differential Equations and Their Solutions, Van Nostrand, 1960.
20.
Pillai
,
K. M.
, and
Advani
,
S. G.
,
1998
, “
A Model for Unsaturated Flow in Woven or Stitched Fiber Mats in Resin Transfer Molding
,”
J. Compos. Mater.
,
32
, No.
19
, pp.
1753
1783
.
21.
Sun
,
X.
,
Li
,
S.
, and
Lee
,
J. L.
,
1998
, “
Mold Filling Analysis in Vacuum-Assisted Resin Transfer Molding. Part I: Scrimp Based on a High-Permeable Medium
,”
Polym. Compos.
,
19
, No.
6
,
807
817
.
You do not currently have access to this content.