JEC COMPOSITES MAGAZINE - Issue #105 - June 2016 - 27

Tab. 1: Parameters used for the reactive 1D filling
simulation

Material parameters

Value

Dimensions of
the cavity (cm3)

74 x 10 x 0.34

Tow geometry

Cylindrical

Tows 1: radius (mm)

1.5

Tows 2: radius (mm)

0.2

Intra-tow porosity

0.4

Channel porosity

1

Average porosity*

0.529

Channel permeability** (m²)

2 x 10-10

Tow radial permeability (m²)

1 x 10-13

Injection parameters

Value

Injection flow rate (m3.s-1)

1.44 x 10-6

Injection viscosity (Pa.s)

8.2 x 10-3

Injection and mould
temperature

140

Injection duration (s)

95

*Porosity used for the single-scale simulation
**Permeability used for the single-scale simulation
and the channels of the dual-scale simulation
Tab. 2: Parameters for the isothermal injection at
constant injection pressure

Material parameters

Value

Length of the cavity (cm)

20

Radius of the tows (mm)

0.812
0.64
10-10

Tow radial permeability (m²)

5 x 10-13

Injection parameters

Value

Injection Pressure (Pa)

10-5

Injection viscosity (Pa.s)

8.2 x 10-3

tions are often made of fibre tows that
are woven, stitched or braided together.
These materials are called dual-scale
porous materials as they present two
types of pores: macro-pores (channels)
between the tows (in the range of the
millimetre) and micro-pores inside the
tows (in the range of some micrometres).
They differ from single-scale porous

materials, which are only composed of
gaps within the same scale. Two major
phenomena (see figure 1) were observed
experimentally while injecting fluid in a
dual-scale textile:
- an unsaturated region is generated
behind the macroscopic flow front
(Region II) and may constitute a poor
mechanical region if it is located in the
part at the end of injection;
- resin storage occurs inside the tows,
stored resins curing may affect the temperature in the part (Region I).
These phenomena affect the process and
may lead to defects in the final part. For
these reasons, simulation tools dealing
both with the reactive and dual-scale
aspects of the injection process are required to optimize the injection strategy.
In dual-scale simulations, fine tracking of
the unsaturated area is very important,
because it makes it possible both to know
if micro-porosities remain in the part
and, most of all, to be familiar with the
filling kinetics of the tows that affect the
flow and the evolution of the different
parameters of interest (degree of cure,
temperature,...) in the part.
Based on this observation, ESI Group
launched a research work with Ecole
Centrale de Nantes (ECN) two years ago
with the purpose of proposing an innovative industrial computation technique for
dual-scale flow simulations that features
both CPU time efficiency and a fine
degree of precision in the unsaturated
area to treat reactive dual-scale problems. The final objective is to implement

these developments in PAM-RTM from
ESI's PAM-COMPOSITES commercial
simulation tool.

Innovative simulation approach
An innovative numerical strategy was developed to simulate the flow of a reactive
resin efficiently in a dual-scale porous
material. The novelty of the approach
is that it reduces the microscopic filling
problem to a sum of 1D tow transverse
fillings. The number and average length
of tows in each macroscopic element
is determined prior to the injection
simulation. Thus, the microstructure
associated to each element depends on
its geometry. The representative tows
are then discretized both in the longitudinal and transverse directions to track
unsaturated areas accurately in elements
smaller or larger than this unsaturated
area. This microscopic filling strategy
enables tow filling without reducing the
time step too much. These features make
the approach more efficient in terms of
calculation time and more flexible in
terms of meshing.
Unidirectional filling simulation of a
rectangular cavity containing a dual-scale
porosity material is presented below to
highlight the characteristics of the developed method.

Dual-scale reactive simulation
A single-scale reactive simulation using
the parameters of Table 1 showed that
the resin reaches the outlet after 95
seconds and prior to gelling. A dual-scale
simulation was conducted using the same
material and injection parameters. The

No105 June 2016 / jec

FEATURE SIMULATION

Average porosity
Channel isotopic
permeability (m²)

Fig. 1: Dual-scale flow in a dual-scale porous material

composites magazine 27
Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #105 - June 2016
