# Experimental and Numerical Study of Vacuum Resin Infusion for Thin-Walled Composite Parts
## 3 Model of the Resin Infusion: Problem Statement
Since temperature effects are neglected at this stage of the study, the viscosity of the resin is assumed to be unchanged and equal to 0.1 Pa\(\cdot\)s. The air pressure does not affect to the air viscosity in a wide pressure range, whereas its value increases according to quasi-linear law from \(1.8\times 10^{-5}\) Pa\(\cdot\)s up to \(3\times 10^{-5}\) Pa\(\cdot\)s in the temperature range (\(20^{\circ}\)-\(300^{\circ}\)) C [54]. In the present study, the air viscosity is accepted as \(2\times 10^{-5}\) Pa\(\cdot\)s.  
The boundary conditions of Equation (14) are present in the Table 3.  
The initial condition for the pressure specified everywhere in the preform's volume is \(p(t=0)=p_{vent}(t=0)\). The system of equations above closes the formulation of the problem of 3D modeling the dynamics of liquid resin in a porous preform. Beyond the scope of this problem, there remains the issue of localization of dry spots-closed air \"traps\" observed experimentally (see Figures 2 and 7). During the infusion process, several traps can form, but the formation of the first such trap indicates a violation of the manufactured structure's quality. Hence, if the modeling module wor  
Figure 11: The dependencies of the air permeability along and transverse CFRP fabric with hexagonal woven arrangement (calculated according to Equation (16)). \begin{table}
\begin{tabular}{c c} \hline \hline
**Boundary** & **Boundary Condition** \\ \hline Resin injection gate: & \(p_{gate}=p_{gate}(t)\) \\ \hline Vacuum pump vent: & \(p_{vent}=p_{vent}(t)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The boundary conditions of Equation (14). the optimization module, the resulting solution may be discarded without further consideration, and calculations can be continued at the changed process design variables. When the module is operating in standalone mode, the simulation can continue to identify all critical time instants and other formed dry spots. To perform such an analysis, a MATLAB algorithm for the processing of simulation results has been developed. In such cases, the simulation continues until the blocking of the vacuum vent by the resin flow. An indicator of this blockage is a condition:  
\[V_{r,out}=\min_{out}(V_{r})\cong 0.25 \tag{17}\]  
at the boundary \(\Gamma_{out}\) surrounding the vacuum port. In order to identify time instant when a first dry spot arises and its localization, the use of change in averaged pressure in the non-filled zones of the prepreg has been proposed. The essence of the method is as follows. Let pressure in the vacuum vent varies rather slowly according to the sinusoidal law so that the period of these oscillations is, e.g., \(\sim\)30 s:  
\[p_{vent}=p_{vac}^{0}+p_{vac}^{amp}\cdot\sin(2\pi t/T_{vent}) \tag{18}\]  
where the mean value and amplitude of the pressure variation are accepted as \(p_{vac}^{0}=2\times 10^{4}\) Pa and \(p_{vac}^{amp}\approx 0.5\times 10^{4}\) Pa, respectively. The pressure in a void area connected to the vacuum vent must be uniform in every point of this area due to the insignificant air viscosity. As the resin front advances, some areas may become blocked from the one connected to the vacuum line. In this area, however, as well as in those connected with vacuum, resin fraction is very small, i.e., \(V_{r}(\mathbf{r})\cong 0\). However, as a result of blocking, this region remains under the pressure at which it was blocked, not under a sinusoidally changing one. As an indicator of the moment of a void trap closure, we introduce the expression:  
\[\left<p_{\phi}\right>=\int\limits_{\Omega}d\Omega\cdot\left[1-H\left(V_{r}^{ low}\right)\right]p/\int\limits_{\Omega}d\Omega\cdot\left[1-H\left(V_{r}^{ low}\right)\right] \tag{19}\]  
where \(H\) is the Heaviside function, and \(V_{r}^{low}\) is the low resin filling, below which integration is performed. Formula (19) calculates at each simulation step the time-varying average value of pressure in all \"low filled\" areas, or, more precisely, in areas separated from the filled ones by the resin front.