Resin Transfer Molding of a Wind Turbine Blade

Resin Transfer Molding (RTM) is a manufacturing process for composite structures. The resin is injected under pressure into the mold cavity. Reinforcement materials like fiber structures can be placed into the empty mold before the resin is injected, which makes it easier to use any kind of reinforcement material and orientation. After the resin has been injected the curing takes place.

To avoid air bubbles that might be trapped within the resin several vents are placed at certain positions of the mold. Simulation can be used to optimize the vent positions.

In this example the RTM process of a wind turbine blade is investigated. The model geometry and setup was inspired by Ref. 1.

Model Definition

The blade consists of five parts of different composites, which have different anisotropic permeabilities. The colors in Figure 1 indicate the different permeabilities. The blade has a thickness of 1 cm. The geometry was constructed using COMSOL Multiphysics and the Design Module. However, in this example we just import the ready-made geometry file.

Figure 1: Geometry of the wind turbine blade. The colors indicate the different porous materials and different permeabilities.

Initially, the blade is filled with air. Resin is injected via the cylindrical inlet pipes at the top of the blade with a pressure of 800 kPa. The air can escape through the outlets which are defined at both short ends of the blade and at four additional vents along the blade rim which are marked by the outgoing arrows in Figure 1. All other boundaries are assumed as solid walls and the No Slip wall condition applies.

The model is set up using the combined multiphysics interface Two Phase Flow, Level Set, Brinkman Equations.

Model Equations

The flow through the porous media within the mold (due to the reinforcement material) is described by the Brinkman Equations for incompressible flow:

(1)

In these equations, where the inertial term has been neglected, μ (SI unit: kg/(m·s)) is the dynamic viscosity of the fluid, u (SI unit: m/s) is the velocity vector, ρ (SI unit: kg/m3) is the density of the fluid, p (SI unit: Pa) is the pressure, εp is the porosity, and κ (SI unit: m2) the permeability of the porous medium.

For the two-phase flow level-set method, an equation for the level-set function

, which describes the interface between the two phases, is solved:

(2)

is a smoothed step function which is zero within one phase and one within the other, ε denotes the porosity, γ determines the amount of reinitialization, and εls describes the thickness of the interface.

Beside defining the interface between the two phases, the level-set function is used in the multiphysics coupling feature node to smooth the density and viscosity jumps across the interface through the definitions

(3)

Table 1 lists the parameters that are used in the model.

Table 1: Material properties.
Material property	Value
Air Density: ρair	1 kg/m3
Dynamic Viscosity of Air: μair Resin Density: ρresin Dynamic Viscosity of Resin: μresin	10-5 Pa·s 1250 kg/m3 0.195 Pa·s
Porosity, Material 1: ε1 Porosity, Material 2: ε2 Porosity Material 3: ε3 Permeability, Material 1: κmat1,ii Permeability, Material 2: κmat2,ii Permeability, Material 3: κmat3,ii	0.45 0.5 0.5 2.9·10-10, 8·10-11, 2.9·10-10 m2 2.5·10-10, 7·10-11, 2.5·10-10 m2 1.7·10-10, 8·10-11, 1.7·10-10 m2

Results and Discussion

Figure 2: Velocity magnitude in logarithmic scale plotted on a cross section in the middle of the mold.

After 1 hour of simulated time, the mold is filled with resin. Figure 2 shows the velocity magnitude in the middle of the mold. The highest velocity values appear near the inlets and the small vents, where the flow channel narrows.

Figure 3 shows the pressure at the external surfaces of the blade. The highest pressure appears at the inlets.

Figure 3: Pressure plotted on the external surfaces of the wind turbine blade.

Figure 4: Volume fraction of resin after 15 minutes simulated time.

The resin front advances as shown in Figure 4 and Figure 5. In Figure 4, the resin front is shown after 15 minutes, in Figure 5, the resin interface is plotted after 5, 10, 20, and 30 minutes of simulated time. After 1 hour, the mold is completely filled with resin. The position of the vents could be optimized to avoid air bubbles within the molding process.

Figure 5: The Resin front advancing during the filling process. The figures show the resin interface position after 5, 10, 20, and 30 minutes.

Reference

1. Y. Jung. An Efficient Analysis of Resin Transfer Molding Process using Extended Finite Element Method. Other. Ecole Nationale Superieure des Mines de Saint- Etienne; Seoul National University, 2013. English. (NNT: 2013EMSE0701). (tel-00937556, https://tel.archives-ouvertes.fr/tel-00937556/)

Polymer_Flow_Module/Tutorials/rtm_wind_turbine_blade

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Geometry 1

Start creating this model by importing the model geometry.

In the window, under click .

In the window for , locate the section.

From the list, choose to make sure that the geometry, which was created using the COMSOL Multiphysics Design Module, can be imported properly.

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file rtm_wind_turbine_blade.mphbin.

Click

Global Definitions

The parameters needed for this model are stored in an external file. You can load them as follows:

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file rtm_wind_turbine_blade_parameters.txt.

Materials

Define the materials in the next step. Introduce them as empty material nodes first; as soon as the physics has been defined, the material node menu will show you which properties are needed for the simulation. You can then just fill in the values defined in the list.

Air

In the window, under right-click and choose .

In the window for , type Air in the text field.

Resin

Right-click and choose .

In the window for , type Resin in the text field.

Porous Material 1 (pmat1)

Right-click and choose .

Select Domains 1, 2, 12, and 13 only.

In the window for , locate the section.

In the εp text field, type epsilon_1.

Porous Material 2 (pmat2)

Right-click and choose .

Select Domains 7–11 only.

In the window for , locate the section.

In the εp text field, type epsilon_2.

Porous Material 3 (pmat3)

Right-click and choose .

Select Domains 3–6 only.

In the window for , locate the section.

In the εp text field, type epsilon_3.

Brinkman Equations (br)

In the window, under click .

In the window for , locate the section.

Find the subsection. From the list, choose . Using the new porous-slip wall treatment accounts for porous walls without resolving the full flow profile in the boundary layer. Instead, a stress condition is applied at the porous surfaces by utilizing an asymptotic solution.

Inlet 1

In the toolbar, click

and choose .

Select Boundaries 44, 60, and 72 only.

In the window for , locate the section.

From the list, choose .

Locate the section. In the p0 text field, type 800[kPa].

Locate the section. Click

In the dialog box, type Inlet in the text field.

Click .

Create selections as you will need the selected groups of boundaries again when defining the boundary settings for the interface.

Outlet 1

In the toolbar, click

and choose .

Select Boundaries 1, 4, 5, 8, 40, 51, 52, 56, 65, 66, and 84–91 only.

In the window for , locate the section.

Click

In the dialog box, type Outlet in the text field.

Click .

Level Set in Porous Media (ls)

Level Set Model 1

In the window, under click .

In the window for , locate the section.

In the γ text field, type 2e-4.

In the εls text field, type 2*d_i.

Initial Values, Fluid 2

In the window, under click .

Select Domains 9–11 only.

Inlet 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose ϕ .

Outlet 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Multiphysics

Two-Phase Flow, Level Set 1 (tpf1)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Materials

Now fill in the material properties.

Air (mat1)

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Density	rho	1	kg/m³	Basic
Dynamic viscosity	mu	1e-5	Pa·s	Basic

Resin (mat2)

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Density	rho	1250	kg/m³	Basic
Dynamic viscosity	mu	0.195	Pa·s	Basic

Porous Material 1 (pmat1)

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Permeability	{kappa11, kappa22, kappa33} ; kappaij = 0	{2.9e-10, 8e-11, 2.9e-10}	m²	Basic

Porous Material 2 (pmat2)

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Permeability	{kappa11, kappa22, kappa33} ; kappaij = 0	{2.5e-10, 7e-11, 2.5e-10}	m²	Basic

Porous Material 3 (pmat3)

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Permeability	{kappa11, kappa22, kappa33} ; kappaij = 0	{1.7e-10, 8e-11, 1.7e-10}	m²	Basic

Definitions

Create a few more selections that are useful for meshing the geometry.

In the window, expand the node.

Upside Boundaries

In the window, expand the node.

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select the check box.

Select Boundaries 2, 14, 27, 36, 43, 59, 71, and 81 only.

In the text field, type Upside Boundaries.

Vent Edges

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Edges 59, 64, 65, 69, 72, 88, 96, 101, 102, 106, 109, 121, 128, 129, 133, and 136 only.

In the text field, type Vent Edges.

Mesh 1

Now mesh the geometry. This example uses a swept mesh. For thin geometries a swept mesh offers a good mesh quality with a moderate number of mesh elements.

Free Triangular 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Size 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Click the button.

Locate the section.

Select the check box. In the associated text field, type d_i/4.

Select the check box. In the associated text field, type d_i/5.

Size 2

In the window, right-click and choose .

In the window for , locate the section.

Click the button.

Locate the section.

Select the check box. In the associated text field, type 1.5*d_i.

Click

Swept 1

In the toolbar, click

First, mesh the blade leaving out the cylindrical inlet ports.

In the window for , locate the section.

From the list, choose .

Select Domains 1–8, 12, and 13 only. You can use the and buttons to zoom into and out of the domain to select small boundaries.

Distribution 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 2.

Click

Now mesh the cylindrical inlet ports separately.

Swept 2

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Domains 9–11 only.

Distribution 1

Right-click and choose .

Study 1

Before solving the model, specify the output times and make sure that the time step is sufficiently small to catch the advancement of the resin front properly.

Step 2: Time Dependent

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the text field, type range(0,1,60).

Solution 1 (sol1)

In the toolbar, click

In the window, expand the node, then click .

In the window for , click to expand the section.

From the list, choose . This way the maximum time step is limited to the output interval of 1 minute.

In the toolbar, click

Definitions

To get Figure 2 you have to modify the default plot as described below. First, however, define another selection to facilitate plotting the velocity on the midsurface of the geometry.

Midsurface

In the toolbar, click