Multiphase Flow Coupling Behavior of Bubbles Based on Computational Fluid Dynamics during AFP Process: The Behavior Characteristics of Bubbles during AFP Process

To investigate the mechanism of the eﬀect of process parameters on bubble ﬂow behavior during automated ﬁber placement (AFP) and the relationship between the bubble and voids, mechanical properties of laminates, this paper analyzes the multiphase ﬂow coupling behavior of the bubble and ﬁber formation using computational ﬂuid dynamics (CFD) and ﬁnite element (FE) method under diﬀerent AFP process parameters. The eﬀects of AFP process parameters on bubble characteristics and ﬁber deformation are then discussed, respectively, including bubble displacement, maximum cross-sectional area, the lowest internal temperature of the bubble, bubble breakup, and maximum deformation of the ﬁber. Furthermore, the AFP and corresponding test experiments are performed to investigate the relationships between diﬀerent bubble characteristics and void content, mechanical properties, mainly interlaminar shear strength (ILSS) and ﬂexural strength (FS). The results show that the maximum cross-sectional area of bubbles is closely related to the AFP process parameters. The FS and ILSS are positively correlated with the maximum cross-sectional area. With the increase of bubble displacement and ﬁber maximum deformation, FS and ILSS are ﬁrst increased and then decreased.


Introduction
Fiber Reinforced Plastics/composites (FRPs) have been widely used for many years in the aerospace, naval, automotive, and civil applications due to their several advantages over traditional materials (e.g., metals), such as high stiffness and strength to weight ratio, more excellent fatigue resistance, better long-term durability, lower thermal expansion and superior corrosion resistance [1][2][3][4]. Such advantages make FRPs an ideal candidate for a wide range of applications involving extreme operational conditions [5][6][7][8]. e manufacturing method of FRP includes hand layup, molding, pultrusion, filament winding, automated tape laying, and automated fiber placement. Among them, automated fiber placement (AFP) appeared in the 1970s in the aerospace industry. It combines the advantages of filament winding and automated tape laying to overcome their limitations and exploit their benefits, which is one of the fastest-growing and most effective fully automated manufacturing technologies for composite materials in recent years [9][10][11][12]. An AFP machine usually consists of a placement head and another functional mechanical structure (a robotic arm or gantry structure). e placement head lays prepreg tows onto a mold to construct the layup. Depending on the shape of the mold surface, the AFP process can use multiple prepreg tows (8∼32 tows), or realize continuous variable angle placement. Additionally, it can cut/refeed the tow to adapt to the change of the manufacturing boundary, which can guarantee the processing requirements of complex structures [13][14][15]; see Figure 1.
Due to the complexity of the AFP manufacturing process, such as multiple process parameters, prepreg defects, and manufacturing errors, the laminates are not exempt from imperfections that include gaps and/or overlaps, twisted tows, fiber waviness, and voids. ey often appear in the final component, thereby affecting the mechanical performance. Among them, voids can significantly affect the mechanical properties of composites [16][17][18], which result from the small bubbles in the prepreg itself, the volatilization of the resin caused by the preheating process, low laying pressure, small air pockets, and so forth. Air bubbles in the process of AFP are an essential cause of voids formation, which are closely related to the AFP process parameters.
With regard to the characteristics of voids during the AFP process, Ranganathan et al. [19,20] proposed a novel model to establish an in situ AFP process of thermoplastic composites using a Newtonian fluid in a two-dimensional geometry, which can predict the final void content and the thickness of a composite part as a function of the laying speed and compaction pressure under nonisothermal conditions. Similarly, Tierney and Gillespie [21] developed some integrated models, such as the heat transfer model, void dynamics model, and multiscale void transport model, for predicting the heat transfer and void dynamics within the laminate. e results indicate that obvious gradients in final void content exist through the thickness and are closely related to processing parameters including the heating temperature, laying speed, and heater height. Simacek et al. [22] established a dynamic model of the voids of thermoplastic composites manufactured by the AFP technique. e model combines the internal pressure of the bubble, the response of the fiber matrix, the pressure of the compaction roller, and the pressure of resin to analyze the process of the resin diffusing from the resin-rich region to fill the bubble. Khan et al. [23] developed a simulation tool from the existing available model in literature [19][20][21]. e effects of compaction force, laying speed, and hot gas flow in the heating region on the void development were investigated through simulation. en, experiments were performed to manufacture composite laminates. Void distributions from simulations were compared with the experiments. e results show that the simulation method is feasible. Seanz-Castillo et al. [24] investigated the effect of process parameters on voids and the mechanical performance of CF/ PEEK composites. ree different out-of-autoclave technologies were used, including vacuum bag, hot-press, and thermoplastic automated fiber placement (TP-AFP) with in situ consolidation (ISC). e void content was obtained using density method, 2D microscopy, matrix acid digestion, and C-scan, respectively, thus summarizing the benefits and scope of various methods. e results find that ISC voids appear mainly in the upper laminates because the bottom layers can suffer more rolling times by compaction roller. is paper only considers the effect of temperature during the TP-AFP process while other process parameters are not considered.
In summary, a few kinds of literature have examined the voids of thermoset materials during the AFP process. However, the bubbles in the thermoset laminates during the AFP process were rarely studied. Due to the curing process, the bubbles during the AFP process are not final defects. But the literature of [25] indicated that a specific relationship exists between the bubbles before curing and the voids in the laminate after curing. Also, the mechanism of the effect of AFP process parameters on bubble flow behavior is not yet clear. So it is difficult to understand the mechanism of controlling defects in process optimization. To aid in such an understanding, this paper investigates the relationship between the bubble behaviors and the AFP process parameters, void content, and mechanical properties using computational fluid dynamics (CFD) and finite element (FE) method. e rest of this paper is organized as follows: in Section 2, the multiphase flow mesomodel is established using the CFD and FE method, including the control equations of CFD, fluid-solid coupling model, fluid-gas coupling model, and their analysis conditions. According to analysis results, the effect of AFP process parameters on bubble characteristics and fiber deformation are then discussed in Section 3. Lastly, the AFP and testing experiments are performed to reveal the relationship between void content, mechanical properties, and bubble characteristics.

Control Equations.
e molten resin is an incompressible fluid with a certain viscosity. e Navier-Stokes equations (N-S Equations) describe the motion characteristics of a viscous incompressible fluid based on momentum conservation. When the differential equation of motion, constitutive equation, state equation, and continuity equation are closed, the density is assumed to be constant, so the continuity equation is set as 0, as described in where div represents divergence. At this time, the simplified equation with three velocity components as variables is N-S Equations. It assumes that the density is constant, so it is suitable for incompressible fluids which conform to the generalized Newtonian viscosity assumption. Because the resin in prepreg could melt and flow under the action of AFP process parameters, the flow state of resin is incompressible. us, N-S Equations can reflect the basic motion law of actual fluids and are suitable for studying the flow characteristics of resins during the AFP process: where ρ is the density of the fluid; u, v, w are the velocity components of the fluid at time t; X, Y, Z are the components of external force; p is the pressure; μ is the dynamic viscosity; and ∇ is the Laplace operator. e Reynolds stress model (RSM) based on N-S Equation is directly embedded in ANSYS-CFD, which can obtain an accurate viscous model and turbulent state. Reynolds number is an important parameter in RSM. e calculation method is as follows: where v, ρ, and μ are the velocity, density, and viscosity coefficient of the fluid, respectively, and D is a characteristic length.
Reynolds number can be used to distinguish whether the fluid flow is laminar flow or turbulent flow and can also be used to determine the resistance of the object in the fluid flow. We can obtain the Reynolds number of resin under different process parameters by Figure 2 and Table 1. Other boundary conditions are shown in Table 2.

Fluid-Solid Coupling Model.
is subsection uses the computational fluid dynamics (CFD), combining ANSYS-CFD and statics modules to construct the mesomodel of prepreg during the AFP process for investigating the behavior of bubbles in preforms and deformation of fibers under different process parameters. is model consists of three phases with fluid-solid-gas, including resin, fibers, and bubble in the resin. e thickness of the model is set as 0.2 mm. e contact length between the rigid roller and the resin is considered as about 0.4 mm, which is in accordance with the prepregs for subsequent experiments. e carbon fibers are wrapped in resin, wherein the diameter of the carbon fiber is set to 0.03 mm. e established fluid-solid two-phase model is shown in Figure 2.

Fluid-Gas Coupling Model.
e fluid part is automatically meshed using the CFD mesh type. When studying the behavior of bubbles in resin, it contains two phases of resin and air, in which these two phases first need to be calculated separately. erefore, the Volume of Fluid (VOF) model in the multiphase flow model is selected, defining the number of phases as 2. Using this model, the phase interface between resin and air can be simulated to evaluate the movement and deformation of bubbles in resin under different process conditions. Related material properties are shown in Table 1.
In order to simplify the model, consider that the preheating temperature has a great influence on the viscosity. Moreover, the resin has a small change in density, specific heat, and thermal conductivity at a low-temperature gradient (changes within 10°C). us, the model only considers changes in resin viscosity with temperature. e air viscosity does not change much with temperature so that it can be ignored in the simulation. rough the experimental test of the prepreg manufacturers, the viscosity of the resin at 30°C (303 K), 40°C (313 K), and 50°C (323 K) is about 10000 MPa·s, 3000 MPa·s, and 1000 MPa·s, respectively.
Since the movement speed of the fluid is determined by both the laying pressure (compaction force) and the laying speed, in order to simplify the model, assuming that the pressure is in a static and constant state, then the movement speed of the fluid is completely determined by the laying speed. In this way, we set the linear speed of the pressure roller (laying speed) as the inlet speed of the fluid in contact with the pressure roller. e laying pressure can be set to constant inlet pressure. e outlet velocity is related to the inlet pressure and laying speed and is a variable. e singlefactor simulation parameters are shown in Table 2.
In order to distinguish between resin and bubbles in the prepreg, it is necessary to provide the air phase region of the fluid region, where a spherical shape with a spherical center coordinate of (0.1 mm, 0.1 mm, 0.075 mm) and a radius of 0.05 mm is divided. en, the phase region is set to air property. us, a fluid-gas coupling initial model is established, as shown in Figure 3(a), which shows the initial state and position of the bubble (the middle section of the 3D model). e air temperature is set at room temperature to investigate the effect of the process parameters on the

Effect of AFP Process Parameters on Bubble
Characteristics and Fiber Deformation e carbon fiber density is set to 1.78 g/cm 3 , Young's modulus is 125 GPa, and Poisson's ratio is 0.34. e principle is that the results calculated by the fluid-gas simulations are applied to the carbon fiber through the fluid-solid coupling interface. e effects of different process parameters on bubble motion characteristics and fiber deformation are explored below. e main characteristics examined include the displacement of the bubble motion (D bm ), the maximum cross-sectional area of the bubble (A max ), the internal lowest temperature of the bubble (T int ), and the maximum deformation of the fiber (D fmax ). Due to the large difference between the color of the bubbles and the resin, the size of the bubble is obtained by the grayscale recognition method using Image-pro Plus to obtain the change of the cross-sectional area of the bubble during the movement. e behavior characteristics of bubbles and the   gray-scale recognition method under different process parameters are shown in Figure 4. Bubble internal temperatures under different preheating temperatures are shown in Figure 5. Fiber deformations under different process parameters are shown in Figure 6. Figures 3-5 are based on the fluid-gas coupling model. Figure 6 is obtained by the fluidsolid coupling model.

Discussions.
e relationship between different process parameters and characteristic parameters is obtained through multiphase flow simulations, which can be listed in Table 3.
From Table 3, the bubble motion displacement in the resin is mainly related to the laying pressure and preheating temperature. e displacement increases with the increase of the laying pressure and preheating temperature. However, the laying speed has little effect on the displacement compared with other process parameters. Air bubbles are compressible fluids, so when the boundary conditions change, the bubble cross-sectional area will change. e results show that the higher the laying pressure has, the smaller the cross-sectional area of the bubble is. Interestingly, the laying speed is opposite to that, which has a positive correlation with the cross-sectional area of the bubble. Additionally, bubbles are easy to break up at higher laying speed and preheating temperature or longer displacement (more than 200 μm). But the bubbles seem to be breaking up at the laying speed of 20 mm/s and 30 mm/s. It is inferred that the slower speed may also result in the bubbles breaking up. Different laying pressures can also affect the internal temperature of the bubble except for the preheating temperature. It may be due to the reduced cross-sectional area of the bubbles and the faster heat conduction. For fiber deformation, except that the laying pressure has a significant effect on the maximum deformation of the fiber, other process parameters have no obvious effect on this parameter.

4.1.
Experiments. According to 7 groups of processing parameters, the laying experiments are carried out using an AFP machine. Considering the subsequent testing of void content and corresponding mechanical properties, it is necessary to perform curing experiments on 7 groups of AFP samples. During curing, the resin in the sample can undergo a cross-linking chemical reaction with the latent curing agent. Here, if air bubbles cannot be discharged from the resin, they will remain inside the sample to form void defects. It can be seen that the bubble content before curing can affect the void content. However, the degree of chemical reaction of the resin is related to the curing pressure and curing temperature, which can change the difference of the voids caused by the AFP process. us, 7 groups of samples are cured by an identical curing process using a vacuum bag and an autoclave to remove any variation at the voids due to the curing. e curing process parameters are the vacuum degree of 2 Pa, curing pressure of 0.5 MPa, curing temperature of 120°C, and curing time of 120 min. Afterwards, the void content is identified by the photomicrography method. Universal Testing Machine further tests interlaminar shear strength (ILSS) and flexural strength (FS) of the samples. e experimental setup is shown in Figure 7.

Bubbles and Voids.
In order to improve the accuracy of the void content, we select three test specimens and their 6 fields of view for each sample. us, each sample uses 18 fields of view to test the voids. So, their average value can be considered as the void content of a sample. According to the obtained void content under different AFP process parameters, the relationship between voids and bubble characteristic parameters is shown in Figure 8. e trends of void variation are fitted by a B-spline curve. From Figure 8, the void content decreases first and then increases as the bubble displacement increases, in which the critical value is about 70 μm (D bm ). It is found that too long or too short bubble displacement is beneficial to increase the void content. When the bubble is extremely moving, it has two functions. First, the bubbles have the phenomenon of expulsion [26], which accelerates the removal of the bubbles from the fluid. e second is that the bubbles will converge, leading to the convergence of microbubbles, which is conducive to the detection of microphotography. From this point, the expulsion effect is significant before the displacement is 70 μm. e longer the displacement is, the more obvious the expulsion is. Also, the convergence effect can increase significantly after 70 μm. Bubble convergence intensifies as displacement increases within this range. Similarly, the relationship between the maximum deformation of fibers and void content shows similar trends as that of the bubble displacement. It can be inferred that fiber deformation may also have a certain effect on the expulsion and convergence of bubbles. Interestingly, bubble cross-sectional area and void content present a negative correlation. is may be due to the fact that the larger cross-sectional area is helpful to bubble convergence and expulsion. But there is an inflection point at 0.85 mm 2 , which reflects that the crosssectional area between 0.78 mm 2 and 0.85 mm 2 has little effect on the void content. Subsequently, the void content decreases rapidly with the increase of cross-sectional area, which is due to the poor motion ability of bubbles with a cross-sectional area of 0.78-0.85 mm 2 , which is not conducive to bubble convergence and expulsion. Also, the decrease of the laying speed could determine the above relationship. Additionally, there is no obvious correlation between void content and bubble internal temperature. It can be seen that temperature has a lower effect on the void content.

Bubbles and Mechanical Properties.
is subsection investigates the relationship between bubble characteristic parameters and mechanical properties, including interlaminar shear strength (ILSS) and flexural strength (FS). Each sample selects three specimens for testing. e results are shown in Figure 9.      Advances in Materials Science and Engineering Void content generally has a negative relationship with mechanical properties, especially the mechanical properties dominated by interlayer properties. When the void content is between 1.7% and 2.3%, the ILSS decreases fastest. Void content also has an adverse effect on FS. When the void content is more than 3%, the FS is only about 75% of that without voids. is explains the trend of the curve in Figure 9.
ese trends are closely related to the different void content caused by bubble motion. us, in most of the curves, the mechanical properties and bubble characteristic parameters show inverse relationships compared with void content. For example, FS and ILSS are positively related to the maximum cross-sectional area of the bubble, while the void content is the opposite. A similar situation presents in the bubble displacement and maximum deformation of the fiber. e curves appear to increase first and then decrease. However, the relationship between temperature and mechanical properties is not obvious, which is in accordance with that of void content. It follows that the multiphase flow coupled simulations, especially the bubble cross-sectional area, can assist in controlling void defects and providing an effective way to improve the efficiency of the AFP process optimization.   Note: "+" represents that the bubble has broken up. "-" represents the normal bubble. "⟶+" represents that the bubble is breaking up.

Conclusions
Based on the presented analysis, the following conclusions can be drawn: (1) e bubble displacement increases with the increase of the laying pressure and preheating temperature. Usually, the cross-sectional area of the bubble reduces with the increase of the laying pressure. Interestingly, the laying speed is opposite to that, which has a positive correlation with the cross-sectional area of the bubble. (2) Bubbles are easy to break up at higher laying speed and preheating temperature or longer bubble displacement (more than 200 μm). e laying pressure has a positive effect on the internal lowest temperature of the bubble as well as the maximum deformation of the fiber. (3) Void content decreases first and then increases as the bubble displacement or maximum deformation of fibers increases. is can be explained by the expulsion and convergence functions of the bubbles during the AFP process. Additionally, the bubble cross-sectional area and void content present a negative correlation. (4) e mechanical properties of FS and ILSS are positively related to the maximum cross-sectional area of the bubble. FS and ILSS increase first and then decrease as bubble displacement and maximum deformation of the fiber increase, which are opposite to that of the void content. Moreover, there is no obvious correlation between FS, ILSS, and the internal temperature of the bubble. e understanding of the relationship between the processing parameters and the bubble characteristics can help to establish a foundation for process optimization and void control during the AFP process. e results presented in this paper can assist in developing a theoretical framework or a mathematical model relating AFP processing parameters to the low-defect of the manufactured FRPs in the future.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.