2022 Volume 63 Issue 7 Pages 993-1000
Sand erosion is a phenomenon in which the collision of solid particles erodes a material surface. The rate of sand erosion is higher in carbon fiber reinforced plastics (CFRP) than in metallic materials. Therefore, CFRP requires a light and protective coating material. Herein, to improve the erosion resistance of CFRP, five polyurethane coated CFRPs with different glass transition temperatures were investigated at elevated temperatures, and a prediction formula of the erosion rate at the elevated temperatures was established. Furthermore, computational fluid dynamics was used to predict the surface temperature and erosion rate of fan exit guide vane (FEGV) when polyurethane coating was applied, and the coating thickness for FEGV in the erosion environment was estimated based on these predictions.
This Paper was Originally Published in Japanese in J. Soc. Mater. Sci., Jpn. 70 (2021) 896–903. The caption of Fig. 10 is slightly modified.
Fig. 13 Comparison of erosion rate of CFRP and UP2 in FEGV.
During sand erosion, solid particles within an airflow collide with and damage the surface of a material. Research on sand erosion first began in Germany in the early 1930s to address the problem of dust collection.1) Since then, many studies have been conducted on predicting damage to a material from particle motion theoretically.2–5)
In recent years, the rise in crude oil prices and global warming have led industrial fields to make active efforts to reducing environmental loads and improving fuel efficiency. In particular, the development of international logistics has increased the movement of people and goods and thus the demand for aircraft.6) The aviation industry requires materials with excellent lightness, strength, and rigidity (i.e., specific strength and rigidity) for weight reduction. Carbon fiber reinforced plastics (CFRPs) are widely used in aircraft, and they have begun to be applied to turbofan engines. However, CFRP has a lower resistance to sand erosion than conventional metallic materials used for aircraft such as aluminum and titanium alloys.7) Turbofan engines can take in large amounts of sand and dust in the air during takeoff and landing. The fan exit guide vane (FEGV), which rectifies the flow of the bypass section, is constantly exposed to an erosion environment. In addition, the blades are heated by the adiabatic compression of the airflow, so the erosion characteristics may be affected by temperature. Therefore, using CFRP in a sand erosion environment such as a turbofan engine requires coating it with a material having excellent sand erosion resistance at high temperatures.
Many studies have been conducted on developing CFRP coatings to improve the sand erosion resistance. Some studies have considered using physical vapor deposition (PVD) and electroplating to coat CFRP with metal thin films.8,9) Metal films have excellent erosion resistance and are not easily affected by temperature, but they are heavy, which may offset the light weight of CFRP. This has led researchers to focus on lightweight resin coatings; in particular, a polyurethane-based coating with excellent erosion resistance has attracted attention.7,10,11) However, the effects of temperature on the erosion resistance and material properties of this coating have not yet been considered.
Uchiyama et al. combined sand erosion experiments on flat plates and computational fluid dynamics (CFD) to predict the amount of damage that sand erosion will cause to an FEGV.6,12) They reported that the experimental and predicted values showed good agreement. However, the effect of temperature on the damage distribution should be considered, especially for materials that are easily affected by the environmental temperature such as polymers. Damage to an engine due to sand erosion not only degrades its performance but can also cause a serious accident. However, tests using actual engines are expensive and energy-intensive. In addition, damage due to sand erosion is inevitable regardless of the material or countermeasures, so maintenance should be carried out at appropriate times. This requires predicting the expected damage in the design stage and setting the coating to an appropriate thickness according to the usage environment.
In this study, the sand erosion characteristics and the life prediction method of polyurethane-based coating materials under high-temperature environment were investigated. First, using five types of polyurethane-based materials with different glass transition temperatures, the CFRP of a flat plate was coated, and a high-temperature sand erosion test was performed on them. The effects of particle impact velocity, impact angle, and temperature on the erosion resistance of polyurethane-based coating materials were investigated. In addition, based on the experimental results, a modified formula that takes into account the effect of temperature in the damage prediction formula of Uchiyama et al. was examined. Furthermore, CFD analysis was performed on the FEGV to determine the temperature distribution at each position of the blade and the particle impact factors (impact velocity, impact angle and striking efficiency), and the results were combined with modified equations for predicting the amount of damage obtained from flat plate experiments. Based on this combination, the amount of damage when the polyurethane coating material was applied to FEGV was predicted. Based on these studies, the design formula that determines the coating film thickness when actually applying the coating was also examined.
Five types (UP1–UP5) of polyurethane or polyurea with different glass transition temperatures (Tg) were considered as coatings. Each coating was applied to a CFRP (T800/3900, [0/45/–45/0]3s) flat plate to fabricate a test piece. For comparison, a test piece of CFRP without any coating was also used. The test pieces had dimensions of 50 mm × 49.5 mm × 4.5 mm. Table 1 presents the type, density, thickness, and Tg of each test piece. The densities for UP1–UP5 are for the coating material, and the density for the CFRP test piece is for CFRP. Tg was measured by using a differential scanning calorimeter (NETZSCH, DSC200 F3).
A suction-type high-temperature sand erosion device was used for the test. Figure 1 shows a schematic diagram of the device. An ejector applied a negative pressure to the flow path, and solid particles supplied from an electromagnetic feeder were swept into the flow path together with air. The particles were then ejected from a nozzle to collide with the test piece in the test chamber. An air heater upstream of the ejector heated the air in the flow path. The test piece was fixed to the test piece holder, which could be tilted to change the impact angle (α) of the solid particles. An aluminum fiberboard with high heat insulation was used as the walls of the test chamber. A heat exchanger was installed behind the test chamber to cool the exhausted high-temperature air, and the particles were then collected by a dust collector.
Schematic diagram of sand erosion test apparatus.
Amorphous alumina particles (Al2O3, Showa Denko K.K., WA-70) were used to represent the solid particles and were not sieved. The particle size distribution was measured by using a laser diffraction/scattering-type particle size distribution measurement instrument (Seishin Enterprise Co., Ltd., LMS-2000e). The average particle size was 290 µm, and the particle density was 3980 kg/m3. The nozzle had an inner diameter of 3 mm, and the distance between the nozzle tip and test piece surface was fixed to 10 mm. The amount of particles supplied was adjusted by the feeder to 1–3 g/min.
The particle impact velocity (Vp) of the solid particles ejected from the nozzle was adjusted by the airflow rate and was measured by using a high-speed video camera (Photron Limited, FASTCAM SA5). The velocities of 10 particles were measured at each airflow rate, and the average value was taken as Vp.
In this study, Vp was set to 30, 40, or 50 m/s. Six particle impact angles (α) were considered: 10°, 15°, 30°, 45°, 60° and 80°. In addition, 90° represented a vertical impact, and an additional 20° test was conducted for UP4. The particle impact angle with respect to CFRP was set perpendicular to the fiber orientation of CFRP at 0°.
The air heater adjusted the airflow temperature (T) to 23°C (i.e., room temperature), 45°C, 60°C, and 90°C. Each test piece was sufficiently preheated before impacted by particles. A thermocouple was installed on the surface of each test piece to ensure that the surface temperature of the test piece matched the airflow temperature.
2.3 Evaluation method of sand erosion resistanceThe erosion rate Rv (m3/kg) is defined as the damaged volume per unit mass of an impacting particle, and it was used to evaluate the sand erosion resistance of the test pieces.6,7,12) After a certain amount of solid particles was collided with the test piece, the test piece was taken out, and the particles adhering to the test piece were removed by air blowing. The volume of the damaged surface was measured by using a three-dimensional shape measurement machine (Keyence Corporation, VR-3200). This series of operations was repeated at least four times to obtain a curve showing the relationship between the damaged volume and amount of impact particles. The erosion rate was calculated from the slope of the straight line when the curve reached a steady state. The number of test pieces for each test condition was one.
Figure 2 shows the relationship between the erosion rate Rv and particle impact velocity Vp of UP2 and UP5 at test temperatures of 23°C and 60°C as a log–log graph. The following power law generally holds between Rv and Vp:1)
| \begin{equation} R_{v} = kV_{p}^{n} \end{equation} | (1) |
Effect of impact velocity on erosion rate (UP2 and UP5).
The experimental results showed that this power law held true for all materials in the test. The exponent n of each material was not affected by the temperature. Table 2 presents the proportional coefficient k and exponent n of Vp for each material.
Figure 3 shows the effect of the particle impact angle α on the erosion rate Rv at different temperatures T for UP2, UP4, and CFRP. The error bars show the standard deviation of the damaged volume in repeated impact experiments for each test piece. UP2 showed a maximum damage angle α0 = 15° regardless of T, which also held true for UP1, UP3, and UP5. In contrast, UP4 showed α0 = 30° at T = 23°C, but increasing T to 90°C decreased α0 = to 15°. CFRP alone showed α0 = 60°. In general, cutting is the dominant damage mechanism for the erosion of ductile materials, which would decrease α0. In contrast, brittle materials show high α0 because the dominant damage mechanisms are crack growth and plastic deformation.13,14) In this study, ductile damage was predominant for the coatings because they had a low α0, and brittle damage was predominant for CFRP because it had a high α0.
Effect of impact angles and temperature on erosion rate ((a) UP2, (b) UP4 and (c) CFRP).
Figure 4 shows the effect of temperature T on the erosion rate Rv at a particle impact angle α = 15° for each coating material. For UP2–UP5, Rv decreased with increasing T, while the opposite trend was observed for UP1. For CFRP, Rv was almost constant regardless of T. Figure 5 shows the relationship between Rv and T for UP2 as a log–log graph. This relationship can be defined by the following power law:
| \begin{equation} R_{v} \propto T^{K'} \end{equation} | (2) |
Effect of temperature on erosion rate at each specimen (Vp = 50 m/s, α = 15°).
Effect of temperature on erosion rate (UP2).
The exponent K′ of temperature was found to depend on α. This shows that the dependence of Rv on T differs according to α. Figure 6 shows that the relationship between α and K′ was linear for UP2. Therefore, K′ can be expressed in terms of α as follows:
| \begin{equation} K' = A\alpha + B \end{equation} | (3) |
Effect of temperature on K′ (UP2).
Table 3 presents the constants A and B for each coating material. Because the absolute value of K′ increased with α, the effect of T on Rv increased with increasing α.
Figure 7 shows the relationship between Rv and the glass transition temperature Tg of each coating at 23°C and 60°C. The broken line represents T. A nearly linear relationship can be observed between Tg and Rv. When T > Tg (i.e., the coating was in a rubbery state), the coating showed high sand erosion resistance. In addition, Tg decreased as T increased for all test pieces, excluding UP1. This may be because the ratio of the rubber phase to the phase of the coating material increased, which increased the elastic deformability. Thus, selecting a coating material with an appropriate Tg for the usage environment is important.
Effect of glass transition temperature on erosion rate (Vp = 50 m/s, (a) α = 15°, T = 23°C and (b) α = 15°, T = 60°C).
Uchiyama et al. simplified the Neilson–Gilchrist equation5) for the damage caused by sand erosion to define the erosion rate Rv as follows:6,12)
| \begin{equation} R_{v1} = K_{1}V_{p}^{n} \cos^{2}\alpha \sin m\alpha + K_{2}V_{p}^{n} \sin^{2}\alpha \quad (\alpha \leq \alpha_{0}) \end{equation} | (4-1) |
| \begin{equation} R_{v2} = K_{1}V_{p}^{n} \cos^{2}\alpha + K_{2}V_{p}^{n} \sin^{2}\alpha \quad (\alpha \geq \alpha_{0}) \end{equation} | (4-2) |
Here, K1, K2 and m are material constants. Equation (4) was then modified to consider the temperature T as follows. As noted above, eq. (2) was found to hold for Rv and T in this study. Therefore, it is assumed that the erosion rate $R'_{v}$ at a certain temperature T can be expressed by the ratio from the reference temperature T0, and that the following equation holds using K′:
| \begin{equation} R'_{v1} = \left(\frac{T}{T_{0}}\right)^{K'}K_{1}V_{p}^{n} \cos^{2}\alpha \sin m\alpha + K_{2} V_{p}^{n} \sin^{2} \alpha \quad (\alpha \leq \alpha_{0}) \end{equation} | (5-1) |
| \begin{equation} R'_{v2} = \left(\frac{T}{T_{0}}\right)^{K'}K_{1}V_{p}^{n} \cos^{2}\alpha + K_{2}V_{p}^{n} \sin^{2} \alpha \quad (\alpha \geq \alpha_{0}) \end{equation} | (5-2) |
In this study, T0 was set to 23°C. Table 4 presents K1, K2, m and the maximum damage angle α0 of each coating material. K1 and K2 were obtained by fitting the parameters to experimental values. The calculation results for eq. (5) are plotted as a curve in Fig. 3. Equation (5) showed good agreement with the experimental values at low α and generally agreed at high α. Figure 8 shows the damage curve of each coating material calculated by using eq. (5) at T = 90°C. UP2 demonstrated the best erosion resistance at all T and α. For example, coating CFRP with UP2 decreased Rv by 89.5% at α = 15° and 98.8% at α = 60° when T = 90°C, compared with CFRP alone. Thus, UP2 showed extremely high sand erosion resistance.
Comparison of erosion rate of coating material.
Based on these, UP2 is considered to be the best sand erosion resistance the coating material. This may be because UP2 is a polyurea-based coating material. However, the reason why polyurea-based coating materials have excellent sand erosion resistance will continue to be investigated in the future.
The damaged surface of each coating material after the test was observed by using a scanning electron microscope (Hitachi High-Tech Corporation, SU-8020). At α = 15°, many cutting marks and intruded particles were observed, which indicates that cutting was the dominant damage mechanism. At α = 60°, crack growth, ripple-like plastic deformation marks, and excavated damage marks were observed. This indicates that cracks developed because of the repeated impacts of particles, and the detachment and the plastic deformation of the material surface were the dominant damage mechanisms. The damaged surfaces at 23°C and 60°C showed that the size of the damage scars decreased with increasing T. This may be also because the coating material transformed into a rubbery state owing to the increase in T. This increased the energy absorption capacity, which decreased Rv.
The damage prediction method for three-dimensional blade shapes of Uchiyama et al.12) was modified to consider the effect of temperature and was applied to the FEGV. First, thermo-fluid analysis software (Software Cradle Co., Ltd., SCRYU/Tetra) was used with an unstructured grid to perform fluid analysis on the airflow around the blades of the FEGV. After the airflow was fully developed, and it had reached a steady state, the temperature distribution on the blade surfaces was calculated. Next, solid particles were generated upstream of the blade, and particle behavior analysis was performed to determine the effect of influencing factors such as the impact velocity, impact angle and striking efficiency at each position on the blade surface. The temperature and influencing factors obtained from the numerical analysis were substituted into eq. (5) to predict the erosion rate at each position on the blade surface.
4.2 Numerical analysis conditionsFigure 9 shows the numerical analysis model used to simulate the engine bypass and FEGV. The number of pitches was set to five, and periodic boundary conditions were applied to the model. A three-dimensional compressible turbulent field was used, and steady-state analysis was performed by using the Navier–Stokes equations, equation of continuity, and energy equation. The finite volume method was used for discretization, and the Spalart–Allmaras model was used for the turbulence model. For the inflow surface, the total pressure, total temperature, and inflow angle were defined in the span direction in a cylindrical coordinate system. For the outflow surface, the static pressure was defined. A non-slip boundary was defined for the FEGV and wall surfaces on the hub and chip sides to provide heat insulation.
Numerical model and analysis area.
Unsteady analysis using the Lagrange method was applied to analyzing the particle behavior. Spherical alumina particles were simulated with an average particle size of 290 µm and density of 3980 kg/m3. Particles were generated on the inflow surface at intervals of 500 µm, and the initial velocity was the same as the airflow velocity. The behavior of the particles did not affect the airflow, and only the first impact of the particles was examined. The analysis results were used to obtain the impact velocity Vp, impact angle α and striking efficiency η at each position on the blade surface based on the approach of Uchiyama et al.12) η represents the impact frequency of particles and can be calculated as follows:
| \begin{equation} \eta = \frac{S_{1}}{S_{2}} \end{equation} | (6) |
As shown in Fig. 10, S1 is the area formed by three adjacent particles at the particle generation position, and S2 is the area formed by the three particles forming S1 at the particle impact position.
Schematic diagram of striking efficiency η.
Figure 11 shows the analysis results for the temperature distribution on the FEGV surface. The temperature was high on the fan case side and leading edge of the blade. Figure 12 shows the distributions of the impact velocity $V_{p}/\overline{U_{0}}$, impact angle α, and striking efficiency η on the pressure side of the FEGV. The black region indicates where the particles did not collide, and $V_{p}/\overline{U_{0}}$ is the particle velocity Vp divided by the average airflow velocity at the inflow surface $\overline{U_{0}}$. In this study, $\overline{U_{0}}$ was assumed to be 160 m/s, which is about half the velocity of sound in a standard atmosphere. $V_{p}/\overline{U_{0}}$ was high on the hub side of the blade and α was high at the leading and trailing edges of the blade. A larger η indicated a higher particle impact frequency per unit area, so the particle impact frequency was higher on the trailing edge of the hub side.
Surface temperature in FEGV.
Impact velocity, impact angle and striking efficiency in FEGV ((a) Impact velocity, (b) Impact angle and (c) Striking efficiency).
The temperature, impact velocity and angle obtained from the numerical analysis can be substituted into eq. (5) to obtain the erosion rate $R'_{v}$ at a given position on the blade surface. In addition, because the striking efficiency η differs depending on the position on the blade surface, η can be used to calculate the erosion rate $R''_{v}$ at the given position on the blade surface:12)
| \begin{equation} R''_{v} = \eta R'_{v} \end{equation} | (7) |
The test results for low impact velocities (30–50 m/s) were extrapolated to high impact velocities to predict the erosion rate. This is because a sand erosion test method for high impact velocities of 150 m/s or more has not yet been established.
Figure 13 shows the distribution of $R''_{v}$ on the pressure side of the blade surface when the FEGV was made of CFRP alone and when it was made of CFRP coated with UP2. The polyurethane coating material was found to significantly reduce $R''_{v}$ and thus improve the sand erosion resistance. $R''_{v}$ was also high on the trailing edge of the hub side and showed the same distribution as η. Thus, the striking efficiency was concluded to have a significant effect on erosion rate.
Comparison of erosion rate of CFRP and UP2 in FEGV.
Practical application of a coating in an erosion environment requires determining an appropriate thickness according to the expected amount of damage. In this study, a design formula was examined to determine the coating thickness under the assumption that UP2 was used as a coating for an FEGV that was mounted on an aircraft.
The particle mass M (kg) that collides with a small damaged area S (m2) of the blade at a unit time t (s) can be expressed by the following equation using the particle concentration Cv (kg/m3) in the airflow upstream of the blade, the flow velocity V (m/s), and the striking efficiency η:
| \begin{equation} M = \eta SC_{v}Vt \end{equation} | (8) |
If the impact angle is constant within S, the erosion rate $R'_{v}$ can be expressed using S and the average depth Δh (m) of S:
| \begin{equation} R'_{v} = \frac{S\Delta h}{M} \end{equation} | (9) |
From eq. (8) and eq. (9), $R'_{v}$ can be expressed by the following equation:
| \begin{equation} R'_{v} = \frac{S\Delta h}{\eta SC_{v}Vt} = \frac{\Delta h}{\eta C_{v}Vt} \end{equation} | (10) |
Therefore, the damage depth per unit time Δh/t (m/s) caused by a particle impact can be expressed as follows:
| \begin{equation} \frac{\Delta h}{t} = \eta R'_{v}C_{v}V = R''_{v}C_{v}V \end{equation} | (11) |
The standard JIS W 4601 (“General specification of turbojet engines and turbofan engines for aircraft”)15) stipulates acceleration tests for the sand erosion of aircraft engines. The conditions covered by this standard were used to set Cv = 53 mg/m3, t = 10 h and V = 1000 km/h. When UP2 was the coating material, $R''_{v}$ was highest on the trailing edge of the hub side at about 5.0 × 10−7 m3/kg, as shown in Fig. 13(b). Therefore, this position required the thickest coating, and eq. (11) was used to calculate a minimum thickness Δh of about 0.27 mm.
The results of this study led to the following conclusions:
This study was greatly cooperated by Kansai Paint Co., Ltd. In addition, the sand erosion test and numerical analysis were conducted at the Composite Materials Laboratory, Department of Mechanical Engineering, Faculty of Science and Engineering, Hosei University, with the cooperation of students. We express our gratitude to them here.
