# Study of Solid Particle Erosion on Helicopter Rotor Blades Surfaces
## 2 Erosion Equations and CFD Setup
### CFD Setup  
Nowadays, blades are constructed mostly from composite structures; the outer layer is wrapped with alloy, and the inner layer is made from a composite. Ti-4 Al-1.5 Mn, Mg-Li9-A3-Zn3, and Al7075-T6 are commonly used aviation materials, and are suitable for simulation experiments with different physical properties [38; 39; 40], the density, hardness and compositional elements of these three materials are listed in Table 1. Among the prices of the three materials, magnesium alloys are the most expensive, while aluminum alloys are the least expensive. Generally, magnesium alloys are used for weight reduction because of their light weight; titanium alloys are used under high-strength conditions; aluminum alloys are mainly used to reduce costs as they are cheap and easy to manufacture. For this reason, these materials in the helicopter blade models were used in this study. The cross-sectional profile of the helicopter rotor blade, and the geometric details, are shown in Figure 1 for the classic airfoil NACA0012. Here, the authors emphasize the blade tip, as this area of the blade experiences the highest linear velocity and can easily become damaged [41]. The particle type is set to silica crystal and its density is 2200 kg/m\({}^{3}\). The Mohs hardness is 7. The flow rate of the particles was set to 0.97 kg/s. Particles with a regular 100-\(\upmu\)m diameter are uniformly ejected from the inlet surface (size: 200 \(\times\) 200 mm\({}^{2}\)) at different impact speeds (70, 150, or 220 m/s) and angles of attack (6\({}^{\circ}\), 3\({}^{\circ}\), or 0\({}^{\circ}\)). The jet velocity at the particle inlet surface was set to the impact velocity. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Ti** & **Al** & **Mn** & **O** & **Others** & **Density** & **Hardness** \\  & & & & & & **(kg/m\({}^{3}\))** & **(Vickers)** \\ \hline Ti-4 Al-1.5 Mn & margin & 3.5–5.0 & 0.8–2.0 & 0.15 & 0.55 & 4500 & 330 \\  & Mg & Li & Al & Zn & others & & \\ Mg-Li9-A3-Zn3 & margin & 8.5–9.5 & 2.5–3.5 & 2.5–3.5 & 0.5 & 1510 & 158 \\ Al & Zn & Mg & Cu & others & & \\ Al7075-T6 & margin & 5.1–6.1 & 2.1–2.9 & 1.2–2.0 & 1.5 & 2800 & 89 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Elemental composition (%) and characteristics of three materials. Figure 1: Geometric details of the helicopter rotor blade. The boundary condition of the rotor blade is defined as the steady state. The simulation materials and parameters are shown in Table 2.  
Figure 2a,b show the boundary conditions and mesh structure, respectively. The surface near the rotor blade was processed with mesh refinement, as shown in Figure 2b. In addition, the mesh independence of the erosion shield was studied by increasing the number of elements. There are 2,154,080 elements in the mesh structure in Figure 2b. The flow plant domain in Figure 2b passes the fluent grid quality test [42]. Table 3 is a grid independence test by increasing the number of elements. The average erosion rate and \(|\Delta E_{Avg. }|\) are the criteria for detecting grid independence. The value of the average erosion rate is the result of Ti-4 Al-1.5 Mn being eroded by solid particles of 220 m/s, and \(|\Delta\)E\({}_{Avg. }|\) is the average erosion rate deviation. Through these two sets of values, the number of elements selected for this simulation is reasonable. After a preliminary blade erosion simulation, in this study, due to the fluent boundary condition setting, only the front end of the blade section was affected by the impact of the particles. As shown in Figure 3, the front end of the blade section is exposed to significant pressure. Therefore, when a bionic coating is added to the blade later, the bionic coating is applied on the front end of the blade section. First, the erosion simulation was carried out on blades of the three materials under general sandstone conditions. The material with the best erosion resistance was determined after processing the simulation dates at three particle speeds and three impact angles.