Numerical Investigations of Film Cooling and Particle Impact on the Blade Leading Edge

: As a vital power propulsion device, gas turbines have been widely applied in aircraft. However, fly ash is easily ingested by turbine engines, causing blade abrasion or even film hole blockage. In this study, a three-dimensional turbine cascade model is conducted to analyze particle trajectories at the blade leading edge, under a film-cooled protection. A deposition mechanism, based on the particle sticking model and the particle detachment model, was numerically investigated in this research. Additionally, the invasion efficiency of the AGTB-B1 turbine blade cascade was investigated for the first time. The results indicate that the majority of the impact region is located at the leading edge and on the pressure side. In addition, small particles (1 m and 5 m) hardly impact the blade’s surface, and most of the impacted particles are captured by the blade. With particle size increasing, the impact efficiency increases rapidly, and this value exceeds 400% when the particle size is 50 m. Invasion efficiencies of small particles (1 m and 5 m) are almost zero, and the invasion efficiency approaches 12% when the particle size is 50 m.


Introduction
The operating temperatures of turbine engines have exceeded 2000 K, which is far beyond the temperature limits of metal materials [1]. Many thermal protective measures have been adopted to protect hot components, such as thermal barrier coating technology [2], transpiration cooling technology [3], regenerative cooling technology [4] and film cooling technology [5]. Film cooling technology is the most optimum cooling method, for its simple structure and high reliability. The film cooling performance is significantly influenced by many factors, such as blowing ratio, injection angle and film hole configuration. To extend the service life of turbine engines, improving film cooling performance has become a hot topic of active research.
In recent years, the concentration of airborne particles has increased gradually because of air pollution and environmental degradation. The expanding airline routes and increasing flight time raise the risk of particle deposition on turboshaft engines [6]. Ingested fine particles affect turbine components in many ways. Bons [7] indicated that particle deposition increased surface roughness and decreased aerodynamic performance. Wang et al. [8] conducted a particle deposition experiment to investigate the effects of surface roughness on particle adhesion. They concluded that the effects of blade roughness on the distribution of deposited particles could be ignored. Alqallaf et al. [9] reviewed the particle erosion behavior and protective coatings for gas turbine blades. They concluded that the solid particles led to erosion and wear in turbine blades. Wammack et al. [10] found that long-term impacts led to spallation of the thermal barrier coating. Furthermore, the ingested particles could deposit on the blade surface, resulting in cooling performance deterioration [11]. Film hole blockage caused by particle accumulation decreased the film cooling effectiveness, and even led to turbine engine failure [12]. Due to engine surge as a result of the rapid accumulation of fly ash on nozzle guide vanes, Bojdo and Filippone [13] investigated the sensitivity of accumulation efficiency to dust properties. Hence, it is indispensable to investigate particle trajectories on turbine blades.
Particle deposition on turbine blades mainly depends on the force exerted on the particles. Hossain et al. [14] tracked particle paths of different sizes, and found that small particles were more likely to follow the mainstream. Dahneke [15] designed a spherical particle ejection device to investigate particle-wall interaction, and he found that all particles could adhere to the surface by adjusting their initial velocity. Brach and Dunn [16] proposed the capture velocity method to determine particle behaviors. Based on the capture velocity method, El-Batsh and Haselbacher [17] proposed a critical velocity model to calculate the capture efficiency of particles. After the particles were captured by the blade surface, the force exerted on them needed to be further analyzed. If aerodynamic force was sufficient to overcome sticking force, particles would be removed from the surface and continue to flow with the mainstream. El-Batsh and Haselbacher [17] proposed a particle detachment model to determine whether the deposited particles could continue their adhesion.
Particle sticking and particle detachment models have been applied in particle transport research, and have shown good agreement with experimental results [18]. Prenter et al. [19] numerically investigated particle behaviors of different sizes and found that large particles were more likely to impact on the suction surface. Xu et al. [20] investigated the effects of surface roughness on the particle-wall interaction, and indicated that the deposition rate increased with surface roughness. Pan et al. [21] found that the deposition region expanded with the increase in the inlet Reynolds number. Zhang et al. [22] found that capture efficiency showed a dramatic increase when the mainstream temperature exceeded the threshold. Suman et al. [23] analyzed historical experimental data on particle adhesion, and they proposed a generalization of particle impact behavior in gas turbines via non-dimensional grouping. Bowen et al. [24] compared the impact locations on the blade surface between rotating and stationary conditions. They found that traditional cascades could not be used to predict deposition on rotor blades. Wasistho [25] proposed a dual Eulerian-Lagrangian particle approach to better predict particle behaviors. Liu et al. [26] used molten wax to simulate fly ash particles, and experimentally investigated the particle deposition on a plate with film cooling holes. They found that the trenches could alter the deposition mass and distribution on the pressure surface. Suman et al. [27] performed an experimental study to investigate the adhesion of particles on a gas turbine. They found that the adhesion ability of particles depended on the roughness of the substrate. Mu et al. [28] numerically investigated the fly ash behaviors on a heat exchanger surface, and they used a dynamic mesh method to predict the morphology evolution. They found that the elliptical tube was beneficial to restraining the deposit formation. Zheng et al. [29] found that increasing the surface temperature of the ash deposition significantly increased the mass of the ash deposition. Han et al. [30] found that vortex generators reduced thermal resistance caused by particle deposition in a heat exchanger channel.
The blade leading edge is a critical region to perform film cooling, and it is also especially vulnerable to particle deposition in the actual condition. However, the combination of leading edge film cooling and particle transportation was seldom investigated in the open literature. Therefore, this study investigated particle trajectories on the blade leading edge under film cooling conditions. A deposition mechanism based on the sticking model and detachment model was incorporated to analyze the particle-wall interaction. Therefore, impact efficiency (ηim), capture efficiency (ηca) and invasion efficiency (ηin) are adopted to evaluate particle behaviors. The effects of blowing ratio, inlet flow angle and particle diameter were taken into consideration.

Computational Model
Based on the periodic distribution of film cooling holes and turbine cascade [31], the computational model with periodic boundary conditions is shown in Figure 1. The hightemperature gas is injected from the mainstream inlet at an incidence angle (β1). More details of blade geometry and film hole configuration are given in Table 1, where there is one film hole on the suction side (SS), and another film hole on the pressure side (PS).
The blowing ratio M is defined to evaluate the coolant strength: Detailed boundary conditions and particle properties are listed in Table 2, where the pressure and temperature of both mainstream inlet and outlet are set as constants. Four blowing ratios (0.68, 1.03, 1.32, 1.53) and three mainstream inlet angles (123°, 133°, 143°) are analyzed in this study. The wall boundary conditions are no-slip and adiabatic. The mainstream inlet turbulent intensity and turbulent viscosity ratios are given as 5% and 100. For the coolant inlet, both turbulent intensity and turbulent viscosity ratios have lower values of 1% and 10. The effects of particle size on particle-wall interactions are also taken into consideration.   The structured multi-block grid mesh of the film-cooled blade is shown in Figure 2a. The first row's height of cell nodes near the blade surface is placed at y + ≈ 1, which fulfills the enhanced wall treatment requirements of the turbulence model. The refined near-wall mesh is favorable to capture particle-wall interactions accurately. The film cooling effectiveness (η) is defined as follows: where T represents temperature. The subscripts aw, 1 and c represent the adiabatic surface, the mainstream inlet and the secondary flow inlet. The centerline film cooling effectiveness (η) for three numbers of meshes is almost overlapped, as given in Figure 2b. To shorten the computational time, 0.3 million cells are adopted for subsequent simulations.

Gas Phase
The commercial software package ANSYS FLUENT 16.2 (ANSYS, Inc., Canonsburg, PA, USA)is applied in this study. The realizable k-ε turbulence model with enhanced wall treatment is used to solve the steady Navier-Stokes equations of the continuous phase. The gas was modeled as compressible air using the ideal gas law in this study. The equation of state is defined as follows: where Mw is the molecular weight of the air. The fluid viscosity is 1.79 × 10 −5 kg/m × s, and the molecular weight of the air is 29 g/mol.
The governing equations are expressed as follows: Mass conservation equation: Momentum conservation equation: Energy conservation equation: Turbulent kinetic energy equation: The rate of turbulent dissipation equation: where the model constants are default as: Other variables in these equations are defined in the nomenclature. The SIMPLEC (Semi-Implicit Method for Pressure Linked Equations Consistent) algorithm [32] is used to solve the pressure-velocity coupling. The second-order upwind scheme computes spatial discretizations of energy, momentum and turbulent equations. For the steady-state calculation of this paper, a residual of 10 −6 is considered to get converged results for all variables except the energy equation (with a residual of 10 −7 ) and continuity equation (with a residual of 10 −5 ).

Particle Phase
The discrete phase model (DPM), coupled with the random walk model (RWM), is applied to simulate particle trajectories on the blade leading edge. Moreover, the momentum equation of an individual particle is defined as follows: where FD is the drag force, and FS is Saffman lift force. Critical velocity and particle detachment models are programmed in the user-defined functions (UDFs) to estimate the interaction between the blade surface and inertial particles. The critical capture velocity is expressed as: where Vcr is the critical velocity calculated by particle diameter dp and composite Young's modulus E. The subscripts s and p represent blade surface and particle. If the normal velocity of an inertial particle is below the critical velocity, it will adhere to the blade surface. Then, the particle detachment model is performed.
The adhesion particles will detach from the blade surface if ufri (wall friction velocity) is above utc (critical wall shear velocity).

Validation of the Simulated Method
Three parameters are defined to evaluate particle-wall interactions: where ηca, ηim and ηin are capture efficiency, impact efficiency and invasion efficiency. Mto represents the total mass of the injected particles. Min is the total mass of particles ingested by film cooling holes. A two-dimensional computational model was established in our previous study to validate the deposition model [33]. As shown in Figure 3a, the particle deposition model predicts surface-particle interactions on the turbine blade leading edge well. Variations of film cooling effectiveness at the mid-span plane of the blade leading edge are shown in Figure 3b. The numerical results agree with experimental data [34], so the numerical method of this study is fully reliable.

Investigation of Film Cooling Performance
The temperature contours on the middle sections of the blade leading edge at four blowing ratios and three inlet flow angles are shown in Figure 4. The coolant air is attached to the blade surface after being injected from cooling holes at low blowing ratios (M = 0.68, 1.03). With the blowing ratio increasing, coolant air is detached gradually from the blade surface, especially on the SS. The jet liftoff is suppressed when increasing the mainstream incidence angle, which moves the stagnation point from the PS to SS. Therefore, increasing the incidence angle results in a better coolant coverage downstream the SS. For the case with β1 = 123°, the cooling film on the SS has detached from the wall. With the increase in the blowing ratio, the cooling film from the outlet of the SS is gradually pressed by the mainstream toward the PS. As shown in Figure 5, for low incidence angle cases (123° and 133°), it can be seen that coolant air is concentrated toward the centerline on the SS, while a better lateral cooling coverage appears on the PS. For a small incidence angle (β1 = 123°), coolant flow gradually diffuses to the leading edge at high blowing ratios. This phenomenon weakens film cooling effectiveness downstream the SS significantly. For the same blowing ratio cases, reducing the mainstream incidence angle results in expanding cooling air coverage on the PS. Film cooling effectiveness can also be regarded as the dimensionless temperature of the blade surface. Low cooling effectiveness meant a high blade temperature, which indicated that the blade in this region was more prone to high-temperature corrosion and high-temperature oxidation [35]. Figure 6 shows variations of the film cooling effectiveness on the centerline. The film cooling effectiveness on the centerline deteriorates when reducing the incidence angle, as shown in Figure 6a. Furthermore, it decreases when increasing blowing ratio, as shown in Figure 6b. This is because the strong momentum of the secondary flow generated by the high blowing ratio results in coolant air directly mixing with the mainstream, which reduces film cooling performance, especially on the SS. In contrast, the blowing ratio has little effect on the centerline cooling performance of the PS.

Investigation of Particle Trajectories
During the working condition, turbine blades are affected by ingested particles. Figure 7 shows the distribution of the local capture efficiency and local impact efficiency of fine particles (dp = 1 m) at different inlet flow angles. It can be seen that few particles impact on the blade surface because of the low inertia, which means most of the particles follow the mainstream. Additionally, there is a similar distribution between impact efficiency and capture efficiency at the same inlet flow angle, which indicates the blade surface captures almost all the impacted particles. Moreover, the collision and deposition mainly occur at the PS. With the increase in the inlet flow angle, both impact and deposition efficiency increase near the film hole on the PS. However, a reverse phenomenon is generated at the trailing edge of the PS.
A comparison of local impact efficiency and local capture efficiency of different particle sizes is shown in Figure 8. For small particle sizes (dp = 1 m, dp = 5 m), both particle impact and capture efficiency are small, and they show a similar distribution. Due to high inertia, large particles are more likely to separate from the mainstream, causing higher impact efficiency. However, the deposition rate increases first, and then decreases with a particle size increase, which indicates that large particles (dp > 10 m) hardly settle on the blade surface. This phenomenon shows that impacted particles with large sizes can rebound from the blade surface more easily. Collision mainly occurs on the PS and leading edge. Moreover, the impact efficiency of particles with dp = 50 m is close to 100%, which indicates that this region is vulnerable to erosion caused by particles, and most of the particles impact on the blade surface more than once. The erosion rates are plotted against the impact energy of the particles [9]. Therefore, with the increase in particle size, the erosion rate increases rapidly. As shown in Figure 8, erosion mainly occurs on the PS, and erosion gradually generates at the SS when particle size is 50 m.  Figure 9 shows a comparison of impact efficiency and capture efficiency, with different particle sizes at four blowing ratios. It can be concluded that impact efficiency increases as particle size increases. The impact rate of particles of dp = 10 m has exceeded 100%, and values even exceed 400% when particle size is dp = 50 m. This phenomenon is ascribed to the fact that particles still have high inertia after collision with the blade surface, which results in several rebounds between two adjacent blades. This also accounts for a high impact efficiency of the SS for particles with a size of 50 m, as shown in Figure 8. Therefore, large particles affect blades mainly by impacting them, which causes substantial damage to turbine blades. With increasing particle size, capture efficiency increases first and then decreases. Deposition seldom occurred on the blade surface for dp > 20 m. Small particles affect blades mainly by deposition, which increases surface roughness and then leads to heat transfer deterioration of turbine blades. The blowing ratio has little effect on impact efficiency and capture efficiency, except for a particle size of 10 m. Because of the flow recirculation near the PS, as found in our previous study, the 10 m particles are more likely to stick to the blade surface at a high blowing ratio. The flow recirculation hardly influences particles with smaller sizes (1 m, 5 m) due to low inertia. While large particles (20 m, 50 m) have much higher inertia, their trajectories are hardly influenced by varying blowing ratios. Therefore, only the capture efficiency of 10 m particles increases with the blowing ratio increasing.  Figure 10 shows variations of ηca and ηim of the 10 m particles at four blowing ratios. Bar charts represent impact efficiency (ηim), and line charts represent capture efficiency (ηca). As discussed above, impact efficiency barely varies with blowing ratio at three inlet angles, while capture efficiency increases with the blowing ratio increasing. Both impact and capture efficiency increase with the inlet angle, increasing from 123° to 143°. Therefore, it is an effective method to reduce the threat of ingested particles by increasing inlet flow angles, which can also enhance film cooling performance. Capture efficiency % Im pact efficiency %  Figure 10. Variation of impact efficiency and capture efficiency with different inlet angles at four blowing ratios, dp = 10 μm.
The fly particles might invade the film hole in actual working conditions, causing partial blockage, which would decrease cooling performance significantly. As demonstrated in Figure 11, invasion efficiencies of small particles (1 m and 5 m) are almost zero. However, the value of invasion efficiency is about 12% when the particle size is 50 m. The invasion efficiency increases with the increase in particle sizes, because high inertia of large particles could overcome the strong momentum of secondary flow.

Conclusions
Particle deposition and trajectories were investigated using critical velocity and particle removal models. The invasion efficiency of the AGTB-B1 turbine blade cascade was investigated for the first time. In addition, film cooling effectiveness was analyzed by considering the effects of blowing ratio, inlet flow angle and particle diameter. The main conclusions are shown as follows: 1. For the film-cooled blade leading edge, film cooling effectiveness on the centerline increases with the inlet flow angle. Film cooling performance decreases with the increase in the blowing ratio, especially at the suction side.
2. Due to low inertia, small particles (1 m and 5 m) hardly impact the blade surface, and particles on the blade are mostly captured. Impact efficiency increases gradually with the increase in particle size. For particles with a size of 50 m, the total impact efficiency exceeds 400%, which indicates that there are multiple bounces between particles and the blade surface.
3. The blowing ratio has little effect on impact efficiency and capture efficiency, except for the capture efficiency of 10 m particles. The particles are more likely to impact blades with an incidence angle of 143°. Moreover, invasion efficiencies of small particles (1 m and 5 m) are almost zero. The value of invasion efficiency is about 12% when the particle size reaches 50 m. Therefore, these results indicate that the film cooling holes are blocked mainly by large particles. Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: Data sharing not applicable.

Conflicts of Interest:
The authors declare no conflict of interest.