Experimental Research on the Effect of Particle Parameters on Dynamic Stall Characteristics of the Wind Turbine Airfoil

Abstract

The frequent appearance of sandy and dusty weather in Northwest China impacts the wind turbine. Meanwhile, the non-constant phenomena, dynamic stall speed during the wind turbine operation, will lead to large load fluctuations and unsafe operation. However, few studies have been conducted at home and abroad on the effect of particle parameters on the dynamic stall of airfoils. This paper investigates the impact of particle parameters on the airfoil dynamic stall through numerical simulation of the coupling between the continuous phase and discrete phase by using the SST k-ω turbulence model for a two-dimensional NACA 0012 airfoil. The effect of particle parameters on the airfoil dynamic stall aerodynamic performance, the impact of the flow field around the airfoil, and the particles motion were studied, respectively. The investigation shows a reduction in the aerodynamic performance of the airfoil, due to the addition of particles. The effect is more prominent under a large angle of attack and less under a small angle of attack. When the angle of attack increases, the loss rate of lift coefficient in the windy and sandy environment gradually decreases, while irregular fluctuations emerge when the angle of attack decreases, and the overall rate of change increases more significantly, compared to the stage of the increasing angle of attack. For the particle diameter under 50 μm, the larger the particle diameter, the more significant the change of lift coefficient becomes, as well as the larger the vortex volume near the airfoil’s leading edge, and a large number of particles gather at the suction surface of the airfoil. For the particle diameter of 50 μm, the lift coefficient decreases at any angle of attack of the airfoil movement to the oscillation cycle, the vortex volume decreases, and a large number of particles gather at the pressure surface of the airfoil. However, for particle diameters above 50 μm, the lift coefficient gets reduced, followed by a decrease in the vortex volume near the airfoil leading edge with the increase of particle diameter, so that plenty of particles gather on the pressure surface of that airfoil. At the stage of increasing the airfoil angle of attack, with the increase of particle concentration, there is a gradual decrease of the peak lift coefficient and stall angle of attack of the airfoil, as well as a corresponding decrease of the drag coefficient divergence angle of attack and peak value. In contrast, when the airfoil angle of attack is decreased, the airflow reattachment process obviously lags behind that of the clean air. As the particle concentration increases, the airfoil separation point occurs earlier, and the higher the concentration, the earlier the separation point. The erosion maximum airfoil erosion rate increases with the particle concentration.

1. Introduction

The Northwest of China is rich in wind resources, yet there are frequent sandstorms, and sometimes strong ones, which makes it really easy for the wind turbines to operate in this environment and to develop certain erosions and tears on their blades, sometimes seriously affecting their aerodynamic performance. During the operation of the wind turbine, there is a more dramatic non-stationarity in the flow field, which leads to dynamic stall and high load fluctuations during most of the wind turbine operating time, resulting in instability phenomenon. Due to the complex working environment of wind turbines, the blades often work in a non-constant incoming flow state, whose yaw, atmospheric boundary layer shear, and other factors will bring about periodic changes in the angle of attack of the wind turbine blades, thus causing an apparent dynamic stall. That is, the lift drag coefficient of the airfoil being affected by the leading edge separation vortex shows an evident hysteresis phenomenon [1]. The sudden change in the airfoil performance and load will affect the wind turbine service life and power generation efficiency.

The windy and sandy environment has two main effects on wind turbines. On the one hand, sand particles will cause the wind turbine blade to change its winding condition, thus affecting the efficiency of the wind turbine to capture wind energy. On the other hand, sand particles will produce a certain degree of erosion on the wind turbine blade, making the blade shape change, resulting in its aerodynamic performance degradation and, eventually, negatively impacting the generation efficiency of the wind turbine and its operating stability. Many studies have focused on the changes in the aerodynamic performance of wind turbine blades or airfoils after erosion occurs. Using numerical simulation methods, Alden [2,3], Fiore [4], Han [5], Douvi [6], and Li Deshun [7,8] et al. studied the effects of particles on the erosion and aerodynamic performance of wind turbine blades and different airfoils and found that, in the stationary state, the prolonged erosion of wind and sand on the leading edge of wind turbine blades and airfoils and the accumulation of sand particles on the blade surface will seriously affect the aerodynamic performance of the wind turbine, and the longer the operation time, the greater the degree of influence and the more serious the erosion, specifically, the airfoil aerodynamic performance will change as the erosion degrees of the leading edge vary. The leading-edge erosion will lead to an increase in the airfoil drag coefficient, a decrease in the lift coefficient, and a decline in the wind turbine annual power generation. In addition, Yasmin [9] and Gharali [10] conducted numerical simulations of air-solid, two-phase flow on the wind turbine airfoils to investigate the effects of particle diameter and mass flow rate on airfoil erosion, aerodynamic performance, and flow field structure. Khalfallah and Koliub [11], Sareen [12], and Gaudern [13] also conducted numerical simulations to study the effect of leading-edge erosion on the aerodynamic performance of wind turbine airfoils by subjecting the leading edge of the airfoil to erosion of different depth and width, respectively. The results showed that the width erosion on the leading edge of the airfoil was the main reason for its aerodynamic degradation.

The leading-edge erosion would increase the drag coefficient and decrease the lift coefficient. The mechanism of generating dynamic stalls in wind turbine airfoils is very complex. For different airfoils, Ekaterinaris [14], Samara [15], and Masdar [16] et al. studied the effects of different parameters on the dynamic stall aerodynamic characteristics and flow field of them, respectively. Zhu [17] et al. analyzed the dynamic stall speed of two-dimensional airfoils, three-dimensional non-rotating blades, and three-dimensional airfoils under pitch oscillation. After the research on the S809 airfoil, Sandeep Gupta [18] et al. found that the dynamic stall aerodynamic performance of the airfoil calculated using the modified B-L model matched with the experimental data very well. Michael V.Ol [19] and Wang [20] carried out an analytical study on the airfoil aerodynamic performance and flow field characteristics under light dynamic stall and deep dynamic stall in combination with experiments. The results showed that the variable incoming flow velocity could suppress the dynamic stall characteristics of the airfoil to a certain extent under the light stall condition, while aggravating its dynamic stall characteristics under the deep stall condition.

To sum up, lots of research has been carried out at home and abroad on the influence of windy and sandy environments on the wind turbine airfoil and dynamic stall of the airfoil. Yet, the studies of the impact of wind and sand on the wind turbine airfoil remain limited to static conditions, without consideration of the influence of particles on the wind turbine airfoil under dynamic stall conditions. In contrast, during wind turbine operation, the blade is often under active stall conditions, which will bring about such problems as significant load fluctuation, reduced power generation efficiency, and shortened service life. Therefore, the study of the effect of windy and sandy environments on the dynamic stall of wind turbine airfoil has a unique theoretical and practical application value, which is of great importance to the safe and stable operation of wind turbines.

This studies the particle parameters effect on the airfoil dynamic stall characteristics using the CFD method for the two-dimensional NACA 0012 airfoil. It uses numerical simulations to verify the accuracy of the SST k-ω turbulence model under clean air and analyzes the feasibility of the discrete phase model. Firstly, a preliminary study on the aerodynamic parameters of the airfoil for particles of 50 μm diameter (concentration 8.56 g/m³) revealed that the addition of particles of 50 μm diameter had some effect on the aerodynamic performance; next, the effects of particles with different diameters on the dynamic stall characteristics of the airfoil were studied at the same concentration (8.56 g/m³); lastly, the effects of different concentrations of particles with the same diameter (50 μm) on the dynamic stall characteristics of the airfoil were studied. Meanwhile, the influence of particle parameters (particle diameter and particle concentration) on the entire flow field of the airfoil were analyzed, and the relevant laws of different particle parameters on the aerodynamic performance, flow field characteristics, and erosion of the airfoil were obtained, which provided a certain theoretical basis for the subsequent research and calculations and, at the same time, provided a certain reference basis for the relevant design of practical engineering applications.

2. Numerical Simulation Methods Setup

Computational Domain and Meshing Strategies

In this paper, the NACA 0012 airfoil is taken as the research object of numerical simulation. The chord length c of the airfoil is 0.5813 m, and the sine wave periodically oscillates around the 1/4 chord length point. It uses ICEM for modeling and structured sliding grid division [21], with the left, upper, and lower boundaries to be 15 c away from the aerodynamic center of the airfoil and the right boundary to be 21 c from the aerodynamic center of the airfoil [22]. Among them, the left and lower boundaries are velocity inlet boundaries, and the right and upper boundaries are pressure outlet boundaries. To accurately simulate the flow field characteristics at the boundary layer, the mesh around the airfoil is encrypted with the boundary layer mesh shown in Figure 1.

To simulate the dynamic characteristics of the airfoil, the computational domain presents itself as the stationary domain and the rotational domain. The rotational domian adopts an O-shaped grid with a diameter of 6 c. The height of the first grid layer is about 0.01 mm, and the regular growth rate is 1.005. The number of the airfoil grid is about 50,000, and the rotation domain grid follows the pitching and oscillating motion of the airfoil. The external stationary domain adopts a structured grid technology with good orthogonality, with a number of about 40,000; the intersection interface between the static domain and the rotational domain is set to have the same size grid spacing, in order to reduce the interpolation error in different grid regions in the airfoil flow field calculation. During the calculation, the rotational domain grid rotates periodically along the intersection interface with physical time. Meanwhile, the flow field information exchange between the rotating and stationary domains is achieved through the grid intersection interpolation [23], as shown in Figure 2.

3. Model Validation and Feasibility Analysis

3.1. SST k-ω Turbulence Model Validation

The transport equations of the SST k-ω model [24] are:

$$\frac{\partial \left(\rho k\right)}{\partial t}+\frac{\partial \left(\rho u_{i}k\right)}{\partial t}={\mathrm{P}}_k-{\mathrm{D}}_k+\frac{\partial }{\partial x_i}\left[\left(\mu +{\sigma }_k{\mu }_t\right)\frac{\partial k}{\partial x_i}\right]$$

(1)

$$\frac{\partial \left(\rho \omega \right)}{\partial t}+\frac{\partial \left(\rho u_i\omega \right)}{\partial x_i}=\alpha \rho S^2-\beta \rho {\omega }^2+\frac{\partial }{\partial x_i}\left[\left(\mu +{\sigma }_{\omega }{\mu }_t\right)\frac{\partial \omega }{\partial x_i}\right]+2\left(1-F_1\right)\rho {\sigma }_{\omega 2}\frac{1}{\omega }\frac{\partial k}{\partial x_i}\frac{\partial \omega }{\partial x_i}$$

(2)

In this equation, k—turbulent kinetic energy; ω—specific dissipation rate; μ—molecular viscosity; $\alpha$, β, σ_ω, σ_ω2—constant coefficients. The right side of the transport equation is the generation term of turbulent kinetic energy, the dissipation term, and the diffusion term. The last term of Equation (2) is the staggered diffusion term.

To conduct numerical simulations under clean air, based on the experiment conditions, the angle of attack $\alpha ={15}^{\circ }{+10}^{\circ }\sin (\omega t)$, Reynolds number $\mathrm{Re}=1\times {10}^6$, reduced frequency k = 0.15, and Mach number Ma = 0.0732, conditions were selected for the validation of the numerical simulation method and compared with the test data from L.W.Carr, NASA Ames Research Center, USA [25], for the analysis. Figure 3 presents the comparison curves of the aerodynamic performance of the airfoil with the test values under different turbulence models. As can be seen, the SST k-ω turbulence model comes closer to the experimental value at the stage where the airfoil angle of attack increases, indicating that the SST k-ω turbulence model has better performance in capturing the flow field of the dynamic stall process of the airfoil. Thus, the SST k-ω turbulence model is applied.

3.2. Discrete Phase Model Feasibility Analysis

The Euler–Lagrange method is applied individually to each particle of the discrete solid phase, and the equation of motion for the particle phase is solved by Newton second law, as follows:

$$m_{\mathrm{p}}\frac{\mathrm{d}{v}_{\mathrm{p}}}{\mathrm{d}t}=F_{\mathrm{fp}}$$

(3)

$$I_{\mathrm{p}}\frac{\mathrm{d}{w}_{\mathrm{p}}}{\mathrm{d}t}=M_{\mathrm{fp}}$$

(4)

In this equation, $m_{\mathrm{p}}$ is the particle mass; $I_{\mathrm{p}}$ refers to the inertia term of the particle, $F_{\mathrm{fp}}$, represents the fluid force of the gas phase acting on the discrete particle, $F_{\mathrm{fp}}=-F_{\mathrm{pf}}$; $M_{\mathrm{fp}}$ means the total rotational moment acting on the particle.

Due to the scarcity of relevant tests for wind turbine airfoils under windy and sandy environments, a cylindrical winding test under windy and sandy conditions is applied, instead of the above tests for the purpose of verifying the feasibility of the discrete phase model. Li Deshun [26] conducted a numerical simulation of the experimental conditions in the literature [27], with particle Stokes number (is a similarity criterion describing the inertia of particles in two-phase flows) and mass concentration ratio of 0.98 and 10%, respectively. The flow velocity distribution of the particles basically matches the measured data with minor errors. The relative error is more prominent only in the center of the cylindrical wake region, with an average relative error of 39.8%. In comparison, the average relative error in other areas is 9.8%, which makes it feasible to adopt the discrete phase model for the simulation of solid phase particles.

4. Calculation Results and Analysis

4.1. Aerodynamic Performance

4.1.1. Effect of Particles on Aerodynamic Performance of Airfoil under Dynamic Stall

To determine the effect of particles on the aerodynamic performance of the airfoil under dynamic stall conditions, an initial exploration of the dynamic stall characteristics of the airfoil begins in the case of 50 μm diameter particles (concentration 8.56 g/m³). Figure 4 depicts the dynamic stall aerodynamic performance of the airfoil under windy and sandy environments. Although the particles have some influence on the aerodynamic performance of the airfoil during the oscillatory motion of the airfoil, the degree of impact varies at different stages. Compared with clean air, the lift coefficient decreases after adding 50 μm diameter particles, and it is more influential at large angles of attack, dropping by about 4% at a 25° angle of attack. The drag coefficient tends to decrease, in general, with a reduction of about 2.5% at a 25° angle of attack. The moment coefficient increases at most angles of attack, about 2.65% increase at 25° angle of attack, but decreases at certain angles of attack. Due to the existence of frequent exchange of momentum between the wind and sand particles, the airflow results in an increase in momentum loss, followed by a decrease in the lift coefficient of the airfoil. Moreover, the reason for the rise in the momentum coefficient is the aerodynamic center position change caused by the particle’s momentum. As is seen in the figure of the lift-to-drag ratio, both the maximum lift-to-drag ratio with clean air and the addition of 50 μm diameter particles correspond to an optimum angle of attack of approximately 5.225°.

In comparison with clean air, the addition of 50 μm diameter particles reduces the maximum lift-to-drag ratio by 6.67%. That is, a reduction happens in the wind turbine output. Thus, evidence suggests that the addition of particles decreases the aerodynamic performance of the airfoil, and it sets the stage for the later study.

4.1.2. Effect of Particle Diameter on Aerodynamic Performance of Airfoil under Dynamic Stall

The effect rate is used for analysis, in order to further study the effect of different diameter particles on the aerodynamic performance of the airfoil under dynamic stall. Equation (5) presents the effect rate of aerodynamic coefficients under the dynamic stall of the airfoil with different diameter particles, compared to clean air, with the results in Figure 5. The upper half of the x axis in the figure indicates that the lift coefficient under clean air is more significant than that after adding particles, e.g., the lift coefficient decreases after adding particles, compared to clean air, as opposed to the lower half of the x axis. In addition, the angle of attack of the x axis corresponds to two variation processes of the aerodynamic coefficient of the airfoil, namely the process of increasing the angle of attack (rising edge) and the process of decreasing the angle of attack (falling edge), and the aerodynamic coefficient of the rising edge is greater than that of the falling edge.

$$\mathrm{\Delta }{C}_l=\frac{C_l{}_{clean}-C_{lparticle}}{C_l{}_{clean}}\times 100\%$$

(5)

According to Figure 5, when the airfoil angle of attack increases (rising edge of the angle of attack), the loss of lift coefficient in windy and sandy environments gradually decreases. This is because the flow field separation zone gradually increases, together with the increase of the angle of attack, so that the influence is weakened on the pressure distribution on the airfoil surface, as the particles mainly concentrated on the outer edge of the airflow separation zone. When the airfoil angle of attack decreases (falling edge of the angle of attack), there are irregular fluctuations. However, the overall rate of change, compared to the angle of attack increasing phase, increases significantly, and the maximum loss of lift coefficient decreases with the rise of particle diameter. Additionally, according to the graph, as the particle diameter increases, the loss of lift coefficient in the increasing angle of attack phase gradually decreases. That is because the inertial force of small-diameter particles is relatively small, and the air drag plays a major role, and the particles show strong followability. The smaller the diameter, the easier the particles are sucked into the airfoil separation zone, and the more frequent the gas momentum exchange between small diameter particles and the separation zone, resulting in an increase of gas momentum loss, subsequently showing a greater reduction in the lift coefficient. However, for the large-diameter particles, the particle inertia force plays a dominant role, and the followability becomes poor, with a limited effect on the airfoil surface.

4.1.3. Effect of Particle Concentration on Aerodynamic Performance of Airfoil under Dynamic Stall

In order to study the effect of different concentrations of particles on the aerodynamic performance of the airfoil under dynamic stall conditions, Figure 6 compares the characteristics of varying concentrations of particles on the aerodynamic performance of the airfoil under dynamic stall. Various concentrations of particles during the oscillatory motion of the airfoil have certain effects on the dynamic stall aerodynamic performance of the airfoil, which, of course, vary at different stages. The general trend of increasing the airfoil angle of attack (rising edge of the angle of attack) is that, as the particle concentration increases, the stall angle of attack of the airfoil gradually decreases, and the maximum lift coefficient also gradually decreases. The general trend of reducing the airfoil angle of attack (falling edge of the angle of attack) is that, at higher particle concentration status, the lift coefficient changes more gently in the airfoil airflow reattachment phase. The drag coefficient comparison reveals that, as the particle concentration increases, the drag coefficient divergence angle of attack decreases, and the peak drag coefficient decreases accordingly. As the concentration of particles in the airflow increases, the percentage of particles in the gas phase increases, and the momentum exchange between the particles and the gas phase becomes more frequent, so that the laminar flow on the upper surface of the airfoil turns into turbulent flow earlier, which suppresses the strength of the leading-edge separation vortex. Consequently, the vortex-induced lift decreases. In terms of aerodynamic performance, the maximum lift coefficient of the airfoil drops, and the peak drag coefficient decreases. Meanwhile, due to the increase in turbulence, the airflow reattachment process significantly lags behind the clean air reattachment process at the airfoil angle of the attack reduction stage. The manifestation of the changing pattern of the aerodynamic performance is that the reattachment phase of the airfoil lift coefficient is smoother than before, and the drag coefficient in the reattachment process is significantly larger than that under clean air.

4.2. Effect of Particles on the Flow Field Characteristics of Airfoil

4.2.1. Effect of Particles on the Distribution of Airfoil Vorticity

Figure 7 presents the vortex volume streamline diagram of the airfoil under clean air at different stages in a dynamic stall cycle, with the aim to study the flow field characteristics of the airfoil under dynamic stall conditions. According to the figure, when the airfoil moves upward from the initial angle of attack of 15° to the angle of attack of 16.2°, the flow is completely attached, with the formation of a thin layer of wake area, and its lift coefficient increases with the increase of the angle of attack. As time goes on, when the airfoil pitches up to an angle of attack of 19.8°, the leading-edge separation vortex on the whole suction surface of the airfoil is formed, whose lift coefficient grows linearly with the change of the angle of attack. At a 21° angle of attack, the leading-edge separation vortex gradually strengthens and moves toward the trailing edge. When the airfoil upstroke is to a maximum attack angle of attack of 24.6°, the leading edge of the airfoil induces many separation vortices, and an obvious trailing edge vortex is generated under the induction of the leading edge separation vortex.

By the time the airfoil moves upward to the maximum angle of attack before moving down to the 21.8° angle of attack, the previous leading edge separation vortex has begun to fall off. The secondary separation vortex induced from the front edge fuses into an enormous vortex, while the trailing edge vortex gradually increases and attaches to the airfoil suction surface. Under the induction of this vortex, the flow velocity of the airfoil suction surface accelerates, and the pressure decreases. Hence, the pressure of the pressure surface is bigger than that of the suction surface. As the downward motion of the airfoil reaches a 20.6° angle of attack, the trailing edge separation vortex gradually falls off. In the meantime, the secondary vortex induced by the leading edge separation vortex gradually shifts toward the trailing edge of the airfoil, causing a noticeable fluctuation of the pressure distribution on the suction surface of the airfoil. Along with the further reduction of the airfoil angle of attack, new small-scale leading edge separation vortices are generated at the leading edge of the airfoil, following the main flow from the leading edge to the trailing edge of the airfoil. It is precisely because of the existence of these vortices that the airflow reattachment on the airfoil suction surface is delayed, causing the airfoil lift coefficient in the dynamic stall condition to be significantly larger than that of the stable state.

4.2.2. Effect of Particle Diameter on the Distribution of Airfoil Streamline and Vorticity

In order to study the relationship between particles and gases, Figure 8 displays the streamline and vorticity distribution at the leading edge of the airfoil with varying particles of diameter. It is observed from the figure that the particle inertial force increases as the particle diameter increases, resulting in a decrease in followability with the airflow, making it easier to collide with the airfoil. As the collision happens most at the leading edge position, the particle bounces in the opposite direction to the airflow, which enhances the momentum exchange between the particle and the airflow. As a result, the vortex volume increases, and a spike perpendicular to the airfoil surface appears near the leading edge. With a further increase in particle diameter (particle diameter > 50 μm), there is a corresponding decrease in the perturbation to the surrounding area, due to the decline of particle number (same concentration) and a reduction in the frequency of momentum exchange between the particles and the surrounding airflow. Additionally, because of the particle increased inertial force, the vortex volume is more obviously spiked, due to the farther bounce distance after the collision with the airfoil. However, the overall vortex volume reduces accordingly.

4.2.3. Effect of Particle Concentration on the Airfoil Velocity Distribution

As an attempt to understand the effect of different concentrations of particles on the flow field around the airfoil, Figure 9 describes the variation of velocity gradient in the boundary layer at the trailing edge of the airfoil under different concentrations of particles. The length of the arrow in the figure represents the magnitude of velocity, and its direction indicates the direction of the speed, where the direction of the velocity changes is the separation point. The velocity pattern diagram of the airfoil surface suggests that the addition of particles allows for the separation point of the airfoil boundary layer to occur earlier, and the greater the concentration, the closer the separation point is to the leading edge. It is because the more the particle concentration increases, the more the air momentum exchanges, the more the momentum is lost, and hence, the trailing edge separation. Additionally, there is a greater airflow velocity gradient in the flow field around the airfoil as the momentum exchange increases.

4.3. Particle Movement Characteristics

4.3.1. Particle Mass Concentration Distributions

In order to study the relationship between the motion state of particles and the airflow under the dynamic stall state of the airfoil, Figure 10 shows the streamlined diagram of particle concentration distribution under the motion of the airfoil to different angles of attack. It is clear from the figure that, when the airfoil moves up to a 16.2° angle of attack, the particles mainly gather at the edge of the separation zone of the airfoil suction surface and present good followability. A weak momentum exchange occurs between the airflow and the particles when the flow state is stable, and the airflow carries the particles around the airfoil, which has less influence on the flow field. During the upward motion of the airfoil from 19.8° angle of attack to 24.6° angle of attack, the particles move away from the airflow vortex as the angle of attack increases. The reason is that the particles centrifugal force and diffusion velocity are greater than the airflow centrifugal force and movement velocity, which makes the motion state of the particles change.

After the upward motion of the airfoil reaches the maximum angle of attack, the downward motion starts. At the angle of attack of 21.8°, because of the downward pitching motion of the airfoil, the particles are mainly gathered in the wake area of the pressure surface of the airfoil, due to the influence of the gradual recovery of the airflow and the settling effect of the particles. As the downward pitching motion of the airfoil reaches a 20.6° angle of attack, the particles suffer more from the vortex and are rolled up and lifted by the large-scale vortex. Since the density of the particles is much larger than that of the airflow [28], and the particles are subject to viscous and centrifugal forces, a large number of particles mostly cluster at the edge of the vortex and can hardly enter the center of the vortex. The particle motion has an intense non-constant characteristic. With short particle relaxation time, the particles fill the entire flow field space under the winding and sucking effect of the vortex. When the airfoil downward motion moves to an 18.2° angle of attack, the particles accompany the vortex to move downstream. The vortex strength spreads and weakens, so the number of those sucked and lifted particles gradually drops, and some particles settle. With the further decrease of the angle of attack, the particles are transported with the airflow for a long distance, and a large number of particles have moved away from the airfoil. Following the decrease of the angle of attack and the settling of the particles, some particles gather at the edge of the wake area of the airfoil pressure surface.

4.3.2. Mass Concentration Distribution of Particles of Different Diameters

In order to study the changing pattern of the mass concentration distribution of particles with different diameters under dynamic stall, Figure 11 shows the mass concentration distribution of particles with varying diameters. When the particle diameter is below 50 μm, the particles mainly distribute in the airfoil suction surface. As the velocity difference between the small-diameter particles and the airflow is small, there is good followability, less particle settling, and a shorter aerodynamic response time. Again, because of the dominant role of air traction, the particles follow the mainstream in airfoil pitching from the front edge to the back edge. When the particle diameter exceeds 50 μm, the particle concentration at the airfoil suction surface decreases when the particle diameter increases. The particle concentration at the pressure surface increases as the particle diameter increases, and the particle distribution near the pressure surface is wider. The particle concentration enrichment area at the suction surface is farther from the airfoil surface, because when the particle diameter increases, the particle Stokes number increases, triggering the increase of the inertia force, and since particle centrifugal force is bigger than that of the airflow, the momentum response time increases, the airflow tracing force to particle decreases, and the momentum exchange frequency between the particles and the airflow is reduced; thus, the force of the airflow on the particles is weakened, so the particle followability becomes worse.

4.3.3. Effect of Different Particle Concentrations on the Erosion Characteristics of Airfoil

In order to study the erosion of different concentrations of particles under the dynamic stall condition of the airfoil, Figure 12 depicts the distribution of the erosion location and erosion degree corresponding to the maximum erosion rate of the airfoil. There is a slight influence of various concentrations of particles on the position corresponding to the maximum erosion rate of the airfoil, which appears near the airfoil leading edge. However, there is a more significant effect of different concentrations of particles on the maximum erosion rate of the airfoil, e.g., the maximum erosion rate of the airfoil surface gradually increases along with the increase in concentration, as shown in

Table 1. Erosion of dynamic airfoil stall at different concentrations of particles.

Concentration of Particle Co/(g/m3)	Erosion Position Corresponding to the Maximum Erosion Rate	Maximum Erosion Rate/(kg/m2s)
8.56	x/c = 0.00508	3.08087 × 10−9
40	x/c = 0.0082	1.31717 × 10−8
200	x/c = 0.00625	1.55057 × 10−7
715	x/c = 2.29374 × 10−4; x/c = 1.90018 × 10−4	2.29401 × 10−7

, because by increasing the particle concentration, the probability of particles colliding with the airfoil surface gradually increases, leading to an increase in the erosion rate. Figure 13 is the variation curve of the maximum erosion rate of the airfoil with the particle concentration, from which it is evident that the maximum erosion rate of the airfoil increases in response to the rise in the particle concentration.

5. Conclusions

An analysis of the feasibility of the discrete phase model is presented in this paper for the two-dimensional NACA 0012 airfoil by verifying the turbulence model using SST k-ω, as well as for determining the reliability and accuracy of this numerical simulation method. Firstly, a preliminary study was conducted on the aerodynamic performance of 50 μm diameter particles, and it was discovered that the addition of 50 μm-diameter particles could affect the aerodynamic performance of the airfoil. Then, the particles with various diameters displayed different effects on the dynamic stall characteristics of the airfoil at the same concentration. Finally, the effects of different concentrations of particles with the same diameter (50 μm) on the dynamic stall characteristics of the airfoil were studied. Meanwhile, the influence of particle parameters (particle diameter, particle concentration) on the entire flow field of the airfoil was analyzed, and the relevant laws of different parameters of particles on the aerodynamic performance, flow field characteristics, and wear of the airfoil were found. The following conclusions came from a closer look at the influence of particle parameters on the dynamic stall aerodynamic characteristics, flow field characteristics, and particle motion state of the wind turbine airfoil.

(1) The addition of particles decreases the aerodynamic performance of the airfoil, e.g., the lift coefficient decreases, the drag coefficient increases, and the moment coefficient decreases, and it is more influential at a large angle of attack and less influential at small angles of attack, but slightly different in some areas. When the attack of angle increases, the lift coefficient loss rate in windy and sandy environment gradually decreases, and irregular fluctuations occur at reducing angles of attack, but the overall change rate increases significantly, compared to the increasing angle of attack phase. Moreover, the lift coefficient maximum loss rate decreases with the increase of particle diameter. As the particle diameter increases, the loss rate of lift coefficient in the increasing angle of attack phase gradually decreases. During the increasing angle of the attack phase, the stall angle of attack of the airfoil gradually decreases as the particle concentration increases, the peak lift coefficient decreases, the drag coefficient divergence angle of attack reduces, and the peak drag coefficient decreases correspondingly. At the airfoil angle of attack reduction stage, the airflow reattachment process obviously lags behind that of clean air.

(2) The detachment of vortices corresponds to a decrease in the lift coefficient. The generation of leading-edge separation vortices and the reattachment process allows the lift coefficient to increase. When the particle diameter is under 50 μm, the airfoil leading-edge vortex increases as the particle diameter increases. When the particle diameter is over or equal to 50 μm, the airfoil leading edge vortex decreases as the particle diameter increases. The separation point of the airfoil boundary layer occurs earlier as the particle concentration increases, and the larger the concentration, the closer the separation point is to the leading edge.

(3) When the particle diameter is below 50 μm, the particles are mainly distributed on the suction surface of the airfoil. When the particle diameter is above 50 μm, the particle concentration on the suction surface of the airfoil decreases as the particle diameter increases, as opposed to the particle concentration distribution pattern on the pressure surface. Meanwhile, the particle distribution near the pressure surface becomes wider, and the particle concentration enrichment area on the suction surface moves farther away from the airfoil surface. Various concentrations of particles have a minor influence on the position corresponding to the maximum erosion rate of the airfoil located near the leading edge, and the maximum wear rate of the airfoil gradually increases, together with the increase of particle concentration.