# Aerodynamic Sensitivity Analysis for a Wind Turbine Airfoil in an Air-Particle Two-Phase Flow
## 1 Introduction  
Wind energy is one of the most important renewable energy resources. However, the performance of a wind turbine is greatly affected by the extremely complex operating environments, such as common sandstorm and rain. For high stability, high efficiency and long life, it is necessary to study the effects of sand particles or rain droplets on the wind turbine aerodynamic performance. In recent decades, the methodology of computational fluid dynamics (CFD) has become increasingly popular to wind turbine aerodynamics [1; 2; 3; 4], and various CFD methods, including Reynolds-Averaged Navier-Stokes (RANS) equations [5], Detached-Eddy Simulation (DES) [6], Large-Eddy Simulation (LES) [2], transition prediction [7], overset grid [8] and hybrid scheme of CFD and blade element momentum (BEM) [9], have been developed. Especially, a handful of CFD-based studies have been conducted to investigate the effects of sand or rain on the airfoil aerodynamic performance. In aviation applications, [PERSON] and [PERSON] [10; 11] developed an iterative, two-way momentum coupled, two-phase flow scheme by linking a thin-layer incompressible Navier-Stokes (N-S) CFDcode with a Lagrangian particle tracking algorithm, and successfully simulated the rain phenomenon and the aerodynamic efficiency degradation of the NACA64-210 airfoil in heavy rain. For the same airfoil, [PERSON] and [PERSON] [12] combined the CFD package of FLUENT with a discrete phase model (DPM) to analyze the aerodynamic influences due to heavy rain and demonstrated that the degradation rate of aerodynamic efficiency increases with the rain rate. [PERSON] and [PERSON] [13] simulated the flow over the NACA0012 airfoil in heavy rain by a two-way momentum coupled Eulerian-Lagrangian approach. Their results showed significant aerodynamic penalties at low angles of attack due to rain effects and an about 3\({}^{\circ}\) rain-induced increase in stall angle of attack. In the field of wind turbine aerodynamics, [PERSON] et al. [14] proposed a CFD model coupled with a deposition model to assess the performance degradation of the wind turbine blade NACA63-215 airfoil, and demonstrated that the operation in the dusty environments can lead to a severe loss of power due to the dust accumulation on the blade surface. [PERSON] et al. [15] employed FLUENT together with a Lagrangian particle tracking scheme to study the effects of sand particles on the aerodynamic performance of the S819 airfoil, including the influences of sand dimensions, sand/air drift velocity and sand/air mass flow rate ratio. [PERSON] et al. [16] presented a multiphase CFD model based on the coupled Lagrangian-Eulerian approach to capture the water-film formation over the S809 airfoil and stated that heavy rain could result in a significant performance loss. [PERSON] and [PERSON] [17] developed a multiphase CFD model to estimate the effect of rain by simulating the water-film formation using the Lagrangian DPM and the Eulerian Volume of Fluid (VOF) model, and observed that the S809 airfoil performance is highly sensitive to the rainfall rate at low rainfall rates. However, if the rainfall rate is high enough to immerse most of the airfoil surface under water, a further increase in the rainfall rate does not have a substantial effect. [PERSON] et al. [18] computed the air-sand particle two-phase flow over the S809 airfoil by combining the N-S equations with a Lagrangian DPM via FLUENT and found that there was an increase in drag as well as a decrease in lift caused by increasing particle concentrations. Most of the above-mentioned studies are limited to the prediction of aerodynamic performance loss for an airfoil in an air-particle flow, and the more sensitive region to particles and the difference between aviation and wind turbine type airfoils are still unclear. In this work, the incompressible N-S equations coupled with a Lagrangian DPM will be presented to simulate the air-particle two-phase flow over the S809 airfoil at different Reynolds numbers, particle concentrations and various angles of attack.