# Aerodynamic Performance of a NREL S809 Airfoil in an Air-Sand Particle Two-Phase Flow

^{*}

## Abstract

**:**

^{6}and Re = 2 × 10

^{6}in a dry, dusty environment were compared with existing experimental data on air flow over an S809 airfoil from reliable sources. Notably, a structured mesh consisting of 80,000 cells had already been identified as the most appropriate for numerical simulations. Finally, it was concluded that sand concentration significantly affected the aerodynamic performance of the airfoil; there was an increase in the values of the predicted drag coefficients, as well as a decrease in the values of the predicted lift coefficients caused by increasing concentrations of sand particles. The region around the airfoil was studied by using contours of static pressure and discrete phase model (DPM) concentration.

## 1. Introduction

^{4}to 2 × 10

^{5}, both drag and lift coefficients experience great changes, while at Reynolds numbers from 2 × 10

^{5}to 5 × 10

^{6}the changes are smoother and very small.

^{6}. The numerical calculations accomplished on the transition shear-stress transport (SST) turbulent model using Fluent and Lewice software under the same icing conditions. However, the researchers have arrived at the conclusion that there was not good agreement between the numerical results obtained with Lewice and the experiments.

_{τ }= 180 combined with Lagrangian heavy particle tracking in a turbulent channel flow in order to characterize the effect of inertia on particle preferential accumulation.

^{6}and Re = 2 × 10

^{6}, using CFD code. The computational results are compared with reliable existing experimental data on air flow over an S809 airfoil, in order to find the impact of sand particles on lift and drag coefficients and, consequently, the aerodynamic performance of the airfoil.

## 2. Discrete Two-Phase Flow over an Airfoil

## 3. Computational Method

#### 3.1. Computational Mesh

^{−5}, corresponding to a maximum y

^{+}of approximately 0.2, a sufficient size to properly resolve the inner parts of the boundary layer. The C-type grid and the detail of the mesh close to the S809 airfoil are presented in Figure 1.

#### 3.2. Turbulence Models

_{μ}originally proposed by Reynolds [23] and a new model equation for dissipation (ε) based on the dynamic equation of the mean–square vorticity fluctuation.

^{3}. Regarding the Reynolds numbers for the simulation, they were chosen to be Re = 1 × 10

^{6}and Re = 2 × 10

^{6}, in order to be validated in the present simulations by being compared to reliable experimental data regarding the air flow over the airfoil. Moreover, the flow can be described as incompressible, an assumption close to reality, so it is not necessary to solve the energy equation. The free stream temperature was chosen to be same as the environmental temperature, in other words, equal to 300 K. Subsequently, the density of the air is ρ = 1.225 kg/m

^{3}and the viscosity is μ = 1.7894 × 10

^{−5}kg/ms.

## 4. Results and Discussion

^{6}and Re = 2 × 10

^{6}. The component of the net affecting force on the airfoil acting normal to the incoming flow stream is known as the lift force, while the component of the net force acting parallel to the incoming flow stream is known as the drag force. The lift and drag coefficients were possible to be predicted by means of the realizable k–ε and SST k–ω turbulence models, and then to be examined and compared with reliable experimental data regarding the one-phase air flow over the S809 airfoil by Somers [18].

^{6}and Re = 2 × 10

^{6}, respectively, for one-phase flow and two-phase flows of two different concentrations of sand particles in the air. Regarding the numerical results for the one phase air flow, it is obvious that the lift coefficient increases linearly with the angle of attack in the range of −9° to 9°. The turbulence models are shown to have the same behavior and good agreement with the experimental data. Nevertheless, for angles of attack higher than 12°, there is a disagreement between the experimental data and the computational results. Furthermore, it can be observed that sand concentration affects the lift coefficients. More specifically, there is a downward translation of the lift coefficient curve as the concentrations of sand particles increase, which has, as a result, a degradation of the aerodynamic performance. This degradation increases as the angle of attack and the concentration of sand particles increase.

^{6}and Re = 2 × 10

^{6}, respectively. For both Reynolds numbers the predicted drag coefficient increases as the angle of attack and the concentrations of sand particles in the air increase. This increase is much more obvious for 10% concentration of sand particles in the air flow. The larger total drag is caused by the mixture of air and sand particles, which results in larger skin frictional drag. Despite that there is a significant difference between experimental data and numerical results.

^{6}and Re = 2 × 10

^{6}with the realizable k–ε model for air flow and air-sand particle two-phase flow consisting of 1% and 10% concentration of sand particles in the air.

^{6}for an S809 airfoil for air flow. Notably, the stagnation points, in other words the points in a flow where the fluid velocity is zero and, thus, the static pressure is equal to the total, are obvious. As can be seen, the pressure on the lower surface of the airfoil is greater than the pressure of the incoming flow stream. As a result, the airfoil is effectively “pushed” upward, normal to the incoming flow stream. Moreover, it can be seen that as the angle of attack increases, the trailing edge stagnation point moves forward on the airfoil.

^{6}for air flow and air-sand particle two-phase flow for 1% and 10% concentration of sand particles in the air are given in Figure 10, Figure 11 and Figure 12 and they seem to have similar behavior with the contours of static pressure at Re = 1 × 10

^{6}. However, as the Reynolds number increases, the upper surface pressure achieves lower values for each angle of attack.

^{6}for 1% and 10% concentration of sand particles in the air, respectively, with the realizable k–ε turbulence model. As can be seen, the sand particles tend to concentrate mainly in the region of the trailing edge to the middle of the airfoil, and as the concentration of them in the air increases, the airfoil is surrounded by more particles.

^{6}with the realizable k–ε turbulence model for 1% concentration of sand particles in the air as shown in Figure 15, and 10% concentration of sand particles in the air as illustrated in Figure 16, the sand particles seem to have the same behavior as the concentration of them in the air increases, as for the case of Re = 1 × 10

^{6}. Furthermore, it can be observed that, as the Reynolds number increases, the sand particles drift towards the trailing edge of the airfoil.

## 5. Conclusions

^{6}and Re = 2 × 10

^{6}.

## Author Contributions

^{6}and wrote the paper; Dimitra C. Douvi and Dionissios P. Margaris analyzed the data; Aristeidis E. Davaris performed the simulations for Reynolds number of Re = 1 × 10

^{6}.

## Conflicts of Interest

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**Figure 1.**(

**a**) C-type grid with 80,000 quadrilateral cells; and (

**b**) detail of the mesh close to the S809 airfoil.

**Figure 3.**Comparison between reliable experimental data and simulation results of the lift coefficient curve for an S809 airfoil for (

**a**) realizable k–ε; and (

**b**) SST k–ω turbulence models at Re = 1 × 10

^{6}for one-phase and two-phase flows consisting of two different concentrations of sand particles in the air.

**Figure 4.**Comparison between reliable experimental data and simulation results of the lift coefficient curve for an S809 airfoil for (

**a**) realizable k–ε; and (

**b**) SST k–ω turbulence models at Re = 2 × 10

^{6}for one-phase and two-phase flows consisting of two different concentrations of sand particles in the air.

**Figure 5.**Comparison between reliable experimental data and simulation results of the drag coefficient curve for an S809 airfoil for (

**a**) realizable k–ε; and (

**b**) SST k–ω turbulence models at Re = 1 × 10

^{6}for one-phase and two-phase flows consisting of two different concentrations of sand particles in the air.

**Figure 6.**Comparison between reliable experimental data and simulation results of the drag coefficient curve for an S809 airfoil for (

**a**) realizable k–ε; and (

**b**) SST k–ω turbulence models at Re = 2 × 10

^{6}for one-phase and two-phase flows consisting of two different concentrations of sand particles in the air.

**Figure 7.**Contours of static pressure at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 1 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air flow.

**Figure 8.**Contours of static pressure at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 1 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air-sand particle two-phase flow and 1% concentration of sand particles in the air.

**Figure 9.**Contours of static pressure at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 1 × 10

^{6}with the realizable k–ε turbulence model for and S809 airfoil for air-sand particle two-phase flow and 10% concentration of sand particles in the air.

**Figure 10.**Contours of static pressure at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 2 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air flow.

**Figure 11.**Contours of static pressure at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 2 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air-sand particle two-phase flow and 1% concentration of sand particles in the air.

**Figure 12.**Contours of static pressure at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 2 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air-sand particle two-phase flow and 10% concentration of sand particles in the air.

**Figure 13.**Contours of DPM concentration at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 1 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air-sand particle two-phase flow and 1% concentration of sand particles in the air.

**Figure 14.**Contours of DPM concentration at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 1 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air-sand particle two-phase flow and 10% concentration of sand particles in the air.

**Figure 15.**Contours of DPM concentration at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 2 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air-sand particle two-phase flow and 1% concentration of sand particles in the air.

**Figure 16.**Contours of DPM concentration at (

**a**) −3°; (

**b**) 0°; (

**c**) 3°; and (

**d**) 9° angles of attack at Re = 2 × 10

^{6}with the realizable k–ε turbulence model for an S809 airfoil for air-sand particle two-phase flow and 10% concentration of sand particles in the air.

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**MDPI and ACS Style**

Douvi, D.C.; Margaris, D.P.; Davaris, A.E. Aerodynamic Performance of a NREL S809 Airfoil in an Air-Sand Particle Two-Phase Flow. *Computation* **2017**, *5*, 13.
https://doi.org/10.3390/computation5010013

**AMA Style**

Douvi DC, Margaris DP, Davaris AE. Aerodynamic Performance of a NREL S809 Airfoil in an Air-Sand Particle Two-Phase Flow. *Computation*. 2017; 5(1):13.
https://doi.org/10.3390/computation5010013

**Chicago/Turabian Style**

Douvi, Dimitra C., Dionissios P. Margaris, and Aristeidis E. Davaris. 2017. "Aerodynamic Performance of a NREL S809 Airfoil in an Air-Sand Particle Two-Phase Flow" *Computation* 5, no. 1: 13.
https://doi.org/10.3390/computation5010013