# Turbulent Flow Over a NACA 0012 Airfoil

In this application, AcuSolve is used to simulate turbulent flow of a fluid over a NACA 0012 airfoil at 3 angles of attack, 0 degrees, 10 degrees, and 15 degrees. AcuSolve results are compared with experimental results for coefficients of pressure, lift, and drag reported by NASA. The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model external aerodynamics.

## Problem Description

The problem consists of a NACA 0012 airfoil located in the center of a cylindrical domain, as shown in the following image, which is not drawn to scale. Fluid enters the domain with a velocity of 1.0 m/s. The domain edges are distant, 500 chord lengths, from the airfoil to minimize any far field effects. The problem is set up to simulate high Reynolds number flow, with Re = 6,000,000.
The simulation was performed as a two dimensional problem by restricting flow in the out-of-plane direction through the use of a mesh that is one element thick.

## AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions for each of the three angles of attack, 0 degrees, 10 degrees, and 15 degrees. For each case, the angle of attack was varied by changing the angle of the incident flow. Note that this enables the use of a single mesh for all of the simulations.

With a 0 degree angle of attack, the flow field is symmetric as the fluid flows over and under the airfoil. The airfoil impedes the flow, causing stagnation at the leading edge. As the fluid passes over and under the airfoil, velocity increases. As the fluid passes over the blunt trailing edge, a minor amount of flow separation occurs. The flow reattaches shortly after it passes the trailing edge and recovers the mean velocity in the distant far field.
With a 10 degree angle of attack, the stagnation point is shifted downward (relative to the airfoil), reflective of the shifted angle of attack. Fluid velocity above the airfoil is markedly different than that below the airfoil. A small low-velocity region is evident on the suction side of the airfoil, indicating some separation toward the trailing edge.
With a 15 degree angle of attack, the stagnation at the front of the airfoil is shifted even farther downward (relative to the airfoil), reflective of the shifted angle of attack. Additionally, the low-velocity wake increases in size, reflecting separation along the suction surface of the airfoil.
Experimental values of coefficient of lift (CL) at angles of attack (α) of 10 degrees and 15 degrees and values of drag coefficient (cd) at angles of attack (α) of 0 degrees,10 degrees, and 15 degrees are presented with the corresponding AcuSolve results in the following table.
Table 1.
CL (α=10) CL (α=15) cd (α=0) cd (α=10) cd (α=15)
Experimental 1.0941 1.5576 0.0082 0.0123 0.0207
AcuSolve 1.0903 1.5424 0.0081 0.0124 0.0208
Percent deviation from experimental 0.35 0.98 1.22 0.81 0.48

AcuSolve values for coefficient of pressure are plotted against experimental results for angles of attack (α) of 0 degrees, 10 degrees, and 15 degrees in the following plots. The results are presented for normalized distance along the airfoil, given by x/c, where x is the distance from the leading edge and c is the chord length.

For each case, AcuSolve is able to predict the flow characteristics at each point along the airfoil surface.

## Summary

The AcuSolve results compare well with the experimental results for flow over a NACA 0012 airfoil. In this application, a constant-velocity flow field impinges on the airfoil surface. As the flow convects in the streamwise direction along the airfoil surface, a boundary layer develops. The rate at which the boundary layer develops has significant impact on the viscous stresses present on the airfoil surface. At low angles of attack these stresses dominate the drag on the airfoil. As the angle of attack increases, the flow over the airfoil is no longer symmetric, which leads to the generation of lift. For non-zero angles of attack, the asymmetric pressure distribution on the airfoil creates another source of drag that is combined with the viscous stresses to determine the total drag on the airfoil. The AcuSolve results for coefficients of lift and drag are within 0.98 percent and 1.22 percent of experimental values, respectively. AcuSolve results for coefficient of pressure closely agree with experimental results along the length of the airfoil for all three angles of attack that were investigated.

## Simulation Settings for Turbulent Flow Over a NACA0012 Airfoil

AcuConsole database file: <your working directory>\airfoil_turbulent\airfoil_turbulent.acs

Global

• Problem Description
• Analysis type - Steady State
• Turbulence equation - Spalart Allmaras
• Auto Solution Strategy
• Convergence tolerance - 0.0001
• Relaxation factor - 0.4
• Material Model
• Fluid
• Density - 1.0 kg/m3
• Viscosity - 1.667e-7 kg/m-sec

Model

• Volumes
• Fluid
• Element Set
• Material model - Fluid
• Surfaces
• +z slip
• Simple Boundary Condition
• Type - Slip
• -z slip
• Simple Boundary Condition
• Type - Slip
• airfoil surface
• Simple Boundary Condition
• Type - Wall
• farfield
• Simple Boundary Condition
• Type - Far Field
• X velocity - cos(α) m/sec
• Y velocity - sin(α) m/sec
Note: The X-velocity is given by cos(α) and Y-velocity is given by sin(α), where α is the airfoil angle of attack in radians. Values contained in the .acs are for a 15-degree angle of attack. You can calculate these values and enter them in AcuConsole, or use built-in calculations in AcuConsole to determine sine and cosine.
• Eddy viscosity - 1.0e-9 m2/sec

## References

NASA - Langley Research Center. http://turbmodels.larc.nasa.gov/naca0012_val_sa.html