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Flow over a NACA0012 Airfoil

 

Problem Description

 

Extensive wind-tunnel measurements were taken for the symmetrical NACA0012 airfoil at the Langley Research Center’s 8-foot transonic pressure tunnel. The tests were conducted at lift coefficients from near-zero through Mach number values from 0.3 to 0.86 for Reynolds numbers of 3.0´10⁶ to 9.0´10⁶ with transition fixed at 5% of chord length. These experimental results serve as a basis for conducting a turbulent simulation using the Spalart-Allmaras model present in the AEROFLO program.

 

The NACA0012 airfoil at an angle of attack, a, of 2.86^o was chosen, since it has long been a standard two-dimensional model for evaluating wind-tunnel test techniques and computational methods. Comparisons of results from AEROFLO’s simulation and the experiments are provided for the condition Ma = 0.86, Re = 9.0´10⁶. Details of the experiment can be found in the NACA Technical Memorandum 81927

 

Mesh

The computational domain employs a block with 245 ´ 50 ´ 3 grid points (Figure 1). The grid is an O-grid with the i direction oriented along the surface of the airfoil.

 

Figure 1. Mesh of the domain

Simulation Parameters

 

 

Table 1. Simulation Parameters

 

The simulation type is simple CFD using both the WENO (33 and 34) and the MUSCL scheme for spatial differencing and the Beam-Warming scheme for time differencing. The problem is solved as though two-dimensional in i and j directions. (Note that although no spatial differencing is done in the k direction, 3 grid points are still required in this direction as this is the minimum number of grid points allowed in any direction.) The Spalart-Allmaras model is used for the simulation with trip points on the surface of the blade: one each on the pressure and suction side.

 

Obtain the Files

 

Both mesh files and project input files can be accessed below. Remember to place the grid files in a subfolder with the set up file /airfoil.

Setup file (foil.afl)

Grid file (foil.in).

 

Another C-Grid files also can be found below. In this case, the grid files should be placed in a subfolder /Carifoil.

 

Setup file (foilC.afl)

Grid file (foilC.PLOT3D).

 

Start the Simulation

 

Change the directory to the subfolder with the selected grid and spatial scheme. Start the simulation by

 

mpirun –np 1 mpiaeroflo.exe < foil.afl

 

Simulation Results

 

Figures 2, 3 and 4 show the pressure plot for the MUSCL, WENO 33 and WENO 34 results. Note the shock present on the suction side at approximately half the chord length.

 

Figure 2. Pressure contours (MUSCL)

 

Figure 3. Pressure contours (WENO 33)

 

Figure 4. Pressure contours (WENO 34)

 

Comparison of Different Spatial Schemes

 

Figure 5 shows the comparison of different spatial schemes for the coefficient for pressure. The results are also compared with the referenced experimental measurements. It shows that WENO 34 scheme provide best result.

 

 

Figure 5. Comparison of the coefficient of pressure, Cp, with experimental measurements for WENO and MUSCL procedures

 

CFL Test

 

The CFL performances for different spatial schemes are also tested for this problem. The test results are summarized in Table 2.

 

*  The CFL condition is computed by CFL= Δt/ Δs, which assume the reference flow velocity u=1.0.

**  Δs=min(Δx_i) is the minimum computational grid spacing

*** CFL_a=(u+a) Δt/ Δs=u(1+1/M)CFL is a measure of how far a sound wave can travel through the flow.

 

Table 2. CFL Number Test for Different Schemes

 

 

Convergence Performance

 

The convergence performances of the different spatial schemes are shown in Figure 6 by comparing the iteration norm.

Figure 6. The comparison of iteration norm for different spatial schemes

 

Reference:

 

1. Harris, C. D., “Two-dimensional Aerodynamic Characteristics of the NACA0012 Airfoil in the Langley 8-Foot Transonic Pressure Tunnel”, NACA Technical Memorandum 81927, 1981.