Flow Past a Two-Dimensional NACA0012 Airfoil

We simulated compressible flow at Mach=0.5, Re=10,000 (based on chord length) past a NACA0012 airfoil at zero angle of attack. This airfoil needs to have good resolution at the leading and trailing edges and to have good boundary layer resolution. We used thin quadrilaterals on the body, and small elements at the nose and tail then blocked out using triangles in the far domain and a regular array of quadrilaterals in the wake. It is important to keep the resolution smoothly varying in the wake since abrupt changes in the resolution there can lead to noise generation.

4180 quadrilaterals and 3307 triangles were used in the mesh which was created by Kirby [82] using SIMPLEX2D [83] and an advancing front/blocking algorithm. A summary of the simulation parameters is given in table 7.4.

In figures 7.6, 7.7 and 7.8 we show instantaneous iso-contours of density, divergence of momentum, and curl of momentum, respectively, in the near wake of the airfoil. The divergence of momentum is equal to minus the rate of change of density due to the conservation of mass equation. Hence, we should expect to see noise generated by the method appearing in this field. The plot shows that this calculated quantity is smooth showing that at this resolution we are well resolved by this measure. The vorticity plot, however, shows some noise near the vortices in the wake, so in this case the vorticity is probably a good measure of accuracy and a small increase in the resolution should reduce this noise to acceptable levels.

 

Parameter Value

Dimension 2d

Re 10,000 based on total chord length

Mach 0.5

$$\Delta t$$ 0.001 to 0.00001

N-Range 1 to 11

K_Tri 3307

K_Quad 4180

Method Discontinuous Galerkin

  

Figure 7.5: Top: Mesh of full domain for simulation of compressible, Mach 0.5, Re=10,000 flow past a NACA 0012 airfoil at zero angle of attack to the mainstream flow, Middle: Mesh around body and wake, Bottom Left: Close up of the airfoil, Bottom Right: Close up of part of the wake region.

  

Figure 7.6: The wake region (from $\frac{x}{L} = 2$ to $\frac{x}{L} = 5$) of a NACA 0012 airfoil at zero angle of attack to the mainstream flow. Mach 0.5, Re=10,000, 3307 triangles, 4180 quadrilaterals, N=11. Instantaneous iso-contours of the density are shown.

  

Figure 7.7: The wake region (from $\frac{x}{L} = 2$ to $\frac{x}{L} = 5$) of a NACA 0012 airfoil at zero angle of attack to the mainstream flow. Mach 0.5, Re=10,000, 3307 triangles, 4180 quadrilaterals, N=11. Instantaneous iso-contours of the divergence of momentum are shown.

  

Figure 7.8: The wake region (from $\frac{x}{L} = 2$ to $\frac{x}{L} = 5$) of a NACA 0012 airfoil at zero angle of attack to the mainstream flow. Mach 0.5, Re=10,000, 3307 triangles, 4180 quadrilaterals, N=11. Instantaneous iso-contours of the curl of momentum are shown.