Step 8: Postprocessing

1.    Plot the $y^+$ distribution on the airfoil (Figure  3.11).

Plots XY Plot Set Up...

(a)   Disable Node Values in the Options group box.

(b)   Select Turbulence... and Wall Yplus from the Y Axis Function drop-down list.

   Wall Yplus is available only for cell values.

(c)   Select wall-bottom and wall-top in the Surfaces selection list.

(d)   Click Plot and close the Solution XY Plot dialog box.

Note:   The values of $y^+$ are dependent on the resolution of the mesh and the Reynolds number of the flow, and are defined only in wall-adjacent cells. The value of $y^+$ in the wall-adjacent cells dictates how wall shear stress is calculated. When you use the Spalart-Allmaras model, you should check that $y^+$ of the wall-adjacent cells is either very small (on the order of $y^+=1$), or approximately 30 or greater. Otherwise, you should modify your mesh.

The equation for $y^+$ is

where $y$ is the distance from the wall to the cell center, $\mu$ is the molecular viscosity, $\rho$ is the density of the air, and $\tau_w$ is the wall shear stress.

Figure  3.11 indicates that, except for a few small regions (notably at the shock and the trailing edge), $y^+>30$ and for much of these regions it does not drop significantly below 30. Therefore, you can conclude that the near-wall mesh resolution is acceptable.

Figure 3.11: XY Plot of $y^+$ Distribution

2.   Display filled contours of Mach number (Figure  3.12).

Graphics and Animations Contours Set Up...

(a)   Enable Filled in the Options group box.

(b)   Select Velocity... and Mach Number from the Contours of drop-down list.

(c)   Click Display and close the Contours dialog box.

(d)   Zoom in on the region around the airfoil, as shown in Figure  3.12.

Figure 3.12: Contour Plot of Mach Number

  Note the discontinuity, in this case a shock, on the upper surface of the airfoil in Figure  3.12 at about $x/c \approx 0.45$.

3.   Plot the pressure distribution on the airfoil (Figure  3.13).

Plots XY Plot Set Up...

(a)   Enable Node Values.

(b)   Select Pressure... and Pressure Coefficient from the Y Axis Function drop-down lists.

(c)   Click Plot.

Figure 3.13: XY Plot of Pressure

  Notice the effect of the shock wave on the upper surface in Figure  3.13.

4.   Plot the $x$ component of wall shear stress on the airfoil surface (Figure  3.14).

(a)   Disable Node Values.

(b)   Select Wall Fluxes... and X-Wall Shear Stress from the Y Axis Function drop-down lists.

(c)   Click Plot and close the Solution XY Plot dialog box.

  As shown in Figure  3.14, the large, adverse pressure gradient induced by the shock causes the boundary layer to separate. The point of separation is where the wall shear stress vanishes. Flow reversal is indicated here by negative values of the x component of the wall shear stress.

Figure 3.14: XY Plot of $x$ Wall Shear Stress

5.   Display filled contours of the $x$ component of velocity (Figure  3.15).

Graphics and Animations Contours Set Up...

(a)   Enable Filled.

(b)   Select Velocity... and X Velocity from the Contours of drop-down lists.

  Scroll up in the Contours of drop-down list to find X Velocity.

(c)   Click Display and close the Contours dialog box.

  Note the flow reversal downstream of the shock in Figure  3.15.

Figure 3.15: Contour Plot of $x$ Component of Velocity

6.   Plot velocity vectors (Figure  3.16).

Graphics and Animations Vectors Set Up...

(a)   Enter 15 for Scale.

(b)   Click Display and close the Vectors dialog box.

(c)   Zoom in on the flow above the upper surface at a point downstream of the shock, as shown in Figure  3.16.

Figure 3.16: Plot of Velocity Vectors Downstream of the Shock

  Flow reversal is clearly visible in Figure  3.16.