NACA 12 AIRFOIL: FIELDS
VELOCITY AND PRESSURE FIELDS, SUPERSONIC INCOMING FLOW
The NACA airfoil is a test profile which has been designed more particularly for supersonic flows; therefore we made simulations with Mach=1.2. We made the following simulations on a non-structured triangular mesh. With this mesh, we avoid oscillations which tend to be generated, and that we encountered with the structured fine mesh.
For an airfoil transsonic flow simulation based on Euler equations, quality criteria are shock waves resolution, stagnation point and prediction of their position. An additional criterion is the prediction of drag and lift coefficients.
The flow around a NACA airfoil is a very well CFD documented test case, it is interesting to compare the results we got with the reference results obtained by Marcello Manna in his PhD thesis.
Mach field, triangular mesh, incidence 7 degrees.
Mach iso-lines, triangular mesh, incidence 7 degrees.
Beam & Warning scheme
Comparison of Mach iso-lines: If we refer to the Vb test case of M. Manna, a NACA 12 profile with Mach(infinity) = 1.2, we can see that the Mach iso-lines we get can be compared with the field he got with an Upwind TVD scheme. At the front of the airfoil the shape of our closed lines can be compared to those obtained with a Beam & Warming scheme: the lines are not perfectly regular. At the back intrado of the airfoil we have a closed line, like for the Upwind scheme. Our shock wave is quite finely captured, almost like the way it is with the Upwind scheme.
Pressure field, triangular mesh, incidence 7 degrees.
Pressure iso-lines, triangular mesh, incidence 7 degrees.
Comparison of pressure iso-lines: If we refer to the Vb test case of M. Manna, we can see that our shock wave is well captured, it is fine like for the Upwind scheme test case. At the back intrado we have a closed pressure line (cyan), that is not closed for the Symmetric TVD and Beam & Warming schemes. We can observe a closed line for the Upwind test case, but it is smaller. Nevertheless, looking at our Mach iso-lines, we can expect this closed pressure line.
Upwind scheme Beam & Warning scheme Symmetric scheme