Up to this point, we have developed a detailed understanding of the shock-expansion theory. Now, we will put this theory to the test and analyze some classic supersonic canonical problems such as flow over a diamond-shaped airfoil, a flat-plate airfoil and a curved symmetric airfoil. The intriguing aspect of each of these problems is that the flow-field comprises both shocks and expansion waves. You can see this in the image below, which is for a supersonic flow over a diamond-shaped airfoil, where the red region is behind a shock wave and the blue region is behind an expansion wave.
Despite the apparent complexity of the flow-field, we will see in this lesson that the shock-expansion theory can still be applied to obtain exact analytical solutions for such practical applications. Furthermore, we will see that we can still achieve accurate lift and drag force prediction by introducing a slender object assumption and simplifying the shock-expansion theory to a thin-airfoil approximation.
Here are the accompanying hand-out slides for this lesson.