Features of "fishtail" shock interaction in transonic flows on a NACA0012 Profile

Slender profiles flying at nearly sonic speed exhibit a peculiar shock pattern, which is commonly referred to in literature as the "fishtail" shock structure. It consists of two oblique shock waves that originate at the trailing edge of the airfoil and interact with a detached, nearly normal shock wave in two triple points located along the oblique shocks. Making use of both shock-fitting and shock-capturing CFD simulations and classical shock polar analysis, we prove that, in the case of a NACA0012 airfoil, the two interaction points cannot be modeled using the three shocks theory that von Neumann developed nearly a century ago to describe triple points arising in Mach reflections. Our analysis suggests that the four-wave interaction model proposed by Guderley should be used instead.