Special properties of transonic flows in a channel with a lenticular bump

The present study focuses on particular properties of transonic flows through a planar channel featuring a circular bump on the lower wall. The selected geometry is reminiscent of the region surrounding the trailing edge of an airfoil at zero angle of attack and the resulting flow pattern is indeed similar to the fishtail shock-pattern that characterizes airfoils flying at nearly sonic speed. Numerical simulations have been conducted by solving the inviscid Euler equations using both a commercial and an in-house CFD code; discontinuities are modeled using shock-capturing in the former and shock-fitting in the latter. Numerical experiments reveal different shock-patterns obtained by independently varying the inlet Mach number and the outlet-to-inlet static pressure ratio. When shock-interactions occur, shock-polar analysis reveals that the branching point can be modeled using either von Neumann's three-shock-theory or Guderley's four-wave-theory, depending on the inlet Mach number. Furthermore, for certain pairs of boundary conditions, multiple solutions have been observed.