Numerical investigation of transonic flow over porous medium using immersed boundary method

A computational study of transonic flow past porous medium has been performed to explore the flow features at the free-stream/porous-medium interface. An immersed boundary (IB) method is used to render the porous medium, modeled as a 2-D matrix of circles (projection of solid circular cylinders in a cavity). Investigation of the flow properties at the interface confirms the presence of a finite (average) slip velocity over the entire interface, which can make the flow more resistant to separation in the presence of an adverse pressure gradient. Lower wall-normal gradients of stream-wise velocity are observed at the interface and in the boundary layer downstream of the porous region, which indicate reduced average shear stress, and hence a lower skin friction drag. However, the results also reveal the formation of an adverse pressure gradient over the porous medium and in the region downstream of it as a result of the flow over porous medium. Parametric studies have also been performed to investigate the effects of changes in the structure of the porous medium on the mean flow properties at the free-stream/porous-medium interface and the boundary layer properties downstream of it. Results indicate that whereas the extents (length and depth) of the porous medium do not have much effect on the value of slip velocity, changes in the porosity and diameter of IB circles result in change of slip velocities. It is further observed that the boundary-layer health worsens as the flow moves past the porous medium and it is affected by the length, porosity, and diameter of circles forming the porous region. Investigation of transonic flow over the DFVLR R-4 airfoil with and without the porous medium indicates that the structure of the flow separation is altered but not attenuated with the introduction of the porous region, at least for the specific porous configuration used in the present study. The simulations are done as steady state Reynolds-averaged Navier-Stokes calculations, using Menter’s k − ω/k − ɛ model for turbulence closure.