Supersonic starting jet impingements upon hemispherical concavities

A numerical study on starting supersonic jets impinging upon hemispherical concavities was conducted using OpenFOAM platform based on rhoCentralFoam transient compressible flow solver. Three concavities of diameter ratios of D/d=0.5, 1, and 2 were studied to understand how the flow and shock structures associated with the initial stages of the jet impingement are affected by concavities smaller or larger than the jet diameter. A separation distance between the nozzle exit and the lowest points of the concavities was maintained at h/d=1.5 for consistency. Numerical simulation results reveal that D/d=0.5 and 1 concavities lead to shocks reflecting off the concavity lips and surfaces, where they travel upstream and interact with the starting vortex-ring, embedded shocks and compressible jet shear layers. Between the two, D/d=0.5 concavity also leads to higher flow unsteadiness due to its smaller size that hastens shock interactions and their upstream propagations. Nonetheless, the jet shear layers/flows would still eventually turn when they encountered the flat-wall sections and convect along them as classical impinging jets. In contrast, D/d=2 concavity results in high flow blockage that sees significant jet flow reversing direction shortly after it has emanated from the nozzle and exit from the concavity in the upstream direction. Insignificant jet flow fluid interacts with or convects along the flat-wall section, representing a significant departure from typical impinging jet behavior. As a result, while centerline flow characteristics are broadly similar for both D/d=0.5 and 1 concavities, D/d=2 concavity produces interesting deviations due to its unique impingement behavior.