Numerical Investigation of Shock-Train Response to Inflow Boundary-Layer Variations

A dataset of normal shock trains in a rectangular cross-section channel has been created from direct numerical simulations in an effort to quantify the impact of inflow confinement ratio on the shock-train structure. To this end, the inlet boundary-layer momentum thickness was varied while the bulk inflow and outflow conditions remained constant. The simulations show that the shock train is displaced upstream as the inflow confinement ratio increases. Also, an increase in boundary-layer momentum thickness results in a reduction of the normal-like portion of the lambda-shock structures in the channel core. This leads to more numerous but weaker bifurcating shocks as well as an increase of the shock-train length. When the inflow boundary-layer thickness is varied temporally, the complex shock train response depends on the excitation frequency. A resonant frequency is observed when different components of the shock train exhibit the highest amplification in terms of pressure jumps. Further, the domain upstream of the leading shock acts as a low-pass filter, which has the end result of limiting the axial shock-train motion. Nevertheless, even a small oscillation in boundary-layer momentum thickness of 0.45 mm (0.6% of the channel height) is seen to increase the shock-train length by two orders of magnitude (4 cm).