Effect of Reynolds number on a normal shock wave-transitional boundary-layer interaction over a curved surface

The interaction between a normal shock wave and a boundary layer is investigated over a curved surface for a Reynolds number range, based on boundary-layer growing length x, of $0.44\times {10}^6\le {\text{Re}}_x\le 1.09\times {10}^6$. The upstream boundary layer develops around the leading edge of the model before encountering a $M$$\sim$1.4 normal shock. This is followed by adverse pressure gradients. The shock position and strength are kept constant as $\text{Re}$ is progressively varied. Infra-red thermography is used to determine the nature of the upstream boundary layer. Across the $\text{Re}$ range, this is observed to vary from fully laminar to fully turbulent across the entire span. Regardless of the boundary-layer state, the interaction remains benign in nature, without large scale shock-induced separation or unsteadiness. Schlieren images show a pronounced oblique wave developing upstream of the main shock for the laminar cases, this is believed to correspond to the separation and subsequent transition of the laminar shear layer. Downstream of the shock, in the presence of adverse pressure gradients, the boundary-layer growth rate is inversely proportional to $\text{Re}$. Nonetheless, across the entire range of inflow conditions the boundary layer recovers quickly to a healthy turbulent boundary layer. This suggests the upstream boundary-layer state, and its transition mechanism, to have little effect on the outcome of its interaction with a normal shock wave. Graphic abstract:

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