Identify the configuration(s) in which steady two-dimensional internal flow may show boundary layer separation if the flow direction is left to right.
Show Hint
Boundary layer separation typically occurs where the flow decelerates due to adverse pressure gradient—often in diverging or suddenly expanding passages.
Boundary layer separation in internal flows occurs when the fluid encounters an \emph{adverse pressure gradient}. This generally happens when the passage diverges or when there is a sudden expansion that forces the fluid to decelerate.
Configuration (A): The lower wall diverges, but the divergence is smooth and mild. For steady internal flow, such a small divergence may not produce strong enough adverse pressure gradient for separation. Configuration (B): Both walls are parallel. The pressure gradient is uniform and zero. Therefore, no separation will occur. Configuration (C): The lower wall diverges more sharply toward the outlet. This increases the adverse pressure gradient significantly. Such geometry is well known to cause boundary layer separation. Hence, separation is expected. Configuration (D): A sudden step expansion produces a strong adverse pressure gradient immediately after the step. This almost always causes boundary layer separation and the formation of a recirculation zone. Therefore, separation will occur.
Thus, configurations (C) and (D) show boundary layer separation.
