( Reference Najafi, Saidi, Sadeghipour and Souhar2005) investigate the complementary case in which a turbulent rotating flow enters a pipe at rest. Up to now, flow separation for a turbulent flow at the inlet of a rotating pipe has not been sufficiently analysed. At part load for small flow numbers $\unicode\approx 0.33$ at $Re=3000$. Turbomachines often operate at part load due to the claim of flexibility and not at the design point where the efficiency reaches its maximum. Below this critical flow number, separation is expected. The extended boundary layer theory predicts a critical flow number which is analytically derived and validated. We show the impact of swirl on the axial boundary layer and conduct experiments in which we vary Reynolds number, flow number and surface roughness to validate the analytical results. The solution of the resulting generalized von Kármán momentum equation takes into account the influence of the Reynolds number and flow number.
To describe this phenomenon analytically, we extended boundary layer theory to a swirl boundary layer interacting with the axial momentum boundary layer.
Below a critical flow number, defined as the ratio of average axial velocity to circumferential velocity of the pipe, there is flow separation, known in the turbomachinery context as part load recirculation. In the centre of the pipe, the fluid is free of swirl and is accelerated due to boundary layer growth. When a fluid enters a rotating circular pipe, an angular momentum or swirl boundary layer appears at the wall and interacts with the axial momentum boundary layer.