The development of transverse velocity profile is directly related to the development of secondary vorticity. In the internal aerodynamics case with potential external flow, although vorticity remains confined inside the viscous shear layer, secondary vorticity induced velocities exist outside of it.

If the secondary vorticity field is known, the induced secondary velocity field is well approximated following Hawthorne’s classical analysis. In the present work, the above analysis is used to separate the velocity field in the transverse plane into a potential and a rotational part. In the case of confined flows, the rotational part is confined inside the viscous shear layer, while the potential part occupies the whole flow field. This last part is the consequence of the “displacement” effects of the shear layer in the transverse plane.

Therefore, the present work allows a re-examination of the flow two-zone model (separation of the flow field in a viscous and an inviscid part) in confined flows.

On the other hand, the limitations of Hawthorne’s theory are examined, while a parallel analysis is presented for the case where the secondary vorticity distribution varies not only along the blade height, but also circumferentially.

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