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National Advisory Committee for Aeronautics, Technical Notes - Flow Surfaces in Rotating Axial Flow Passages

In order to investigate the deviation of flow surfaces from their
assumed orientation in the usual type of two-dimensional solution, three-
dimensional, incompressible, nonviscous, absolute irrotational fluid
motion is determined for flow through rotating axial—flow passages
bounded by straight blades of finite spacing and infinite axial length
lying on meridional planes. Solutions are obtained for five passages
with varying blade spacing and hub-tip ratio. The results are presented
in such a manner as to apply for all ratios of axial velocity to passage
tip speed. It is concluded that, for conditions in typical axial-flow
blade rows, the deviation of flow surfaces from their assumed orienta-
tion in two-dimensional solutions is small.

A flow surface in the passage between two blades of a compressor
or turbine is generated by the motion through the passage of any fluid
line consisting of the same fluid particles and extending from one
boundary to another in a plane normal to the axis of rotation. In two-
dimensional analyses of flow in compressors and turbines, the fluid
motion is usually assumed to occur on flow surfaces that are: (1) sur-
faces of revolution about the axis of the turbomachine (blade—to4blade
solutions, references 1 and 2, for example) or (2) mean passage surfaces
that are congruent with the mean blade surfaces (hub—to—shroud solutions,
references 5 and 4, for example). Actually, the flow surfaces deviate
from the orientation assumed for the two-dimensional solutions and, in
the direction of flow, become progressively more tilted and distorted.

This deviation of the flow surfaces from.their assumed orientation is
caused by spanwise variations of blade loading and, in rotating blade
rows, by rotation of the fluid particles relative to the passage in a
plane normal to the axis of the'blade row. This rotation is required
to maintain the rotational or irrotational character of the absolute
fluid motion.