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National Advisory Committee for Aeronautics, Technical Notes - A Rapid Approximate Method for Determining Velocity Distribution on Impeller Blades of Centrifugal Compressors

A rapid approximate method of analysis was developed for both com-
pressible and incompressible, nonviscous flow through radial— or mixed-
flow centrifugal compressors with arbitrary hub and shroud contours and
with arbitrary blade shape. The method of analysis is used to deter—
mine approximately the velocities everywhere along the blade surfaces,
but no information concerning the variation in velocity across the
passage between blades is given.

In eight numerical examples for two—dimensional flow, covering a
fairly wide range of flow rate, impeller-tip speed, number of blades,
and.blade curvature, the velocity distribution along the blade surfaces
was obtained by the approximate method of anaLysis and compared with the
velocities Obtained.by relaxation methods. In all cases the agreement
between.the approximate solutions and the relaxation solutions was
satisfactory except at the impeller tip where the velocities obtained
by the approximate method did not, in general, become equal on both
surfaces of the blade as required.by the Joukowski condition.

In impellers of centrifugal compressors, part of the viscous losses
and the phenomena of surge and Choke are related to the velocity dis—
tribution on the blade surfaces. Viscous losses in impellers are
associated with the boundary layer along the flow surfaces. The growth
of this boundary layer depends on the velocity variation along the flow
surfaces just outside of the boundary layer. In particular, if the
velocity decelerates rapidly along the blade surfaces, the boundary
layer may separate causing large mixing losses. Also, if the velocity
at any point along the blade surface is sufficiently greater than the
local speed of sound, shock losses will result. The choke phenomenon
occurs when the average velocity between blades is sonic. This average
sonic velocity is characterized.by local supersonic velocities along
portions of the suction surface of the blade. One possible cause of
surge in centrifugal impellers is the formation of relative eddies on u
the pressure surface of the blade (reference 1). These eddies are
characterized by negative velocities, opposed to the general flow
direction, along portions of the pressure surface. In order to analyze
the performance of centrifugal impellers it is therefore necessary to
determine the velocity distribution on impeller blades.

Several methods of analysis that can be used to determine the
variation in velocity along blades with finite spacing have been
developed for two—dimensional incompressible flow (references 2 to 5,
for example) and compressible flow (references 1 and 6). All these
methods require considerable labor and therefore are not convenient
tools for analyzing the performance of an arbitrary impeller design.