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National Advisory Committee for Aeronautics, Technical Notes - Two Axial Symmetry Solutions for Incompressible Flow Through a Centrifugal Compressor with and Without Inducer Vanes

Solutions for axially symmetric flow through an impeller with and
without inducer vanes were obtained'by relaxation methods using an
analysis developed herein. The fluid was considered inviscid and '
incompressible. The impeller selected was of arbitrary design except
that the impeller blades were assumed to have zero thickness and to
consist of radial elements. Plots of streamlines, lines of constant
velocity, and lines of constant tangential blade force (related to the
pressure difference between blade surfaces) are presented.and dis— '
cussed.

For impellers with thin, high-solidity blades, the effects of
inducer vane curvature on the streamlines and on the axial and radial
components of velocity were found to be small and'were restricted to
those regions in which the vanes were curved.

Although trial-and—error methods of develOpment may result in
centrifugal compressors of acceptable efficiency, they can provide only
design information based on geometric properties and not on fundamental
aerodynamic principles. Without design information based on funda-
mental principles, the experience of previous developments cannot
easily be applied to the design of new compressors with different geo—
metry or operating requirements, nor in general can essential features
of a good design be separated from those having little effect on per-
formance. The flow must therefore be experimentally and theoretically ‘
investigated in order that fundamental laws of design may be formulated
which can'be codbined with designing skill to produce consistently good
compressors.

For a given set of operating conditions, the flow in a centrifugal
compressor depends on the compressibility and viscosity of the fluid '
and on the three—dimensional geometry of the conmressor. In order that
the flow may be analyzed withmlt prohibitive effort, the fluid is
usually assumed to be inviscid, and for some investigations the effects
of compressibility are neglected. Also, in most analyses, variations
in the flow are limited to two dimensions lying either on a plane con-
taining the axis of the impeller (designated the meridional plane) or
on a surface of revolution (designated the blade—to-blade plane) gen—
erated by rotating some characteristic line in the meridional plane
(for example, the mean line between the hub and the shroud) about the
axis of the impeller.