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Measurements of Temperature Variations in the Atmosphere Near the Tropopause with Reference to Airspeed Calibration by the Temperature Method

A solution is presented for three-dimensional, incompressible, non—
viscous, potential flow in a rotating impeller passage with zero through
flow. The solution is obtained.for a conventional impeller with
straight blades but with the inducer vanes removed and the impeller
blades extended upstream.parallel to the axis of the impeller. By super-
position of solutions two additional examples are obtained for different
ratios of compressor flow rate to impeller tip speed. The three—
dimensional solutions are compared with corresponding two-dimensional
solutions and it is concluded that, at least for the type of impeller
geometry investigated, two-dimensiOnal solutions can be combined to
describe the three-dimensional flow in rotating_impellers with suffi-
cient accuracy for engineering analyses.

As an aid to better understanding of flow conditions in rotating
impeller passages, methods of analysis have been developed in the past
for potential_nonviscous-flow. In order to achieve solutions with a
reasonable expenditure of effort, all methods are based on two—
dimensional assumptions, in that the flow is restricted, by assumption,
to specified flow surfaces in space. Either of two types of surface
are usually assumed for the flow: first, the mean blade (or passage)
surface on which flow conditions vary from.hub to shroud but are con—
sidered constant in the circumferential direction (axial-symmetry solu-
tions, references I and 2), or, second, surfaces of revolution on which
flow conditions vary from one blade to.the next, but normal to which
the flow conditions are considered constant (blade-to—blade solutions,
references 5 and 4).

If the streamlines of an axial symmetry solution are used to
generate surfaces_of revolution around the axis of the impeller, the
totality of the blade-tonlade solutions on these surfaces of revolution
constitute a quasi-three-dimensional solution (reference 5) because the
solutions indicate variations in flow conditions throughout the impeller
passage. However, because the flow is constrained to surfaces of revo-
lution, the solution is not three dimensional in the exact sense of the
word. No complete three-dimensional solutions for rotating impeller
passages exist in the.literature, and a solution has therefore been
obtained at the NACA Lewis laboratory.