Preliminary Analysis of Problem of Determining Experimental Performance of Air-Cooled Turbine 2: Methods for Determining Cooling-Air-Flow Characteristics Page: 3 of 22
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NACA M E50A06
The evaluation of the cooling and performance characteristics
of a turbine (and of an engine in which the turbine may be used)
with blades through which cooling air is circulated requires knowl-
edge of the characteristics of the cooling air; that is, pressure,
temperature, and velocity as the air proceeds from the roots to the
tips of the blades. These characteristics are required in the
determination of such factors as the heat flow, blade temperatures,
blade-to-cooling-air heat-transfer coefficients, and effective
cooling-air temperatures. These factors are discussed in refer-
ence 1. In addition, the cooling-air characteristics are required
to evaluate the work of pumping the air through the blades and the
work required in the compressor to compress the air to the pressure
required at the blade roots. The turbine-pumping work is usually
insufficient to raise the air pressure from atmospheric to that
required at the blade tip to permit the air to flow out of the blade
and mix with the combustion gas stream. The air must consequently
be raised above atmospheric pressure at the blade root by some
means external to the turbine, for example, by the compressor. If
the required pressure is known, it is possible to determine the
bleedoff point on the compressor. In the investigation of a tur-
bine, certain data must be obtained and formulas developed so that
evaluations of the type discussed can be made for various flight
conditions.
Formulas for determining the cooling-air-flow characteristics
in the turbine-blade cooling-air passages are suggested herein.
The formulas must be verified and the coefficients appearing therein
evaluated by investigation of cooled turbines. Discussions of work
that leads to the suggested formulas are given in some cases, so
that readers unfamiliar with the subject may obtain some background
knowledge.
ANALYSIS OF FORMULAS FOR COOLING-AIR-FLOW CHARACTERISTICS
Mach Number in Blade Cooling-Air Passage
An analysis of the cooling-air flow through turbine blades based
on one-dimensional flow has been developed (reference 2). The work
in general is based on the analysis of Shapiro and Hawthorne (refer-
ence 3); the main additions of reference 2 to this work is the
evaluation of the generalized body force in the equations of refer-
ence 3 for the case of a rotating body and the method of numer-
ically solving the equations. From this analysis, the variation of
Mach number of the air through the turbine-blade passage was deter-
mined as2
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Ellerbrock, Herman H., Jr. Preliminary Analysis of Problem of Determining Experimental Performance of Air-Cooled Turbine 2: Methods for Determining Cooling-Air-Flow Characteristics, report, June 7, 1950; (https://digital.library.unt.edu/ark:/67531/metadc58404/m1/3/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.