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National Advisory Committee for Aeronautics, Research Memorandum - Cooling of Gas Turbines - VIII - Theoretical Temperature Distributions Through Gas Turbine with Special Blades and Cooling Fins on the Rim

A theoretical analysis of the radial—temperature distribu-
tion through a turbine with specially designed turbine blades was
made for a turbine with and without cooling fins on the rim. The
effect on blade life and effective gas temperature of the addi-
tion of cooling fine on the rim was investigated for selected
turbine operating conditions. The accuracy: of the radial-
temperature distribution was then determined by finding a two-
dimensional temperature distribution through the turbine rim and
rotor for the turbine with and without cooling fine on the rim.
The two-dimensional distribution was obtained by consideration
of radial- and axial-temperature gradients and by application of
the relaxation method to the resulting differential equation. A
three-dimensional temperature distribution for a section of the
turbine rim near a blade root was then determined by use of three-
dimensional relaxation.

The results showed that, for the selected conditions, the
addition of cooling fins on the rim permitted only a slight increase
in the effective gas temperature. The two-dimensional investigation
proved the radial distribution to be sufficiently accurate for most
applications. The three-dimensional study indicated the type of
temperature gradients to be expected in a section of the rim sur-
rounding a blade root and may be applied to determinations of rim
thermal stresses.

High-temperature materials now available for gas turbines
limit turbine -inlet temperatures to about 1500° r,- consequently,
some method of turbine cooling is necessary if inlet temperatures
above this value are to be used. Investigations have been con-
ducted at the NACA Cleveland laboratory (references 1 to 9) to
determine the relative merits of indirectly cooling turbine blades
(by conducting heat away from the blades) and of directly cooling
them (by passing air or liquids through hollow passages in the
blades). Increases in gas temperatures of the order of 100° to
200° F were found possible for indirect cooling; considerably
greater increases in gas temperatures were made possible by direct
cooling with either air or water as the coolant.