A Solution of the Direct and Inverse Potential Problems for Arbitrary Cascades of Airfoils Page: 3 of 51
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NACA ARR No. L4K22b
(1) Methods that regard a blade of the cascade as
an isolated airfoil operating in a flow composed of a
free-stream velocity and a disturbance velocity due to
all the other blades of the cascade. The method applies
best to cascades of thin airfoils with small solidity.
(See reference 1, p. 70, and bibliography contained-
(2) Stream-filament methods, which regard the
space between the blades of the cascade as channels of
varying area but in which the streamlines are uniform
or of simple curvature. These methods apply best to
cascades of high solidity in which, moreover, the flow
is smooth (shock free) at entrance.
(3) Methods based on conformal transformation of the
cascade. These methods may be subdivided as follows:
(a) Methods based on the concept of the equiva-
lent cascade of flat plates; that is, the cascade
of flat plates with spacing equal to that of the
given cascade, with blade angle equal to the zero-
lift angle of the given cascade, and into which the
given cascade can be transformed conformally.
Extensive use of this concept is made in reference 1,
on the basis of which are given approximate solu-
tions of the direct and inverse problems for cascades
of various types of shape and for various ranges of
solidity. The solutions are approximate mainly
because of the methods given for the determination
of the equivalent cascade from the given cascade
or vice versa.
(b) Particular conformal transformations that
yield special classes of shape for which the flow
can be calculated exactly (such as those of refer-
ence 1, p. 55, and reference 2).
(c) Exact methods for arbitrary airfoils
or pressure distributions in cascade, such as
those that exist for isolated airfoils. For
this purpose, Weinig (reference 1, p. 90) uti-
lizes the basic known transformation from a cas-
cade of flat plates to a single circle. By this
transformation, the given cascade transforms to
a near circle. The near circle, p'-plane, i- then
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Mutterperl, William. A Solution of the Direct and Inverse Potential Problems for Arbitrary Cascades of Airfoils, report, December 1944; (https://digital.library.unt.edu/ark:/67531/metadc61263/m1/3/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.