<DOC>
<DOCNO>
987
</DOCNO>
<TITLE>
a general theory of three dimensional flow in subsonic and supersonic
turbo-machines of axial-radial-and mixed-flow types .
</TITLE>
<AUTHOR>
wu, c.
</AUTHOR>
<BIBLIO>
naca tn 2604, 1952 .
</BIBLIO>
<TEXT>
a general theory of steady three-dimensional flow of a nonviscous fluid
in subsonic and supersonic turbomachines having arbitrary hub and casing
 shapes and a finite number of blades is presented . the solution of the
 three-dimensional direct and inverse problem is obtained by investigating
an appropriate combination of flows on relative stream surfaces
whose intersections with a z-plane either upstream of or somewhere inside
the blade row form a circular arc or a radial line . the equations
obtained to describe the fluid flow on these stream surfaces show
clearly the several approximations involved in ordinary two-dimensional
treatments . they also lead to a solution of the three-dimensional
problem in a mathematically two-dimensional manner through iteration .
the equation of continuity is combined with the equation of motion in
either the tangential or the radial direction through the use of a
stream function defined on the surface, and the resulting equation is
chosen as the principal equation for such flows . the character of this
equation depends on the relative magnitude of the local velocity of
sound and a certain combination of velocity components of the fluid . a
general method to solve this equation by both hand and high-speed
digital machine computations when the equation is elliptic or hyperbolic
 is described . the theory is applicable to both irrotational and rotational
absolute flow at the inlet of the blade row and at both design
and off-design operations .
</TEXT>
</DOC>
