Handbook of Turbomachinery Second Edition Revised - Ventech!

St Stanton number h/(rCpu?)
u? Free-stream fluid velocity (m/s)
V Control volume (m 3 )
Vx, Vy, Vf Velocity components in the x, y, r directions, respectively (m/
s)
x Axial direction in an orthogonal cylindrical coordinate
system (m)
e Fluid turbulence kinetic energy dissipation rate (kg/m-s)
g Intermittancy
n Kinematic viscosity (m 2 /s)
y Azimuthal coordinate in an orthogonal cylindrical system
(rad)
r Fluid density (kg/m 3 )
EARLY COMPUTATIONAL METHODS
The first turbines representing what we now think of as ‘‘modern’’
turbomachinery appeared with the invention of the axial flow steam turbine
by Parsons in the 1880s. (See, for example, Horlock [1].) Turbine
aerodynamic design methods at that time consisted of little more than
guess work as to the nozzle guide vane and rotor blade shapes, the optimum
number of blades, reaction, and other features. However, World War II led
to quasi-empirical databases and design methods from marine, ground
power turbines, and aircraft turbo-supercharger designs. Heat transfer to
the airfoils was generally not a major consideration, as the maximum
material use temperatures were higher than inlet gas total temperatures.
After the war, the development of computers allowed the use of
computational fluid dynamics (CFD) in many engineering fields including
turbomachinery, albeit primitive by today’s standards. As simplified as these
early CFD tools were—dealing with only inviscid flow, for example—their
results were often quite successful, and many are still in use today. In Fig. 2,
we illustrate one of the first major advances in turbomachinery CFD after
World War II: Wu’s Quasi-3-D stream surface model of the mainstream
flow [2]. Wu’s calculation method introduced the concept of the blade-toblade
stream surfaces (S1) and the meridional (hub-to-tip) stream surfaces
(S2) on which sets of 3D models (the governing equations) of the flow could
be written. In writing a 3D model on a 2D surface, we mean that one must
assume the surface normal velocity component to S1 or S2 is known. The
surface normal component at a point on, say, the S1 surface will be one of
Copyright © 2003 Marcel Dekker, Inc.