Handbook of Turbomachinery Second Edition Revised - Ventech!

available to explore fully viscous solutions of the 3D Navier–Stokes
equations in reasonable times. Because external surface heat transfer is
essentially driven by the main stream flow conditions (through the structure
of the intervening boundary layer), standard heat-transfer correlations
could be used along the predicted streamlines to compute the heat transfer
to the surface.
Wu’s method was ‘‘packaged’’ and improved by researchers at what is
now the USA’s NASA/Glenn Research Center as the well-known computer
codes MERIDL and TSONIC [3, 4]. These codes are still used in many CFD
calculations, for example, to quickly generate an approximate starting
solution for more complex and time-consuming Navier–Stokes numerical
solutions. A major drawback of Wu’s Quasi-3D method is that it is only
approximate (by design, of course). The procedure also requires much
human intervention and application of design experience during the iterative
solution process to obtain the most useful results. Researchers therefore
continued to look for both faster and more accurate methods, particularly
those that incorporate viscosity and other effects naturally.
The first major step for including viscosity became available in the late
1960s and early 1970s through numerical analysis of flow-path boundary
layers. The publication that started much of the work was by Patankar and
Spalding [5] in which the authors numerically solved the 2D, steady
boundary-layer equations (simplified forms of the Navier–Stokes equations)
using a scaled coordinate system that adapts to the boundary-layer
thickness as it grows downstream. The boundary-layer differential
equations are of the parabolic type; thus only the values of the upstream
independent variables are needed to solve for the downstream values.
Variation in the solution is wholly determined by the variations in the free
stream and the solid surface over which the fluid flows. This technique
formed the vehicle for many, many studies of skin friction drag and heat
transfer, for attached boundary layers. Patankar–Spalding also became the
workhorse numerical technique for many studies of boundary-layer
turbulence that popularized the k-e turbulence model [6] and others.
Parabolic boundary-layer solvers using the Patankar–Spalding procedure
were written by NASA and others under the names of STAN5 [7] and
TEXSTAN [8]. Many others were developed in academia and industry.
These codes were used with the TSONIC/MERDIL passage-flow solvers to
give a technique fast and robust enough for design work but with greater
accuracy than the part-calculation, part-correlation techniques used
previously. Separation still had to be dealt with empirically because of the
inability of the parabolic equations to be solved under conditions favoring
separation, i.e., strong adverse pressure gradients. The transition starting
point and transition lengths also need empirical expressions for their
Copyright © 2003 Marcel Dekker, Inc.