Handbook of Turbomachinery Second Edition Revised - Ventech!

volume will be equal to the accumulation rate in the control volume with
time. In this general scheme the continuity, energy, and x-momentum
equations to be solved on the grid are
mass : SðrVx dAx þ rVy þ rVrdArÞ ¼
energy : SðrVxhodAx þ rVyhodAy þ rVrhodArÞ ¼
x momentum : SððP þ rV 2 xÞdAx ðDV=DtÞDr
ðDV=DtÞDðrEÞ
þ rVyVxdAy þ rVrVxdArÞ ¼DV=DtðDðrVxÞÞ
Similar relationships govern the r-momentum and the moment of
momentum.
There are many important details left unmentioned here on Denton’s
method concerning the numerical solution technique, stability and damping,
convergence, etc. These are available in the extensive literature on his
method that Denton and his colleagues have published. Some other early
developers of similar fully 3D methods deserving mention include Rai [23],
Ni [24], and Ha [25]. Most of these follow the basic finite-volume, multigrid
idea. For details on these methods, the reader is referred to the respective
citations.
CALCULATIONS AND MEASUREMENTS—FULLY 3D
METHODS
Figure 7shows asingle-stage, high rim speed, high-pressure turbine with a
significant 3D design studied by Kingcombe et al. [26] at the Defense
Equipment Research Agency (DERA) in the United Kingdom. The rigmeasured
turbine aerodynamics were compared to the 3D Denton code. The
vane drawing, Fig. 8, shows measured and computed isentropic Mach
number profiles over the vane pressure surface. Agreement with the
experiment is reasonably good, demonstrating the power of applying a
true 3D code to the analysis of this very 3D geometry.
For the heat transfer, Fig. 9gives the measured vane midspan heattransfer
coefficient, expressed as Nu, taken from the vane cascade in
DERA’s test facility. Also shown on the plot is a prediction using the
Denton 3D Euler method and the STAN5 boundary-layer code incorporating
the Van Driest damping function (see [11]), transition start length
correlation by Seyb [27], and transition length correlation by Chen and
Thyson [28]. (Note that contrary to usual custom, the suction side is on the
left.) Kingcombe et al. state that the transition location and length were
‘‘quite well’’ predicted although at some points the predictions and
measurements were in better agreement than others. What is important is
Copyright © 2003 Marcel Dekker, Inc.
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