Handbook of Turbomachinery Second Edition Revised - Ventech!

tend to be large, due to the necessity of modeling in three dimensions not
only multiple blade rows but also multiple blade passages, in order to
achieve a periodic segment of the annulus. Such computational requirements
can rapidly exceed the time constraints and computer resources of
most component design efforts at the present time.
One approach to avoid the massive amounts of calculation time
required for an unsteady 3D blade-row interaction analysis is to perform a
steady-flow solution for each individual blade row, and communicate
circumferentially averaged flow conditions between adjacent blade rows via
a mixing plane. Because the flow field at each mixing plane is essentially
time-averaged, nonperiodic circumferential conditions that result from
dissimilar blade counts are not an issue. Therefore, only one passage needs
to be analyzed for each blade row. As a result, the problem size and
calculation time are considerably reduced, compared to an unsteady bladerow
interaction analysis. The mixing plane approach has been taken by
Dawes [62], with his multistage program, and has also been applied to the
method of Hah and Wennerstrom [63].
Adamczyk [64] has developed an alternative approach for multiple
blade-row analyses, which utilizes an ‘‘average-passage’’ model. The
governing equations in this model provide a time-averaged 3D representation
of the flow through a typical passage of each blade row. Individual
solutions are performed for each blade row, with the effects of adjacent rows
being modeled by averaged blockage and body forces. A correlation model
is used to represent the interaction between blade rows. The computational
cost of the average-passage model is intermediate between the mixing plane
model and the unsteady blade-row interaction analysis. However, the
average-passage simulation becomes more complex and costly as the
number of blade rows increases.
The decision to utilize a full unsteady analysis technique depends
largely on what type of information is desired. If only time-averaged flow
properties are of interest, then a steady, isolated blade-row analysis or a
simplified blade-row interaction model should suffice, with a considerable
savings in computational effort. However, in other cases, the ability to
resolve the time-unsteady nature of the flow is essential, to model such
effects as vortex shedding, wake passage, or blade-row interaction. Then a
full unsteady analysis is required.
Numerical Solution Techniques
The subject of numerical solution techniques is too extensive to be covered
in any detail in this chapter. Only a cursory discussion of methods
appropriate to the solution of the time-dependent Reynolds-averaged
Copyright © 2003 Marcel Dekker, Inc.