Handbook of Turbomachinery Second Edition Revised - Ventech!

passage domain is required. The method is currently extended to a
multistage environment to analyze rotor–stator and rotor–rotor (stator–
stator) interaction (aperiodic and clocking) effects on both aerothermal and
aeromechanical performances. The whole annulus unsteady flow field is
reconstructed from the single-passage result according to the phase-shifted
periodicity. By introducing the nonrotating spatial harmonics, representing
upstream wakes, the aperiodic disturbances due to different rotor–rotor
blade counts as well as the clocking effects are efficiently included in a
single-passage solution.
Some further comments need to be made on this kind of unsteady flow
modeling based on flow decomposition, which is seemingly more complex
(undesirable!) than the straightforward time-domain unsteady CFD
methods. First, the unsteady disturbances we are dealing with are generally
small in magnitudes, though their effects may not be. To ensure small
unsteadiness to be adequately resolved, numerical errors (artificial dissipation
and dispersion) need to be much smaller compared to the physical
signals to give a reasonable ‘‘signal-to-noise’’ ratio. For instance, in the field
of computational aeroacoustics, it has been evident that conventional
unsteady CFD algorithms with second-order temporal and spatial
discretizations are unable to adequately extract small but meaningful
physical acoustical disturbances from a background flow. In the context of
unsteady turbomachinery flows, it won’t be difficult to find situations where
physical unsteady disturbances are easily ‘‘washed off’’ by numerical
dissipations. Since magnitudes of numerical errors are normally in
proportion to those of flow variables, it would be more accurate to directly
solve the unsteady perturbations. Second, by decomposing the timeaveraged
flow and the unsteady part, we can use the same numerical
algorithms and boundary condition treatments for both a time-averaged
flow and a pure steady flow. The past experiences suggest that usefulness of
comparing different unsteady CFD computations depends measurably on
the consistency of the ways these computations are carried out. Hence use of
the same numerics in both steady and time-averaged calculations should
help to identify and understand true unsteady effects.
Some Comments on Turbulence/Transition Modeling
It has been a standard practice that turbulence models tuned for steady
flows are used quasisteadily for unsteady flows. The uncertainties associated
with this must be recognized. At the same time, it is felt that this should not
always be used as an explanation (or excuse!) for poor agreements between
computational and experimental results. For instance, one may find the
turbulence/transition modeling will strongly affect blade aerodynamic
Copyright © 2003 Marcel Dekker, Inc.