Handbook of Turbomachinery Second Edition Revised - Ventech!

Aerodynamic Interaction (Unsteady Losses)
Regarding aerothermal influences of a wake shed from an upstream blade
on a downstream relatively moving blade row, there are several different but
related issues:
1. How do we quantify flow loss in an unsteady environment?
2. How is the mixing loss of wake velocity deficit influenced by the
presence of a downstream blade row?
3. How does a wake disturbance affect the loss generation of
downstream blade rows?
Entropy/stagnation Pressure Decoupling. This is a basic issue concerning
transportation of flow losses in an unsteady environment, relevant to
presentation and interpretation of unsteady losses computationally and
experimentally. For a thermodynamic process, we have
1
T0dS ¼ dh0 dP0
r 0
Hence, in a steady adiabatic flow situation, a higher entropy is always
associated with a lower stagnation pressure, because the stagnation enthalpy
h0 remains constant along a streamline. Essentially, stagnation pressure
deficit is a proper measure of entropy rise (loss) in steady flows. For an
unsteady flow, however, this is not the case. Neglecting the viscous and heat
conduction terms, the unsteady energy equation can be written as
dh0
dt
1 qP
¼
r qt
Therefore, h0ðT0Þ will not be constant along a stream line if static pressure is
varying in time, as it would be once an unsteady wake impinges on blade
surface.
An inviscid unsteady flow calculation by the author [2] for a lowpressure
turbine cascade subject to periodic unsteady incoming wakes is
used to illustrate this point. Wakes shed from the upstream blade row are
modeled by specifying inlet wake profiles, traveling relatively in the
circumferential direction at the rotor rotating speed. As can be seen from
the instantaneous entropy contours (Fig. 1), for the region upstream of the
blade passage, wakes are convected at an essentially uniform velocity, and
the time-averaged stagnation pressure and entropy would be more or less
uniformly distributed along the pitch upstream of the blade row. By looking
at the velocity triangles, we can see that within the wake there would be a
relative velocity component. The entropy within a moving wake is thus
convected relatively along the wake. Each wake first hits the pressure surface
Copyright © 2003 Marcel Dekker, Inc.
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