Handbook of Turbomachinery Second Edition Revised - Ventech!

SOURCES AND EFFECTS OF UNSTEADINESS
Propagation of Wake and Pressure Disturbances
Unsteady disturbances travel in the form of flow characteristics. Each
characteristic has a distinct traveling velocity (magnitude and direction).
Although the basic characteristics are obtained from the linear Euler
equations (hence inviscid without any dissipation mechanisms), they are
extremely useful as the basis for developing computational models,
understanding flow physics, and interpreting computational (as well as
experimental) results. For a 2D inviscid compressible flow with ‘‘V’’ being
the local flow velocity and ‘‘A’’ the local speed of sound, there are four flow
characteristics: (1) entropy disturbance, convected at a local flow velocity V,
running downstream; (2) vorticity disturbance, convected at local velocity
V, also running downstream; (3) an acoustic (pressure wave) disturbance,
propagated at a speed of V þ A, always running downstream; and (4)
another acoustic (pressure wave) disturbance, propagated at a speed of
V A, which runs either upstream for a subsonic flow, or downstream for a
supersonic flow.
In a turbomachinery context, the spatial nonuniform velocity and
pressure distributions in a blade row are sensed as unsteady disturbances in
adjacent blade rows. More specifically, wakes shed from upstream blades
contain both entropy and vorticity components and normally have little
static pressure nonuniformity (until they impinge on downstream blades).
Therefore, a wake disturbance is convected downstream at a local flow
velocity. Anexample is shown in Fig. 1,whereincoming unsteady wakes are
convected through a turbine passage and distorted in the nonuniform
velocity field. For both compressor and turbine situation, a wake
disturbance mainly affects downstream rows, though unsteady pressures
generated when it hits the downstream blade also propagate upstream.
On the other hand, nonuniform ‘‘steady’’ static pressure necessarily
associated with blade loading in one blade row can be seen as unsteadiness
by both upstream and downstream relatively moving blade rows, assuming
that the axial-flow velocity is subsonic. The propagation of acoustic
(pressure) waves is largely an inviscid phenomenon, which is probably why
an interference with unsteady pressure disturbances is often called
‘‘potential interaction.’’ Wakes have measurable velocity gradients and
therefore viscous dissipation always coexists with wake convection,
although the kinemics of wake convective transportation itself can be
described in an inviscid manner. An example of the potential interaction can
be seen in Fig. 2for atransonic turbine stage, where pitchwise nonuniform
pressures of the upstream stator interact with the rotor in a complex
manner, largely due to reflection of pressure disturbances. It is noted from
Copyright © 2003 Marcel Dekker, Inc.