THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS
Three Park Avenue, New York. N.Y. 10016-5990
99-GT-452
The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the Society or of its Divisions or
Sections, or printed in Its publications. Discussion is printed only lithe paper is published in an ASME Journal. Authorization to photocopy
for internal or personal use is granted to libraries and other users registered with the Copyright Clearance Center (CCC) provided
$3/article is paid to CCC, 222 Rosewood Dr., Danvers, MA 01923. Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department.
Copyright 1999 by ASME
All Rights Reserved
Printed in USA
STRUCTURE AND PROPAGATION OF ROTATING STALL
IN A SINGLE- AND A MULTI-STAGE AXIAL COMPRESSOR
11110111119,111 11111111
H. M. Saxer-Felici, A. P. Saxer, F. Ginter, A. Inderbitzin, G. Gyarmathy
Turbomachinery Laboratory
Institute of Energy Technology
Swiss Federal Institute of Technology (ETHZ)
8092 Zurich, Switzerland
ABSTRACT
The structure and propagation of rotating stall cells in a single- and
a two-stage subsonic axial compressor is addressed in this paper using
computational and experimental analysis. Unsteady solutions of the 2o inviscid compressible (Euler) equations of motion are presented for
one operating point in the fully-developed rotating stall regime for both
a single- and a two-stage compressor. The inviscid assumption is
verified by comparing the single-stage 2-D inviscid/compressible
solution with an equivalent 2-D viscous (Navier-Stokes) result for
incompressible flow. The structure of the rotating stall cell is analyzed
and compared for the single- and two-stage cases. The numerical
solutions are validated against experimental data consisting of flow
visualization and unsteady row-by-row static pressure measurements
obtained in a four-stage water model of a subsonic compressor.
The CFD solutions supply a link between the observed experimental
features and provide additional information on the structure of the stall
flow. Based on this study, supporting assumptions regarding the driving
mechanisms for the propagation of fully-developed rotating stall cells
and their structure are postulated. In methodical respect the results
suggest that the inviscid model is able to reproduce the essentials of the
flow physics associated with the propagation of fully-developed, fullspan rotating stall in a subsonic axial compressor.
p0
70
TRS
U2
ww
a, R
ACp
stagnation pressure
stagnation temperature
rotor period
rotating stall period
time
rotor speed at Euler radius
axial & tangential relative velocity components
absolute and relative flow angles (from axial)
blockage factors from unsteady pressure trace
Eq.( I) & from instantaneous cell width Eq. (2)
static density
pressure coefficient = (p 13)/( I -p l U22 )
flow coefficient at Euler radius = ux /U2
stage static-to-static pressure coefficient
2
= (h3 — h 1 )/ Cl; (air), = (p3 — p l )/(p U2 ) (water)
—
Subscripts
1,11. 12, 2. 22, 23, 3
axial stations, see Fig. 1
Superscripts
time-averaged value
I. INTRODUCTION
NOMENCLATURE
Abbreviations
CFD
IGV
RS
tot
computational fluid dynamics
inlet guide vanes
rotating stall
frame of reference
Symbols
F. R
front, rear boundaries of stall cell
It
static enthalpy
static pressure
For decades, the operational stability of compression systems has
been a major concern of industrial and aeroengine gas turbine designers,
see for example the early work of Emmons etal. (1955). In this respect,
rotating stall (RS) is a key flow phenomenon limiting the operational
stability of compressors. In order to better predict its occurrence, and
ultimately to control it, further research is required. RS is identified by
large scale flow distortions propagating around the compressor annulus
at a fraction of the rotor speed. It often precedes surge, a phenomenon
involving mass flow pulsations within the whole compression system.
RS, as well as surge, detrimentally affects the performance and
sometimes the structural integrity of the machine.
Presented at the International Gas Turbine & Aeroengine Congress & Exhibition
Indianapolis, Indiana — June 7-June 10, 1999
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
Ranging from stall inception, see for example (Gamier et al., 1993),
(Tryfonidis et al., 1995), (Camp & Day, 1997). to operation in deep stall
with or without surge (Day et at, 1978), (Das & Jiang, 1984),
(Breugelmans et al., 1985), (Mathioudalcis & Breugelrnans, 1988), the
studies describing and analyzing the unstable behaviour of compressors
are mainly based on experimental work. From these observations a
number of theoretical linear and non-linear models (Greitzer, 1976a,b),
(Moore & Greitzer, 1986), (Demargne & Longley, 1997) have been
developed and applied to study the dynamics of the whole compression
system with a view to ultimately control RS and surge (Paduano at al.,
1993), (Gysling & Greiner, 1994). An other approach is to use CFD to
focus on the phenomenological understanding of the structure of
rotating stall from a fluid dynamics point of view (Outa et at, 1994),
(Nishizawa & Takata, 1994), (Saxer-Felici et al., 1998a). Some
approaches combine CFD with semi-empirical models (Hendricks eta].,
1996), (Longley, 1997). A comprehensive review of compressor
stability models is given by 1,ongley (1993).
The present work concerns the fluid dynamic behaviour of fullydeveloped, full-span RS in high hub-to-tip ratio axial compressors using
computational analysis and experimental data. The configuration
presented here is relevant for repeating stages as found in the rear part
of modern land-based compressors. The base flow is not far from being
2-D in such low aspect ratio bladings.
The present objective is to study the structure of fully-developed
rotating stall and the mechanisms for its propagation in a single- and
two-stage axial compressor using two numerical methods and
experimental results. This is somewhat unusual as the classical CFD
research approach is to focus on RS inception (He, 1997), (Gong et at,
1998), (Hoying et al., 1998). The first numerical method, MULTI2
(Saxer, 1992), uses the Euler equations to solve the inviscid
compressible flow while the second, FENFLOSS (Ruprecht, 1989),
(Ginter, 1997), solves the incompressible Navier-Stokes equations with
a mixing-length turbulence model.
Both numerical techniques are based on the 2-D unsteady equations of
fluid motion. The 2-D assumption is motivated by experimental
observations, see for example (Day et al., 1978), which point out the
essentially axial-tangential nature of full-span RS in low aspect ratio
bladings. Also the experiments of (Das & Jiang, 1984) with a high hub/
tip ratio blading indicate that 3-D effects are markedly reduced as the
axial gaps are reduced.
The use of the Euler equations for propagating rotating stall cells is
prompted by previous experimental and theoretical studies (Cumpsty &
Greitzer. 1982), (Longley, 1993), (Gyarmathy, 1996), (Gong et al.,
1998), which clearly indicate the crucial impact of fluid inertia for stall
cell propagation. Furthermore, as shown in external (Rizzi & Eriksson,
1984) and internal (Felici, 1992) aerodynamics, the Euler equations
allow the generation and capture of strong vortical flows as encountered
during rotating stall operation.
The two numerical methods are applied to a single- and a two-stage
axial compressor bearing similarity (File et al., 1997) with any of the
repeating stages of the four-stage water model of a subsonic axial
compressor (Hof et at, 1996). Because of the limitations linked to the
choice of the CFD models applied (no 3-D effects, number of stages)
and the differences between CFD and experimental setups, only the
general mechanism of RS cell propagation and cell structure is
discussed, while overlooking detailed flow features which are much
smaller than, say, the size of the blade pitch. Reference is made
throughout the paper to previous experimental work on other relevant
configurations to point out the validity of the current CFD approach as
well as the existing discrepancies. This step is required in order to apply
the present inviscid CFD method for the control of RS in a future phase.
Due to the limited computational resources available, a full-annulus, 3D unsteady, viscous multi-stage simulation is here not possible. Instead,
different contributions to the RS phenomenon are pointed out by a
stepwise removal of different levels of simplifications (for example
inviscid vs. viscous, single-stage vs. two-stage).
The paper is organized as follows. Both the inviscid/compressible and
viscous/incompressible numerical schemes are briefly described,
together with the in-house experimental setup. CFD and experimental
global data such as performance map and blockage are discussed first
Then, detailed unsteady solutions for the single-stage compressor are
presented by cross-comparing the inviscid/compressible and the
viscous/incompressible solutions with in-house experimental data. This
supports the validity of the inviscid assumption and provides the basis
to discuss the structure of the rotating stall cell. The time-variations of
the flow parameters in the two-stage compressor are then shown and
discussed together with CFD and experimental flow visualization in the
absolute and RS cell-based frame of reference. Finally a summary of the
essential results and the conclusions are drawn regarding the flow
physics associated with full-span. fully-developed RS in low subsonic
axial compressors.
II. NUMERICAL PROCEDURES
As described hereafter, the time-marching solvers MULT12 (Saxer,
1992) and FENFLOSS (Ruprecht, 1989), (Ginter, 1997) differ both in
the physical assumptions for the flow to be solved, as well as in their
basic numerical schemes and grid structures.
11.1 Inviscid flow solver (MULT121
A multi-block grid generator MELLIP (Saxer-Felici, 1996) and an
unstructured flow solver MULTI2 (Saxer, 1992) are used. MELLIP
solves the Poisson equations in the blade-to-blade plane. An iterative
successive line over-relaxation technique is applied on blocks of C and
H grid types with moving block boundaries, resulting in an overall
unstructured smooth grid. The source terms are calibrated to control
spacing and orthogonality at the blade surfaces.
MULTI2 solves the time-dependent Euler equations for compressible
flow with an explicit, finite-volume, node-based Ni-Lax-Wendroff type
algorithm (Ni, 1981) extended to 3-D unstructured meshes and hexahedral cells (Saxer, 1992). MULTI2 can solve the time-dependent as well
as the steady-state interaction in multistage configurations. In this study,
the 3-13 solver is used in 2-D mode with three 2-D meshes piled up to
form a two-cell-height 3-D control volume. A combined second- and
fourth-difference numerical smoothing consistent with the second-order
accuracy (both in space and time) of the discretization scheme is added
to prevent high frequency oscillations and to capture shock waves. In the
present subsonic cases, the second-difference smoothing is turned off.
11.2 Viscous flow solver (FENFLOSS)
The commercial grid generator ICEM (ICEM, 1997) and the 2-D
flow solver FENFLOSS (Ruprecht, 1989), (Ginter, 1997) are used. The
finite-element code FENFLOSS solves the Navier-Stokes equations for
incompressible flows based on a Petrov-Galerkin formulation on a
2
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
multi-block grid with 4-node elements. The momentum equations are
solved by a segregated solution algorithm with a preconditioned
conjugated gradient algorithm for non-symmetrical sparse matrices and
a modified Uzawa pressure correction algorithm. Time-dependent flows
are simulated by a fully-implicit three-level time discretisation of
second-order accuracy and the rotor/stator interaction is obtained by
overlapping grids over one grid element (Ginter, 1997). Since no
interpolation is required at the interface, the balance equations are
satisfied. An algebraic mixing-length turbulence model is used in the
solver. This code has been applied to several flow problems in hydraulic
turbomachinexy (Ruprecht et al., 1994), (Gentner et al., 1998).
and stator, and solidity are retained from the experimental model. The
geometry used in the simulation corresponds to a cut at the (RMS) Euler
radius of any of the repeating stages of the four-stage water model
described in Chapter III and in (Saxer-Felici et al., 1998a). The domain
used in the inviscid two-stage calculation is shown in Figure 1 with the
location of the rotor inlet (station 1), a station ahead of the first rotor
(station 11), the rotor/stator interface of stage 1 (station 12), the exit of
stage 1 = inlet stage 2 (station 2), the rotor/stator interface of stage 2
(station 22), a section downstream of stator 2 (station 23) and finally the
exit boundary (station 3). Both the inviscid and viscous procedures use
block-structured grids which are shown in a blow-up of the near-blade
region. In both the inviscid and viscous procedures the grids are attached
to the local blade row and the governing equations are solved relative to
this coordinate system. Hence, for the grid region attached to the moving
rotor blades the equations are solved in the relative frame of reference
(for example in the regions limited by the sections Ito 12 and 2 to 22 in
Fig. 1a). In the regions attached to a stator the grid is stationary and
absolute flow variables are used (regions 12 to 2 and 22 to 3). In
comparison to the inviscid grid (Fig. 1W), the viscous mesh presents
JI.3 Computational domains
Whereas inviscid solutions have been obtained on a single- and
two-stage compressor, the viscous procedure is applied only on the
single-stage configuration. In order to reduce CPU time, the
circumferential domain is reduced to 15 blades (30 blades are used in the
test rig compressor), see also Section IV.3. Axial spacing between rotor
stations
I
11 12 2 22 23
stage 1
3
stage 2
a)
ostationary
numerical probe
stations II
12
2
23
22
Figure 1: a) Two-stage computational grid on 15 channels for inviscid calculation, b) blow-up of near-blade region for inviscid calculation (twostage, 59085 nodes/mesh plane), c) blow-up of near-blade region for viscous calculation (single-stage, 124853 nodes/mesh plane). Location of
stationary numerical probes is indicated.
3
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
EXPERIMENTAL SETUP
A not quite usual test rig to study RS in an axial compressor is in operation at the Turbomachinery Laboratory of the ETHZ. It builds upon
previous experimental work on a single-stage centrifugal air compressor
(Hunziker & Gyarmathy, 1993) and its water-driven model designed using the principle of hydrodynamic analogy (File et al., 1997).
discontinuities in the metrical properties at the block interfaces and a
faster coarsening of the grid within the inlet and exit regions. Whereas
the trailing edge is cut in the viscous computation, the inviscid grid
includes a wedged trailing edge. Also, the two grid densities differ
largely in the blade-to-blade region. However, these differences do not
significantly influence the RS flow structures under investigation, see
Chapter IV.
11.4 Boundary conditions
Damnation
Axial
Compressor
Inviscid flow solver MULTI2. As described in Saxer & Giles (1993)
non-reflecting boundary conditions are used. Long inlet and exit
farfields (as compared to the actual setup of a test rig stage) are adopted
and steady-state non-reflecting boundary conditions are applied based
on circumferentially averaged quantities at the inlet and the exit. In this
respect, any uncertainty in modelling the unsteadiness reaching the
farfield boundaries should be minimized, despite the large perturbation
produced by the RS cell.
At the rotor inlet, the average entropy (or stagnation pressure), the stagnation temperature, and the tangential flow angle are set in the absolute
frame of reference with pi? = I bar, To = 300K, a = -31.3 °. This is in
contrast to calculations performed in the stable branch of the characteristic, where in standard practice the rothalpy and relative flow angles are
set at the rotor inlet. In the rotating stall regime, when setting the absolute inlet flow angle (corresponding to the metal angle of the upstream
existing IGV's trailing edge, see Chapter III and Fig. 2), the relative
flow angle and the flow coefficient are free to adjust to the local flow
conditions. The circumferentially averaged conditions allow local flow
adjustments due to potential effects. At the exit, the average static pressure is prescribed in order to reach the desired throughflow coefficient
Fr0.25 in the RS regime. At the rotor/stator interfaces an unsteady numerically non-reflecting procedure based on the local characteristic variables ensures a physically consistent boundary condition even in the
presence of the strong backflow characteristic of the RS regime (Saxer,
1992). A no mass flux condition is enforced at the pseudo hub and tip
walls as well as on the stator and rotor blades, A periodic condition is
applied between the circumferential upper and lower boundaries of the
multiple blade passage domain. In this low Mach number application,
the rotor speed U2= 164.08 m/s is derived by matching the non-dimensionalized velocity triangle from the design values at iti=0.39 together
with an inlet axial Mach number of 0.18 (ratio of specific heats x=1.4).
This value of Mach is chosen sufficiently low to mimic incompressible
flow and high enough to ensure a reasonable convergence of the flow
solver.The instantaneous error in the continuity equation applied on the
computational domain is lower than 1% of the inlet mass flow.
Viscous flow solver FENFLOSS. The rotor-relative inlet velocity vector is imposed with w, = 0.537 m/s, w = 1.821 m/s. For incompressible
flow calculation, the pressure level is arbitrary, and for convenience is
set to p3 = 0 bar at the stator exit. The rotational speed U2 = 2.142 in/s
is as in the experiment. With these, the flow coefficient is set to
(N—y=0.25 and the rotor-relative inlet flow angle to [3 1 =13 1 = 73.6°. A no
slip condition is assumed at the blade surfaces. 210 time-steps are used
for one rotor revolution (14 time-steps/pitch). 12 iterations are applied
for each time-step of the implicit algorithm with data exchange at the interface at each iteration.
Throttle Valve
111
II
If
Flow Straightener
a)
Venturi Tube
IN N.,
Dimensions
In [mm]
position
tO
9
8
6
5
4
3
2
c)
IGV's
0
Pitot Tube
Figure 2: a) Schematic of closed-loop water model rig, b) 4-stage
axial compressor with plexiglas casing, c) indication of pressure
measurement locations.
4
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
between the computed cases, the RS cell shown in Fig 7a) is represented
at an instantaneous and slightly larger flow coefficient of 9=0.27. In
addition, the experimental correlations by Day et al. (1978) show that
the blockage increases with the number of stages. Between stage I and
2, within the RS cell, the flow in the absolute frame of reference is
nearly tangential in the direction of rotation with a velocity up to twice
the rotor speed. This high-speed tangential motion produces trailing
edge flow separation and vortex roll-up in stator I, blocking the stator
passages as seen in the middle of Fig. 8a).
Flow visualization near the trailing edge of the last stator. A blowup of the stator flowtield represented by trajectories of numerical
bubbles set in three channels (representing the middle portion of the RS
cell) is displayed in Figure 9 for the inviscid/compressible single- and
two-stage solutions together with photographs taken near the stator
trailing edge of stage 4 in the test rig. The time-lag At corresponds to the
passage of 113 of the RS cell. The video camera shutter time is 4 ms
corresponding to a streak length of 0.22 blade pitch for particles
travelling at 1.12=2.1 m/s. To produce a similar effect in the CFD
solution, the position of three ghost bubbles are shown in addition to the
current bubble position corresponding to a streak length of 0.21 blade
pitch for particles travelling at C/ 2=164.08 m/s. Almost identical flow
features are found in the two CFI) solutions. As mentioned above, the
suction pulse at the cell front drives exit-domain fluid back into the
stator passages, producing a separation at the trailing edge. The
suction side due to a trailing edge separation. This vortex grows and
decays in size as the cell passes by and is finally expelled at the cell rear
due to the pressure pulse seen in Fig. 6b). The evolution of this vortical
feature is explained in more detail below when comparing flow
visualization in the single- and the two-stage case with in-house
experimental data.
Whereas these global flow structures agree well between the two
computed solutions, the size of the recirculation bubble upstream of the
rotor is larger in the inviscid solution than in the viscous one. In the
stator channels, identical flow features are found in the two CFD
solutions, though the magnitude and size of the trailing edge vortex may
differ.
IV.4 Two-staae inviscid solution
Rotating stall cell structure. Instantaneous streamlines drawn in
the absolute and in the cell-based frame of reference are depicted in
Figure 8 for the two-stage in viscid/compressible computation at =O.25.
One point to notice first is that the flow features located upstream of the
first rotor and behind the last stator are very similar to the single-stage
cases as described above. The blockage and the axial extent, though, as
inferred from the limiting streamlines in the cell-based frame of
reference, are larger than in the single-stage inviscid/compressible case
(compare Fig. 8a) with 6a) & Fig. 8b) with 7a)). This is consistent with
the observation that although the mean operating points are the same
stagnation
point
at
stagnation point
tagnation point
a) single-stage
b) two-stage
c) experiment
Figure 9: Trajectories of tracer particles in the last stator, shown in the absolute frame of reference at two instants separated by a time lag ha
corresponding to the passage of the third of the RS cell (At = XTR513). a) single-stage computation, b) two-stage computation, c) experiment. In
the experiment the streak length is 0.22 blade pitch for particles travelling at U2=2,I m/s and 0.21 blade pitch in the CFD solutions for particles
travelling at C12=164.08 m/s.
9
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
The experimental stage average data obtained in the four-stage axial
compressor water model is also marked in Fig. 3 for design conditions
and at iT=0.24 & c=0.26. As expected, the viscous and experimental
values are close for design conditions, while the inviscid computation
produces a much larger stage pressure rise due to the absence of the
viscous effects influencing the work of the stage. Interestingly, within
RS operation the experimental mean pressure rise per stage lies in
between the two single-stage computed solutions for both 11:=024 and
.(1)=0.26. The magnitude of the difference between the two CFD
solutions is of the order of the difference between the first and fourth
stage in the experiment (individual experimental stage pressure rises are
not shown here). This seems to indicate that within fully-developed fullspan RS inviscid mechanisms generating the circumferential blockage
are of importance.
The stage average pressure coefficient for the two-stage inviscid
computation is also indicated in Fig. 3. As expected for a repeating stage
machine, the average values closely match the ones computed for the
single-stage, both in the stable and RS regimes. At the computed RS
operating point, the first stage is producing most of the pressure rise, a
phenomenon also observed in the in-house experiment.
Figure 4: Computed and measured blockage factors as a function of
the flow coefficient.
IV.2 Circumferential blockage
IV.3 Siogle-stage solutions
As observed in the experiment, all CFD solutions produce a single
RS cell. The measured and computed flow blockages are shown in
Figure 4 as a function of the flow coefficient. As expected and similarly
described by Day et al. (1978), the experimental blockage A defined by
Unsteady static pressure traces. In Figures 5a) & 5b), the inviscid and
viscous computed traces of static pressure coefficient are shown for 6
rotor revolutions for 9=0.25 and for a stationary numerical probe
located in the middle of a blade passage at the rotor/stator interface. In
Figure 5c), the measured casing wall pressure trace taken at the rotor/
stator interface of stage 4 (pos. 8 in Fig. 2c)) is displayed for(70.24. It
also shows the passage of a single RS cell.
Both computed results show the passage of a time-periodic fullydeveloped single rotating stall cell with sharp static pressure gradients
corresponding to the cell width and weaker gradients within the sound
flow regions.
The RS frequency is larger in the inviscid solution than in the viscous
case (64% of the rotor speed compared to 55%), but the amplitudes of
the static pressure fluctuations are comparable. The blockage coefficient
marked in Fig. 5 is obtained from the pressure traces according to the
definition given by Eq. (1).
In both computations bumps appear in the pressure traces and therefore
variations occur in the blockage. As discussed in (Saxer-Felici et al.,
1998a) and (Saxer etal., 1999), the shape of the rotating stall cell varies
periodically from compact (low blockage) to diffused (large blockage)
for a given mean flow coefficient. In the inviscid computation, the
blockage varies from 32% to 47%. In the incompressible viscous flow
computation shown in Fig. 513) the volume flow is kept constant through
the setting of the boundary conditions, but the solution still exhibits a
variation in RS cell blockage (20% to 41%) due to the presence of
fluctuations in the head rise. Note the smoothness of this pressure trace
compared to the experimental and inviscid cases.
Compared to the CFD solutions (shown at the Euler radius), the
amplitude of the measured pressure traces is smaller (by a factor 2
approximately, which corresponds, as expected to the ratio of
experimental to numerical blade count per row). This is consistent with
the momentum exchange theory discussed below. The shapes of the
traces are in good agreement between the CFD and the experimental
data. The measured RS cell travels at 54% of the rotor speed, nearly
matching the computed value in the viscous/incompressible case. The
_ time between suction peak and next pressure peak
time between two suction peaks
interface of stage 2 (station 22), in agreement with the experimental data
taken at the rotor/stator interface of stage 4 (pos. 8 in Fig. 2c)). Overall,
the comparison suggests that the computed blockage and its variation
with tp are consistent with experimental results.
0.15 _
9
(I)
varies linearly with the flow coefficient in the RS regime. It ranges from
—30% at RS inception to 85% where full annulus stall is developed.
Consistent with experimental observations, no RS operation with a
blockage below —30% can be sustained in the computations, i.e. the flow
solution jumps back to the stable branch of the characteristic. For the
single-stage computational solutions two values of blockage are given.
This is required since in the inviscid computation, the blockage varies
periodically with tp for a given mean operating point (Saxer-Felici et al.,
I998b). This corresponds to a surge-like mechanism (±-10% of the inlet
mass flow) superimposed upon the rotating stall phenomenon, see
dashed fine in Fig. 4. Hence, the following definition for the blockage is
used instead of Eq. (1) and applied to two instantaneous operating points
at times corresponding to a local high and a local low flow coefficient,
while ja0.25.
— circumf dist. between suction peak and next pressure peak ( 2)
periphery
The analysis presented in Saxer-Felici et al. (1998b) indicates that computed blockage values follow this correlation for different grid sizes.
For the viscous solution, the two values of blockage indicated for
ri=0.25 correspond to the extreme values inferred from Fig. 5b) (discussed below), i.e. corresponding to a high and low head rise, see also
(Saxer, 1999). Both pulsations encountered in the inviscid and viscous
solutions lead to a change in the cell shape and are discussed in the next
Section.
In the two-stage computation, the mass flow pulsation is reduced, hence
the variation of blockage with tp is smaller than in the single-stage computation. A mean blockage value of 40% is computed at the rotor/stator
6
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
0.25
The opposite occurs at the rear of the cell (R). In this theory, the
magnitude of the pressure pulses at the front and rear boundaries of the
RS cell is inversely proportional to the width of the cell boundary zone,
i.e. of the circumferential extent of the pressure spike. By allowing only
15 channels in the computation instead of 30 in the experiment, the
extent of this zone is reduced by approximately a factor 2 for a given
blockage.
Overlooking the local blade-to-blade effects, the shape and magnitude
of the static pressure tracts at the rotor/stator interface agree well
between the two CFD solutions. Both exhibit a severe change in static
pressure at the cell rear and front boundaries, although the gradient is
steeper at the rear than at the front, a phenomenon which is consistent
with experimental observations (Cumpsty & Greitzer 1982), (Das &
hang, 1984). The front (F) and rear (R) boundaries of the inviscid RS
cell are marked in Fig. 6 using the modified blockage coefficient X,
based on the static pressure trace defined by Eq. (2) for a given time
occurrence.
For the viscous RS cell, the front and rear boundaries are defined by the
occurrence of the same flow features in the streamline field as in the
inviscid calculation. see Fig. 6c). Hence, by inspection of the velocity
field the inviscid and viscous blockages agree well, although a strict
application of Eq. (2) (based on static pressure) to the viscous/
incompressible solution would result in a lower blockage than in the
inviscid solution.
For the flow coefficient profiles, the characteristic behaviour is identical
in both cases. Note that a good approximation for the blockage can also
be obtained by considering the width of the RS cell as the peripheral
distance formed by the bisection of the mean flow coefficient with the
local throughflow.
Rotating stall cell structure. The cell structure is shown in Figure 7 by
instantaneous streamlines drawn in the RS cell frame of reference for the
single-stage cases: a) inviscid/compressible computation and b)
viscous/incompressible computation. Clearly the two CFD solutions
exhibit a strikingly similar RS cell structure, which is discussed first. In
the RS cell frame of reference, the incoming flow presents a tangential
component opposed to the rotor speed and the cell appears steady apart
from the local effects of the blade passing and the low-frequency change
in cell shape due to the periodic variation of blockage with p (SaxerFelici et at, 1998a). In this frame of reference the cell is characterized
by a large recirculation bubble upstream of the rotor, a broad lowvelocity region with large scale vortex shedding downstream of the
stator, and tangential counter-current flows within the rotor and stator
rows. The large recirculation bubble ahead of the rotor comprises two
opposing vortices dividing the incoming flow in two streams to the front
and the rear of the RS cell. The upstream vortex is undisturbed, while
the other one is disrupted by the sequence of rotor blades crossing it. In
the sound flow outside the RS cell the axial velocity is larger and the
incidence angle on the rotor blade is lower than at the inlet boundary,
making the stage operate at a higher flow coefficient than at the average
_
p. This can be viewed as the presence of a cylindrical body formed by
two counter-rotating vortices placed in a potential flow field.
Downstream of the stalled stator blades, near the trailing edge, the
suction pulse formed at the front of the cell (see Figs. 6a) and 6c)), tends
to drive downstream fluid back into the stator channels. Part of this fluid
is transported ahead of the stator and then tangentially in the direction
of rotation, and finally washed out in a stator passage closer to the front
of the RS cell. Another part of this fluid rolls up into a vortex near the
experimental blockage for stage 4 varies between 34% to 40%, and lies
in the range of the obtained CFD values.
I.5
1.0
a) inviscid
a Cp
0.5
0.0
-0.5
-1.0
4.5
0
4
2
yr(Rotor Revs.)
1.5
1.0
0.5
b) viscous
aCp
0.0
-0.5
4.0
-1.5
0.6
04
0.2
c) experiment
wd MN=
oCp 0.0
11111111111a1
MUM
a
cm=
-0.2
-0.6
0
2
tif (Rater
4
6
)
Figure 5: Computed static pressure coefficient at Tp0.2.5 for singlestage computations at a stationary probe located along the rotor/
stator interface for a) inviscid computation and b) viscous
computation. c) Measured value for cifl.24 between rotor and
stator at pos. 8 shown in Fig. 2.
Circumferential variations of pressure and throughflow. A
comparison between the inviscid/compressible and viscous/
incompressible solutions for the single-stage axial compressor is given
below. More details can be found in a parallel study in (Saxer et al.,
1999).
In Figures 6a) and 6c), the instantaneous streamlines are drawn in an
absolute frame of reference showing the RS cell captured by the two
CFD methods. The solutions outline identical basic flow features,
though the axial extent of the RS cell in the viscous solution seems
smaller. Also shown are the static pressure coefficient and flow
coefficient profiles along the rotor/stator interface for both CFD
solutions (Fig. 6b)). This type of pressure and axial velocity profile
agrees well with idealized 1-D inviscid models (Cumpsty & Greitzer,
1982), (Gyarmathy, 1996), which consider momentum exchange
between sound and stalled flow. At the cell front (F), a pressure low
accelerates the stagnant fluid in the rotor channels leaving the cell and
decelerates the sound flow in the stator channels as these enter the cell.
7
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
ACp
\
.\
b '
\--'
\
•
viscous
-
) single-stage abs.
) single-stage abs. los ,
Figure 6: a) Instantaneous streamlines in absolute frame of reference from inviscid computation, b) momentary profiles of static pressure and
flow coefficients along the rotor/stator interface, c) instantaneous streamlines in absolute frame of reference from viscous computation.
viscous
inviscid
) single-stage cell lot
) single-stage cell fox.
Figure 7: Instantaneous streamlines in RS cell frame of reference for a) single - stage inviscid and b) single - stage viscous computations.
inviscid
inviscid
a) two-stage abs. fox.
b) two-stage cell for.
Figure 8: Instantaneous streamlines in a) absolute frame of reference and b) cell frame of reference for two-stage inviscid computations.
8
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
between the computed cases, the RS cell shown in Fig 7a) is represented
at an instantaneous and slightly larger flow coefficient of 9=0.27. In
addition, the experimental correlations by Day et al. (1978) show that
the blockage increases with the number of stages. Between stage I and
2, within the RS cell, the flow in the absolute frame of reference is
nearly tangential in the direction of rotation with a velocity up to twice
the rotor speed. This high-speed tangential motion produces trailing
edge flow separation and vortex roll-up in stator I, blocking the stator
passages as seen in the middle of Fig. 8a).
Flow visualization near the trailing edge of the last stator. A blowup of the stator flowtield represented by trajectories of numerical
bubbles set in three channels (representing the middle portion of the RS
cell) is displayed in Figure 9 for the inviscid/compressible single- and
two-stage solutions together with photographs taken near the stator
trailing edge of stage 4 in the test rig. The time-lag At corresponds to the
passage of 113 of the RS cell. The video camera shutter time is 4 ms
corresponding to a streak length of 0.22 blade pitch for particles
travelling at 1.12=2.1 m/s. To produce a similar effect in the CFD
solution, the position of three ghost bubbles are shown in addition to the
current bubble position corresponding to a streak length of 0.21 blade
pitch for particles travelling at C/ 2=164.08 m/s. Almost identical flow
features are found in the two CFI) solutions. As mentioned above, the
suction pulse at the cell front drives exit-domain fluid back into the
stator passages, producing a separation at the trailing edge. The
suction side due to a trailing edge separation. This vortex grows and
decays in size as the cell passes by and is finally expelled at the cell rear
due to the pressure pulse seen in Fig. 6b). The evolution of this vortical
feature is explained in more detail below when comparing flow
visualization in the single- and the two-stage case with in-house
experimental data.
Whereas these global flow structures agree well between the two
computed solutions, the size of the recirculation bubble upstream of the
rotor is larger in the inviscid solution than in the viscous one. In the
stator channels, identical flow features are found in the two CFD
solutions, though the magnitude and size of the trailing edge vortex may
differ.
IV.4 Two-staae inviscid solution
Rotating stall cell structure. Instantaneous streamlines drawn in
the absolute and in the cell-based frame of reference are depicted in
Figure 8 for the two-stage in viscid/compressible computation at =O.25.
One point to notice first is that the flow features located upstream of the
first rotor and behind the last stator are very similar to the single-stage
cases as described above. The blockage and the axial extent, though, as
inferred from the limiting streamlines in the cell-based frame of
reference, are larger than in the single-stage inviscid/compressible case
(compare Fig. 8a) with 6a) & Fig. 8b) with 7a)). This is consistent with
the observation that although the mean operating points are the same
stagnation
point
at
stagnation point
tagnation point
a) single-stage
b) two-stage
c) experiment
Figure 9: Trajectories of tracer particles in the last stator, shown in the absolute frame of reference at two instants separated by a time lag ha
corresponding to the passage of the third of the RS cell (At = XTR513). a) single-stage computation, b) two-stage computation, c) experiment. In
the experiment the streak length is 0.22 blade pitch for particles travelling at U2=2,I m/s and 0.21 blade pitch in the CFD solutions for particles
travelling at C12=164.08 m/s.
9
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
separated flow rolls-up into a vortex near the suction side (solid box).
As the RS cell moves through the stator, this vortex grows, lifts up from
the suction surface and moves towards the pressure side.
Simultaneously, the stagnation point on the pressure surface moves
towards the trailing edge and the flow behind the stator becomes more
tangential (solid box at a later time). As the RS cell is leaving this
portion of the stator, the positive pressure pulse at the cell rear drives
sound flow coming from the rotor into the stator channel and confines
the vortex near the trailing edge on the pressure surface, until it is
washed out in the exit region. The location of the stator trailing edge
vortex, its motion, the location of the stagnation point and the direction
of the flow behind the stator are consistent with the experiment (Fig.
9c)).
Unsteady static pressure traces. The computed inviscid/compressible,
normalized static pressure traces for the two-stage axial compressor are
shown for 6 rotor revolutions and five axial stations at(T0.25 in Figure
I Oa). These represent the unsteady pressure fluctuations recorded by
spatially stationary numerical probes, which are located as indicated in
the figure at axial stations II, 12, 2, 22 and 23 (see also Fig. I). It has to
be mentioned that the mean pressure rise per stage is only 0.5, which is
not apparent in Fig. 10a) due to the normalization. This means that the
pressure fluctuations associated with RS are quite intense in comparison
to design flow pressure differences. The traces indicate the passage of a
time-periodic fully developed single RS cell travelling at 62% of the
rotor speed. The comparison between the traces at the rotor/stator
interfaces in stage I and 2 (stations 12 and 22) indicates that a more
clearly defined RS pattern is computed in stage 2. In the unstalled
portion of the flow, the circumferential pressure gradient is more
uniform in stage 2 (station 22) than in stage 1 (station 12). This is
consistent with our experimental observations, which show the
measured casing wall pressure traces between the rotor and stator of
stages 2 and 4 (pos. 2 & 8 in Fig. 2c)) for Tc=0.26 in Figures I la) & c),
respectively.
Considering the flow inbetween stages, i.e. station 2 in Fig. 10a), notice
that the 14% blockage value is somewhat misleading. Indeed the
circumferential extent of the RS cell is almost constant throughout the
two stages, as deduced from the inspection of the cell structure in Fig.
8b). Notice the plateau in the circumferential pressure distribution
outside the RS cell, which contrasts with the pressure gradient found at
the rotor/stator interfaces of stage 1 & 2 (stations 12 and 22,
respectively). This plateau is qualitatively observed in the experiments
(Fig. 11b), i.e. between stage 3 and 4 in the water model (pos. 7 in Fig.
2c)).
Ahead of the first rotor in Fig. 10a) (station 11), the drop in static
pressure corresponds to the passage of a vortex trapped in a large
recirculation bubble forming the RS cell, as explained above.
Overlooking the local blade passing effects, a fairly smooth pressure
gradient within the sound flow between the peaks is computed. This
suggests that the RS cell acts as an obstruction like a cylindrical solid
body placed in a potential flow producing a potential field deflecting the
incoming flow, as postulated above. Behind the last stator (station 23),
the amplitude of the fluctuations due to the passage of the RS cell is
about 1/3 of the one encountered within the stages. This behaviour is
consistent with the experimental observations of (Das & Jiang, 1984).
In our measurements (see Fig. 1 I d)) taken at the stator exit of stage 4
(pos. 9 in Fig. 2c)), the trace shows a similar behaviour with the CFD
one shown in Fig. 10a) at station 23.
Unsteady flow coefficient Similarly to the unsteady pressure, timetraces of the local flow coefficient are plotted in Figure 10b) for the axial
stations 11, 12. 2, 22 and 23. The passage of the RS cell is associated
with regions of low throughflow and strong backflow within its center.
In the sound flow region, the flow coefficient is increasing from inlet to
exit. Interestingly, the mean throughflow in the sound flow region
= 0.46) corresponds to the value obtained for operation in the stable
branch of the characteristic at the same pressure rise (see Fig. 3), as
originally con-elated from experimental data by Day et al. in 1978.
Unsteady tangential flow angle. The evolution of the absolute
tangential flow angle during RS is plotted in Figure 10c). As already
inferred from Fig. 8 the passage of the RS cell is marked by an abrupt
change of flow direction. Three different patterns are seen within the
two-stage machine. Ahead of the first rotor (station 11), the angle within
the sound flow region evolves smoothly from the value set by the inlet
guide vane (i.e. inlet boundary conditions) to almost tangential
conditions as the RS cell approaches the numerical probe. Within the RS
cell near the cell front, the flow is nearly tangential in the direction of
the rotor rotation, as experimentally observed by Das & Jiang (see Figs.
6 & 12 in Das & Jiang, 1984) and Mathioudakis & Breugelmans (see
Fig. 8 in Mathioudakis & Breugelmans, 1988). At the rotor/stator
interfaces of stage I and 2 (stations 12 and 22. respectively), the flow
changes abruptly from tangential in the direction of rotor rotation to the
opposite direction during the passage of the RS cell. This produces
strong vortical flow, as seen in Fig. 8. The third pattern is identified
between stage I and 2 and downstream of stator 2 (stations 2 and 23,
respectively). In the sound flow region, the tangential angle closely
matches the value obtained in the unstalled branch of the characteristic
obtained at a throughflow above the design value (since c s„no fl ow >
o• Within the RS cell the flow is almost tangential. The small
bump observed
bserved during stall downstream of stator 2 (station 23) is an
indication of the vortex shedding mentioned in Section IV.3.
Absolute velocity. The time-variation of the absolute velocity
normalized by the rotor speed U2 is plotted in Figure 10d). Within the
RS cell the above mentioned nearly tangential velocities ahead of rotor
I and 2 are much larger than the velocity in the sound flow. At the rotor/
stator interfaces 12 and 22, the opposite is computed with fluid of low
velocity found ahead of stators. This behaviour is confirmed by the
measurements of Das & hang (1984) at midspan.
The 2-D assumption is supported by cross-analysis with experimental
data obtained in other subsonic compressors, for example (Das & Jiang,
1984), which indicate that 3-D effects strongly diminish as the axial gap
between blade rows decreases for this type of high hub/tip ratio blading.
This is pointed out as the axial gap in the geometry under investigation
is even smaller than the smallest axial gap studied in (Das & Jiang,
1984), (i.e. 0.29 chord length compared to 0.4, and 0.7 hub/tip ratio
compared to 0.82 in this study). On the other hand these same
experiments (midspan values at a normalized axial gap of 0.4) confirm
most of the key flow features defining the structure of the RS cell
computed in this study.
10
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
_
11
\-7C, \:°
b)
1.1
0.8
d)
2.4
c)
1.0
0.6
90
0.5
0.4
60
0.0
0.2
-0.5
0.0
• 1.0
2
1.5
1.5
0.8
1.0
0.6
0.5
0.4
0.0
0.2
•03
0.0
-1.0
.2
4
-1.5
1.5
RS
eel
0.8
1.0
0.6
0.5
0.
00
0.2
.0.5
0.0
60
a2 &sip= -30.3°
a2
1
16
0.8
2
0.4
0.0
0.8
2.4
TV T44.40.621
1.5
1 .0
aCp22
C22IU'
0.6
0.5
0.4
0.0
0.2
1.6
30
0.0
4.54 Some
60
90
• 1.5
1.5
0.8
I 02
0.6
,14,.
0.0
I
4
2
30
.2
i
2.4
90
30
0.2
i
00
60
0.4
.
0.8
-30
2
-1.0
so
1.4
6 0
VT (Rotor Revs.)
4
90
6 0
VT (Rotor Revs.)
00
6 0
2
t/T (Rotor Revs.)
2
4
6
VT(Rotor Revs.)
Figure 10: Variation of flow parameters in time at different axial positions during RS operation for the two-stage computation at T:=0.25. Top:
first rotor inlet, bottom: last stator outlet. a) Static pressure coefficient, b) flow coefficient, c) absolute flow angle, d) ratio of absolute velocity
to rotor speed. Values are recorded by stationary probes placed at different axial positions.
81)
b)
ACp pos. 2
2
VT (Rotor Revs.)
6
ACp pos. 7
C)
d)
ACp pos. 8
0
6 0
VT (Ro(or Revs.)
VT (Rotor Revs.)
2
aCp pos. 9
4
6
VT (Rotor Revs.)
Figure 11: Variation of static pressure in time at different axial positions (see Fig. 2c)) during RS operation for the experiment at j= O.26.
II
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
V. SUMMARY AND DISCUSSION
VI. CONCLUSIONS
Rotating stall is analyzed in a single- and two-stage subsonic axial
compressor using two numerical methods for unsteady flows and
experimental data. One method (MULT12) is based on the Euler
equations for an inviscid/compressible fluid, while FENFLOSS solves
the Navier-Stokes equations for incompressible flow. With solutions
presented for one operating point in the RS regime at 64% of design
flow, the two methods are able to consistently reproduce the periodic
propagation of a fully-developed single rotating stall cell in more than
qualitative agreement with the experimental observations.
When comparing the inviscid/compressible with the viscous/
incompressible solution in the single-stage configuration, the global
structure of the RS cell and the essentials of its dynamic behaviour are
found to be remarkably similar, although no "optimization" (grids,
parameters) of the two methods has been attempted here. For example,
a noteworthy common feature is the formation of a moving recirculation
bubble ahead of the rotor (i.e. in the inlet region) comprising two
counter-rotating vortices dividing the incoming flow in two streams
suggesting that the stagnant fluid contained in the RS cell acts as an
obstruction like a cylindrical solid body placed in an otherwise potential
flow. The major differences between the inviscid and viscous cases
concern essentially the strength of recirculation areas and, to a lesser
extent, the RS speed of propagation. This suggests that the speed of
propagation of the RS cell could be finked not only to the row-to-row
momentum exchange mechanism but also to the strength of the large
recirculation bubble upstream of the rotor. The use of numerical
techniques involving different physical assumptions (inviscid vs.
viscous, compressible vs. incompressible) to generate RS suggests that
the inception mechanism does not appear to influence the final structure
of the fully-developed rotating stall pattern.
A two-stage MULTI2 solution is presented for the same operating point
in the RS regime. Ahead of the first rotor and behind the last stator the
flow features are similar to the single-stage solutions. Both at the first
and second stage rotor/stator interfaces a momentum exchange
mechanism takes place between the blade rows entering and leaving the
stalled cell, i.e. at the RS cell front and rear boundaries. This
phenomenon is also identified in the single-stage CFD solutions and
confirmed experimentally by analysis of the circumferential static
pressure traces. It is also consistent with 1-D idealized models (Cumpsty
& Greitzer, 1982), (Gyannathy. 1996). In the interspace between stage
I and stage 2 a tangential flow in the direction of rotation is produced
with a velocity much larger than the rotor speed. This generates trailing
edge separation and vortex roll-up blocking the stator passages of the
first stage. Downstream of the last stator, tangential flow, vortex roll-up
and vortex shedding is computed in both the single- and two-stage cases.
Both CFD solutions of the single-stage and two-stage cases are
compared with experimental data obtained in a water model of a fourstage subsonic axial compressor of equivalent geometry. The static
pressure traces and the flow visualization compares well with the CFD
solutions. The major difference lies in the amplitude of the pressure
spikes, which scales like the ratio of experimental to CFD blade count
number per row. The 2-D assumption in the computations is supported
by comparisons with in-house experimental data on key flow features as
well as by other experimental studies with a similar hub/tip ratio, for
example (Das & Jiang. 1984), where 3-D effects are shown to be small
for the short axial gaps modelled in this study.
A numerical study of the structure and propagation of fullydeveloped, full-span rotating stall is presented for a single- and twostage subsonic 2-D axial compressor. The conclusions derived from the
analysis of the CFD results (inviscid/compressible and viscous/
incompressible) and the experimental data obtained in a 4-stage water
model can be summarized as follows.
• A strong recirculation bubble comparable in size to the
circumferential width of the RS cell lies ahead of the first rotor. High
speed flow occurs between this recirculation zone and the first rotor.
This feature is common to both the single- and the two-stage solution.
• The momentum exchange between blade rows at the rotor/stator
interface applies in both the single- and the two-stage machine. This
confirms the essentially inertial nature of the driving mechanism for the
propagation and structure of full-span, fully-developed RS.
• A different RS flow structure is found at the stator/rotor interface
(in between stages) compared to the one observed within stages at the
rotor/stator interface. In this respect, the blockage value based on
unsteady static pressure traces seems to be a poor indicator of the cell
width, when applied in between stages.
• In the two-stage solution, the flow in the interspace between stage
1 and stage 2 is characterized by a large tangential velocity (up to twice
the rotor speed) within the RS cell producing a multiple flow separation
and corresponding blockage of the first stage stator passages.
• Using CFD flow visualization in both the absolute and cell-based
frames of reference offers a more complete picture of the structure of
RS. This provides the missing link between the features observed in the
in-house and other experiments.
REFERENCES
Breugelmans, F. A. E., Mathioudalcis, K. Casalini, F., 1985:
"Rotating Stall Cells in a Low-Speed Axial Flow Compressor", AIAA
Journal of Aircraft, Vol. 22, No. 3, pp. 175-181, March.
Camp T. R. and Day I. J., 1997: "A Study of Spike and Modal Stall
Phenomena in a Low-Speed Axial Compressor", ASME Paper 97-GT526.
Cumpsty N. A. and Greitzer E. M., 1982: "A Simple Model for
Compressor Stall Cell Propagation", ASME Journal of Engineering for
Power, Vol. 104. pp. 170-176. Also ASME paper 81-GT-173, January.
Das, D. K. and Jiang, H. K., 1984: "An Experimental Study of
Rotating Stall in a Multistage Axial Flow Compressor", ASME Journal
of Engineering for Gas Turbines and Power, Vol. 106, pp. 542-551.
July.
Day I. J., Greitzer E. M. and Cumpsty N. A., 1978: "Predictions of
Compressor Performance in Rotating Stall", ASME Journal of
Engineering and Power, Vol. 100, No. I.
Day I. J., 1993: "Stall Inception in Axial Flow Compressor",
ASME Journal of Turbomachinery, Vol. 115, pp. 1-9.
Demargne A. A. J. and Longley J. P.: "Comparisons Between
Measured and Calculated Stall Development in Four High-Speed MultiStage Compressors", ASME paper 97-GT-467, 1997.
Emmons H. W., Pearson CE, and Grant H. P., 1955: "Compressor
Surge and Stall Propagation", Trans. ASME, Vol. 79, pp. 455-469.
Felici H. M., 1992: "A Coupled Eulerian/Lagrangian Method for
the Solution of Three-Dimensional Vortical Flows", Ph. D. Thesis, Dpt.
Aeronautics & Astronautics, Massachusetts Institute of Technology,
Cambridge, MA. USA, June, also GTL Report #211, MIT, Cambridge,
12
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms
MA. June 1992.
File G., Gyarmathy G.. Staubli T., 1997: "Water Model of a SingleStage Centrifugal Compressor for Studying Rotating Stall",
Proceedings of the 2nd European Turbomachinery Conference,
Antwerpen, Belgium.
Gamier V. H., Epstein A. H., Greitzer E. M., 1991: "Rotating
Waves as Stall Inception Indication in Axial Compressors", ASME
Journal of Turbomachinery. Vol. 113, pp. 290-301.
Gentner Ch., Kin G., Code E., 1998: "Experimental and Numerical
Investigation of the Unsteady HOW in an Axial Turbine at Different
Points of Operation", Ninth International Symposium on Application of
Laser Techniques to Fluid Mechanics, Lisbon, Portugal.
Ginter F., 1997: "Berechnung der Instationaren, Turbulenten
Stn5mungsmaschinen", Ph.D. Thesis, Institut air Strijmungsmechanik
und Hydraulische Strdmungsmaschinen, University of Stuttgart,
Germany.
Gong Y., Tan C. S., Gordon K. A., and Greitzer E. M., 1998: "A
Computational Model for Short Wavelength Stall Inception and
Development in Multi-Stage Compressors", ASME Paper 98-0T-476,
1998. Accepted for Publication in the Transactions of the ASME.
Greitzer. E. M. "Surge and Rotating Stall in Axial Flow
Compressors, Part I: Theoretical Compressions System Model", ASME
75-GT-9, also ASME Journal of Engineering for Power, Vol. 98. April
1976, pp. 190-198. I 976a. Part II: Experimental Results and
Comparison with Theory". ASME 75-GT-10. alsoASME Journal of
Engineering for Power, Vol. 98, April 1976, pp. 199-217, I976b.
Gyarmathy G., 1996: "Impeller-Diffuser Momentum Exchange
During Rotating Stall", ASME Paper 96-WA/F'ID-6, ASME Winter
Annual Meeting, Atlanta, November.
Gyarmathy G., Inderbitzin A.. Staubli, T., 1997: "Rotating Stall in
Centrifugal Compressors", Video, Turbomachinery Laboratory of the
Institute of Energy Technology, Swiss federal Institute of Technology,
Zurich.
Gysling D. L., Greitnr E. M., 1994: "Dynamic Control of Rotating
Stall in Axial Flow Compressors using Aeromechanical Feedback",
ASME paper 94-GT-292.
He L.. 1997: "Computational study of Rotating-Stall Inception in
Axial Compressors", AIAA Journal of Propulsion and Power. Vol. 13,
No. I, pp. 31-38, January-February.
Hendricks G. J.. Sabnis J. S., Feulner M. R., 1996: "Analysis of
Instability Inception in High-Speed Multi-Stage Axial Flow
Compressors". ASME paper 96-GT-360.
Hof A., Hauser M.. Aeschlimann B., 1996: "The "Rheinfall" Water
Model of an Axial Compressor: Design and Measurements" (internal
report in German), Semester-Project, Turbomachinery Laboratory of
the Institute of Energy Technology, Swiss Federal Institute of
Technology, Zurich.
Hoying D. A.. C. S. Tan, H D. Vo, E. M. Greitzer, 1998: "Role of
Blade Passage Flow Structures in Axial Compressor Rotating Stall
Inception", ASME paper 98-GT-588.
Hunziker R., Gyarmathy G.. 1993: "The Operational Stability of a
Centrifugal Compressor and its Dependence on the Characteristic of the
Subcomponents", ASME Journal of Turbomachinery. Vol. 116, pp.
250-259.
10EMTm Software System CFD/CAE Version 3.3.3
Langley J. P., 1993: "A review of Non-Steady Row Models for
Compressor Stability". ASME paper 93-GT-17.
Langley J. P., 1997: "Calculating the Flowfield Behaviour of HighSpeed Multi-Stage Compressors". ASME paper 97-GT-468, 1997,
Mathiaudalcis, K. and Breugelmans, F. A. E„ 1988: "ThreeDimensional Flow in Deep Rotating Stall Cells of an Axial
Compressor", AIA A Journal of Propulsion and Power, Vol.4, No.3, pp.
263-269, May-June,
Moore F. IC., Greitzer E. M., 1986: "A Theory of Post-Stall
Transients in Axial Compression Systems, Parts I & II", ASME Journal
of Engineering for Gas Turbines and Power, Vol. 108, pp. 68-97, 1986.
Ni R.-H., November 1981: "A Multiple Grid Scheme for Solving
the Euler Equations", AIAA Journal, Vol. 20, No. 11. pp. 1565-1571.
Nishizawa T., Takata H., 1994: "Numerical Study on Rotating Stall
in Finite Pitch Cascades", ASME paper 94-GT-258.
Outa E., Kato D., Chiba K., 1994: "A N-S Simulation of Stall Cell
Behavior in a 2-D Compressor Rotor-Stator System at Various Loads",
ASME paper 94-GT-257.
Paduano J. D.. Epstein A. H., Valvani L., Langley J. P.. Greitzer E.
M., 1993: "Active Control of Rotating Stall in a Low-Speed Axial
Compressor", ASME Journal of Turbomachinery, Vol. 115, pp. 48-56.
Rizzi A.. Eriksson L.-E., 1984: "Computation of Row Around
Wings Based on the Euler Equations", JFM, Vol. 184. pp. 45-71.
Ruprecht A., 1989: "Finite-Elemente zur Bertchnung
Dreidimensionaler, Turbulenter Stn5mungen mit Komplexen
Geometrien", Ph.D. Thesis, Institut fur Stromungsmechanik und
Hydraulische Stromungsmaschinen, University of Stuttgart. Germany.
Ruprecht A.. Bauer C., Chihab W., Gentner C., Ginter F., Maihdfer
M., Wetzel B., 1994: "Einsatz der Numerischen Suomungsmechanik in
der Entwicklung Hydraulischer Stromungsmaschinen", Alctuelle
Forschungsarbeiten des Instituts ftir Stromungsmechanik und
Hydraulische Stnimungsmaschinen, University of Stuttgart, Germany.
Saxer A. P., 1992: "A Numerical Analysis of 3-D Inviscid Stator/
Rotor Interactions Using Non-Reflecting Boundary Conditions". Ph. D.
Thesis, Dpt. Aeronautics & Astronautics. Massachusetts Institute of
Technology, Cambridge, MA, USA, June, also GTL Report* 209, MIT,
Cambridge, MA. March 1992.
Saxer. A. P. and Giles, M. B., 1993: "Quasi-Three-Dimensional
Nonreflecting Boundary Conditions for Euler Equations Calculations",
AIAA Journal of Propulsion and Power. Vol. 9. No. 2, pp. 263-271,
March-April.
Saxer A. P., Saxer-Felici H. M., Ginter F., Inderbitzin A.,
Gyannathy G., 1999: "Structure and Propagation of Rotating Stall Cells
in an Axial Compressor", to be presented at the 3rd European
Turbomachinery Conference, London, UK, March.
Saxer-Felici H. M., 1996: "MELLIP: A Block-Structured Grid
Generator for Turbomachinery B lading". Internal Report
Turbomachinery Laboratory of the Institute of Energy Technology.
Swiss Federal Institute of Technology, TN-LSM-96-02,
Saxer-Felici H. M., Saxer A. P., Inderbitzin A., Gyarmathy G.,
1998a: "Prediction and Measurement of Rotating Stall Cells in an Axial
Compressor". ASME paper 98-GT-67, 1998. Accepted for Publication
in the ASME Journal of Turbomachinery.
Saxer-Felici H. M., Saxer A. P., Inderbitzin A.. Gyarmathy G.,
I 998b: "Numerical and Experimental Study of Rotating Stall in an
Axial Compressor Stage". AIAA Paper 98-3298, Presented at the 34th
AIAA/ASME/SADASEE Joint Propulsion Conference & Exhibit, July
13-15, 1998, Cleveland. OH.
Tryfonidis M., Etchevers 0., Paduano J. D., Epstein A. H.,
Hendricks G. J., 1995: "Pre-Stall Behavior of Several High-Speed
Compressors", ASME Journal of Turbomachinery, Vol. 117, No. I, pp.
62-80.
13
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/22/2014 Terms of Use: http://asme.org/terms