# Simulation of Casing Treatments ofa Transonic  Compressor Stage

Authors: M. Hembera; H.-P. Kau; E. Johann
Journal: International Journal of Rotating Machinery
 (2008)

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## Abstract

This article presents the study of casing treatments on an axial compressor stage for improving stability and enhancing stall margin. So far, many simulations of casing treatments on single rotor or rotor-stator configurations were performed. But as the application of casing treatments in engines will be in a multistage compressor, in this study, the axial slots are applied to a typical transonic first stage of a high-pressure 4.5-stage compressor including an upstream IGV, rotor, and stator. The unsteady simulations are performed with a three-dimensional time accurate Favre-averaged Navier-stokes flow solver. In order to resolve all important flow mechanisms appearing through the use of casing treatments, a computational multiblock grid consisting of approximately 2.4 million nodes was used for the simulations. The configurations include axial slots in 4 different variations with an axial extension ranging into the blade passage of the IGV. Their shape is semicircular with no inclination in circumferential direction. The simulations proved the effectiveness of casing treatments with an upstream stator. However, the results also showed that the slots have to be carefully positioned relative to the stator location.


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## Body

## 1. Introduction

In order to reduce weight and enhance efficiency of
compressors for modern jet engines, the requirements for the power density are
further rising. This is among other things achieved by increasing the
rotational speed so that the blade tips of the first rotor stage are operating
in transonic conditions. Developments lead to an increase of the aerodynamic
loading of the blades, also rise the risk of rotating stall and surge during
operations. This risk can be countered through the application of casing
treatments.In the last 40 years, many casing treatments above
the rotor have been tested and simulated. It is proven that these devices can
extend the stall margin of a compressor. The treatments are only useful when
the rotor tip is responsible for stall. The rotor has to be tip-critical.The casing treatment can be classified into two
categories according to their geometric configuration:(1)
circumferential treatments such as circumferential grooves, which are typically
axis-symmetric,(2)
axial treatments such as axial slots, which are non-axis-symmetric.
These two categories and the different shapes therein
are not equally effective in terms of stall margin enhancement and efficiency
loss [1–16]. In general, the most successful treatments in terms of mass flow
reduction at stall are axial slots, which are used in this study.Many studies were conducted to identify and analyze
the flow mechanisms in these highly loaded transonic compressor stages at
design point and at operation points close to surge, both for design and
off-design speeds. The investigations identified two main groups of stall
mechanisms: flow instabilities resulting from complex blade tip effects and
common blade stall (Greitzer et al. [4]). The latter occurs due to an excessive
flow deflection resulting in an increased aerodynamic loading of a compressor
blade. This overloading causes the onset of widely spread flow separations at
the suction side of the blade hence blocking the passage flow. It was shown
that blade stall effects can be delayed successfully through increasing the
airfoil's solidity. However, compressor stages can also experience stall
although the aerodynamic loading of the blades does not exceed a stability
limit. Here, complex flow mechanisms, which occur near the blade tip clearance,
are found to be the key factor for the limited stability.Most of the investigated casing treatments in the
last decades enhance flow stability, but, unfortunately, also most of them come
along with an often significant drop in efficiency. Many investigations were
conducted with the goal to understand the specific impact of casing treatments
on the compressor flow, but many basic questions still remain unsolved. Until
now, for example, it is not yet clear why some casing treatment configurations
perform very well in some compressor systems at certain speeds, but fail at
other operation speeds or on other compressor systems. No design guidelines, for
casing treatments in order to apply a specific geometry of a casing treatment
to the individual requirements of a compressor stage, exist so far. The only
fact that is proven is that blade tip effects have to be responsible for the
onset of stall mechanisms so that the application of casing treatments can
successfully enhance the stability of the compressor (Greitzer et al. [4]).The first part of the following study is dealing with
the understanding of stall inception mechanisms in transonic compressor stages.
The second part of the study presents the results of axial slots successfully
simulated on a transonic rotor-stator configuration (Wilke and Kau [11])
applied on this specific transonic IGV-rotor-stator configuration.


## 2. Considerations on Designing a Casing  Treatment for Transonic Compressors

Casing Treatments for compressors are designed in order to effectively enhance its
flow stability under critical flow conditions without dropping the performance
of the compressors. This is possible if the casing treatment is able to
manipulate the specific flow mechanisms which are responsible for compressor
stall and at the same time minimizing unnecessary casing treatment flow in
normal compressor operations. The two different phenomena, blade tip stall and
tip blockage stall were identified as the two basic mechanisms of tip stall in
transonic compressors in detailed simulations conducted in previous
investigations with different transonic compressors. Both stall classes can
occur in combination or as isolated phenomena depending on the aerodynamic design.
This fact is one of the explanations why the impact of casing treatments can
change significantly with the speed of rotation or the type of compressor.


### 2.1. Blade Tip Stall

At blade tip stall, the angle of attack of the inflow
is very steep especially near the blade tip. Thus, the inflow cannot completely
follow the direction given by the blade profile. This results in an extended
separation zone at the blade suction side and a significant deceleration or
even stagnation of the inflow at the upstream part of the following blade
pressure side (see Figure1). The tip leakage flow and the tip leakage vortex
rather just fill up the separation zone at the suction side of the blade than
blocking the incoming flow. The trajectory of the tip leakage vortex is almost
parallel to the direction of the inflow.Blade tip stall and tip blockage stall.
(a)(b)Figure 2
Simulated compressor stage.Figure 3
Block topology.Figure 4
Mesh topology at Rotor 1 tip leading edge.


### 2.2. Tip Blockage Stall

At tip blockage stall conditions, the inflow
direction of the compressor's main flow is very similar to that of the design
point, even close to surge. The angle of attack corresponds with the stagger
angle of the rotor blades and the deflection of the flow over the blade passage
is moderate. No aerodynamic overloading of the blade tip occurs at the tip
blockage stall mechanism. However, at higher pressure loads, the tip leakage
flow and the tip leakage vortex can cause a characteristic stagnation zone at the
blade passage shock, which leads to a critical blockage of the main flow. The
stagnation zone can be the result of a vortex breakdown occurring after the
blade passage shock. The angle between the vortex trajectory and the blade
chord is significantly bigger than that between the inflow and the blade chord
(see Figure1).In contrast to blade tip stall, the tip blockage
stall mechanism is in general characteristic for high rotational speeds as the
phenomenon seems to be a characteristic property of transonic compressors
(Wilke et al. [11, 12], Hofmann and Ballmann [17, 18], Schlechtriem and
Lötzerich [19], Furukawa et al. [20], Hoeger et al. [21]).The strategies in designing a casing
treatment must be to prevent or to reduce any blockage and stagnation zones
induced by the tip leakage flow. Additionally, the inflow near the outer casing
should be deflected in the direction of the blade chord in order to avoid an
aerodynamic overloading of the blades. Minimizing the tip leakage flow induced
stagnation or blockage zones can be achieved through three different
arrangements:(1)
reduction
of the tip leakage flow, for example, by reducing the blade tip gap;(2)
removing
of stagnating leakage flow, for example, by axial slots (Wilke and Kau [22]);(3)
deflection
of the flow direction of the tip leakage parallel to the main flow, for
example, by circumferential grooves (Wilke and Kau [23]).
A decrease of the inflow angle of attack
near the blade tip requires a significant increase of the local mass flow which
can be achieved by bleeding additional air out of the blade passage and reinjecting
it upstream into the blade passage.Tip blockage stall effects occur at
higher mass flows than blade tip stall mechanisms. Hence, in compressors, in
which the flow stability is limited by tip blockage stall effects, the
application of casing treatments is generally more effective than in those that
show mainly blade tip stall mechanisms. A compressor that experiences tip
blockage stall can be stabilized by treating the tip leakage flow until the
mechanisms of blade tip stall finally dominate the aerodynamics.For blade tip stall, the local mass flow
near the blade tip has to be increased significantly by the casing treatment so
that this mechanism is more loss-intensive in order to stabilize the compressor
stage. This means, in the end, that the compressor efficiency is negatively
influenced.


## 2.1. Blade Tip Stall

At blade tip stall, the angle of attack of the inflow
is very steep especially near the blade tip. Thus, the inflow cannot completely
follow the direction given by the blade profile. This results in an extended
separation zone at the blade suction side and a significant deceleration or
even stagnation of the inflow at the upstream part of the following blade
pressure side (see Figure1). The tip leakage flow and the tip leakage vortex
rather just fill up the separation zone at the suction side of the blade than
blocking the incoming flow. The trajectory of the tip leakage vortex is almost
parallel to the direction of the inflow.Blade tip stall and tip blockage stall.
(a)(b)Figure 2
Simulated compressor stage.Figure 3
Block topology.Figure 4
Mesh topology at Rotor 1 tip leading edge.


## 2.2. Tip Blockage Stall

At tip blockage stall conditions, the inflow
direction of the compressor's main flow is very similar to that of the design
point, even close to surge. The angle of attack corresponds with the stagger
angle of the rotor blades and the deflection of the flow over the blade passage
is moderate. No aerodynamic overloading of the blade tip occurs at the tip
blockage stall mechanism. However, at higher pressure loads, the tip leakage
flow and the tip leakage vortex can cause a characteristic stagnation zone at the
blade passage shock, which leads to a critical blockage of the main flow. The
stagnation zone can be the result of a vortex breakdown occurring after the
blade passage shock. The angle between the vortex trajectory and the blade
chord is significantly bigger than that between the inflow and the blade chord
(see Figure1).In contrast to blade tip stall, the tip blockage
stall mechanism is in general characteristic for high rotational speeds as the
phenomenon seems to be a characteristic property of transonic compressors
(Wilke et al. [11, 12], Hofmann and Ballmann [17, 18], Schlechtriem and
Lötzerich [19], Furukawa et al. [20], Hoeger et al. [21]).The strategies in designing a casing
treatment must be to prevent or to reduce any blockage and stagnation zones
induced by the tip leakage flow. Additionally, the inflow near the outer casing
should be deflected in the direction of the blade chord in order to avoid an
aerodynamic overloading of the blades. Minimizing the tip leakage flow induced
stagnation or blockage zones can be achieved through three different
arrangements:(1)
reduction
of the tip leakage flow, for example, by reducing the blade tip gap;(2)
removing
of stagnating leakage flow, for example, by axial slots (Wilke and Kau [22]);(3)
deflection
of the flow direction of the tip leakage parallel to the main flow, for
example, by circumferential grooves (Wilke and Kau [23]).
A decrease of the inflow angle of attack
near the blade tip requires a significant increase of the local mass flow which
can be achieved by bleeding additional air out of the blade passage and reinjecting
it upstream into the blade passage.Tip blockage stall effects occur at
higher mass flows than blade tip stall mechanisms. Hence, in compressors, in
which the flow stability is limited by tip blockage stall effects, the
application of casing treatments is generally more effective than in those that
show mainly blade tip stall mechanisms. A compressor that experiences tip
blockage stall can be stabilized by treating the tip leakage flow until the
mechanisms of blade tip stall finally dominate the aerodynamics.For blade tip stall, the local mass flow
near the blade tip has to be increased significantly by the casing treatment so
that this mechanism is more loss-intensive in order to stabilize the compressor
stage. This means, in the end, that the compressor efficiency is negatively
influenced.


## 3. Investigated Compressor Stage and  Numerical Model

The investigated compressor stage is a
transonic front stage of a modern high-pressure compressor (HPC). The
compressor-rig totally consists of 4.5 stages. At design point, the total
pressure ratio of the front stage including the IGV at the point of maximum
efficiency is about 1.63. The compressor operates at a speed of 12 960 rpm and
has a relative Mach number at the rotor 1 blade tip of about 1.3. The tip
clearance of the rotor 1 is 0.5% span. Tip clearances of IGV and stator 1 were
also modeled as a simplification of the gap resulting from the mechanism for
the variable vanes.The compressor-rig has been run in the past and is
now numerically simulated in order to investigate different casing treatment
geometries. After the selection of the most promising geometry, new experiments
will be conducted in order to validate the results gained by the numerical
simulations.In order to save computational time and to be able to
conduct unsteady simulations, the domain scaling approach was applied. The
compressor stage was reduced to the blade numbers shown in Table1.Table 1
Simulated compressor blades.
RowOriginalAdaptedSimulatedIGV40462Rotor 123231Stator 136462The reduction in simulated passages for the discretization is based on the assumption that the flow is identical inside
all blade passages of the rotor 1 and inside every 2nd blade passage of the IGV
and stator 1, respectively. The IGV and stator 1 were not aerodynamically
scaled due to the fact that the casing treatment is applied to the rotor and
hence effects that destabilize the compressor have to appear at the rotor 1 tip
and not at the IGV or stator 1, so that the difference in their aerodynamic
loading due to the increased blade numbers is of no importance. The commercial
solver NUMECA/EURANUS was used for the simulation. The integration in time is
implemented through the implicit pseudo-time scheme. For the time-accurate
investigations, 41 physical time steps per blade passage and 15 pseudo-time
iterations with a CFL number of 1-2 within each physical time-step were
simulated. The choice of a prim number for the number of time steps was made to
dampen possible numerical oscillations excited by any blade periodicity.
Turbulence is introduced with the one-equation turbulence model from
Spalart-Allmaras. The simulations were conducted on 4 3.8 GHz Pentium IV
processors with 2 GB RAM. Without an initial solution, about 4 weeks and several
rotor rotations were required in order to achieve convergence. The numerical
stall point was determined with an accuracy of 2500 Pa in static back pressure.
Numerical stall appears as a transient flow field characterized by a continuous
decrease in mass flow, total pressure, and efficiency. Numerical stall in the
simulations was never a purely numerical phenomenon, but always arose from
physical consequences due to distinctive flow mechanisms.One blade passage is meshed with a block
structured topology consisting of 4 H-blocks and 1 O-block around the blade.
The H-blocks are located upstream of the leading edge, downstream of the
trailing edge and, seen in circumferentially direction, in front and behind the
blade O-grid. The whole grid for all meshed passages including 2 IGVs, one rotor and 2 stator passages, consists of 2.3 million mesh points without the mesh for the casing treatment. 77 grid
points were used to model the blade passage in the span-wise direction in all
rows. For the blade-to-blade direction, in the rotor 59 grid points were used,
whereas in the stators 29 per passage were used. In order to resolve phenomena
occurring near the shroud, the radial distribution was refined in the direction
toward the casing. The O-grid of Rotor 1 has 193 grid points in the
circumferential direction to ensure a high-quality mesh at the leading and
trailing edge of the rotor blade. The tip clearance is modeled by 21 grid
points in radial direction. The tip gap is modeled with an H-Block in the
middle and a surrounding O-Block. Because of the low-Reynolds description of
the boundary layer in the Spalart-Allmaras model used to simulate the
turbulence, the mesh was refined toward the solid boundaries in order to meet
the resolution requirements ofy+≤2. Mesh studies
were conducted in steady simulations by coarsening and refining the mesh. This
mesh size seemed to be the ideal compromise between accuracy and computational
demands.The casing treatments are resolved with
about 100 000 grid points in a butterfly-mesh. The nonrotating grids of the
casing treatments are mounted on a very thin circumferential socket (5% of the
tip clearance) and linked to the moving rotor and fixed IGV passage by an
unsteady rotor-stator interface using a sliding plane directly at the casing.


## 4. Investigated Casing Treatments

The design and the position of the tested casing
treatments is a well-known type. It has a significant impact on the stability
on rotor flows as shown by several authors (e.g., Takata and Tsukuda [3]). The
shape of the tested slots is a semicircle. This was done in order to improve
flow circulation inside the casing treatment and to avoid unnecessary
stagnation or secondary recirculation zones. No information is available about
the ideal number of slots per passage: the slot height or slot width for a
given compressor configuration in order to optimize both, efficiency and
stability. The simulated casing treatments use the pressure gradient in the
blade passage as well as the axial momentum of the main flow to create a flow circulation
inside the slots. Additionally, the pressure gradient from the blade pressure
to the blade suction side causes a secondary flow inside the casing treatment
when the rotor passes underneath. The slots remove blockage fluid out of the
blade passage and reinject the fluid further upstream near the IGV trailing
edge. This type of casing treatment is often called self-recirculating casing
treatment.Main parameters of the casing treatment
configurations can be seen in Figures5 and 6. Due to spatial limitations, stator 1 is not shown in
Figure 5. In configuration 1 and 2, the slots are parallel to
the rotational axis, whereas in the inclined configurations 3 and 4, the slots
have an angle of about 30° relative to the machine axis, so that they are
parallel to the IGV's flow exit angle. Both configurations, the axial and the
inclined one, were run with 4 equal slots per passage providing an open area of
50% in circumferential direction to the passage, and 2 equal slots per passage
providing an open area of 25% to the passage. The axial extension of the slots
is 80% of the axial rotor chord length. The axial position of the slots covers
30% of the blade chord length. The slots have a radial extension, thus are not
inclined against a meridian plane in the direction of blade rotation.Figure 5
Simulated casing treatments.Figure 6
3D view of casing treatment 1.


## 5. Flow Mechanisms inside the  IGV-Rotor-Stator Configuration without  Casing Treatment

Many authors have already described the mechanisms
and characteristics of tip leakage flow and its resulting vortex in transonic
compressor stages (Hofmann and Ballmann [17], Wilke and Kau [23]). Therefore,
the description of the flow in the stage without the casing treatment will
concentrate on the most important aspects in order to understand the occurring
phenomena.The tip leakage vortex develops because of the pressure difference between the
pressure and suction side at the blade tip gap. The vortex core emerges near
the leading edge of the blade, with a tendency to move more toward the blade
leading edge when increasing static back pressure. Additionally the aerodynamic
blade loading and thus the pressure difference at the blade tip increases when
approaching stall, so that the tip leakage flow is also increased. This leakage
flow rolls up around the vortex core coming from near the leading edge and
forms the tip leakage vortex. This rotation of the tip leakage vortex results
in the formation of a characteristic trough in the static pressure distribution
(Figures7 and 8). This trough indicates the vortex trajectory. Note
that in the figures, only one time-step out of 41 is shown.Figure 7
Static pressure in the blade passage at maximum efficiency, 98% blade height.Figure 8
Static pressure in the blade passage at the onset of vortex breakdown,
98% blade height.At maximum efficiency, the tip leakage vortex is able to cross the blade passage
shock without being significantly disturbed (see Figure7). Blockage effects are very small and can be
neglected. The λ-Shock is attached to the leading edge of the blades
and impinges on the suction side of the precursory blade at about 3/4 of the axial blade chord length. Hence, the
low-energy tip leakage vortex emerging from the forward tip gap has enough time
to be mixed and thus re-energized by the main passage flow. The trajectory of
the vortex is straight, with a very small angle relative to the blade chord of
the blade where it emerges, and it does not impinge on the pressure side of the
following blade.Near the onset of vortex breakdown, which is an operating point close to numerical
stall (see Figure8), the tip leakage vortex crosses the blade passage
shock with a significant enlargement of the cross section of the vortex.
Additionally, the trajectory turns into a direction more perpendicular to the
blade main flow. This phenomenon is often called vortex breakdown. Blockage
effects of the main flow are significant (Figures
8 and 9). The λ-Shock is detached from the blade leading edge and
impinges on the suction side of the precursory blade at about 1/2 of the axial blade chord length. Hence, the
mixing distance for the low-energy tip leakage flow with the main flow is
reduced to about 65% of the distance at the maximum efficiency operating point.
As a consequence, the vortex does also not get the same level of re-energetization.
Furthermore, the difference in static pressure before and after the shock is
increased at operation points close to stall, marking an additional hurdle for
the vortex to pass through. As a consequence, the vortex breaks up when passing
the shock, increases its diameter, and changes direction. Additionally, what
cannot be seen on the pictures, the inward radial extension increases
significantly after the shock. In Figure
9, an additional loss mechanism at the operating point
close to stall can be observed. As the vortex changes direction after the
shock, it impinges onto the second half axial blade length on the pressure side
of the following blade. This low-energy fluid passes the tip gap and creates a
secondary loss area on the blade's suction side. The relative total pressure in
Figure 9 illustrates these losses. The relative total pressure
in front of the blade passage shock can even be lower than the static pressure right after
the shock. This lack of energy blocks the core part of the leakage vortex from
passing through the pressure barrier of the blade passage shock. As a
consequence, the vortex core breaks down and the onset of a stagnation zone can
be observed. Low-energy fluid, which cannot be transported through the shock,
gets caught inside the stagnation zone. Under stable flow conditions, the fluid
inside the stagnation zone gets re-energized continuously by mixing and
diffusion processes between the core and outer parts of the vortex. This energy
input prevents the breakdown area from continuous expansion. At surge, however,
the re-energizing effects are no longer sufficient to dampen an expansion of
the stagnation zone. Hence, more low-energy fluid is transported into the
stagnation zone. The volume of the breakdown zone grows rapidly until the
resulting blockage causes vast flow separations in the rotor flow. This
mechanism finally leads to compressor stall.Figure 9
Relative total pressure at the onset of vortex breakdown,
98% blade height.


## 6. Classification of Critical Flow Mechanisms

The classification of critical flow
mechanisms in this compressor stage is determined based on the parameters
defined by Wilke [24]. With these parameters, it can be decided whether the
primary stall mechanism in the rotor is blade tip or tip blockage stall, as
described in the second chapter. Several angles and the Mach number in front
and after the shock near stall are required. For a detailed description, please
refer to [24]. The Mach number in front of the passage shock is about 1.55, and
after the shock about 0.8. To decide whether a blade tip stall is present, the
factor BP can be used.This factor is defined in (1), the required flow angles close to stall can be found
in Figure 10:
(1)BP=α−ξχ−ξ=0.35. For this compressor stage, this value is 0.35. In the case the value is 1, it is
very likely that blade tip stall occurs, in case it is 0, it is very unlikely.
Hence, for this stage, it is not very likely that blade tip stall occurs, which
is a good condition for the application of axial slots. The second parameter to
decide whether tip blockage stall is likely to occur is BS:(2)BS=M2,P,critM2,P=0.772. The critical Mach number M2,P,crit can be determined according to the
following equation:(3)M2,P,crit=M1tan(90°−β)cos(180°−(α+β)). In case the value for BS equals 1, it is very likely that tip blockage
stall occurs. This compressor stage has a value of 0.772, so that it is very
likely that this type of stall is present in this rotor. As a consequence, this
rotor seems to be an ideal candidate for the application of axial slots to
enhance the stall margin.Figure 10
Flow angles at 99% blade height (flow angle: blue = 90°, red = 45°).


## 7. Flow Mechanisms inside the  IGV-Rotor-Stator Configuration with  Casing Treatments

Due to the time requirements of the calculations, only for the most
promising—smallest loss of efficiency—configurations,
the complete compressor lines were calculated. The configurations 2 and 4 with
only 2 treatments per passage showed the smallest loss of efficiency. In the
following figure, the passage flow is analyzed on the basis of configuration 2
and at one time step out of 41. In Figure11, the static pressure distribution at 98% blade height
with the casing treatment configuration 2 is shown. By comparing to Figure 7, which is at about the same mass flow level, it can
be observed that the shock has moved a bit downstream, thus increasing the
mixing distance of the vortex with the main flow. Additionally, the vortex
trajectory has moved more toward the blade suction side from where it emerges.
In the sketched slot outline, the mass flow density in the casing treatments is
plotted. In this operation point, it can be seen that fluid enters as expected
on the pressure side of the blade (red colored) and exits the slots (blue
colored) upstream near the trailing edge of the IGVs. The main driving force
for the slot circulation is the high-pressure zone in front of the blade's
pressure side and after the shock. It takes place every time, when the blade
leading edge passes the slot. The slot flow has a highly unsteady character. It
is described in detail in the next chapter. For a point near stall, the
observations as described above are similar. Important to note is that the
characteristic low static pressure trough of the vortex between the leading
edge and in front of the shock is reduced. That means that a higher static
pressure occurs in the situation with the casing treatment at the same mass
flow levels (not shown).Figure 11
Static pressure in the blade passage with CT at maximum efficiency, 98% blade height.


## 8. Flow Mechanisms inside the  Casing Treatments

Figure12 illustrates the flow mechanisms in the casing treatments for configuration 1
with 4 slots per passage, in order to be able to describe the difference of the
location of the slots near the IGV suction side trailing edge or in between two
IGVs. The pictures illustrate the situation at a static back pressure of 140 kPa,
still with a certain margin from stall. Only the most important phases of a
period are shown. These are time steps 1 and 8, as well as time steps 21 and
28. The pictures on the left show the static pressure distribution in a plane
located in the middle of the regarded casing treatment as well as the static
pressure distribution in 98% blade height at time steps 1, 8, 21, and 28 of 41.
The right sketches explain the occurring primary and secondary flow phenomena
in the slots of CT1. Due to mass inertia effects, the pressure-induced flow
mechanisms in the slots appear with a delay, so that the pressure patterns in
time step 1 (and 21) (left picture) show their effect on the flow only in step
8 (or 28, resp.) (see right sketch). Effects from the blade, here the vortex
and the shock, show immediate impact on the flow and are here secondary flow
effects.Figure 12
Casing treatment flow phenomena.


### 8.1. Time Step 1

In time step 1, a typical flow for axial slots is present. The flow enters the
casing treatment on the right side, forming the main slot vortex, which is
leaving the treatment upstream of the main flow near the IGV. The flow is
mainly pressure driven, induced by a high-pressure field, which enters the slot
directly after the shock. This is the primary cause for the development of the
vortex in this time step. Secondary flow effects appear due to the shock
itself. The main flow develops radially inwards in front of the shock, and is
oriented radial outwards directly after the shock. The pressure pattern inside
the slot shows a high pressure on the right side, resulting from the shock, and
a low pressure on the left side.


### 8.2. Time Step 8

In time step 8, this pressure pattern of time step 1 shows its effect, so that the
main flow direction is from the right to the left, without any vortex. This
main flow direction is supported by an additional impulse resulting from the
blade tip that just passes the opening of the slot. Secondary flow effects
result again from the shock itself, and from the tip gap vortex, producing a
low-pressure field with an anticlockwise circulation. This extended vortex area
also picks up some fluid, so that a small secondary flow appears above the
vortex.


### 8.3. Time Step 21

In time step 21, the high-pressure field from the shock which moved from the right
to the left reaches the exit area of the main flow. However, the high-pressure
field from right behind the blade passage shock also just passes underneath
that area, so that the exiting flow gets decelerated and deflected. In this
phase, the general flow inside the slot again looks like a typical casing
treatment flow with a main slot vortex. In contrast to time step 1, the
pressure pattern is reversed. The high-pressure field is on the left side,
resulting from the shock, and the low-pressure field is on the right side,
resulting from the low static pressure trough caused by the tip gap vortex.
This pressure pattern has a strong influence on the flow phenomena in the next
time step.


### 8.4. Time Step 28

In this time step, the flow follows, again time-delayed, the pressure gradient and
hence flows mainly from the left to the right, with only a small portion of the
flow running in the “normal” anticlockwise direction near the outer part of the
slot.


## 8.1. Time Step 1

In time step 1, a typical flow for axial slots is present. The flow enters the
casing treatment on the right side, forming the main slot vortex, which is
leaving the treatment upstream of the main flow near the IGV. The flow is
mainly pressure driven, induced by a high-pressure field, which enters the slot
directly after the shock. This is the primary cause for the development of the
vortex in this time step. Secondary flow effects appear due to the shock
itself. The main flow develops radially inwards in front of the shock, and is
oriented radial outwards directly after the shock. The pressure pattern inside
the slot shows a high pressure on the right side, resulting from the shock, and
a low pressure on the left side.


## 8.2. Time Step 8

In time step 8, this pressure pattern of time step 1 shows its effect, so that the
main flow direction is from the right to the left, without any vortex. This
main flow direction is supported by an additional impulse resulting from the
blade tip that just passes the opening of the slot. Secondary flow effects
result again from the shock itself, and from the tip gap vortex, producing a
low-pressure field with an anticlockwise circulation. This extended vortex area
also picks up some fluid, so that a small secondary flow appears above the
vortex.


## 8.3. Time Step 21

In time step 21, the high-pressure field from the shock which moved from the right
to the left reaches the exit area of the main flow. However, the high-pressure
field from right behind the blade passage shock also just passes underneath
that area, so that the exiting flow gets decelerated and deflected. In this
phase, the general flow inside the slot again looks like a typical casing
treatment flow with a main slot vortex. In contrast to time step 1, the
pressure pattern is reversed. The high-pressure field is on the left side,
resulting from the shock, and the low-pressure field is on the right side,
resulting from the low static pressure trough caused by the tip gap vortex.
This pressure pattern has a strong influence on the flow phenomena in the next
time step.


## 8.4. Time Step 28

In this time step, the flow follows, again time-delayed, the pressure gradient and
hence flows mainly from the left to the right, with only a small portion of the
flow running in the “normal” anticlockwise direction near the outer part of the
slot.


## 9. Difference of Flow Mechanisms in Casing  Treatment 1 and 2

The main reason why configuration 1 is shown in Figure12 is to illustrate the
differences in the flow of casing treatment 1, located right at the suction
side of the trailing edge of the IGV, and casing treatment 2, located in the
middle of the two IGVs. The basic flow phenomena are the same, however there is
one important difference as a result from the interaction of the shock and the
IGVs suction and pressure side. In Figure 13, the time-averaged static pressure
distribution around the IGV for the smooth wall case at 98% blade height is
plotted. The high-pressure area behind the shock interacts with the IGV and its
pressure distribution. As the pressure difference near the IGV trailing edge is
about 100 000 Pa from the pressure to the suction side, the resulting local
pressure from the interaction of the shock induced high-pressure field and the
pressure distribution from the IGV is also different. The local bubble at the
suction side has a lower static pressure than on the pressure side,
consequently the deceleration
and deflection of the flow as described for time steps 21 and 28 are weaker in
this slot (CT1) than in the slot located between the IGVs (CT2).Figure 13
Static pressure around IGV at smooth wall, time averaged, 98% blade height.


## 10. Compressor Stage Maps

Figures14 and 15 show the total pressure ratio and
the normalized efficiency for the configurations 2 and 4 with casing treatments. For both
configurations, a slight enhancement in total pressure ratio could be achieved
at the same mass flow levels. However, the efficiency of configuration 2 is
negatively influenced and is reduced by about 0.26% in comparison to the smooth
wall configuration. For the configuration 4, the efficiency was even decreased by about 0.45%.Figure 14
Total pressure
ratio for smooth wall configuration and casing treatment configurations 2 and 4.Figure 15
Normalized
efficiency for smooth wall configuration and casing treatment configurations 2
and 4.In order to evaluate the improvement in stall margin, the following equation is
used for the determination:(4)ΔSMCT=Πmax,CTΠmax,SWm˙min,SWm˙min,CT−1. According to (4), the stall margin for both casing treatment configurations could be
improved by about 8.6%.


## 11. Conclusion

This article has presented a numerical investigation
on axial slots for a transonic axial compressor stage including IGV. Therefore,
the stage was investigated with the methodology of Wilke. Tip blockage stall
was identified as the primary stall mechanism in the rotor, so that the rotor
is an ideal candidate for the application of axial slots for enhancing the
stall margin. Four different casing treatment configurations were tested. The
flow in the casing treatments has been analyzed in detail, with special focus
on the interaction of the casing treatment flow and the influence of the IGV.
At operating points on the right side of the compressor line, when the
compressor is dethrottled, the flow phenomena in the slots are very similar,
almost independent from the location of the slots relative to the IGV. At
operating points close to surge on the left side of the compressor line, there
is a significant difference in the flow phenomena inside the slots due to the
interaction of the shock with the pressure distribution of the IGV. The typical
slot vortex is more stable over time in the slots near the suction side leading
edge of the IGV than in the slots between the IGVs. All casing treatment
configurations decreased the overall stage efficiency, but they were also able
to shift the stall margin by almost 9%. In future investigations, one special
focus will be put on the shape of the casing treatment in order to reduce the
efficiency losses. Furthermore, the IGV will be closed for part speed. It can
be expected that effects described in this article will get even stronger in
that case.



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*Source: 657202-2008-12-10.xml*