Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

51, 4, pp. 903-913, Warsaw 2013

EFFECT OF CIRCUMFERENTIAL GROOVES CASING TREATMENT ON

TIP LEAKAGE FLOW AND LOSS IN A TRANSONIC MIXED-FLOW

COMPRESSOR

Xiao-Qing Qiang, Ming-Min Zhu, Jin-Fang Teng

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, China

e-mail: jackzhushen@sjtu.edu.cn

A numerical simulation of a single stage transonic mixed-flow compressor is presented. The
simulation is runwith amulti-passagegrid thatmodels the 3D, viscous, steadyandunsteady
flow field. The effect of circumferential grooves casing treatment on the compressor overall
performance, tip leakage flow and loss has been studied. The results show that the narrow
operating range has been significantly broaden by the casing treatment grooves, while the
mismatching between the rotor and stator still exists andbecomes evenworse.Detailed ana-
lysis indicates that the fluid from circumferential grooves is injected into the blade passage
near the suction surface and re-energizes the leakage flow,whichmakesmainly contribution
to manipulation of the tip leakage flow and stall margin improvement. Since the pressure
difference across the blade tip section has a great impact on the effectiveness of circumferen-
tial grooves, the positions of shockwave and tip leakageflowaswell aswhere the interaction
takes place ought to be taken into account through the casing treatment design procedure.

Key words: compressor, casing treatment, tip leakage, flow loss, numerical simulation

Nomenclature

SC – smooth casing [–]
CT – casing treatment [–]
PE – peak efficiency [–]
NS – near stall [–]
SM – stall margin [–]
π – pressure ratio [–]
ṁ – mass flow rate [kg/s]
Zone 1,2 – low momentum region near leading and trailing edge, respectively [–]
TLF 1,2 – tip leakage flow from fore and rear chord, respectively [–]

1. Introduction

Mixed-flow or diagonal-flow compressor stages have been regarded as providing advantages over
both axial and centrifugal compressors. Combining these merits of high pressure ratio, a wi-
de operating range and small frontal area, mixed-flow compressors have a bright prospect of
application of small-sized military/civil turbofan or turbo-shaft engines.
In the late 1950s, several researchworks about the design andperformance test ofmixed-flow

compressor stages were conducted (Goldstein, 1948;Osborn andHamrick, 1952). Alongwith the
rapid development of axial and centrifugal compressor design techniques, transonic mixed-flow
compressors with high rotating speeds and pressure ratios were designed and studied since the
1980s (Musgrave and Plehn, 1987; Mönig et al., 1993). The increasing rotor blade loading and
tip tangential velocity,Mach number at the inlet blade tip resultes, in consequence, a higher loss



904 X.-Q. Qiang et al.

and intensive interaction between the shockwave and tip leakage flow aswell as boundary layer,
which made a great impact on the endwall flow stability in modern transonic compressors.

Dominant features of the compressor endwall flow include the tip leakage flow; interactions
among the tip leakage flow, the passage shock and the endwall boundary layers; and accumu-
lation of the low momentum fluid due to radial migration (Hah et al., 2010). Particularly, flow
characteristics of the tip leakage flow keep attracting considerable attention from researchers.
A great number of experimental and computation studies on the tip leakage flow in transonic
compressors were reported (Hah et al., 2010; Suder and Celestina, 1994; Hah and Rabe, 2001).
The tip leakage flow as well as its interaction with the shock wave manifests intensive unsteady
characteristics and are considered as a key role in compressor stall inception. Additionally, some
studies have proposed tip leakage vortex breakdown as a possible cause of stall inception in
transonic compressors (Schlechtriem and Loetzerich, 1997; Hoffman and Ballman, 2003). Bre-
akdown of the tip leakage vortex occurs downstream the shock wave at the near stall condition,
leading to large blockage effect near the tip and also the unsteady flow phenomena in the ro-
tor passage, which may be related to the spillage of the tip leakage flow at the stall inception
(Yamada et al., 2007).

Casing treatments have proved adequate to manipulate the specific flow mechanisms which
are responsible for compressor stall and, thereby, enhance the stall margin. Numerous studies of
casing treatment applied to transonic compressors have been carried out to identify the funda-
mental flowmechanisms and their influence on the operating range enhancement as well as flow
stabilization (Hembera et al., 2008; Beheshti et al., 2004; Wilke et al., 2005). A better under-
standing of the complex flowcharacteristics has beenachieved through time-resolved simulations
and accuratemeasurements such as fast response pressure transducer andPIV technique (Voges
et al., 2011). Circumferential-groove casing treatments have been applied very successfully to
certain transonic compressors with a moderate stall margin enhancement and acceptable effi-
ciency penalty. Particularly, recent researches reported that grooves with amuch smaller depth
than conventional designs are shown to be similarly effective in increasing the stall margin, and
the stage efficiency at design speed is shifted to slightly higher values (Müller et al., 2007).

This paper documents a numerical study of a single stage transonic mixed-flow compressor
aimed at addressing these issues. By both steady and unsteady simulation, the behavior of tip
leakage flow and its influence on the stall process are specifically discussed.The flowphenomena
changes caused by the circumferential grooves casing treatment are emphasized in detail.

2. Descriptions of investigated model and numerical method

The present study is based mainly on numerical simulation carried out by Numeca/FINE. The
investigated mixed-flow compressor stage is a transonic front stage of a four-stage high-pressure
compressor. It consists of a low-aspect-ratio blisk rotor equippedwith 21 blades (with 1% blade
height tip clearance, 3mm hub fillet) and a stator with 49 typical straight blades. The inlet
relative Mach number at the rotor tip reaches 1.4 at the design condition, whereas the hub
runs at subsonic conditions. Figure 1 illustrates the cross section of this transonic mixed-flow
compressor stage.

The casing treatment consisted of five grooves lies between 10% and 94% of the rotor axial
chord. Since a deeper groove produces a higher efficiency loss, a moderate-depth (6mm) groove
configuration is chosen. All of the grooves in a given configuration have the same shape. Accor-
ding to the previous study, the ratio of the groove width to gap between each groove has to be
larger than 2 (Prince et al., 1974). To fulfill the requirement, the axial extent of the groove is
chosen to be 12% of the rotor axial chord, while the gap length to be 6%. A schematic of the
casing treatment grooves is presented in Fig. 2.



Effect of circumferential grooves casing treatment on tip ... 905

Fig. 1. Cross section of the mixed-flow compressor stage

Fig. 2. Schematic of the casing treatment grooves

Both steady and unsteady numerical simulations were performed. In particular, the domain
scaling approach was applied in the unsteady simulation. Considering the constraints of this
approach (rotor/stator periodicities must be equal), 3 rotor passages and 7 stator passages
(shown in Fig. 2) were simulated in total so as to identify the behavior of the tip leakage flow
and to capture instantaneous flow structuresnear stallmore accurately.Anumberof 4.73million
grid points was used, including 1.33 million grid points in the rotor blade passage, 2.89 million
in the stator passage, 0.16 million in the tip clearance, and additional 0.35 million in the casing
treatment grooves. The rotor and stator blades weremeshed inH-O-H topology, while the rotor
tip clearance geometry wasmeshed with a butterfly topology. The circumferential grooves were
modeled in a separated block with straight H-block. For each groove, 65 nodes in the tangential
direction, 33 nodes in radial and 33 nodes in axial were used to represent the groove geometry.

The RANS equations were discretized in space using a cell-centered explicit finite volume
scheme. Spalart-Allmaras model was applied to introduce turbulence. The steady-state flow
solution was achieved at the convergence of a fourth-order explicit Runge-Kutta integration
scheme. The time-marching algorithmwas stabilized using scalar eigenvalue-based second-order
and fourth-order difference smoothing operators. Unsteady simulations were implemented in the
Jameson implicit dual time-stepping scheme, which allowed for the solution of a steady state
problem at each physical time step. This methodology enables keeping the main advantages of
the explicit time integration scheme already implemented for resolving steady-state problems as
well as retaining the local time stepping and implicit residual smoothing. For the timedependent
simulation, 30 physical time steps per stator passage and 50 pseudo-time iterations with a CFL
number of 3 within each physical time step were performed. The local time stepping, implicit
residual smoothing andmultigrid techniques were applied to reduce the computation cost.

At the inlet, the flow direction was assumed to be axial. A constant total pressure of
101325Pa and a constant total temperature of 288.15Kwere applied. At the outlet, the average
static pressure was given at a channel extension downstream the stator row to avoid numerical
reflections. The side boundaries of the passage were modeled with matching periodicity. Solid
boundaries were applied at the hub, casing and blade surfaces with no slip and impermeability
conditions.



906 X.-Q. Qiang et al.

3. Results and discussions

3.1. Effect of the casing treatment on compressor performance

The compressor speed line was obtained by raising the exit back pressure incrementally.
When closing to the stall point, the converged solution of the last point was used as the initial
solution. The mass flow rate continued to decrease with rising the exit back pressure until the
convergent solution no longer existed. The last steady and converged solution point would be
considered as the near stall (NS) point.

Fig. 3. Overall performance for the compressor stage at 100% design speed

Figure 3 presents the overall performance for the mixed-flow compressor stage at 100%
design speed both with the smooth casing (SC) and casing treatment (CT). As a comparison,
the unsteady solutions at NS condition are also marked in the figure. The total pressure ratio
and isentropic efficiency are plotted as a function of the mass flow. The figure shows a peak
efficiency (PE) of 0.8215 and maximum total pressure ratio of 2.119 with SC. At PE mass
flow, the total pressure ratio reaches 2.097. At a normalized mass flow of 91.7%, the last steady
converged solutions are gained with a pressure ratio of 2.114. As shown in Fig. 3, values of
unsteady solution are almost equal to the steady solution atNScondition.Thus, in consideration
of computation economy, the compressor speed line is attained by steady solutions. The stall
margin is calculated by

SM=
(π

NS
/ṁ

NS

π
PE
/ṁ

PE

−1
)

·100% (3.1)

where π and ṁ are the value of total pressure ratio andmass flow rate at NS or PE conditions.
Hence, thismixed-flow compressorwith SCgains a stallmargin of 6.57%,which is badly in need
of improving.

Seen from the figure, the impact of casing treatment on the mixed-flow compressor stage
performance is just obvious. The casing treatment consisting of 5moderate-depth grooves is able
to enhance the compressor flow stability effectively with a slight drop of 1% in the isentropic
efficiency atPEmassflow.Furthermore, the casing treatment raises the stage total pressure ratio
significantly. The normalized stall mass flow reduces by 2.7% and total pressure ratio increases
by 2.9%atPEmass flow.Thus, the SMwithCT rises to 11.25%, 1.7 times from the stallmargin
with SC, according toEq. (3.1). As themass flowdecreases fromPEtoNScondition, the growth
of total pressure ratio keeps increasing.

In order to evaluate the influence of the casing treatment on the main passage flow, pitch
averaged radial profiles of several flow parameters are discussed at PE and NS conditions. Fi-
gure 4 presents the spanwise distributions of total pressure ratio as well as isentropic efficiency



Effect of circumferential grooves casing treatment on tip ... 907

at the rotor outlet and incidence angle at the stator inlet. Apparently, the installation of this
circumferential casing treatment has a noticeable impact on these flow parameters. Figure 4a
shows a pretty high aerodynamic loading near the tip region both at PE andNS conditionswith
SC. Dramatic growth of the total pressure ratio is observed above 70% span. At NS condition,
the maximum pressure ratio near the tip region is about 3% higher than that at PE condition
at the same span.WithCT, themaximummagnitude is achieved at 75% span,much lower than
95% span of SC case, which means the highly loaded region is shifted to a lower position by
casing treatment. Furthermore, the pressure ratio below 85% span rises remarkably in compari-
son with SC case, especially at NS condition. The greatest growth in the total pressure ratio at
NS condition comes up to about 9.5% at 73% span. In Fig. 4b, efficiency drop owing to casing
treatment is noticed above 70% and 60% span at PE and NS conditions respectively, and the
difference resulted fromCT at NS condition is larger than that at PE condition. These changes
along the spanwise indicate that the region influenced by CT on the efficiency distribution lies
above higher span near the tip region, contributing to the efficiency drop shown in the compres-
sor performance map. Figure 4c shows the impact of casing treatment on the incidence at the
stator inlet. At PE condition, the incidence angle distribution does not change a lot with CT.
However, it increases by 2◦ to 6◦ in a wide range of span at NS condition. Although this casing
treatment configuration is capable of enhancing the flow stability and rising pressure ratio for
the investigated mixed-flow compressor effectively, it aggravates the incidence distribution at
NS condition rather than improving thematching status between the rotor and stator.

Fig. 4. Spanwise distributions of performance at PE andNS conditions; (a) total pressure ratio at the
rotor outlet, (b) isentropic efficiency at the rotor outlet, (c) incidence angle at the stator inlet

3.2. Tip blockage and tip leakage flow with SC

Figure 5 shows the comparison of the relativeMach number distribution betweenPEandNS
conditions at 98% span. At PE condition, a small area of low momentum (Zone 1) has already
formed behind the detached shockwave, nearly in themiddle of tip passage, followed by amuch
larger one (Zone 2) closed to the pressure surface. The shock-boundary layer interaction can also
be observed near the blade suction side. As the mass flow decreases to NS condition, Zone 1 as
well as Zone 2 grows larger, and Zone 1 in themiddle of the tip passagemoves further upstream
and towards the pressure surface, almost reaching the leading edge. The detached shock wave is
pushed away from the leading edge by the increased back pressure, thereby the position where
the shock wave interacts with the boundary layer moves forward from 33% to 29% of the rotor
axial chord.
Figure 6 presents the tip leakage vortex and leakage flow inside the blade passage at two

conditionswith particle traces released from the region 0.6%axial chord downstream the leading
edge. The color of particle traces describes its velocity. The isolines of the relativeMach number



908 X.-Q. Qiang et al.

Fig. 5. RelativeMach number at 98% span; (a) PE condition, (b) NS condition

ranging from 0.99 to 1.01 at 98% span are also plotted in black lines to represent the shock
wave.

At PE condition, as described in Fig. 6a, the tip leakage vortex core is formed by the fluid
originating near the blade tip section, as the consequence of the pressure difference between the
pressure and suction side at the blade tip. Once the trajectory of vortex core encounters the
shock wave, the velocity of particle traces drops dramatically with a remarkable enlargement of
vortex diameter. This phenomenon is supposed to be the onset of so-called vortex breakdown,
which could be a triggering of stall inception (Hoffman and Ballman, 2003). Right behind the
shockwave, the tip leakage flow originating from the leading edge (TLF1) strides over the blade
tip perpendicularly to the main flow direction at the position between about 30% to 40% axial
chord and travels above the core vortex. This leakage flow rolls up around the vortex core and
forms the induced tip leakage vortex. After passing through themiddle of the blade tip passage,
TLF 1 turns direction sharply into main flow and moves towards the pressure surface of the
adjacent blade passage near the tailing edge. The direction-changing area forms the small-sized
lowmomentum zone (Zone 1) shown inFig. 5a. Both vortex core and leakage flowmove radially
inward as theymove downstream. Another part of the tip leakage flow (TLF 2) strides over the
blade tip between 40% to 84% axial chord and moves towards the pressure surface, above the
vortex core and TLF 1. The vortex core and two parts of the leakage flow accumulate at the
middle and the rear portion of the blade passage near the pressure surface and concur to bring
about the formation of the large-sized low momentum region (Zone 2).

Fig. 6. Particle traces near rotor tip; (a) PE condition, (b) NS condition

As themass flow reduces to NS condition, since the tip leakage vortex core strengthens and
becomesmoreparallel to the leading edge plane, the shockwave has beenpushedupstream(seen
Fig. 6b).Thevortex core encounters the shock frontier at 13%of the axial chord downstreamthe



Effect of circumferential grooves casing treatment on tip ... 909

leading edge, earlier than 19% at PE condition. Besides, TLF 1 travels further across the blade
passage than at PE condition, turning its direction into the main flow closer to the pressure
surface. This tip leakage flow always rolls up around the vortex core right behind the shock
wave, where the so-called vortex breakdownmight occur. It implies that the vortex breakdown
mightmake an effort to drive the tip leakage flow to stride over the tip clearance in the direction
perpendicular to the main flow besides the pressure difference across the tip clearance.
The phenomena of “blade tip stall” and “tip blockage stall” have been identified as the two

basic classes of tip stall mechanisms in transonic compressors (Brignole et al., 2005). Based on
the previous description of these two phenomena, the tip stall mechanism in this compressor
stage is supposed to be the “tip blockage stall” one. The present paper is focused on this aspect.
The effect of tip leakage flow is taken into account to improve the understanding of the “tip
blockage stall” (as Fig. 7 shows). The tip leakage flows can be divided into two types according
to the leaking position and flow behavior inside the blade passage. Both two types play an
indispensable role in formation of the low momentum area (Zone 1 and 2). The radial inward
moving and direction-changing of TLF 1, which might be induced by vortex core breakdown,
results in low momentum area Zone 1, as the “blockage of inflow”mentioned by Brignole et al.
(2005). The vortex core as well as TLF 1 and 2 arrives at themiddle and rear part of the blade
passage near the pressure surface at a low velocity, jointly leading to the formation of Zone 2, as
the “vortex stagnation zone” in the previous research. Since the vortex core breakdown and tip
leakage flow are relevant to the “tip blockage stall”, the application of casing treatment should
be able to manipulate such flow behavior.

Fig. 7. The effect of tip leakage flow on the tip blockage stall mechanism at NS condition

3.3. Effect of the casing treatment on tip leakage flow

The flow field details of casing treatment case at smooth casing PEmass flow rate (91.7% of
chokedmass flow) calculated by steady simulation are discussedhere. The relativeMach number
contour at 98% span and particle traces near rotor tip are presented in Fig. 8. Compared with
Fig. 5a, which is at the samemass flow level, it is observed that the lowmomentum area Zone 1
and 2 no longer exists at 98% span. The blockage inside the blade passage has been dampened
or vanished dramatically after the installation of casing treatment. Particle traces in Fig. 8b,
also originating from the region of 0.6% of the axial chord downstream the leading edge, shows
that the position where the shock wave interacts with the tip leakage vortex moves further
downstream compared with Fig. 6a. Besides, the trajectory of the tip leakage vortex coremoves
more towards the suction surface. No more leakage flow behaving in the same way as TLF 1
is found in SC case, providing an explanation to the repression of blockage Zone 1. The vortex
core and tip leakage flow exit the blade passage in a higher velocity than in SC case at 98%



910 X.-Q. Qiang et al.

span, which weakens the low momentum area Zone 2. Hence, it can be concluded that this
configuration consisting of 5 grooves can effectively manipulate the flow behavior of the tip
leakage vortex and leakage flow, depress the tip blockage and, therefore, delay the occurrence of
stall inception.

Fig. 8. RelativeMach number at 98% span and particle traces near the rotor tip at smooth casing PE
condition; (a) relativeMach number at 98% span, (b) particle traces near rotor tip

Entropy distributions on a series of cross-flow planes with particle traces near the rotor
tip with SC and CT are compared at smooth casing PE condition in Fig. 9. Particle traces
presenting the tip leakage vortex originating from the leading edge are painted in light color,
while the tip leakage flow is painted in deep color, originating from the region very close to the
pressure surface at 98% span, from approximately 30% to 40% of the axial chord. As previously
mentioned, particle traces in deep color, regarded as the TLF 1, enters the blade passage from
the pressure surface andmoves upstream and radially inward. ThenTLF1 arrives in themiddle
of the tip passage at a low speed (seen in Fig. 6a) and turns its direction into main flow.
Figure 9b shows changes in the flow field with 5 CT grooves. Particle traces, starting from the
same position as in Fig. 9a, turn into main flow right after striding over the blade tip and roll
up around the leakage vortex core (in light color). Consequently, the leakage flow in CT case
passes through the blade passage closer to the suction surface than that in SC case.

Fig. 9. Entropy distributions on cross-flow planes and particle traces near the rotor tip at smooth casing
PE condition; (a) with SC, (b) with CT

3.4. Effect of casing treatment on loss at the rotor tip

Figure 9a shows a high loss region at the 2nd cross-flow plane downstream the leading edge,
near the position where TLF 1 changes its direction, as a consequence of a low speed flow and
the resulting blockage here. Owing tomanipulation of the tip leakage flow by casing treatment,



Effect of circumferential grooves casing treatment on tip ... 911

Zone 1 resulted from TLF 1 is remarkably damped as well as Zone 2, as depicted in Fig. 8a.
However, much higher loss regions are observed at the top of 3rd to 7th planes downstream the
leading edge, very close to the endwall. 8th to 10th planes also showhigher andwider loss regions
than that in SC case. Since the leakage flow does not pass through these high loss regions, the
applied casing treatment is supposed to be the dominant because of high loss near the endwall.
The radial velocity distribution at the interface between the rotor casing and circumferential
grooves is also shown in Fig. 9b. The positive radial velocity zone in each groove is located very
close to the pressure surface of the tip passage, while negative zones near the suction surface.
Circumferential grooves draw the fluid near the pressure surface out of the blade passage and
feed it back near the suction surface, bringing about complex interactions between the main
flows and casing treatment, which certainly have a great impact on endwall flow and causes high
loss regions.

On the one hand, the introduction of circumferential casing treatment manipulates the tip
leakage flow behavior and, consequently, removes the tip blockage Zone 1 and 2, reducing the
tip blockage loss. On the other hand, interactions between the blade passage flow and casing
treatment result in a high loss region near the endwall. Whether the circumferential casing
treatment can increase or decrease the overall efficiency depends on the combined effect of all
these factors. In addition, the influence of casing treatment on the efficiency ranges from the
casing to the middle-upper span according to Fig. 4b, not only limited to the tip region. More
future work needs to be given to evaluate the loss variation caused by CT quantitatively, in
order to optimize the design of circumferential casing treatment with less efficiency drop.

3.5. Re-energizing process and its role in casing treatment design

In Fig. 9b, zones with the maximum magnitude of positive and negative radial velocity are
both located in Groove 2 from the leading edge as a result of the greatest change in pressure
difference across the blade tip section. The negative radial velocity zone in Groove 2 just lies
above the area of fairly low static pressure near the detached shock wave. The fluid migrating
circumferentially inside the groove is re-injected into themain flow at the low pressure location,
where TLF 1 passes through in SC case. The fluid from the groove re-energizes TLF 1 and
enforces it into the main flow directly, interpreting the depression of the low momentum zone
and flow blockage caused by TLF 1. Except Groove 5, the left three grooves show both obvious
positive and negative radial velocity zones, making the removal/injection procedure possible.
It implies that the pressure difference across the blade tip section near the trailing edge is not
adequate to complete the fluid transport.Comparedwith the highly loss regions in the front part
of the blade tip passage, lower losses at the top of 8th to 10th planes also provide an evidence
of weak interaction between main the flow and Groove 5. Since Groove 5 lacks the capacity of
re-energizing the leakage flow with only a highly loss at the tip region, the casing treatment of
front 4 grooves is expected to be a better configuration on this mixed-flow compressor stage.

Unsteady simulation at NS condition with CT provides the time-averaged radial velocity
distribution at the interface between the casing and grooves in Fig. 10. Particle traces near the
rotor tip and isolines of the shock wave are also presented. Due to the increased back pressure
at NS condition, the shock wave is pushed further upstream as well as the position where the
interaction with the tip leakage vortex occurs. As a result, themaximummagnitude of negative
radial velocity is achieved in Groove 1, above where the interaction between the shock wave
and tip leakage vortex takes place. Owing to the upstreammotion of the passage shock, a lower
pressure difference is achieved across the blade tip section beneath Groove 2. In consequence,
Groove 2 no longer provides enough energy to drive TLF 1 into themain flow directly. Backflow
of TLF 1 is observed after entering the blade passage, and it turns back into the main flow
direction pretty close to the adjacent pressure surface. It is not difficult to expect that as the



912 X.-Q. Qiang et al.

mass flow continues to decrease, the shock wave keeps moving upstream and provides a much
less driving force to complete the injection procedure in Groove 2. ThusTLF 1without enough
re-energizing keeps moving upstream and brings about the low momentum region as Zone 1
again, making an effort to the onset of the stall process. The above discussion reveals that the
pressure difference across the blade tip section determines the impact of circumferential grooves
on the flow field and overall performance to some degree. Specifically, the positions of the shock
wave and tip leakage flow as well as where the interaction takes place ought to be taken into
account through the design procedure of circumferential grooves.

Fig. 10. Time-averaged radial velocity distribution at the interface between the casing and grooves and
particle traces near the rotor tip at casing treatment NS condition

4. Conclusions

A mixed-flow compressor stage with and without casing treatment has been numerically simu-
lated to study the effect of circumferential grooves casing treatment on the tip leakage flow and
loss. By analyzing the detached shock wave, the tip leakage vortex and leakage flow as well as
the interaction among them, the following conclusions have been drawn:
• The shock wave, tip leakage vortex and leakage flow concur to bring about the formation
of two low momentum regions. Induced by pressure difference and shock-leakage vortex
interaction, the tip leakage flow from the fore chord moves upstream and builds up a
blockage zone at the pressure surface near leading edge;

• The circumferential grooves casing treatment is capable of enhancing flow stability and
raising pressure ratio on the investigated mixed-flow compressor stage effectively. Howe-
ver, it aggravates the incidence distribution at NS condition rather than improving the
matching status between the rotor and stator. It manipulates the endwall flow field via
re-energizing the tip leakage flow from the fore chord and drives it into themain flow. The
impact of grooves on the low momentum fluid is closely corresponding with the position
where the shock wave interacts with tip leakage vortex.

Acknowledgements

This work was supported by the Initiative Projects of SJTU Young Teachers under Grant

No. 12X100040080.

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Manuscript received November 21, 2012; accepted for print March 5, 2013