CFD Investigation on Stall Mechanisms and Casing

Treatment of a Transonic Compressor

Chen Haixin1 Huang Xudong2 Fu Song3

School of Aerospace Engineering, Tsinghua University, Beijing, China, 100084

[Abstract] With an in-house developed highly accurate and efficient code, the authors

simulate the flow in a transonic axial compressor NASA Rotor 37. Based on the code

validation, the stall mechanism is studied. The simulation shows that with different tip gap

height, the stall processes exhibit different characteristics with a smooth casing. Two kinds

of stall mechanisms are revealed. The study on the effects of the Circumferential Grooves

Casing Treatment (CGCT) is performed subsequently. The difference of the triggering to

stall also strongly affects the effectiveness of the CGCT.

Nomenclature

CGCT = Circumferential Grooves Casing Treatment

BTLV = Blade Tip Leakage Vortex

DPH = Dynamic Pressure Head

SW = Smooth Wall, no groove

G1 = only the 1st groove effective, which is most near the leading edge

G23 = the 2nd and the 3rd grooves effective

I. Introduction

ith the development of the modern air-breath engine, the compressor is required to have higher performance

with less stages. This trend challenges people’s understanding of the stall process of the compressor much.

Many efforts have been made on the revealing of the stall mechanism. Adamczyk et al. [1], Copenhaver et al. [2],

Hah and Loellbach [3], Chima [4], Suder and Celestina [5], Van Zante et al. [6], Rabe and Hah[7] studied the flow

structures near the endwall both experimentally and numerically. Schlechtriem and Loetzerich [8], Hoffmann and

Ballmann [9], Yamada et al. [10] and Stephan Kablitz et al. [11] believe that the stall is triggered by the breakdown of

the leading edge blade tip leakage vortex (BTLV). However, Hah, Rabe and Wadia [12] find that for the forward

swept rotor the vortex breakdown won’t happen even the compressor operates in a stalled condition, but the shock

oscillation and the BTLV oscillation induced by the shock-

boundary layer interaction is a possible reason for the stall. The

CFD results on a swept rotor by Bergner et al. [13] indicate that

the “spill forward” flow near the pressure side at leading edge

induces the stall precursor. These studies help us comprehend

the behavior of the compressor little by little.

The application of Circumferential Grooves Casing

Treatment (CGCT) has been found for years to be able to

improve the stall margin of axial flow compressor. Some

researchers attempted to uncover the mechanism of CGCT too.

Recently, Rade & Hah[7] studied the effects of the CGCT on the

flow field of a transonic compressor both experimentally and

computationally. Aamir & John’s [14] most recent work studied

the physical mechanism of the CGCT on a low speed rotor.

1 Associate Professor, Dr.-Ing , Laboratory of Advanced Simulation of Turbulence, chenhaixin@tsinghua.edu.cn 2 Ph. D. Candidate, Laboratory of Advanced Simulation of Turbulence, huangxudong00@mails.tsinghua.edu.cn 3 Professor, Dr. –Ing, Deputy dean , School of Aerospace Engineering, fs-dem@tsinghua.edu.cn, AIAA Senior

Member

W

Figure 1. Geometry of NASA Rotor-37 with

Circumferential Grooves on Casing

42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit9 - 12 July 2006, Sacramento, California

AIAA 2006-4799

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

CFD is becoming more and more important in this area of study. However, so far, because of the extremely

complexity, neither experiments nor CFD could give a completely clear description of the flow in transonic axial

compressor. The understanding about the mechanisms of the stall and casing treatment is still not complete. More

efforts are needed not only on the mechanisms but also on the providing of a guideline for the turbomachinery

design. This paper mainly focuses on the influence of the tip clearance to the stall process and further to the effects

of the CGCT, with the hope to contribute the authors’ efforts to these problems.

II Configuration of Current Study

The transonic compressor, NASA Rotor 37, is

selected for this research. Table 1 gives the

parameters of the test rotor. Self-assigned CGCT,

which involves 7 circumferential grooves,

distributes averagely from the blade’s leading

edge to the trailing edge (Fig 1). Table 2 gives the

parameters of groove configurations for this study.

The original smooth wall configuration is first

simulated for the code validation. Then the

influences of the height of the tip clearance are

studied for the stall mechanism analysis by three

cases: no tip gap configuration; the baseline

configuration with the tip gap of the height about

0.4% of the blade span; and the configuration

with a larger 1.0% span tip gap. For the CGCT

study, only the latter two cases are studied.

III Numerical Method

With the Cartesian coordinate system fixed on and rotating with the rotor, the flow field considered by this paper

can be computed by a steady solver. The governing 3-D RANS equations can be written in the conservative form:

01

=++∂

∂+

∂

∂SD

Rx

F

t

Q

ei

i

, Where

=

rE

w

w

w

Q

ρ

ρ

ρ

ρ

ρ

3

2

1

,

+

+

+

=

i

r

ii

ii

ii

i

i

wH

pww

pww

pww

w

F

ρ

δρ

δρ

δρ

ρ

33

22

11

,

1

2

3

0

i

i

i

i

ij j i

Dx

w q

τ

τ

τ

τ

∂ = − ∂ − ,

−ΩΩ

+ΩΩ∂

∂−=

0

)2(

)2(

0

0

23

32

wx

wxx

Si ρ

ρ

,

( ) eij

l

l

ij

i

j

j

i

tij kRx

w

x

w

x

wρδδµµτ

3

2

3

2−

∂

∂−

∂

∂+

∂

∂+=

,

it

t

t

ix

hq

∂

∂

+−=

PrPr

µµ

Where 2/)( 22rwwkeE ll

r Ω−++= and 2/)( 22rwwkhH ll

r Ω−++= are the rotary total energy, and

the rotary total enthalpy respectively.

A self-improved k-ω TNT SST model [15] is adopted for the closure of Reynolds stress. Although modified, the

model keeps its so-called low Reynolds number property. No wall function is needed.

The Roe’s Flux Difference Splitting (FDS) scheme is selected for the discretization of the convective terms.

For the purpose of robustness, the scheme is formulated in the finite volume approach. The 3rd order MUSCL up-

Table 1. Parameters of NASA Rotor 37

Number of Blades 36

Rotation Speed 17188.7rpm

Tip/Hub Diameter 0.5074/0.3576m

Designed Pressure Ratio 2.106

Designed Mass Flow Rate 20.19kg/s

Tested Choking Mass Flow

Rate

20.93kg/s

Table 2. CGCT configurations Investigated

Num. of Grooves 7

Width (Tip Chord %) 10

Grooves Area Ratio 66.7%

Depth (Local Radius %) 2

wind bias interpolation is employed to ensure that the scheme is 2nd order accurate on non-uniform and curvilinear

grid. The smooth and continuously derivable van Albada limiter is used to restrict the high-order spurious oscillation

in the numerical solution.

The solving of model equations for k and ω are decoupled

from those of N-S equations. 2nd order upwind scheme are used for

spatial discretization.

The LU-SGS implicit scheme developed by Yoon and Jameson

is chosen as the time stepping method for both N-S equations and

the turbulence model equations.

Block-structured grids are generated about the flow passage of

rotor and the cavity of CT. Both of them are H-H type. The

technique of Quasi-Point-to-Point patch and “Overlap Area

Weighted Reconstruction” [16] for the convective fluxes exchange is

used on the grooves’ interfaces with the blade passage grid, as is

shown in Fig.2. The grid number of passage grid is 132×60×60.

And one 30×25×60 grid block is used for each groove.

Previous study [15, 17] indicates that these numerical methods were accurate, efficient and robust for this problem.

IV Results and Discussion

A. Code validation

For the choking mass flow rate, our prediction, which is 20.924kg/s, agrees with the experimental value 20.93

kg/s very well. Fig 3 shows the comparison of the overall performance of Rotor 37 between our calculation and the

experiment results, where the lines represent the calculated results and the solid diamonds show the experimental

data. Fig 3 a) indicates that our code can simulate the whole operation line well, from choking to stall, except that

our prediction on the peak efficiency is about 1% lower than the experimental data. But this seems to be a common

problem of nearly all

the other researchers’

calculation [18]. Fig 3 b)

shows a more or less

over predicted total

pressure ratio and the

possible reason may be

originated from the

grid we used, which

will be discussed later.

Fig 4 illustrates the comparison between our results and some other researchers’ results, on the pitch-wise

averaged total pressure ratio, total temperature ratio, and the adiabatic efficiency at the blade exit. The pictures

a) Total Pressure Ratio b) Total Temperature Ratio c) Adiabatic Efficiency

Figure 4. Pitch-wise Averaged Results at Blade Passage Exit

Figure 2. Patch of Grid Blocks

a) Adiabatic Efficiency b) Total Pressure Ratio

Figure 3. Overall Performance

above are our predictions while the pictures below are the CFD results from literatures [18]. Generally, our results are

comparatively good, especially on the adiabatic efficiency. But at the near hub region, like most of the other

researchers, our code over predicted all the three parameters. This may result from the disability of the turbulence

model, and may need more work in the future.

Fig. 5 shows the relative Mach number distribution at 50% span, 20% chord. Our code captures the location of

the shock wave precisely. However a lower post-shock Ma value is predicted than the experiment result. In Fig.6, on

the relative Mach number at the blade passage exit, our prediction is quite good.

Fig. 7 shows the flow field images, where a) is the contour of relative Mach number at 50% span and b) is the

contour of axial velocity at 98% span. From Fig. 7 a) we can see that our code can capture the main structure of the

flow field well, but the predicted angle between the leading edge shock wave and the blade is a little larger than the

measured value [18], which may result to a larger loss of the velocity and a higher prediction of pressure rise. This

may be a reason for the disagreements in Fig. 3 b) and Fig. 5 a). We believe that this error can be attributed to the

relatively bad grid quality in the blade passage limited by the H-H topology. This can be improved by a combined

O-grid and H-grid in the future work. Fig.7 b) also shows a good agreement between the simulated and the measured

results [18] on the more complex flow field near the casing. However, there are still some problems. First we predict a

stronger shock wave in the middle of the blade suction side; second the wake we predict is too short. The former

problem may again be improved by a high quality grid, while the latter one may need better turbulence model,

lower dissipate numerical methods and more orthogonal grid, in the wake region.

a) Present Result b) CFD Results from Literatures

[18]

Figure 6. Relative Mach Number Distribution at 50% Span, Blade Passage Exit

a) Present Result b) CFD Results from Literatures

[18]

Figure 5. Relative Mach Number Distribution at 50% Span, 20% Chord

a)Relative Mach Number at 50% Span b) Axial Velocity at 98% Span

Figure 7. Flow Images

B. Stall process at different tip gap height Validated by the experimental data, the code is used to study the relations of stall with tip gap height. From the

calculation we find that the mechanisms of stall are quite different with different tip gap height.

No tip gap cnfiguration

As we all know that the rotor can stall without a

tip gap, we consider the no tip gap configuration

first as a limit condition, with the desire to make it

clear the stall process without the influence of the

tip leakage flow. Fig. 8 shows the calculated results

at the near stall condition of Rotor 37 with no tip

gap. Fig. 8 a) shows the DPH contours on the slices

vertical to the axial, where the blue color represents

the low DPH region. There is a remarkable low

DPH region starts from about 1/3 chord and

expands to occupy 1/3 of the blade passage pitch-

wisely at the trailing edge. This region is also

revealed by the streamlines as a separation zone near the blade

suction side in Fig. 8 b). The airflow near the hub at the blade

suction side goes up to the casing sharply and at the same time

goes upstream from the trailing edge to the leading edge

following the surface of the blade suction side, as the result of

the centrifugal force and the pressure gradient. When this part

of flow shears with the passage main flow, the “suction side

upward vortex” (Fig. 8 b)) and “blade tip trailing edge vortex”

(Fig. 9) are formed. It is those vortices that induce the large

separation zone near the blade trailing edge at suction side. The

separation region is so large that make us believe it is

responsible for the triggering of the stall.

Further research shows that, the “suction side upward

vortex” is not a special phenomenon at the near stall condition,

but a very common thing even at the maximum efficiency

operating condition. However,

when the operating point is

far away from stall point, the

passage main flow has an

axial momentum high enough

to suppress the low DPH area

to a very thin region near

blade surface (Fig. 10). So

there is no obvious “blade tip

trailing edge vortex”, and

those vortices can not cause

great effect to the main flow.

With the increase of the back pressure,

the suppressing effect turns weak

gradually, and the affected region of

the shearing between the main flow

and the reversal flow grows larger, and

finally burst up and causes the stall.

Moreover, at the leading edge of

the blade tip at the near stall condition,

we found the so called “spill forward”

region suggested by Bergner et al. [13].

Figure 10. Streamlines Near the Blade Suction Side

at Maximum Efficiency Condition

a) DPH contour b) Streamlines Near Suction Side

Figure 8. Near Stall Condition (No Tip Gap)

Figure 9. Vortex at the Blade Tip Trailing

Edge at Near Stall Condition with No Tip

Gap (Streamline)

a) 95% Span b) 98% Span c) 99% Span

Figure 11. “Spill Forward” Region at the Leading Edge at Near

Stall Condition (Top View)

Suction side upward vortex

Fig. 11 illustrates this, where the arrow represented the velocity vector and the contour shows the DPH value (again

the blue means low DPH region). This region takes the position in front of the blade leading edge upon 98% span,

and can do some blockage to the inflow near blade tip. But it is hard to say now whether it is a reason for the stall, or

just a phenomenon at the near stall condition.

Small tip gap ( 0.4% of blade span) configuration

The practical compressors usually have a tip gap, so there must be the influence of the blade tip leakage

flow/leakage vortex in the actual stall process. Fig. 12 shows the flow field in the near stall condition with a tip gap

of 0.4% of the blade span, which is the case in experiments. The influence of the blade tip gap is revealed by the

obvious BTLV in Fig. 12. Just like the no tip gap configuration, there is still a large separation zone and obvious

vortex near the trailing edge at suction side, at the near stall condition. However the injection of the blade tip

leakage flow at the trailing edge makes the vortex more complex and enhanced the separation undoubtedly. The

comparison between Fig. 12 c), d) well illustrates this, which shows 24 streamlines from identical points in the

passage respectively. At the same time the leading edge BTLV seems to twist tightly and has no evidence to

breakdown (Fig. 12 a)). Since its effect region is a very flat region attached to the casing, as is shown clearly in Fig.

12 b), it can not influence much to the main flow directly. But both the DPH contour in Fig. 12 b) and its counter-

clockwise rotation direction implies that the leading edge BTLV can inhale and roll up part of the flow in the trailing

edge vortex, and hence exert an enhancement to the separation.

In the 0.4% tip gap condition, we can find an obvious “spill forward” region at the leading edge of the blade tip

too. In Fig. 13, a comparison of the flow field near the blade tip’s leading edge is made between the maximum

efficiency condition and the near stall condition. The arrows again represents the velocity vector and the contour

lines show the magnitude of the the velocity’s span wise component. It can be found that accompanied with the

existence of the “spill forward” region, there is a remarkable span-wise flow region at the near stall condition. There

is no spill-forward/reverse flow region at the maximum efficiency condition, and the span-wise flow region is

restricted to be near the blade tip; while at the near stall condition, both of the “spill forward” region and the span-

wise flow region are quite obvious. We believe that the “spill forward” region and the span-wise flow region are all

the consequences of the upstream moving of the shockwave-vortex intersection point with the increase of the back

pressure. This intersection blocks the inflow to

the blade tip as well as the inflow to the tip gap,

and induces the “spill forward” region and the

span-wise flow region respectively.

Fig. 14 gives the overall top view of the

calculated results at maximum efficiency

condition and the near stall condition at 98% span.

From which we can see clearly the upstream

moving of the shockwave-vortex interaction point,

the “spill forward” region and the large separation

zone at trailing edge. Although the existence of

the “spill forward” region can greatly block the

inflow and enlarge the local attack angle, which

a) Maximum Efficiency b) Near Stall

Figure 13. “Spill Forward” Region and Span-wise Flow

Region

Leading edge BTLV

Trailing edge Vortex

a) b) c) d)

Figure 12. Near Stall Condition a) Streamlines at 0.4% Tip Gap Case b) DPH Contour at 0.4% Tip Gap Case

c) Streamlines near SS without Tip Gap d) Streamlines near SS with0.4% Tip Gap

may aggravate the trailing

edge separation, it was still

too early to say that it is the

origin of stall. To judge

whether it is the trigger of the

stall or just a phenomenon at

the near stall condition may

need more work in the future

with unsteady calculation.

Currently we can only

confirm that it is the trailing

edge separation at the suction

side which directly induces

the stall, basically the same as

the no tip gap configuration.

The tip leakage flow, both from the leading edge and from the trailing edge, greatly enhances this process.

Large tip gap (1% of blade

span) configuration

With a larger tip gap,

things are totally different.

Fig. 15 indicates that far

before the full development

of the trailing edge separation

zone, the leading edge BTLV

starts to breakdown. The

location of the breakdown is

right after the shockwave-

vortex interaction point, as is

shown in Fig. 15 b), which

implies that the breakdown of

the vortex is a consequence of

its interaction with the shock.

Fig. 16 gives the process of

stall: the expanding of the

recirculation region in Fig.16

a); and finally the substantial

blockage of the blade passage

in Fig.16 b). In this case,

there is no obvious trailing

edge vortex and no leading

edge “spill forward” region,

even in Fig.16 a), where stall

has developed to a certain

extent. Therefore it is

believed that stall is directly triggered by the breakdown of the leading edge BTLV.

C. CGCT results with different tip gap height

It is reasonable that the difference of the stall mechanism with different tip gap height should have a reflection on

the effect of the CGCT. The investigation on CGCT on configurations with different tip gap verified this.

It should not be strange that the adding of grooves on the casing increases the drag to the passage flow. In

Fig.17 a), For the SW configuration, the whole region adjacent to the casing, ranging from the blade’s leading edge

to the trailing edge, are occupied by the vectors in the direction reverse to the main flow, which is just the leakage

flow jet. When the grooves are added, the leakage flow jet is obviously affected. The reverse velocity vectors are

a) Developing b) Deeply Developed

Figure 16. Process of Stall with Large Tip Gap

a) Maximum Efficiency b) Near Stall

Figure 14. Top View of 98% Span

Trailing Edge Separation Zone

“Spill Forward” Region

a) DPH Contour & Streamlines b) Pressure Contour & Streamlines

Figure 15. Breakdown of the Leading Edge BTLV with Large Tip Gap

limited in only the regions between

two grooves. In the regions adjoin to

grooves, the flow direction changes

abruptly. From the zoom-in view in

Fig.17 b), it can be seen that the tip

leakage flow tends to rush into the

cavity of grooves. The energy of the

leakage flow is dissipated in driving

the vortexes in the grooves.

Small tip gap ( 0.4% of blade

span) configuration

Fig.18 shows the choking mass

flow rate, maximum efficiency and

stall margin computed for different

combinations of the activated grooves. Carefully comparing the data, some statistical conclusion can be drawn. First,

all the configurations with grooves near leading edge, i.e. G1-3, have a lower choking mass flow rate than SW

condition. The more the leading edge grooves activated, the lower the choking mass flow rate is. While the grooves

near the trailing edge, i.e. G4-7, have the opposite effect. It seems that G2 influences the choking mass flow rate

most. Second, in all the configurations the peak efficiency is not obviously affected, the largest departure is less than

0.2%. Among all the grooves, G4 and G5 even tend to produce a higher value of the peak efficiency. Third, for the

stall margin the leading edge grooves also perform poorly, while the rest grooves, especially the grooves at the mid-

chord can actually delay the stall of the compressor.

As a summary, the circumferential grooves near the leading edge tend to induce losses in choking mass flow rate,

the efficiency and even the stall margin. While the rest grooves, especially the grooves in the mid-chord tend to

improve these performances.

The poor performance of G1 to G3 on this

tip gap configuration can be explained by the

computed BTLV traces in Fig.19. Without

the grooves, the trace of BTLV has a larger

angle to the suction side of the blade, which

makes it able to touch the pressure side of the

next blade within the passage, as in Fig.19 a).

However, with the leading edge grooves, the

BTLV’s trace is dramatically changed to be

of a smaller angle to the blade. Such a trace

keeps the BTLV more close to the trailing

edge separation region on the suction side.

As has been explained in Fig.12, the separation is undesirably enhanced and consequently the stall margin is

decreased.

On the contrary, the grooves near the trailing edge can block the leakage flow there and prevent it from

a) Choking Mass Flow Rate b) Peak Efficiency c) Stall Margin

Figure 18. Performance of Rotor 37 with Small Tip Gap and CGCT

a) SW b) With Grooves

Figure 17. Effect of the CGCT to the Blade Tip Leakage Flow

a) SW b) G23

Figure 19. Effect of the Grooves on the Trace of BTLV

enhancing the suction side separation/vortex. Not only the bursting up of the separation region is delayed, the loss

in it is also decreased.

Large tip gap (1% of blade span) configuration

Because the leading edge BTLV is mainly responsible for the stall in this situation, a straight forward thought is

that the leading edge grooves should be effective. The numerical simulation results verify this hypothesis. Fig 20

shows the effects of the leading edge CGCT. The leading edge grooves still cause some mass flow rate loss in this

condition, but they induce better peak efficiency and much better stall margin. Configurations G12 and G123 almost

give a doubled stall margin. However with only G1 it seems useless for the extension of stall margin.

Fig.21 briefly explains the reason. With the existence of the edge grooves, the formation of the leading edge

BTLV is greatly interrupted and the effect of vortex breakdown is certainly mitigated. Therefore the stall can be

delayed. However the location of the G1 groove makes it have little influence to the BTLV, hence the BTLV in

Fig.21 c) remains almost the same shape and intensity as in the SW configuration.

I. Conclusion

From CFD simulation, two different stall processes with different tip gap configurations are found, which

should be cured by different CGCT.

When the tip gap is small, stall is found to start from the burst up of trailing edge separation/vortex, which is

enhanced by the blade tip leakage flow.

When the tip gap is large enough, the leading edge BTLV breakdown will trigger the stall instead.

For the small tip gap configuration, the grooves in the mid-chord are more effective, while for the large tip gap

configuration the leading edge grooves work well.

a) SW b) G23 c) G1

Figure 21. Effects of Leading Edge CGCT at 1.0% Tip Gap (DPH Contour)

a) Choking Mass Flow Rate b) Peak Efficiency c) Stall Margin

Figure 20. Performance of Rotor 37 with Large Tip Gap and CGCT

Acknowledgments

This research work is supported by the GEAE USA Programme and National Science Foundation of China

(NSFC) project No.10477012.

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