International Journal of Heat and Fluid Flow 58 (2016) 19–29

Contents lists available at ScienceDirect

International Journal of Heat and Fluid Flow

journal homepage: www.elsevier.com/locate/ijheatfluidflow

Unsteady influence of Self Recirculation Casing Treatment (SRCT) on

high pressure ratio centrifugal compressor

Yang Mingyang a,∗, Martines-botas Ricardo b, Deng Kangyao a, Zhang Yangjun c,Zheng Xinqian c

a Institute of Internal Combustion Engine, Shanghai Jiao Tong University, Shanghai 200240, Chinab Mechanical Engineering Department, Imperial College London, London SW7 2AZ, UKc State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o

Article history:

Received 5 September 2015

Accepted 14 December 2015

Available online 13 January 2016

Keywords:

Turbocharger

Centrifugal compressor

Self-recirculation-casing-treatment

Unsteady

a b s t r a c t

Self-Recirculation-Casing-Treatment (SRCT) is a widely employed method to enhance aerodynamic stabil-

ity of a centrifugal compressor. This paper investigated unsteady effects of SRCT on the flow in a transonic

centrifugal compressor via numerical method validated by experimental test. Firstly the static pressure

distribution in the compressor without SRCT is measured for information of boundary conditions as well

as validation. Then a 1-D unsteady model of a single passage is built and validated based on the experi-

mental results. Next, the 1-D model of a passage with SRCT is built to investigate the unsteady influence

of the SRCT on the flow in the passage. Finally 3-D unsteady CFD is employed to investigate the detailed

influence of SRCT on the flow field in impeller passages. Results show that the topology of the passage

with SRCT can remarkably damp the distortion propagating from downstream, hence depress the mag-

nitude of the inlet flow distortion. Furthermore, the width of the rear slot in SRCT is the key factor for

the damping effect. The 3-D simulation results further show that the fluctuations of the re-circulated

flow rate via the front slot is depressed by the SRCT which is attributed to the damping effect of its

configuration.

© 2015 Elsevier Inc. All rights reserved.

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. Introduction

The increasing demand of low carbon vehicle has forced the

ndustry towards highly efficient and downsized engines. One of

he key enablers for the engine downsizing is the turbocharger

hich reclaims the energy from exhaust gas to boost the intake

ir. Self Recirculation Casing Treatment (SRCT) is one of the most

idely used methods to enlarge the performance map width of

high pressure ratio centrifugal compressor. Extensive researches

ave been carried out via the experimental method and CFD sim-

lation to investigate the influence and the mechanism of SRCT

or the stability enhancement (Hunziker et al., 2001, Hu et al.,

009, Sivagnanasundaram et al., 2010, Gao et al., 2010, Galindo et

l., 2005). The recirculation flow in the device driven by the in-

erse pressure gradient is considered to be the main reason for

he performance enhancement. It can compensate the inlet flow

ate when the compressor is approaching to surge condition, thus

ostpones the surge limit.

∗ Corresponding author. Tel.: +86 2134206850.

E-mail address: myy15@sjtu.edu.cn (Y. Mingyang).

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ttp://dx.doi.org/10.1016/j.ijheatfluidflow.2015.12.004

0142-727X(15)00154-X/© 2015 Elsevier Inc. All rights reserved.

It has been confirmed that the flow in a centrifugal compressor

s not axial-symmetrical. The asymmetrical geometry of the volute

n a compressor results in the distorted flow in the diffuser, espe-

ially at off-design flow rates (Ayder et al., 1993, Hagelstein et al.,

997, K. and Van den Braembussche, 1999). Intensive investigations

ave already been conducted to study the interaction between the

olute and impeller, of which most are performed via steady or un-

teady 3-D CFD method. Sorokes et al. (1998) and Sideris and Van

en Braembussche (1987) have showed that the distortion resulted

rom the volute can reach the inlet of impeller which may degrade

he stability of compressor. A simplified 3-D unsteady model was

mployed by Fatsis et al. (1997) to investigate the unsteady inter-

ction between volute and impeller. A single passage was modeled

nd the static pressure at impeller outlet from experiment was im-

osed. At the meantime, a “phase lag” method was used to reduce

he demand for computational resources. Results showed that the

erturbation from impeller outlet had an obvious influence on the

nlet incidence as well as other flow parameters. Gu and Engeda

2001) and Hunteler (2009) studied the interaction via steady 3-D

imulation and concluded that the influence of volute made the

erformance of compressor quite different from that of the one

ithout volute.

20 Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29

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Nomenclatures

A area mm2

Am amplitude

br width of rear slot mm

bf width of front slot mm

bb width of the recirculation channel mm

Cr radial component of velocity m/s

D diameter mm

E power through an area kW

Fco coriolis force N

Fcen centrifugal force N

Fps pressure force N

hb height of the recirculation channel mm

I power density at an unit area kW/m2

L length mm

LE leading edge

N design speed RPM

n rotational speed RPM

P pressure Pa

Sf distance from LE to front slot mm

Sr distance from LE to rear slot mm

TVD total variables diminish

t time s

U blade velocity m/s

V absolute velocity m/s

W relative velocity m/s

Z acoustic impedance Pa•s/m

Greek letters

α sonic speed m/s

β relative flow angle degree

θ circumferential angle degree

Subscripts

ave average

in inlet

max maximum

min minimum

out outlet

The interaction between volute and impeller notably influences

the compressor performance thus the effect of volute should not

be ignored in the investigation of SRCT influence by numerical

method. Indeed Zheng et al. (2010) have numerically proved that

SRCT can depress the distortion of inlet flow angle at main blade

Fig. 1. Measurement point

ip, which has a positive effect on the compressor stability. The

symmetrically distributed re-circulated flow rate at the impeller

nlet is considered to be the reason for the distortion depres-

ion. The conclusion was drawn based on the steady simulation,

here the interfaces between the volute, SRCT and the impeller are

frozen”. However, in the real phenomenon, the impeller spins at

igh speeds when it is confronted by the flow distortion caused by

he volute. Therefore, the propagation of the distortion in the im-

eller happens in the rotating coordinates instead of the fixed one

s the assumption in the steady simulation. On the other hand, it

s accepted that the unsteadiness effect shouldn’t be ignored when

he Strouhal number of the compressor is larger than 0.1, of which

he characteristic length is the average length of the impeller pas-

age (Fatsis et al., 1997). For a high pressure ratio centrifugal com-

ressor, Strouhal number is most likely much larger than this cri-

erion. As a result, the unsteady simulation method is necessary

or the investigation on the interaction between the volute and the

mpeller in a high pressure ratio centrifugal compressor.

The 3-D unsteady simulation on the whole compressor stage

ith SRCT might be conducted for the investigation purpose, but

o doubt that immense computational resources are required. An

lternative route is to apply a method which can simplify the

omplexity of the computation based on the physics of the phe-

omenon without losing the correct pictures.

This paper focuses on the unsteady influence and its mecha-

ism of the SRCT on the flow in a passage. 1-D unsteady model

f SRCT was established based on the model of passage validated

y experimental results. A key geometrical parameter of the im-

action was confirmed by the model. Furthermore, a 3-D unsteady

imulation on a single passage is carried out for detailed investiga-

ion on the evolution of the flow in the impeller with SRCT.

. Experimental testing

The circumferential distribution of static pressure at different

ocations in the impeller and diffuser were measured by pressure

ransducers on the turbocharger test facilities. Fig. 1(a) shows a

ectional view of the compressor. As shown in the figure, there are

wo measured locations in the impeller shroud (referring as 1 and

), which are near main blade leading edge and splitter leading

dge, respectively. Another two positions locate at the inlet and

utlet of the diffuser respectively. To obtain the pressure distribu-

ion in annulus, eight pressure tapings are mounted evenly in cir-

umference for each location, as shown in Fig. 1(b).

Figs. 2 and 3 show the static pressure distribution in annulus

t diffuser inlet and outlet near surge for 4 rotational speeds as

s in the compressor.

Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29 21

Fig. 2. Pressure distributions at outlet of the diffuser (location 4).

Fig. 3. Pressure distributions at inlet of the diffuser (location 3).

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Fig. 4. Pressure distributions at splitter leading edge (location 2).

Fig. 5. Pressure distributions at main blade leading edge (location 1).

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05% N, 100% N, 84.6% N and 69.2% N. The static pressure is di-

ensionless by the circumferential averaged value at each location

or the convenience of comparison. At both locations, there is an

bvious flow distortion around 90° in the diffuser, where the static

ressure falls to the minimum value. This distortion results from

he disturbance of the volute tongue at small mass flow rate con-

itions when the pressure upstream the tongue is evidently dis-

inct from the pressure downstream. Because of the lower averaged

ressure at the diffuser inlet compared with the value at the exit,

he dimensionless magnitude of the distortion is notably higher

t the diffuser inlet. Furthermore, by checking the distribution at

he diffuser inlet, it can be observed that the magnitudes of di-

ensionless distortion are rather similar among all the speeds ex-

ept 69.2% N, which is marginally smaller than others. Therefore, a

tatic pressure distortion with fixed phase is imposed at outlet of

he rotating impeller. Its shape and dimensionless magnitude can

e considered as the same at most of speeds. As it will be dis-

ussed later, this phenomenon brings convenience to the boundary

onditions for 1-D model.

Figs. 4 and 5 show the static pressure distribution in circum-

erential direction at splitter and main blade leading edge near

urge at 4 rotational speeds. The pressure distribution at splitter

eading edge varies significantly with rotational speeds. The dis-

ribution is relatively uniform at 69.2% N, while two valley val-

es appear around 90° and 250° at 84.6% N. As the speed goes

p to 100% N and 105% N, the fluctuation becomes severe and a

ominated valley appears in the distribution around 220°. Appar-

ntly, the flow distortion at the impeller exit produces an evident

ow distortion in the impeller passage in annulus. Different from

he phenomenon at the impeller exit shown in Fig. 3, the distor-

ion distribution is heavily dependent on the rotational speed. On

he other hand, the pressure distribution upstream the main blade

eading edge is much more uniform than that at splitter leading

dge, as shown in Fig. 5. It is inferred that the pressure fluctu-

tions in the impeller is evidently damped in the inducer. For a

ransonic centrifugal compressor, a local supersonic region usually

xists near the tip of main blade leading edge at high rotational

peeds. The region eventually stops and reflects the propagation of

istortion and thus reduces the magnitude at inlet.

In order to investigate the detailed influence of SRCT on the

ow in the compressor, the experimental results discussed above

re applied for the establishment of the numerical model which is

oing to be discussed in details in follow sections.

. Unsteady behavior via 1-D unsteady model

.1. 1-D unsteady model of an impeller passage

For a passage of the impeller, the distorted flow at the im-

eller exit can be considered to be an unsteady boundary condition

hich varies at the rotational frequency. When the passage sweeps

cross the circumferential location of the distortion, the flow dis-

urbance is imposed on and tends to propagate upstream along the

assage. At the meantime, the passage rotates as the disturbance

ropagates, thus the distortion appears at different phase angles in

he passage depending on the rotational speed. This process is the

eason for the distorted flow distribution shown in Figs. 4 and 5.

he same process happens in each passage but with a phase shift

ue to the sweeping in sequence. Therefore, it is possible to obtain

he information of this unsteady phenomenon in the impeller via

single passage which is imposed by an unsteady outlet boundary

22 Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29

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Table 1

The geometries of a single passage.

Geometries Values Geometries Values

Lmain 93.3 mm Aout 3850 mm2

Lsplitter 48.8 mm Ain 4140 mm2

θwrap 17° Dave 73.6 mm

Fig. 6. Main geometries of SRCT.

Table 2

Geometries of a SRCT.

Geometries Values Geometries Values

br 5 mm bf 10 mm

Sr 10.5 mm hb 13 mm

Sf 15 mm bb 8 mm

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Fig. 7. 1-D model of single passage without SRCT.

Table 3

Details of the passage model without SRCT.

Geometries Values Geometries Values

D0 73.6 mm L0 13 mm

D1 73.6 mm L1 80.3 mm

condition. The circumferential location of the distortion in the im-

peller can be calculated by propagation time and rotational speed.

Since the phenomenon can be simplified as a 1-D unsteady gas

dynamics event, it is reasonable and effective to apply a 1-D un-

steady model for the unsteady behavior prediction.

Therefore, the computational gas dynamics 1-D code ONDAS

developed by Imperial College is utilized to establish the model

(Costall et al., 2006). One dimensional flow equations, including

equations of continuity, momentum conservation and energy con-

servation are used as governing equations. Two-step Lax–Wendroff

scheme is used to discrete the equations. Total variation diminish-

ing (TVD) terms are added in the scheme for high definition of

flow discontinues.

Total pressure and total temperature are given as inlet bound-

ary condition. Because the inlet duct is exposed to atmosphere at

the location of the inlet boundary, the flow disturbance can be re-

flected at the location due to dramatical change of flow density.

Therefore, “open-end” type boundary which allows the wave re-

flection is used on the inlet boundary. The circumferential distri-

bution of the static pressure at impeller outlet from experiment is

transformed and used as the outlet boundary condition. Accord-

ing to the discussion above, the pressure distribution in annulus

is converted into the variation with time according the revolution

speed n, as following:

P(t) = P

(θ

60/n · 360

)(1)

where, P(t) is the converted unsteady boundary and P(θ ) is the cir-

cumferential pressure distribution from the experimental measure-

ment.

A transmissive type of boundary condition is imposed on the

exit of the passage. For this boundary type, the measurement lo-

cation (impeller outlet) can be considered as a ‘dummy’ interface.

The reflected pressure distortion from upstream can penetrate the

interface and go into the diffuser without interaction instead of

being reflected back into the passage. Orifice boundary condition

is used to connect two pipes with different diameters. Bassett-

interbone pressure loss junction boundary condition is used to

connect three or more pipes at a common joint (Bassett et al.,

1999).

In a real impeller passage, the flow is sucked in from the inlet

duct although the static pressure near the inlet is lower than at

outlet due to the centrifugal force. However, because there is no

inducer and no centrifugal force in the simplified 1-D model, the

flow can’t go through the passage if there is no positive pressure

gradient between two boundaries. In order to be representative to

the real flow direction, the pressure at inlet boundary is adjusted

to guarantee that the flow in pipes go in the same direction as

the real situation. Furthermore, the pressure gradient is adjusted to

guarantee a reasonable flow velocity which is similar as the mean

velocity in the impeller, through which the behavior of the wave

dynamic in the passage predicted by the model can be similar as

the real situation. This compromise implies that the absolute value

of pressure in the passage cannot be predicted by the model. How-

ever, the gas dynamic behavior in the passage, thus the shape of

the distortion caused by its propagation which is considered to be

the more important information can be expected to be reasonably

evaluated.

As discussed before (Fig. 3), the magnitude and the phase an-

gle of dimensionless pressure distortion at diffuser inlet (the im-

peller outlet) can be considered to be independent from rotational

speeds. Therefore, it is feasible that a dimensionless static pressure

distribution is given as outlet boundary condition at all speeds.

Based on the experimental results, 1-D model of a single pas-

age without SRCT is established to investigate the propagation of

he disturbance firstly. The main parameters of the compressor are

isted in Table 1.

The length of pipe is determined by the main blade chord

ength. The diameter of pipe simplified from the passage is eval-

ated according to the inlet and outlet areas:

ave =√

4π Ain +

√4π Aout

2(2)

The geometries of SRCT are given in Fig. 6 and Table 2.

The model of the passage without SRCT is shown in Fig. 7. Since

RCT is connected to the passage at a junction, two pipes (pipe 0

nd pipe 1) are utilized in the model. The length of the first pipe

s the distance from inlet to rear slot of SRCT. Detailed geometries

f the model are listed in Table 3.

The model of the passage with SRCT is established based on the

ne without SRCT, as shown in Fig. 8. Other two pipes (pipe 0 and

ipe 1) are added in front of the passage pipes (pipe 2 and pipe 3)

o model the inlet domains which are connected with SRCT. Three

ther pipes (pipe 4, pipe 5, and pipe 6) are used to model the SRCT

onfiguration. Considering that the influence of SRCT on the flow

Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29 23

Fig. 8. 1-D model of single passage with SRCT.

Table 4

Details of the passage model with SRCT.

Geometries Values Geometries Values

D0 5 mm L0 20 mm

D1 5 mm L1 20 mm

D2 5 mm L2 13 mm

D3 5 mm L3 80.3 mm

D4 5 mm L4 8 mm

D5 13 mm L5 33 mm

D6 10 mm L6 8 mm

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Table 5

Predicted locations of valley values.

Speed 1-Model Experiment

69.2%N 85° 280° 120° 270°84.6%N 87° 260° 90° 255°100%N 220° 220°105%N 205° 205°

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eld in passage concentrates near impeller shroud, it is reasonable

o model the upper section of the passage so that the prediction

ill focus on unsteady behavior at the vicinity of shroud. Except

he distinction of the configurations, the boundary conditions are

ept the same for the cases with/without SRCT. Detail geometries

re given in Table 4:

Fig. 9. Predicted static pressure at splitter leading edge

.2. Results analysis of the 1-D unsteady model

.2.1. Model of the passage without SRCT

Fig. 9 compares the predicted dimensionless static pressure

istribution at splitter leading edge with experimental results at

he 4 rotational speeds. The reference value for the dimensionless

ressure is the averaged pressure in a rotational period. For speeds

t 69.2% N (a) and 84.6% N (b), there are two valley values (local

inimum values) in the distribution of experimental results, while

here is mainly one valley value at 100% N (c), and 105% N (d).

oth the phase of the valleys and shape are predicted reasonably

ell by the 1-D model. The circumferential phases of distortion

y simulation and test results are compared in details in Table

. The phase angle of the left valley value at 69.2% N is 29.2%

maller than the experimental results, while the phase angle of

ight valley value is 3.6% larger. And the predicted phase angles

re highly consistent with test at other 3 speeds (no larger than

%). Therefore, the 1-D unsteady model is considered to be reliable

at 4 rotational speeds by the 1-D unsteady model.

24 Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29

Fig. 10. Static pressure variations at the location between the front and rear slots

of SRCT.

Fig. 12. A sketch of energy splitting at the junction of SRCT.

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to predict the pressure fluctuations and hence the unsteadiness of

the flow disturbance in an impeller passage.

3.2.2. Model of the passage with SRCT

The 1-D model of passage with SRCT is established based on

the one without SRCT which has been validated by the test results.

Then the influence of SRCT on the distortion in the passage is in-

vestigated by the model.

Fig. 10 shows the dimensionless pressure fluctuation at the po-

sition which is 10% Lmain downstream the main blade leading edge

at speed as 100% N. This position locates between front slot and

rear slot in the inducer. For the qualification of the flow distortion,

a dimensionless magnitude of the distortion Am is defined as fol-

lowing:

Am = Pmax − Pmin

Pave(3)

It clearly demonstrates that flow distortion is impressively de-

pressed by the SRCT in the inducer section of an impeller passage.

Specifically, the magnitude of the distortion Am of the passage with

SRCT is only 25.5% of the one without SRCT.

Fig. 11 shows the comparison between static pressure fluctua-

tions at the splitter leading edge for the cases with/without SRCT

at 100% N. This location is downstream the rear slot of SRCT. Dif-

ferent from the phenomenon in Fig. 10, the result shows that the

magnitude of the distortion is rather similar between two cases.

Specifically, both two valleys can be observed in the two cases, al-

though the magnitude of the smaller one is notably different, as

shown in the figure. It is implied that the flow distortion down-

stream the rear slot is slightly influenced by SRCT. Depression of

the flow distortion by the SRCT mainly focuses on the section of

the passage between the two slots.

Fig. 11. Static pressure variations at the splitter leading edge (downstream the rear

slot).

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It was concluded in Ref. (Yang et al., 2010) that SRCT can allevi-

te the inlet flow distortion by the re-circulated flow in circumfer-

ntial direction via the 3D steady CFD method. It is true that the

symmetrical distributed re-circulation flow rate can compensate

he non-uniform inlet mass flow rate in impeller passages. How-

ver, the effect of distortion depression predicted by the 1-D un-

teady unveils another aspect of the mechanism of the depression,

hich is going to be discussed in following contents.

Fig. 12 shows the topology of a junction at the rear slot in SRCT.

onsidering the propagation of the fluctuation from the passage

xit, as the fluctuation approaches to the rear slot of SRCT, the

opology of the SRCT nearby can be transformed as the junction

hown in the lower part of the figure. At the junction the fluctu-

tion in the passage is split into two portions. One portion propa-

ates along the passage towards the inlet of the passage (pipe 2);

t the meantime, another portion propagates along the channel of

RCT (pipe 4) via the rear slot.

The energy density of static pressure wave (distortion) is de-

ned as following:

= P2

Z · α (4)

here Z is the acoustic impedance, P is the magnitude of pressure

ave (distortion) and α is the speed of sound.

Then the energy on a sectional area is:

= I · A (5)

here A is the area of the section.

According to the energy conservation in a junction, in a pe-

iod the energy density of energy should be balance in three pipes.

hus following equation can be obtained:

3 · A3 = I2 · A2 + I4 · A4 (6)

Since A2 and A3 are the section area of a passage, hence:

2 = A3 (7)

According to Eqs. (6) and (7), in the SRCT:

3 − I2 = I4 · A4

A3

> 0 (8)

As a result, the energy density of the distortion reduces af-

er the distortion propagates by the rear slot, and the magnitude

f pressure distortion between the two slots of SRCT is reduced

onsequently.

Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29 25

Fig. 13. Pressure variations with different br at the location between the front and

rear slots of SRCT.

Fig. 14. Influence of geometrical parameters of SRCT on the magnitude of pressure

fluctuations.

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Regarding to the discussion above, it can be concluded that

he reason for depression of flow distortion in the impeller is the

opology of SRCT. The rear slot becomes a bypass of the passage

nd has ability of absorbing the portion of energy in the pressure

uctuation.

It can be further inferred that more fluctuation energy of the

istortion can be absorbed by SRCT with larger branch area (A4).

o prove this, Fig. 13 shows the static pressure variations near

ain blade leading edge with two different br in SRCT model.

he magnitude of static pressure distortion Am is about 0.041

or the model with br as 10 mm, which is 30.5% lower than the

odel with br as 5 mm. The flow fluctuation has been effectively

epressed by a larger rear slot.

Furthermore, the effect of the geometries of SRCT on the fluc-

uation depression is studied for allocation of the key geometry.

ig. 14 compares the influence of five geometrical parameters on

he magnitude of the pressure fluctuations via the 1-D unsteady

odel, which are hb, bb, bf, br and Sr. The magnitude of the

istortion is insensitive to the variation of bb and bf; while it

ecreases by 10.3% and 11.8% respectively as hb and Sr increases

o 140%. The most sensitive geometrical parameter is the width

f the rear slot br, as shown in the figure. It drops dramatically

rom 7.74% to 5.02% as the parameter increase from 80% to 140%.

herefore, the width of the rear slot is concluded to be the most

mportant parameter in SRCT to depress the pressure fluctuation

n a passage of centrifugal compressor. The root for this depression

ffect is the energy absorption of slot in SRCT.

It is worth being noticed that the parameter br also has an

mportant influence on the compressor surge mass flow rate

ccording to Ref. (Zheng et al., 2010). According to the discussion

bove, the effect of the stability enhancement should be attributed

o its significant effect on the depression of flow distortion in the

assage.

. Unsteady flow field via 3-D CFD

.1. Unsteady 3-D CFD model

1-D unsteady model discussed in above section has demon-

trated the effect of SRCT on the unsteady behavior in the pas-

age. In order to obtain more detailed flow field information, 3-D

nsteady CFD method is applied on the passage simulation.

A single passage with the unsteady outlet boundary is used

n the model. CFD software NUMECA Fine/Turbo is employed to

arry out the simulation. 3-D unsteady compressible finite volume

cheme is adopted to solve Reynolds-averaged Navier–Stokes equa-

ions in conservative formulation. The Spalart–Allmaras turbulence

odel is used for the closure of governing equations, which fea-

ures numerical accuracy in prediction of viscous boundary layer

urbulence flow, small or medium scale separation flow and free

hear turbulence flow (Spalart and Allmaras, 1992). Central scheme

s used for spatial discretization and 4-order Runge–Kutta for tem-

oral discretization. Dual time stepping method is used for time

tepping technique and there are 10 steps for inner iteration. In or-

er to capture reasonable flow behavior, 20 calculation stations are

et in a passage (NUMECA International, 2015), which makes the

assage to rotate at 2° per station. Totally 2700 physical time steps,

ence are 15 rotations, are performed to obtain a converged result.

Grid domains with/without SRCT are shown in Fig. 15. There

re 418,300 cells for the passage without SRCT and 997,000

ells for the one with SRCT. Similar as 1-D model, the measured

ressure distribution in circumferential direction is converted into

he static pressure variation with time according to rotational

peeds. Total pressure and total temperature are imposed as inlet

onditions. Non-slip, impermeable as well as adiabatic conditions

re used in solid wall. Results of steady simulation are used as

nitial condition.

.2. Unsteady 3-D results

Fig. 16 compares the predicted pressure distribution at the

plitter leading edge with the experimental results of the model

ithout SRCT at 100% N. The phase angle of static pressure distor-

ion at splitter leading edge is around 220°, which is in very good

ccordance with the experimental result. However, there is notable

iscrepancy between shapes of the distributions. There is a small

stair” near 90° for experimental result while a larger one around

70° for the prediction. The “stairs” in the experiment results are

pparently the result of wave reflection in the passage.

The discrepancy between the prediction and experiment might

e caused by the non-reflection boundary conditions (at inlet

oundary) in the 3-D CFD simulation. Regardless of the discrep-

ncy of the shape of fluctuations, the phase angle of the distortion

s predicted in a satisfied accuracy, thus the unsteadiness propaga-

ion is considered to be reasonable by the 3-D simulation.

The outlet static pressure distortion imposes an influence on

he flow angle at impeller outlet. Fig. 17 shows the force balance

f a fluid particle near impeller outlet under steady flow condition.

n circumferential direction, the Coriolis force Fco, which is caused

y rotation and relative movement, is balanced by pressure gradi-

nt Fps between pressure/suction surfaces. In radial direction, the

entrifugal force Fcen is balanced by inversed pressure gradient Fps

n streamwise direction. When the unsteady boundary condition is

mposed at outlet of the impeller, the balance between the cen-

rifugal force and the pressure gradient in streamwise direction is

o longer maintained.

As the outlet pressure decreases with time, the flow perturba-

ion propagates upstream into the passage. The inverse pressure

radient in the passage is reduced at the frontal interface of

he pressure perturbation. Thus the flow nearby is accelerated

26 Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29

Fig. 15. Grid domains of single passage for 3-D unsteady simulation.

Fig. 16. Static pressure variations at splitter leading edge by simulation and exper-

iment.

i

d

C

a

b

o

s

w

t

l

g

t

p

t

a

p

fi

t

e

v

c

h

c

c

r

t

w

in radial direction driven by the overwhelming centrifugal force.

According to the velocity triangle at impeller outlet as shown in

right subfigure, the relative flow angle β i (minus value) increases.

On the other hand, as the outlet static pressure increases with

time, the pressure perturbation enhances the inversed pressure

gradient in streamwise direction, which decelerates the flow near

the frontal interface of the perturbation. As a result, the relative

flow angle β i will decrease. In a revolution, the outlet static

pressure experiences a peak value and a valley value as shown in

Fig. 3, thus a flow disturbance with swing flow angle is produced

at the impeller outlet due to the instantly unbalanced force.

Fig. 18 shows the evolution of contours of relative Mach num-

ber at 95% blade height near impeller outlet in one revolution. The

Fig. 17. Forces balance of the flu

nfluence of the static pressure on the evolution of the flow angle

istribution is clearly manifested in the series of figures. From A to

the static pressure falls to the minimum value. In panel (1) there

re two low-relative-flow-angle regions (referring to A1 and A2)

etween the main blades and splitters near impeller outlet. The

ne between main blade SS and splitter PS (A1) is in thumb-like

hape; while the other one (A2) is strand-like and penetrates up-

ard to the splitter leading edge. As discussed above, the reduc-

ion of the pressure produces higher flow angle at impeller out-

et. As a result, in panel (2) where the pressure decreases, the re-

ion A1 shrinks to a dot-shape and the region A2 is drawn back to

he middle chord of the splitter, and later disappear gradually in

anel (3). As the static pressure recoveries to peak from D to F, the

wo regions appears again at the similar locations in the passage,

s shown in panels (4)–(6). Then the phenomenon repeats from

anel (1).

Because of the flow fluctuations at the impeller exit, the flow

eld in the passage is disturbed by the propagation of the fluctua-

ions. Consequently, this disturbance imposes an unfavorable influ-

nce on the compressor stability by a distorted flow distribution at

icinity of the compressor leading edges.

The SRCT has an evident influence on the propagation. Fig. 19

ompares the evolution of relative Mach number at 95% blade

eight with/without SRCT at 100% N. The propagation of distortion

an be seen in the passage without SRCT by the evolution of

ontours (left column). As discussed before, a region with low

elative flow angle at splitter leading edge (A2) develops towards

he impeller inlet. This propagation forces the expansion region

ith high Mach number to migrate towards the inlet. The shape

id particle in the passage.

Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29 27

Fig. 18. Relative flow angle evolution at 95% blade height of the passage without SRCT at 100% N.

28 Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29

Fig. 19. Relative Mach number at 95% blade height of the passage with/without

SRCT at 100% N.

Fig. 20. Variation of static pressure at splitter leading edge and the recycling flow

at rear/front slot of SRCT.

a

i

b

p

e

e

t

S

p

A

i

l

p

d

i

r

fl

t

s

d

a

t

c

t

fl

a

5

s

i

s well as the strength of the region is significantly influenced,

ndicated by the variation of the size and color. As a result, the

lade loading near leading edge is evidently influenced by the

ropagation of distortion in the passage without SRCT.

However, for the case with SRCT, it can be noticed that the

xpansion region with high Mach number at main blade leading

dge is much less influenced although the flow downstream of

he rear slot varies evidently (right column). The rear slot of

RCT intercepts the flow perturbation from downstream, which

revents the flow field from the disturbance at the impeller outlet.

s a result, the impeller inlet flow condition will be significantly

mproved by the device.

Fig. 20 shows the variation of static pressure near splitter

eading edge and re-circulated flow rate via rear/front slot of the

assage with SRCT at 100% N. There is a small phase shift between

istributions of the pressure and mass flow rate at rear slot, which

s the results of the distance between the splitter leading edge and

ear slot. It can be observed from the figure that the re-circulated

ow via the rear slot is directly influenced by static pressure near

he rear slot: the higher the pressure is, the more the flow is

ucked into the SRCT via the slot because of larger pressure gra-

ient between two slots. The amplitude of mass flow fluctuation

t the front slot is 56.3% smaller than at the rear slot, as shown in

he lower part of the figure. Therefore, the unsteadiness of the re-

irculated flow is dramatically damped in the chamber of SRCT. At

he meantime, it can observe that the shape of the mass flow rate

uctuation is different between distributions at two slots, which

gain confirms the unsteady influence of the chamber of SRCT.

. Conclusions

The influence of SRCT on the unsteady flow in an impeller pas-

age is investigated by 1-D and 3-D unsteady simulation methods

n the paper. The conclusions are drawn as follows:

(1) The flow fluctuation amplitude in the passage can be sub-

stantially depressed by SRCT. The depression is attributed by

the effect of energy bypass by the topology of the passage

with SRCT. Furthermore, the width of rear slot (br) is the

most important geometry to absorb the fluctuation energy,

hence to depress the flow distortion.

Y. Mingyang et al. / International Journal of Heat and Fluid Flow 58 (2016) 19–29 29

R

A

B

C

F

G

G

G

H

H

H

H

H

NS

S

S

S

Y

Z

(2) The distortion of the pressure at impeller outlet forces

the flow to swing towards rotational direction when the

pressure drops, while towards opposite direction when the

pressure increases. It is caused by the instantly unbalance

between the centrifugal force and the pressure gradient in

radial direction. The flow perturbation propagates upstream

towards the inlet of passage and is intercepted by the

rear slot of SRCT, which significantly alleviates the flow

distortion at impeller inlet.

(3) The propagation of the flow distortion has an influence on

the re-circulated flow rate in SRCT: higher static pressure

near the rear slot produces more re-circulated flow rate. The

fluctuation magnitude of re-circulated flow rate at front slot

is much smaller than at rear slot due to damping effect by

the SRCT.

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