Investigation of Unsteady Flows and Noise in Rotor-stator Interaction with Adjustable Lean Vane

Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 2, pp. 299–307 (2014)

299

INVESTIGATION OF UNSTEADY FLOWS AND NOISE IN ROTOR-

STATOR INTERACTION WITH ADJUSTABLE LEAN VANE

Haijian Liu*, Hua Ouyang*^, Yadong Wu**, Jie Tian* and Zhaohui Du*

*School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

**School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

^E-Mail: [email protected] (Corresponding Author)

ABSTRACT: The paper is a study of the noise reduction effects of the stator lean angle. Firstly, a numerical study

has been carried out to investigate the unsteady characteristics of the flow induced by the rotor-stator interaction. To

obtain the rotor‟s wake, the distribution of the RMS pressure and the pressure disturbance coefficient, the

compressor with an adjustable stator lean angle has been numerically studied. Then the compressor was

experimentally tested at 11 different lean angles to obtain the free field noise spectra. Both the unsteady flow

property and noise characteristics are discussed on the basis of the Computational Fluid Dynamics (CFD) results.

The results indicate that (1) the pressure fluctuation of stator is the main source of the interaction noise; (2) the phase

of rotor‟s wake can be tuned by the lean angle of the stator; (3) the distribution of the first harmonic of tone noise

decides the distribution of total Sound Pressure level (SPL); and (4) stator with positive lean angle has better noise

reduction than negative one and the lean angle should exceed 10° for better noise reduction.

Keywords: rotor-stator interaction, tone noise, unsteady simulation

1. INTRODUCTION

With the development of high bypass ratio of the

turbofan, it is important to satisfy passengers‟

demand for comfort and quiet of the flight, and

the reduction of noise of the aeroengine becomes

more and more crucial. The decrease of the rotor-

stator interaction noise requires profound

understanding of the complex unsteady flow field.

There are two types of noise in turbofan: tone and

broadband noise. The interaction between rotor

and stator makes the flow field highly unstable. It

will also make strong tone noise because the flow

field alters periodically and the most prominent

component of interaction noise is tone noise.

Stator lean and sweep have been suggested as one

mechanism to reduce the interaction noise. Blade

lean angle is the circumferential displacement of

the blade stacking line relative to the radial

direction; it assumed that the lean angle is

positive when the blade is leaned in the direction

of rotor rotation.

It has been proved that the Sound Pressure Level

(SPL) of the first Blade Passing Frequency (BPF)

tone and the total noise are decreased by the

proper combination of the lean and sweep angle

of stator by NASA (Envia and Nallasamy, 1999,

Woodward et al., 2001 and 2002). Their research

had shown that the maximum noise decrease of

the tone noise was about 6 dB. The tone noise

level of modified stators was significantly

reduced beyond what was achieved by simply

relocating the conventional radial stator to the

downstream location. The broadband noise level

was also reduced by the swept stators. In order to

obtain the details of flow field for noise

prediction, both numerical simulation and

experiment techniques should be adopted. It is

impossible to capture all characteristics of the

flow field by experimental methods, and the

numerical calculation becomes an important

technique to obtain the details of it. Ferrecchia et

al. (2003) utilized numerical simulation to capture

the development process of rotor wakes. The

noise source was separated into several

components through numerical methods by Nark

et al. (2009) and Peters and Spakovszky (2012),

and noise prediction was carried out. Cooper and

Peake (2006) used the wake evolution and the

quasi-3D strip method to develop an asymptotic

technique and a new model for the wake

interaction. For experimental research, Sentker

and Riess (2000) obtained the velocity and

turbulent intensity distribution of S1 and S3

surfaces in a 1.5 stage compressor. S1 is the

stream surface formed by fluid particles lying on

a circular arc of radius of the blade row. S3

surface is the plane of the blade row which is

perpendicular to the axis of rotation. The dynamic

flow field data and velocity fluctuation from the

same surface between the gaps had also been

captured by PIV measurement (Ottavy et al.,

Received: 4 Mar. 2013; Revised: 11 Dec. 2013; Accepted: 4 Feb. 2014

mailto:[email protected]

Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 2 (2014)

300

2003) and hot wire anemometer (Oro et al.,

2011). The spectra of pressure fluctuation on the

blade surface had been measured by pressure

sensors, which were buried beneath the surface of

the rotor and stator (Wang et al., 2006).

The literature about the rotor-stator interaction

indicates that previous researches were aimed at

unsteady effect of flow field and noise prediction,

but less attention was paid to the combination of

unsteady property of flow field with noise

generation. The flow field and noise

characteristics of a 1.5 stage compressor with an

adjustable stator are investigated in this paper.

Detailed discussion is carried out based on CFD

studies and the acoustic measurement.

Firstly, a compressor with three stator lean angles

has been employed for numerical studies to obtain

the pattern of rotor‟s wake, the RMS pressure

fluctuation and the disturbance coefficient

distribution of blade surface. Then the compressor

is acoustically tested to capture the free field

noise spectra. A comparison is made between

results of numerical calculation and aeroacoustic

test.

Table 1 Parameters of compressor.

Parameters Number

Rotation speed n(rpm) 3000

Hub ratio 0.7

Vane : rotor : stator 13:21:21

Design pressure rise (pa) 1800

Mass flow (kg/s) 4.9

Stator blade lean angle ξ(°) (-25~25)

Rotor tip speed(m/s) 94.25

Rotor solidity 1.598

Stator solidity 1.548

2. COMPRESSOR

A 1.5 stage low-speed axial flow compressor has

been employed to study the flow field and

interaction noise. Fig. 1 shows the sketch of the

test rig, and the main parameters of the

compressor are listed in Table 1. There is an inlet

bellmouth and one throttle installed at the inlet

and outlet of the compressor, and the mass flow

can be tuned by the position of the throttle.

The compressor has an adjustable stator, whose

blades can be leaned positively or negatively

relative to the center. The lean is defined by the

angle ξ, and it is positive in the direction of rotor

rotation as shown in Fig. 2. The lean angle of

stator can be altered from -25° to 25° with 1°

resolution by the handle fixed at the shroud.

Fig. 1 Sketch of test rig.

(a) Sketch of lean blade driving mechnism

(b) Photos of stator

Fig. 2 Definition of lean angle ξ.

0.30 0.35 0.40 0.45 0.50 0.55 0.600.40

0.45

0.50

0.55

0.60

0.65

0.70

N25

S0

P25

(a) Eefficiency versus mass flow rate

0.30 0.35 0.40 0.45 0.50 0.55 0.601.004

1.006

1.008

1.010

1.012

1.014

1.016

1.018

N25

S0

P25

(b) Total pressure ratio versus mass flow rate

Fig. 3 Experimental performance of compressor for

cases N25, S0 and P25.


301

Fig. 3 is the experimental test results of the

aerodynamic performance of the compressor with

25°, 0° and -25° stator lean angles named cases

P25, S0 and N25, respectively. The prefix „N‟

means that the stator has negative lean angle,

while prefix „P‟ means positive lean angle. It is

obvious that cases P25 and N25 have little

difference in efficiency and total pressure ratio

compared with the baseline case S0.

3. NUMERICAL STUDY

3.1 CFD setup

The compressor has 13 vane blades, 21 rotor

blades and 21 stator blades. In order to avoid full

channel computation and to reduce the

consumption of the computational resources, the

number of inlet vanes has been tuned to 14 and

the chord length of blade has been reduced at the

same time to keep the solidity. The ratios between

the 1.5 stage compressor components become

vane: rotor: stator = 2:3:3. Three lean angles -25°,

0°, and 25° have been adopted for numerical

studies, which are correspondingly cases N25, S0

and P25.

The numerical simulations were undertaken with

the commercial computational fluid dynamics

code FINE/Turbo of NUMECA, which has been

extensively used in the turbomachinery industry.

Its continuous development over the years has

extended its versatility to a number of aero-

engines design applications. Spalart-Allmaras

turbulence model is used to predict the turbulence

viscosity in the flow fields because of its excellent

stability. Central spatial discretization scheme is

adopted and domain scaling method is utilized to

deal with the rotor-stator interface. The inlet and

outlet boundary are set to total pressure 101325

Pa and 102426 Pa, respectively, to make sure the

mass flow is 4.9 kg/s for every lean angle. At the

beginning of unsteady simulation, steady

simulation results are employed as initial flow

field. The dual time stepping technique is adopted

for the unsteady calculations, and the single rotor

passage is divided into 64 time steps and the

unsteady time step size is 1.488×10-5

s. Each time

step contains 40 inner subiterations. Enhanced

implicitness method is utilized and the CFL

number is set to 3 to obtain a good computation

accuracy and affordable convergence time.

To assess the uncertainty of grid number, a spatial

refinement mesh study has been carried out by

evaluating three meshes with total cell numbers of

approximately 2.9, 3.8, and 4.9 million. The grid

independence convergence study was limited to

steady computations to diminish the need of

resources. Table 2 shows the validation of the

grids independence sensitivity. The grid of

medium refinement with 3.8 million cells has

been adopted in the present work as it is a good

compromise between accuracy and time cost. The

compressor model for numerical calculation has 8

passages. Fig. 4 shows the grid topology and its

details.

Table 2 Grid independence study.

No. of Grids

(million)

2.9 3.8 4.9

Mass flow(kg/s) 4.875 4.891 4.905

Pressure ratio 1.01489 1.01587 1.01598

Efficiency 0.7981 0.8078 0.8096

Fig. 4 Computational grids.

3.2 Numerical results

3.2.1 RMS pressure

RMS pressure is defined as following:

2

0

1 1 ( ) (1)

T

RMS pressure p p dtTp

where is the time averaged pressure. Fig. 5

shows the RMS pressure fluctuation of the stator

blade surface for the three cases. S is the

dimensionless arclength of blade surface from the

leading edge to trailing edge, and H is the

dimensionless span height, with -1<S<0 on the

pressure side and 0<S<1 on the suction side.

According to the distribution of RMS pressure,

the high fluctuation region is near the leading

edge, and the most intense fluctuation region


302

N25(ξ=-25°)

S0(ξ=0°)

P25(ξ=25°)

Fig. 5 RMS pressure contour of stator.

N25 10% span(-25°)

S0 10% span(0°)

P25 10% span(25°)

N25 50% span(-25°)

S0 50% span(0°)

P25 50% span(25°)

N25 90% span(-25°)

S0 90% span(0°)

P25 90% span(25°)

Fig. 6 0.1, 0.5 and 0.9 spans ΔCp time-space contours of stator.



303

locates at pressure side from the root to 80%

height near the leading edge. The flow angle gets

increased when the wakes sweep from the stator‟s

leading edge, which increases the pressure on the

pressure side; and pressure decreases on the

suction side with a positive attack angle at the

same time. All the reasons above cause the

pressure fluctuating intensely near the leading

edge. Compared with baseline case S0, the range

of RMS pressure fluctuations of cases N25 and

P25 are smaller, especially at the pressure side of

case P25. The lean negative blade has more

constraint than positive and straight one for the

radial flow on pressure side, and the radial flow

on the pressure side of P25 is weaker than that of

cases S0 and N25.

3.2.2 Pressure disturbance coefficient ΔCp

The pressure disturbance coefficient ΔCp is

defined as follows:

0

2

0

(2)

( ) / (0.5 ) (3)

Cp Cp Cp

Cp p p v

where Cp is the pressure coefficient, and Cp0

presents the time averaged pressure coefficient. p0

and 0.5ρv2 are the inlet total pressure and dynamic

pressure at stator‟s inlet, respectively.

Fig. 6 shows the pressure disturbance coefficient

time-space distribution at 10%(root), 50%(middle

span), and 90%(top) of span height. S is the

dimensionless arclength of blade surface from the

leading edge, and T is time period. The maximum

pressure disturbance coefficient is near the

leading edge, the high pressure and low pressure

area distribute alternately with time period. The

lean negative blade(case N25) has more constraint

for radial flow at pressure side than straight and

positive ones, so its ΔCp varies more intensely

and widely on pressure side at the root region.

Correspondingly, the ΔCp of case P25 has more

intense fluctuation at suction side of root region

than others. At the middle span 50% and top 90%

region, the lean positive stator blade(case P25)

has minimum pressure disturbance coefficient.

Compared with case N25 and S0, the range and

the intensity of ΔCp of case P25 are minimum,

especially at the pressure side.

3.2.3 Pattern of rotor wake

To obtain the time and frequency domain

distribution of rotor‟s wake, a monitoring line L is

placed at 85% of the gap between rotor and stator

from the trailing edge of the rotor, and there are

65 monitoring points on the monitoring line. Fig.

7 shows the sketch of the monitoring line L and

stator, and point P locates at the middle span of

monitoring line L.

P

Fig. 7 Monitoring line.

0 20 40 60 80 100 120 140 1600.0

0.2

0.4

0.6

0.8

1.0

N25

S0

P25

Sp

an

Amplitude

1st

2nd

Fig. 8 Pressure harmonics of monitoring line L.

The amplitudes of the first and second harmonic

of pressure of the monitoring line L are shown in

Fig. 8. It is obvious that the first harmonic

component is dominant on the whole span height.

The first harmonic of case P25 stator has a sharp

growth from root-to-tip, especially above the 30%

span height; and those of cases N25 and S0

increase gently compared with case P25. Under

the 10% span height, the first harmonic of case

N25 is stronger than those of S0 and P25. The

second harmonic is stronger than its first

harmonic at blade root region of case P25, and the

fluctuation energy in the root region has been

transferred to the higher-order harmonics.

Fig. 9 shows the time-space dimensionless Vz′

distribution on monitoring line L. H is the

dimensionless blade span height, and T is time

period. According to the motion of the rotor‟s

wake time-space distribution, the main axial

velocity loss of the wake locates at 0-80% span

height. Compared with baseline case S0, the



304

Case N25 Case S0 Case P25

Fig. 9 Vz’ time-space contours at monitoring line L (non-dimensionalized by rotor tip speed).

-180 -120 -60 0 60 120 1800.0

0.2

0.4

0.6

0.8

1.0

N25(=-25o)

S0(= 0o)

P25(25)

leading edge

H

phase lag(degree)

Fig. 10 Phase of wakes on L line.

0.00

0.06

0.12

0.18

N25

S0pcle

P25

Fig. 11 Phase close leading edge distribution.

flow

Fig. 12 Noise measurement.

0 2000 4000 6000 8000 10000-20

0

20

40

60

80

100

120

>30dB

S0 measurement

Environment

SP

L(d

B)

f(Hz)

>30dB

Fig. 13 Noise spectra for case S0 and environment.

wake of case N25 is straighter at the lower part of

the blade and the direction of the wake is

reversed. The wake of case P25 has the same lean

direction as that of case S0, and the time for the

wake passing through the leading edge is

lengthened. The longer is the time needed for the

wake to pass through the leading edge, the weaker

is the pressure fluctuation on the blade surface.

This is consistent with the distribution of the

RMS pressure and pressure disturbance

coefficient shown in Figs. 5 and 6, respectively.

The phase of the wake can be obtained by the

cross-correlation analysis about the point P with

other points on the monitoring line. Fig. 10 shows

the phase pattern of rotor‟s wakes for three cases,

the positive phase means that the arrival of local

wake is ahead of point P. Compared with the

baseline case S0, the phase of case N25 reverses

at the monitoring point P. There is a great

increase in phase angle at the root and top region

for case P25. The phase angle of case P25 is

greater than those of cases S0 and N25 on the

whole span height. It is obvious that the phase of

rotor‟s wake is tuned with the stator blade lean

angle.



305

_mic position

_le

an

angle

45 60 75 90 105 120 135-25

-20

-15

-10

-5

0

5

10

15

20

2597 98 99 100 101 102 103 104 105 106 107 108 109 110 111

SPL_dB(A)

(a) total noise SPL (b) tone noise SPL

(c) broadband noise SPL (d) 1st BPF SPL

Fig. 14 Contour of total, tone, broadband and 1st BPF SPL dB(A).

(a) αtone_total (b) α1st_total

Fig. 15 Ratio of tone and 1st BPF noise.

In order to evaluate the phase lag on whole span

height, phase skewing parameter Phase Close

Leading Edge (pcle) is adopted and defined as

following:

1(3)

2

top

hubpcle phase lag dh

The pcle is the phase skewing distance of the wake with stator leading edge, and pcle = 0 means

the stator leading edge. Fig. 11 is the phase

skewing parameter pcle of three cases. The

distribution of pcle shows that case N25 has the

minimum phase skewing control, and the rotor‟s

_mic position

_le

an

angle

45 60 75 90 105 120 135-25

-20

-15

-10

-5

0

5

10

15

20

250.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85

tone_total

_mic position

_le

an

angle

45 60 75 90 105 120 135-25

-20

-15

-10

-5

0

5

10

15

20

250.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

1st_total

_mic position

_le

an

angle

45 60 75 90 105 120 135-25

-20

-15

-10

-5

0

5

10

15

20

2597 98 99 100 101 102 103 104 105 106 107 108 109 110 111

SPL_dB(A)

_mic position

_le

an

angle

45 60 75 90 105 120 135-25

-20

-15

-10

-5

0

5

10

15

20

2597 98 99 100 101 102 103 104 105 106 107 108 109 110 111

SPL_dB(A)

_mic position

_le

an

angle

45 60 75 90 105 120 135-25

-20

-15

-10

-5

0

5

10

15

20

2597 98 99 100 101 102 103 104 105 106 107 108 109 110 111

SPL_dB(A)

_mic position

_le

an

angle

45 60 75 90 105 120 135-25

-20

-15

-10

-5

0

5

10

15

20

2597 98 99 100 101 102 103 104 105 106 107 108 109 110 111

SPL_dB(A)



306

wakes of case P25 has the maximum phase lag.

4 AEROACOUSTIC EXPERIMENT

4.1 Setup

Due to the length of the compressor, the acoustic

test was carried out outside of the laboratory. Fig.

12 presents the aeroacoustic test configuration.

The noise spectra were measured by the B&K

4189 microphones with 0.2 dB uncertainty; the

output signals were received by NI PXI

1033&4472 multichannel data acquisition system.

Seven microphones were fixed around R=1m

circle from θ=45° to 135° by 15° interval, and the

center of the microphones was the interface of the

rotor and stator. The microphones and the axis of

the compressor were in the same measuring plane

parallel with the ground, and the distance of

measurement plane to the ground was 1.2 m. The

evaluation about the outside environment had also

been carried out to make sure that the

environment was satisfactory for the noise

measurements. The total sound pressure level

(SPL) of the 1m circle was at least 5 dB(A) higher

than the 2m circle when the compressor was

running, and it was accorded with the noise

degression. The environmental noise was about

42-44 dB(A) when the tests were carried out at

midnight. Typically the environmental noise was

30 dB less than the measurement as shown in Fig.

13, and the effect of environmental noise could be

neglected.

The downstream stator lean angle ξ was altered

from -25° to 25° by 5° interval, repeated 7 times

for each case.

4.2 Experiment result

The tone noise (BPF and its harmonics) and

broadband noise were separated from the noise

spectra, and the SPL measurement results for all

components are shown at Fig. 14, where θ is the

position of microphone, and ξ is the stator blade

lean angle. The SPL of the broadband component

is about 102.9-103.9 dB for all cases; the tone

noise is maximum when the lean angle ξ is 0°.

Compared with the baseline case S0, lean positive

stator has better noise reduction than lean

negative one. Fig. 14d shows the 1st harmonic of

the tone noise and it has the same distribution as

the tone and total SPL distributions. The different

distribution of the 1st BPF harmonic leads to the

different total and tone noise SPL distributions. It

is obvious that the SPL of total, tone, and 1st BPF

is stronger at the angle of |ξ|<10°. The tone noise

SPL is decreased when the lean angle |ξ|>10°, and

the noise reduction amplitude of lean negative

angle (ξ<-10°) is smaller than that of lean positive

angle (ξ>10°).

The proportion of the SPL b in the total SPL c is

defined as follows: 0.1

0.1( )

_ 0.1

1010 (4)

10

bb c

b c c

Fig. 15a shows the proportion of tone noise SPL

in total SPL αtone_total. The αtone_total is larger than

50% in almost the whole range of |ξ|<10°, and the

αtone_total exceeds 70% when the lean angle is 0°.

Fig. 15b is the proportion distribution of the 1st

BPF in total SPL α1st_total. The α1st_total can reach up

to 50% in |ξ|<10° region and decrease to 30% and

even lower when |ξ|>10°. According to the

analysis, the 1st BPF of tone noise is reduced by

the technique of adjusting the stator‟s lean blade.

The lean positive stator has more noise reduction

than lean negative one, and the lean angle should

exceed 10° for better noise reduction.

5 CONCLUSIONS

Three stator blade lean angles have been

employed for the rotor-stator interaction noise

study. The numerical study reveals the pressure

fluctuation on the stator and the phase skewing of

rotor wakes. The compressor with a series stator

lean angle has also been investigated

experimentally through acoustic measurements.

Both numerical calculations and acoustic

measurements results show that:

1. The leading edge region is the main pressure

fluctuations zone. The first harmonic of the

wake is greater than the other harmonics, and

the dramatic change occurred for case P25

from the blade root-to-tip. It has also been

proved that the first harmonic is the main

component for total SPL in the acoustic

measurement.

2. Compared with case S0, the phase of wake of

case N25 reverses, and the phase of wake of

case P25 increases. The adjustment for the

wake‟s phase of case P25 has better effect

than those of N25 and S0, and it is consistent

with noise test result.

3. The downstream stator lean angle has little

effect on the aerodynamic performance for

the compressor at low speed. The tone and 1st

harmonic of SPL distribution show that the

tone noise is determinant for total SPL. The

lean positive stator has better effect than lean

negative. And the lean angle of the stator

should exceed 10° for better noise reduction.


307

ACKNOWLEDGEMENTS

This work has benefited from the generous

support of National Natural Science Foundation

of China under grant Nos. 11202132 and

51306110. The authors would also like to express

their appreciation of “2011 Aero-Engine

collaborative Innovation Plan” for its support.

NOMENCLATURE

Cp = Pressure coefficient

Cp0 = Time average pressure coefficient

H = Dimensionless span height

m = Mass flow, kg/s

p = Static pressure, Pa

p = Time average pressure, Pa

S = Dimensionless curve length

t = Time, s

T = Time period, s

R = Test radius of microphone, m

Vz′ = Dimensionless axial velocity

ΔCp = Pressure disturbance coefficient

αb_c = Ratio of sound pressure

ρ = Density, kg/m3

ξ = Stator lean angle, °

θ = Microphone position, °

φ = Mass flow rate

π = Total pressure ratio

η = Efficiency

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Investigation of Unsteady Flows and Noise in Rotor-stator Interaction with Adjustable Lean Vane

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