剥離を伴う航空エンジン用低圧タービン翼面境界層の遷移挙動 ... ·...

剥離を伴う航空エンジン用低圧タービン翼面境界層の遷移

挙動に関する研究

*岩手大学工学部船﨑健一†

岩手大学工学部谷口英夫

岩手大学大学院博士前期課程斎藤拓

(株)グローバル・ニュークリア・フュエル・ジャパン酒井宏

Studies on Transitional Behavior of Separated Boundary Layer on the

Suction Surface of an LP Turbine Airfoil for Aeroengines

Ken-ichi Funazaki, Faculty of Engineering, Iwate University

Hideo TANIGUCHI, Faculty of Engineering, Iwate University

Taku SAITO, Graduate Student, Iwate University

Hiroshi SAKAI, Global Nuclear Fuel-Japan Co, Ltd.

1 INTRODUCTION

In modern high bypass turbofan engines,

low-pressure turbine (LPT) stages are required to

provide very huge power output to drive large fan for

propulsion and additional booster stages very efficiently.

Due to the relatively low-speed rotation, the

aerodynamic loading of the LPT stages is usually quite

high and inevitably the blade count in the LPT stage

tends to be very large for maintaining the stage

efficiency as high as possible. As a result, LPT section is

one of the heaviest parts of the engine, which could

amount to about one-third of the engine’s total weight.

The current design trend of aeroengines is therefore to

decrease the number of blades in LPT stages in order to

achieve a drastic reduction of engine weight,

manufacturing and maintenance costs and total sfc

(specific fuel consumption) of aircraft. However, the

reduction of the blade number surely induces an increase

of the aerodynamic loading on each blade, resulting in

the appearance of large separation or separation bubble

on the blade suction surface due to the strong adverse

pressure gradient, particularly under low Reynolds

number conditions. Since this separated flow around the

blade causes a significant loss in engine efficiency, there

have been a number of relevant studies on separated

boundary layer on high-lift LPT blades. Mayle1)

classified the boundary layer transition on LPT blade

into three modes in his pioneering paper, describing that

separated-flow transition mode could be the most

important one for LPT. Nevertheless, it is still necessary

to investigate the separated boundary layer because of

relatively few studies dealing with its transitional

behavior in detail under realistic flow conditions such as

Reynolds number and freestream turbulence. Since

boundary layer transition and separation depend strongly

on these two factors and their interaction2,3)

, it is quite

obvious that understanding of the separated boundary

layer subjected to such flow disturbance and

development of an accurate method to predict its

transition is crucial for lighter and more efficient

aeroengines.

The objective of this paper is to investigate the

influence of Reynolds number and freestream turbulence

intensity (FTI) on the process of boundary layer

transition over the suction side of LPT airfoil. Detailed

boundary layer measurements are performed by use of a *〒020-8551 盛岡市上田 4-3-5

†E-mail: [email protected]

〔特集〕注目研究 in年会 2011

479ながれ30（2011）479－487

hot-wire anemometer. Large test airfoils are used in the

experiment, which can provide a high resolution for the

hot-wire measurement near the airfoil surface. This paper

focuses on how the freestream turbulence affects the

transitional behavior of the boundary layer before and

after the separation at three Reynolds numbers in terms

of intermittency factor as well as streamwise growth rate

of velocity fluctuation. Flow visualization using a

high-speed video camera is conduced to capture

time-resolved behavior of the separation bubble

accompanied with vortex shedding.

2 EXPERIMENTAL METHODS

2.1 Test Cascade

Figure 1 shows the test apparatus, showing the test

linear cascade and the position of the turbulence grid.

The three-blade cascade configuration was chosen for

the sake of making each of the blades as large as possible

in order to increase the spatial resolution of the

measurement. The cascade characteristics are listed in

Table 1. The cross-section of the cascade blade is a

typical profile of modern commercial aeroengine LPT.

Two guide plates, shown in Fig. 1, were needed to

produce the design exit flow angle from the cascade and

the pitchwise periodicity.

The measurements were carried out at Reynolds

number Re = 130,000, 170,000 and 210,000, where the

Reynolds number was based on the chord length C and

averaged exit velocity. The exit velocity distribution was

carefully measured, averaged and then adjusted for every

test case until the specified averaged exit was obtained.

The velocity distribution was measured with a 3-hole

pressure probe traversing 15% chord length downstream

of the cascade outlet plane.

2.2 Measurement Instruments

Single hot-wire probes (DANTEC 55P11) and a

constant temperature anemometer (Kanomax

model-1011) were used for the boundary layer

measurement over the airfoil suction surface. The probe

was moved using a 2-axis computer-controlled traversing

mechanism with minimum linear translation step of

0.02mm.

The inlet freestream turbulence was measured with the

single-wire probe positioned 30%Cx upstream of the inlet

plane of the cascade, as shown in Fig. 1. Three types of

turbulence grids, which consisted of a number of thin

wires, cylindrical or square bars and the frame, were

used in the present study to change the inlet freestream

turbulence, as shown in Table 2. Each of the grids,

designated Grid A, Grid B and Grid C, was placed in

parallel to the cascade, 400 mm upstream of the inlet

plane of the cascade.

Fig. 1 A schematic of experimental apparatus and test

cascade

Fig. 2 A photograph of the experimental apparatus

viewed from the rear of the cascade

Table 1 Cascade characteristics

Chord C [mm] 308

Axial chord Cx [mm] 270

Span h [mm] 300

Inlet flow angle 1 [deg] 45

Exit flow angle 2 [deg] 60

Table 2 Turbulence grids used in the experiment and

turbulence intensities generated by these grids

Re×105 no grid grid A grid B grid C

1.3 0.5% 1.0% 3.4% 5.8%

1.7 0.5% 1.0% 4.5% 6.1%

2.1 0.5% 1.0% 4.5% 6.1%

剥離を伴う航空エンジン用低圧タービン翼面境界層の遷移挙動に関する研究480

2.3 Flow Visualization

Pointwise measurements like hot-wire probe

measurement is not suitable to capture time-resolved

images of the flow field characterized with flow

instability and vortex shedding, both of which were

expected to occur in this study. Therefore, flow

visualization using high-speed video camera was

attempted here to deepen the understanding of

transitional behavior of the LPT boundary layer

accompanied with the separation bubble and inlet flow

disturbances. Phantom 9.1 (Vision Research) with 16GB

memory was used as a high-speed video camera along

with Ray Power 2000 (Dantec Dynamics) that provided

laser sheet from the suction side of the target airfoil. Fog

was created by Safex Fog Generator 2010 (Dantec

Dynamics), which was smoothly injected into the

wind-tunnel at the far upstream position, which was

carefully chosen in order to prevent the fog injection

from inducing any serious flow disturbances in the flow

field.

3 RESULTS

3.1 Time-Averaged and Unsteady Velocity Field

Figure 3 shows time averaged velocity contours for

each FTI cases at Re = 170,000, where dots denote peak

positions of velocity fluctuation in rms at each

streamwise location. In addition, the time variations of

velocity over 0.1 seconds are plotted for the several

positions. The position where boundary layer separation

occurs can be determined by the information on time

averaged velocity, velocity fluctuation in rms, power

spectrum of velocity fluctuation, shape factor and so on.

The separation location was identified in this study as the

one at which the spatial growth rates of time averaged

velocity and the velocity fluctuation at the measurement

point closest to the wall turned from positive value to

negative value. The separation location was found to be

about 69%Cx, almost regardless of the Reynolds number

and FTI. The separation occurred in the case of Tu =

0.5% (top of Fig. 3) and 4.5% (middle of Fig. 3) and was

not observed clearly in Tu = 6.1% (bottom of Fig. 3). The

velocity time traces in Fig. 3(a) show that periodic

small-amplitude fluctuation began to appear near the

separation location, growing into large-amplitude

fluctuation, ending up with transition to turbulence. On

the other hand, Figure 3(b) shows that the velocity trace

under the influence of enhanced freestream turbulence

contained large-amplitude fluctuations at 60%Cx, which

was sometimes disturbed rapidly by high-frequency flow

events at 70%Cx. Thereafter the appearance count and

the duration of these high-frequency flow events

increased, leading to the completion of transition within

relatively short distance.

Figure 4 shows velocity fluctuation contours for each

FTI case at Re = 170,000. The reattachment location was

identified as the one where both of time averaged

velocity and the velocity fluctuation near the wall began

to rise sharply after the separate location. The

reattachments occurred at around 78～80%Cx for the

case of Tu = 0.5% and at around 75～76%Cx for the case

Fig. 3 Time-averaged velocity contours and velocity

traces measured at local peaks of velocity rms

(Re=170,000) ((a) top: Tu = 0.5%, (b) middle：Tu

= 4.5%, (c) bottom：Tu = 6.1%)

船﨑健一・谷口英夫・斎藤　拓・酒井　宏 481

Fig. 4 Time-averaged velocity contours (Re =170,000)


fluctuation in rms (Re=130,000)


fluctuation in rms (Re=210,000)

of Tu = 4.5%. In the case of Tu = 0.5%, the velocity

fluctuation was observed to develop slowly in the

separated shear layer. But strong turbulence emerged and

spread rapidly normal to the wall after the reattachment.

In the case of Tu = 4.5%, the growth of the velocity

fluctuation along the shear layer was observed from the

beginning of the measurement region, followed by the

appearance of high turbulence region after the

reattachment. In the case of Tu = 6.1%, the intense

velocity fluctuation existed near the airfoil surface with

no clear indication of separation. Figures 5 and 6

demonstrate time-averaged velocity contours as well as

velocity fluctuation contours measured at low turbulence

and highest turbulence conditions for Re = 130,000 and

210,000 cases. It follows from Figure 5 that even at the

highest FTI condition there appeared separation bubble

or its separation shear layer. In Figure 6, one can spot

only a slight clue for separation bubble for Tu = 1.0%,

while separation bubble was completely eliminated due

to this high Reynolds number and FTI.

3.2 Intermittency Factor

In order to understand transitional behavior of each of

the measured boundary layers for various test conditions,

its intermittency factor distribution was calculated. The

intermittency factor was calculated as follows4,5)

,

(1)

(2)

where the turbulence detector function D(t) defined by

(3)

was used. D(t) was based on a windowed averaged value

of (u/t )RMS, local boundary layer edge velocity Ue

and local boundary layer thickness . The timescale ts,

the window period tw and the non-dimensional window

period Cwp were defined as

(4)

The values of Ctr and Cwp were chosen in a

trial-and-error manner. The value of N was more than

2000 although N varied with Cwp. The intermittency

factor obtained in the above was then compared with the

famous Narasimha’s correlation6)

given by

(5)

where s is the surface length from the leading edge, st

indicates the position of transition onset and is

transition length which is the distance between s=0.75

and s=0.25. In this study, the transition onset and

transition ending point were determined to be the

positions where became 0.1 and 0.9, respectively.

1

1( ) ( , )

N

kk

x I x tN

1 when ( )( , )

0 when ( )tr

ktr

D t CI x t

D t C

RMS2

e

( / )( )

/

u tD t

U

s e wp w s/ , /t U C t t

2

t2

( )1 exp 0.412

s s


Figure 7 shows intermittency factor distributions

determined by the above-mentioned process at three

Reynolds number conditions, where each of those data

Fig. 7 Intermittency factor distributions measured at

three Reynolds number conditions, in

comparison with Narashimha’s correlation

was curve-fitted with the corresponding curve calculated

by equation (5). Several interesting features are found in

these distributions.

At the lowest FTI condition (no grid case), in which

boundary layer transition is probably dominated by

instability behavior of the separation shear layer as will

be explained later, transition lengths among the three

Reynolds numbers did not significantly differ each other,

while it seems the transition length at Re =130,000 was

slightly shorter than the other higher Reynolds number

cases. Besides, the transition onset moved upstream at

higher Reynolds numbers.

For Tu = 1.0%, the transition onset, defined as the

location where = 0.1, gradually shifted toward the

upstream with the Reynolds number. In addition, in

comparison with the other FTI cases, this FTI condition

yielded the shortest transition length, irrespective of the

Reynolds number. From the fact that the transition length

tended to elongate as the FTI increased, it can be inferred

that the observed rapid completion of the transition was

caused by the enhanced growth rate of the separation

shear layer instability due to the freestream turbulence.

For higher FTI cases, in which the separation bubble

became smaller, the bypass transition mode of attached

boundary layer was apt to dominate the transition

process.

Table 4 summarizes the transition onset and ending

points in terms of percentage of the axial chord length.

Table 4 Transition onset and ending points determined

from the intermittency Re×10

5 Tu (%) Onset Ending

1.3

0.5 81%Cx 86%Cx 1.0 79%Cx 82%Cx 5.8 72%Cx 79%Cx

1.7 0.5 78%Cx 82%Cx 2.1 0.5 77%Cx 84%Cx

3.3 FFT Analysis

Figure 8 shows power spectra of velocity fluctuation

for no grid condition at Re =170,000. These plots

represent the results of FFT analysis of the velocity data

acquired at the dots as shown in Figure 3. In order to

analyze spectrum peaks, frequencies of

Kelvin-Helmholtz (K-H) instability and

Tollmien-Schlichting (T-S) wave were calculated by the

same manner as Chandrasekhar7)

and Walker8)

, where the

Walker’s correlation that gives the frequency of TS

instability wave with maximum amplification rate．

(6)

These correlations with the relevant experimental data

yielded that the dominant frequency of KH instability

could be around 300Hz and fTS for TS wave was about

180Hz. There appeared two clear peaks at 312Hz and

187Hz in the power spectra, evidently the former

corresponding to KH instability and the latter

corresponding to TS wave. Figures 9, 10 and 11 show

power spectra of velocity fluctuation measured for

various FTI conditions at three Reynolds numbers. In

examining the lowest FTI case, it is found that there have

2

e e

*3/2

*

3.2 *,

2TS

U Uf Re

Re


appeared many peaks in the spectra including the effect

of KH instability and probably TS wave, regardless of

the Reynolds number. As the FTI increased, only the

peak of KH instability was likely to remain in the spectra,

ending up with the disappearance of the peak with the

highest FTI.

Fig. 8 Power spectra of velocity fluctuation for no grid

condition (Re=170,000)

Fig. 9 Power spectra for various FTI (Re=170,000)



Fig. 12 Velocity fluctuation profiles within the

boundary layers before the separation for various

FTI conditions (Re = 170,000)

Figure 12 demonstrates several velocity fluctuation

profiles measured for various FTI conditions at Re

=170,000. The abscissa of this plot is the velocity rms

value normalized with the corresponding local maximum

value of the rms value for each of the streamwise

positions, while the ordinate of this plot is the distance

from the wall normalized with the local displacement

thickness (*). In the case of Tu = 0.5% (no grid), the

velocity rms value tended to decrease gradually near the

airfoil surface, indicating that the boundary layer before

the separation had a typical feature of laminar boundary

layer. As the FTI was enhanced from 1.0% to higher, the

profiles of the normalized velocity rms values exhibited

clear peaks around y/* =1.3, with slow the value

decaying slowly with the distance from the surface.

From these findings, it can be concluded that there

existed streamwise streak structures inside the boundary

layer, which situation is called Klebanoff mode9)

. Since it


is believed that the growth of near-wall streaks is a key

phenomenon triggering the bypass transition leading to

breakdown and turbulent production, information on the

evolution of these streaky structures is vital to develop a

more precise transition model suitable for airfoils used in

turbomachines.

Fig. 13 Streamwise evolution of velocity fluctuation

energy for Tu=4.5% and Tu=6.1% at Re=170,000 and

Re=210,000

Figure 13 illustrates how the maximum of velocity

fluctuation energy observed at each of the measurement

locations developed in the streamwise direction under

the enhanced FTI conditions at two different Reynolds

numbers. These plots reveal that the fluctuation energy

was first linearly growing towards the downstream,

followed by a rapid increase until the energy reached the

maximum. This linear growth could be attributed to the

instability enhancement of the streaky structure inside

the boundary layer that was affected by FTI. It can be

also stated that the growth rate of the fluctuation energy

strongly depends on FTI as well as Reynolds number.

Fig. 14 A series of photographs of separation bubble on

the suction surface for Tu=0.5% at Re=130,000

Fig. 15 Body-fitted contour of time-averaged velocity

fluctuation in rms for Tu = 0.5% at Re

=130000


4 FLOW VISUALIZATION

Figure 14 shows a series of photographs of the

separation bubble taken by the high-speed camera for Tu

= 0.5% at Re = 130,000. These figures contain lines

parallel and normal to the surface, the former being

iso-height lines distant from the surface by 5 mm and 10

mm, the latter being iso-distance lines from the airfoil

leading edge. The flow field was clearly visualized by

the laminar fog under the illumination, where the

separation bubble was easily spotted by the dark area.

The interface between the illuminated and dark areas,

which can be regarded as shear layer, tended to fluctuate

at 78%Cx and rolled up to be a vortex at 80%Cx (Fig.

14(a)). This vortex, designated V1, was then advected

downstream as growing shed vortex (Fig. 14(b)). This

process was repeated so that another vortex V2 was

created as seen in Fig. 14(c).

The flow visualization using high-speed camera

clearly captured the shear layer instability followed by

the occurrence of vortex shedding from the separation

bubble. It was found from Fig. 14 that the emerging

frequency of the shed vortices was about 180Hz, which

almost matched the dominant frequency of KH

instability observed in Fig. 10. Figure 15 shows a

contour of time-averaged velocity fluctuation in rms

expressed in the body-fitted coordinate system. The

contour indicates a clear evidence of velocity fluctuation

appearing at 78%Cx, followed by the emergence of

highly fluctuating zone near the surface from 80%Cx.

From the comparison of Fig. 15 with Fig. 14, the highly

fluctuating zone was closely related the vortex shedding

and the vortex advection.

5 CONCLUSIONS

This paper described experimental studies on bypass

transition of separated boundary layer on a LPT airfoil of

aeroengines. Effects of FTI and Reynolds number upon

the transition process of suction surface boundary layer

was examined in detail by use of hot-wire probe

combined with several techniques to analyze the velocity

data. Several important findings in this study are

summarized as follows;

1. As the FTI as well as Reynolds number increased,

the size of separation bubble tended to become small

likewise in the previous findings.

2. At the lowest FTI condition, the transition process

was dominated by separation-induced transition. At

Tu =1.0%, the transition length was shortest among

the other FTI conditions. It can be stated that this

rapid transition process was caused by the enhanced

growth rate of the separation shear layer instability

due to the freestream turbulence. The velocity

fluctuation due to Kelvin-Helmholtz instability was

clearly observed in the shear layer of the separation

bubble. In addition, the power spectra of the velocity

fluctuation contained the peak at the frequency that

almost corresponded to TS wave.

3. For higher FTI cases, the streak structures appeared

upstream of the separation, indicating that the

bypass transition mode of attached boundary layer

tended to govern the transition process.

4. The peak value of the velocity fluctuation energy

was likely to grow in a linear manner before it

rapidly arose. The growth rate of the peak value

increased with the FTI as well as Reynolds number.

5. The flow visualization using high-speed camera

clearly captured the shear layer instability followed

by the occurrence of vortex shedding from the

separation bubble. The emerging frequency of the

shed vortices was found to match dominant

frequency of KH instability.

REFERENCES

1) Mayle, R. E. : The Role of Laminar-Turbulent

Transition in Gas Turbine Engines, ASME J. of

Turbomachinery, 113 (1991) 509-537.

2) Huang, J., Corke, T. C., and Thomas, F. O. : Plasma

Actuators for Separation Control of Low-Pressure

Turbine Blades, AIAA papers 2003-1027.

3) Volino, R. J., Hultgren L. S. : Measurements in

Separated and Transitional Boundary Layers Under

Low-Pressure Turbine Airfoil Conditions, ASME J.

of Turbomachinery, 123 (2001) 189-197.

4) Koyabu, E., Funazaki, K. and Kimura, M., 2005,

Experimental Studies on Wake-Induced Bypass

Transition of Flat-Plate Boundary Layers under

Favorable and Adverse Pressure Gradients, JSME

International Journal Series B, 48-3 (2005) 579-588.

5) Solomon, W.J. : Unsteady Boundary Layer Transition

on Axial Compressor Blades, Ph.D. Thesis, (1996),

University of Tasmania.

6) Narashimha, R. : On the Distribution of Intermittence

in the Transition Region of a Boundary Layer,

Journal of Aeronautical Science, 24 (1957) 711-712.

7) Chandrasekhar, S:Hydrodynamic and Hydromagnetic

Stability, (Clarendon Press, Oxford 1961).

8) Walker, G., J. : Transitional Flow On Axial

Turbomachine Blading, AIAA J., 27 (1989) 595-602.

9) Fasel, H.F: Numerical Investigation of the Interaction

of the Klebanoff-Mode with a Tollmien-Schlichting


Wave, Journal of Fluid Mechanics, 450 (2002) 1-33.

NOMENCLATURE

C : chord length

Ctr, Cwp : constants used for determining intermittency

Cx : axial chord length

D(t) : detection function

Re : Reynolds number

s : surface length

Tu : turbulence intensity

Ue : edge velocity

: boundary layer thickness

* : displacement thickness

: intermittency factor

: transition length

: kinematic viscosity

Abbreviation

FTI : Freestream Turbulence Intensity

rms : root-mean-square


剥離を伴う航空エンジン用低圧タービン翼面境界層の遷移 挙動 ... ·...

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剥離を伴う航空エンジン用低圧タービン翼面境界層の遷移挙動 ... ·...