J. of Thermal Science Vo114, No.3

Unsteady Tip Clearance Flow in an Isolated Axial Compressor Rotor Hongwu ZHANG 1

X i a n g y a n g D E N G 1' 2

Jingyi C H E N 1

Weiguang HUANG 1

]. Institute o f Engineering T h e r m o p h y s i c s , Chinese A c a d e m y o f Sciences, P.O. Box 2706, Beijing, 100080, China 2. Graduate School, Chinese A c a d e m y o f Sciences

The paper investigates effects of operating conditions, tip clearance sizes and external unsteady excitations on the unsteady tip clearance flow in an isolated axial compressor rotor by unsteady 3D Navier-Stokes simulations. The results show that the unsteady tip clearance vortex takes a periodic flow behavior in the rotor tip region. With the decrease of the flow coefficient, the unsteady tip clearance vortex is enhanced and its frequency becomes lower. A larger tip clearance size can cause bigger unsteady fluctuation amplitude and a lower fluctuation frequency of the tip clearance vortex at the near stall operating condition. The unsteady excitation with the natural frequency of the tip clearance vortex can enhance the unsteadiness of the tip clearance vortex and improve the overall rotor performance. The frequency of the unsteady tip clearance vortex is independent of external unsteady excitations with different frequencies.

Keywords: tip clearance flow, compressor, unsteady. C L C number: TK474.8+1 Document code: A Article ID: 1003-2169(2005)03-0211-09 Introduction Background It is well known that the rotor tip clearance flow has profound effects on the performance and stability of axial compressor (Wisler tlj, HowardE2]). Numerous studies on the tip clearance flow were carried out in the past fifty years. Rain TMproposed a model to predict the loss due to tip leakage flow assuming that the kinetic energy of the leakage flow velocity component normal to the mean chamber line would be dissipated. Lakshminarayana t41 developed a model to predict the flow angle assuming that the tip leakage vortex had a Rankine vortex core formation. Storer and Cumpsty TM thought that the mixing of the tip leakage flow and the mainstream was the principal loss mechanism around the blade tip, and predicted the tip leakage loss in terms of conventional design variable. Kang and Hirsch [6j experimentally observed that the flow in the linear cascade tip had a multiple vortex structure, consisting of the tip leakage vortex, the tip separation vortex and the secondary vortex. Inoue et al. [7-9] studied the influence of the tip clearance size on the tip leakage vortex in an isolated rotor. Foley and Ivey [~°] observed that the leakage jet from both stators and rotors rolled up into a vortex downstream of Received June 2, 2005 Hongwu ZHANG: Associate Professor

their respective blade rows in the third stage of a low-speed four-stage axial compressor. These studies for the structure and physics of the tip clearance flow have been carried out in various arrangements and have encompassed cascades, isolated rotors and complete compressor stages, mostly in the framework of a steady flow assumption. However the flow mechanism of tip clearance flow cannot be fully explained based on steady methods and its unsteady characteristic does have a great influence on the compressor performance. Valkov [111 investigated the effect of upstream rotor wakes and tip clearance vortex on the compressor stator performance. The result showed that the energy benefit from tip vortex recovery scaled in the same manner as that associated with wake recovery, and 50 to 67 percent of efficiency gain obtained by Smith []21 can be attributed to the energy recovery in the unsteady tip clearance vortex and wakes. Graf[131numerically investigated the effect of downstream stator on upstream rotor performance. He found that the unsteady downstream stator pressure fluctuations reduced the loss and blockage in the rotor tip region, but increased the overall loss in the rotor. Furthermore he observed that the unsteady rotor tip clearance flow had a fluctuation period, which scaled with rotor flow-through time. Sirakov [14]investigated

212

BPF C

C,p % f

F+

5

Journal of Thermal Science, Vol.14, No.3, 2005

Nomenclature

P__RT

blade passing frequency (Hz) chord length at rotor blade tip (m) static pressure coefficient = ( P - Pr) / O.5 / p

P T / U 2m

disturbance pres sure coefficient = (p - P) / 0.5 / p /Um 2

frequency (Hz) reduced frequency reference pressure (Pa)

the effect of the interaction between downstream rotor tip clearance flow and the upstream stator wake on the time-averaged rotor performance. The result showed that the interaction had a beneficial effect on rotor performance, and the performance benefit became significant at high loading due to strong interaction. Sirakov explained this performance changes by a mechanism that the timeaveraged double leakage flow through the rotor tip clearance was reduced by the interaction between the rotor tip clearance flow and the pressure pulses, induced on the rotor blade pressure surface by the upstream stator wakes. Besides Graf [13], the periodic unsteadiness of the tip clearance flow was also observed by Mailach et al. t151 who performed a detailed experimental investigation on the time-resolved behavior of the flow in the rotor tip region in a four-stage low-speed axial compressor. The experiment results showed that the unsteady periodic fluctuating tip clearance flow induced the propagation of rotating instabilities. More recent work by Bae et al. t161 also showed that the tip clearance flow has an intrinsic fluctuating frequency in a linear compressor cascade.

Objectives It can be seen that the research for the tip clearance flow in its long history of development has gone gradually from steady to unsteady flow framework. Most of the current researches about unsteady tip clearance flow were concerned with the unsteady interactions between the tip clearance flow and upstream or downstream blades. Although unsteady fluctuating frequency of tip clearance flow was also found in these studies, little attention was paid to the detailed intrinsic unsteady characteristic of tip clearance flow, for example, how would the unsteady tip clearance flow behave in the detailed flow structure, and how would some geometr-y and aerodynamic parameters affect the unsteady characteristic of tip clearance flow. Therefore, in pursuing the research along this direction, the specific questions that will be addressed in this paper are as follows: 1. In time-dependent frame, how does the unsteady tip clearance flow behave in rotor blade passage? 2. How would the operating condition influence the unsteady characteristic of tip clearance flow, such as the time-dependent flow fields, the fluctuating frequency and relations between frequency and operating condition?

Um V

relative total pressure (Pa) time-averaged pressure (Pa) rotor blade passing period (s) blade speed at mean diameter of rotor (m/s) axial velocity at rotor inlet (m/s)

Greeks P

air density (kg/m3) flow coefficient = V / U

m

3. How would the tip clearance size influence the unsteady characteristic of tip clearance flow, such as the time-dependent flow fields, the fluctuating frequency and relations between frequency and tip clearance size? 4. How would an unsteady excitation at different frequencies influence the unsteady characteristic of tip clearance flow, such as the time-dependent flow fields, the fluctuating frequency and performance?

Approaches Numerical methods are utilized to tackle the research tasks setting up in the paper. An isolated axial low-speed compressor rotor has been chosen as the computational object. Time-accurate, three-dimensional, Reynolds-averaged, Navier-Stokes equations are solved to obtain unsteady solutions. Three different tip clearance sizes, varying from 2%, 3.4% to 5% chord, have been taken to investigate the effects of the tip clearance size on the unsteady tip clearance flow. Detailed unsteady behavior of tip clearance flow is discussed for 3.4% chord at four operating conditions: near stall, high, middle and low loading conditions, corresponding to the flow coefficients ~=0.498, 0.51, 0.56 and 0.67. Effects of an unsteady excitation on the unsteady tip clearance flow are investigated by specifying the sine signals with different frequencies at the rotor inlet boundary, at the tip clearance size of 3.4% chord, at the high loading condition.

Description of Computed Compressor and Computation Scheme Basic parameters of the isolated compressor rotor The isolated compressor rotor selected for this investigation is actually the first stage rotor in a lowspeed three-stage axial compressor, on which a series of researches for flow instability in compression system have been completed (Nie et al.I171). The design parameters of the compressor are presented in Table 1.

Numerical tool and computation scheme A commercial solver package, FLUENT, has been used for the current study. The solver adopted is a three-dimensional, viscous, time-accurate code employing an implicit second-order accurate scheme to solve the unsteady Reynolds-averaged Navier-Stokes equations.

Hongwu ZHANG et al. Unsteady Tip Clearance Flow in an Isolated Axial Compressor Rotor

The standard k - e turbulence model and non-equilibrium wall function are used to account for the turbulence flow. Several numerical researches on unsteady flow have been conducted in recent years for the same compressor as in this paper by using this solver, and the computational results for the performance of isolated rotor and of three-stage compressor are quantitatively good in comparison with experiment. Table 1 Design parameters of the compressor Rotational speed (r/min) Outer diameter (mm) Hub-tip ratio0. Tip clearance (% of tip chord) Tip and midspan chord (ram) Tip stagger (deg) Tip camber (deg) Blade number of rotor Midspan stagger (deg) Aspect ratio

2400 500 75 3.4 33.3 38 22 60 44 1.86

Steady boundary conditions were given at both inlet and outlet. Total pressure, total temperature and flow angles were specified uniformly at inlet, and static pressure distribution was specified at outlet by means of simple radial equilibrium law. Non-slip and adiabatic conditions were imposed on all solid walls. The grid sensitivity was investigated before this study through comparing the computation results for different grid densities. The grid resolution adopted in the present study is the one, which gives the result not different from that of higher grid densities. This grid is a structured H-mesh with 205 streamwise x 45 pitchwise x 50 spanwise nodes. For the tip clearance, an embedded H-mesh grid with 70 streamwise x 13 pitchwise x13 spanwise nodes is applied. Fig. 1 shows the rotor geometry and grid distributions on the blades and hub.

Fig.1 The computational geometry and grid distributions on the blades and hub

213

Results and Discussions Unsteady flow behavior in the rotor tip region As a starting point for later discussion, the timedependent flow pattern in the rotor tip clearance region is given first to show the unsteady behavior building up and its structure. Fig.2 shows the transient axial velocity coefficient (Cav = U x ] U m ) contour at 98% span in the rotor tip region for tip clearance of 3.4% chord at high loading operation condition. Six time instants during two rotor blade passing periods (T) are given, and A1, A2, A3 and A4 represent the reverse regions. It can be seen clearly that these regions move downstream and their size changes with time. For example, in the first frame (0/40T), A3 is near the suction surface of the blade. A2 lies in the middle of the blade passage, and A1 lies in the aft part of the passage. In the following frames (16/40T, 32/40T), all reverse regions move downstream, but A1 and A3 become weaker with A2 becoming stronger, and a new region of A4 originates from the suction surface near the blade leading edge at 32/40T. In the following frames of 48/40T, 64/40T and 80/40T, A2 becomes weaker, A3 and A4 become stronger, and A1 disappears after the frame of 48/40T. According to the experimental result of Mailach E~51,these reverse regions can be identified with the reverse component of the tip clearance vortex, so the moving path of these regions can approximately represents the tip clearance vortex trajectory, and their moving downstream with size changing at different time, also shows that tip clearance vortex experiences an obvious unsteady fluctuation along its trajectory. Fig.3 shows the transient static pressure coefficient ( Csp ) and disturbance static pressure coefficient ( Cup ) in the transverse plane ($3), 50% chord from the blade leading edge, which helps us to further understand the unsteady fluctuation of tip clearance vortex. Only three time instants in half blade passing period are shown to save the length of this paper. According to the research of Inoue and Kuroumaru ~8~, static pressure in the center of tip leakage vortex is lower, so it is convenient to find the location of the tip leakage vortex marked by the symbol C in Fig.3. It can be found that the tip leakage vortex moves toward the pressure surface of the neighboring blade from the middle of flow passage, then has an interaction with the neighboring blade tip. In Fig.3, it can also be found that there always exists a transient disturbance around the tip leakage vortex, and the strongest disturbance always lies in the center of the tip leakage vortex, which confirms that the tip clearance vortex has unsteady fluctuating characteristic, and forms the primary fluctuating resource in the rotor tip region when it moves downstream. Moreover, the periodic fluctuating behavior of unsteady tip clearance vortex is revealed by the similar time-dependent flow pattern of 0/40T and 80/40T in Fig.2,

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Journal of Thermal Science, Vol.14, No.3, 2005

-0.20

~0.15

-010

-0.05

0.00

0.06

0.11

0.16

0.21

0.26

0.31

0.36

0 . 4 1 0.46

0.51 .,,.,

Fig.2 Transient Axial velocity coefficient contour at 98% span in the rotor tip region showing unsteady tip clearance flow

i

O28 0~8 oo2 -006 •D~,1 4)22 *0.2Q 435! -045 -053

0/40 T

10/40 T

20/40 T

0~0

-081 -069

-O 17 -0 ~J5

(a) Static pressure coefficient

0.2'3

10/40 T

0/40 T

20•40 T

0.27 024 0.22

0.19 OJ7 0.14 0.12

0.I0 0.07 O~ 01}2 0,00

c

(b) Disturbance static pressure coefficient Fig.3 Transient static pressure and disturbance static pressure in the tip region, 50% chord from the blade leading edge

which also indicates that the unsteady tip clearance flow approximately has a half of the rotor passing frequency. In order to accurately quantify the frequency of the unsteady tip clearance vortex, detailed dynamic pressure signals are collected at a series of monitor points located in the rotor tip region to perform the frequency analysis for the tip clearance vortex. Fig.4 shows the locations of these monitor points with static pressure isobars near the blade tip. Five points (TI~T5) are disposed approximately along the low static pressure trough, corresponding to the tip clearance vortex trajectory. Fig.5 shows the FFr of the signals for these monitor points at high loading operating condition for the tip clearance of 3.4% chord. It can be found that the dominating frequencies are 0.5275 BPF (Blade passing frequency) for all points, which approximately corresponds

Fig.4 Location of monitor points in the rotor tip region

Hongwu ZHANG et al. Unsteady Tip Clearance Flow in an Isolated Axial Compressor Rotor

to the fluctuation frequency of tip clearance vortex in Fig.2. But this is somewhat different from the result measured by Bae t~61 in a linear compressor, which shows that the frequency gradually increases with tip clearance flow moving downstream. Though there is no frequency change along the tip clearance vortex trajectory, the fluctuating amplitude experiences a change of increasing and then decreasing. 1000 500 -500 ,, ~l] ~.~n m!l. ~l ,/~i~ I ...... i:~l I ,; !~,,!~ -1000 -1500 ~I~':#/~,~I~:~N~I~%I~;~I~:¢II~ ~ -2000 : : . . . . : . . . . : . . . . : . . . . ', . . . . : . . . . 0.04 0.05 0.06 0.07 0.08 0.09 0 .~ 200 0.5275 A Time / s -.................... T1 T2 t-~

"~,~ <

IO0 ......

~. t _ _ ' / ' 5 , O.6 Frequency/Blade passing frequency

0.4

Fig.5 Frequency characteristic in the rotor tip region Effects of the operating condition on the unsteady behavior of the tip clearance flow After discussing the time-dependent flow pattern and periodic flow behavior of the tip clearance flow at high loading operating condition ( (o=0.51) in the first section, this section will discuss the effects of the blade loading on the unsteady behavior of the tip clearance flow at the tip clearance of 3.4% chord. Four operating conditions are studied in this paper, which corresponds to the flow coefficient (o=0.498, 0.51, 0.56 and 0.67. In order to

215

quantify the unsteady behavior, the static pressure Root Mean Square value (RMS) is applied here, which is defined by the following equation: I PRMS =

N-1 1 )-'[P(t) - P] 2 i=o

where P(t) is the instantaneous static pressure and is the time-averaged static pressure over two rotor blade passing periods. The non-dimensional PRMS for four calculated operating conditions at 98% span blade height are shown in Fig.6, from which the unsteady fluctuation of tip clearance is found for all calculated operating conditions except for ¢~=0.67. The unsteady pressure fluctuation locates around an immovable line (black dash dot line in the figure) in the flow passage, which starts from the blade leading edge and ends at the neighboring blade pressure surface. This line actually coincides with the time-averaged tip leakage vortex trajectory, according to the time-averaged low static pressure trough on the casing (Inoue and Kuroumaru N) but not drawn here. This indicates that the unsteady tip clearance flow fluctuates around the time-averaged tip clearance vortex trajectory. The stronger fluctuations mainly lie in the regions: S~ and $2. With flow coefficient decreasing, the unsteady fluctuations at $2 enhance quickly, which result from the stronger and stronger unsteady interaction between the tip clearance flow and the neighboring blade. The fluctuation amplitude at S~ also has an increase with flow coefficient decreasing, but changes little compared with that at $2. Besides fluctuation amplitude, frequency characteristic of the tip clearance flow also changes with operating

PRMS

0.5pU,,U~ /

0.00

0.02

0.05

0.07

0.09

0.12

0.14

0.16

0.19

0.21

"///'-

/,1 //'

/- /

/

7

'

It i

= 0.67

¢~ = 0.56

(1)

(0 = 0.51

¢~ = 0.498

Fig.6 Time-averaged unsteady fluctuations of static pressure at 98% span in rotor tip region for different operating conditions

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Journal of Thermal Science, Vol. 14, No.3, 2005

conditions as shown in Fig.7. The frequency analysis method used is the same as that in the first section. For ¢~ =0.56, 0.51 and 0.498, the frequencies at the monitor points are 0.6252, 0.5275 and 0.5168 BPF respectively, but no fluctuation frequency is observed for ¢~=0.67. Together with Fig.6, it can be regarded that the unsteady characteristic of tip clearance flow depends on the operating condition. It occurs only when a stronger tip leakage vortex is formed by the flow coefficient reducing to some level. 150 100

~p= 0.56

~ 0.6252 BPF

50 200 "-- 150 ~= 100

q~= 0.51

1

~0.5275BPF ............ [I

Also in Fig.8, it can be found that because of the tip leakage vortex trajectory moving downstream with tip clearance size increasing, the interaction region between the tip clearance vortex and the neighboring blade also moves downstream, which is coincident with the result by Inoue et al[7~9]. The effects of tip clearance size on the frequency characteristic are also investigated as shown in Fig.9. The frequencies are 0.5384, 0.5168 and 0.5087 BPF respectively for the tip clearance size of 2% chord, 3.4% chord and 5% chord at near stall points. It must be pointed out that for the three tip clearance sizes, the near stall points are not the same. For the tip clearance sizes of 2% chord, 3.4% chord and 5% chord, the corresponding flow coefficient are 0.478 0.498 and 0.533 respectively, so the operating conditions also contribute to the frequency shifting.

13

50

<

150 100

o.5p~r;W-,u~

~o= 0.498

0.0 0.02 .............................. r -2.0% chord

50 0 0.3

0.05

0.07

0.09

0.12 ]

r -~3. 4% c h o r d

0.14 0.16 .............

i i

0.19

r -%. 0% c h o r d

i ' J

0.4 0.5 0.6 0.7 Frequency/Blade passing frequency

0.21

"6

0.8

Fig.7 Frequency variation of tip clearance flow with different operating conditions Effects of the tip clearance size on the unsteady behavior of tip clearance flow The tip clearance size has great influence on the tip leakage vortex according to the previous steady researches [7~91. In this section, effects of tip clearance size on the unsteady behavior of tip clearance vortex are investigated by setting the tip clearance size at 2%, 3.4% and 5% chord. The tip clearance flow at the near stall point is normally tied up with the stability of compressor, so the discussion mainly aims at the flow at the near stall point. As in the second section, the static pressure RMS is analyzed and shown in Fig.8 for the three tip clearance size. It can be found that the unsteady fluctuation still locates around the time-averaged tip leakage vortex trajectory, marked by the black dash dot line, for all tip clearance sizes. Because of the interaction of tip leakage vortex and neighboring blade, the strongest fluctuating region occurs near the neighboring blade pressure surface. With the tip clearance size increasing from 2% to 5% chord, the fluctuation intensity enhances quickly and the fluctuation distributed region extends from the tip leakage vortex trajectory to the whole flow passage, which indicates that unsteadiness of the tip clearance vortex grow up with the tip clearance size enlarging.

Fig.8 Time-averaged unsteady fluctuations of static pressure at 98% span in rotor tip region for different tip clearance size 200 r = 2.0% chord 100 0.5384 BPF 200 r = 3.4% chord 100 ¢-~

BPF - __f(,~k_~ 8 0"516 A


0.2

- ~

T

T1 2

~ T 3 T4

roT5

r = 5.0 % chord ~,/0.5087 BPF 11

0.4 0.6 0.8 Frequency/Blade passing frequency

'

'

Fig.9 Frequency variation of tip clearance flow with different tip clearance sizes

"

1.0

Hongwu ZHANG et al. Unsteady Tip Clearance Flow in an Isolated Axial Compressor Rotor

To estimate the range of the fluctuating frequency and compare with the results by other researchers, a reduced frequency F ÷ = fC / W is applied as done by Bae [16~,where C is the rotor tip chord length and W is the time-averaged rotor inlet relative velocity. As the results shown in Fig.10, the dimensional frequencies in the current rotor are different from that of Bae [16] and Mailach et al. ~51, but the reduced frequency are all in the range of F+=0.6-0.9. For the current rotor, F + are about 0.70 at z-=2% chord, 0.67 at r=3.4% chord and 0.65 at =5% chord for the corresponding near stall operating conditions. With the help of reduced frequency, a quantified estimation of the fluctuating frequency of the tip clearance flow could be made based on the blading design parameters before operating the compressor. 2.0

• ~ Bae • Mailach et al • • Current rotor

1.5

217

condition, the natural fluctuating frequency ( f n ) of the tip clearance vortex is 1265 HZ from the first section. Seven unsteady excitations with different frequencies corresponding to 0.25, 0.5, 0.8, 1, 1.25, 1.5 and 1.9 times of the natural frequency of the tip clearance vortex ( 0 . 2 5 f n - 1.9fn ) are investigated here, while the amplitude A is considered as a constant in all the simulations. Fig. 11 shows the static pressure rise coefficient ( Cs ) and total pressure loss of the rotor at the seven unsteady excitations. The performance without unsteady excitation is also shown for comparison. It can be seen that there exist different effects of unsteady excitations with different frequencies on rotor performance. An optimal rotor performance of 0.2% increase in pressure rise and 0.6% decrease in loss can be acquired when the frequency of the excitation equals the natural frequency of the tip clearance vortex. That is well consistent with the experiment result of Bae [16], which shows that the unsteady tip clearance vortex is most receptive to external forcing at its natural frequency.

Different tip clearance size

0.608

A r = 3.4% chord, ¢p= 0.498

1.0

//'~\\\

0.607

d

0.5

0.606 Different Reynolds number ......

I

......

100

I No unsteady excitation

0.605 0.093

z = 2.0% chord, ~p= 0.478

J

I

1000

2000

i

~. 0.092

F r e q u e n c y / Hz

0

,a

Fig,10 Reduced frequency of rotor tip clearance flow

0.091

0.090 0

Effects of unsteady excitations on the rotor performance and the unsteady tip clearance flow In recent years, some researches [18,19]have proved that an unsteady excitation can control the unsteady flow separation on the blade surface, especially the suction surface in the compressor to improve the performance, but it is still not clear whether an unsteady excitation can influence the unsteady behavior of the tip clearance vortex. So in this paper, several sine signals with different frequencies are respectively specified at the rotor inlet boundary to investigate the effects of an unsteady excitation on the unsteady behavior of the tip clearance flow. The sine signals are defined by the following equation: Pr = A sin(2zroJt)

.

i

(2)

where A and COis the amplitude and frequency of the unsteady excitation. All simulations are carried out at the tip clearance size of 3.4% chord, at q~=0.51. For this

0.5

1.0

1.5

2.0

Excitation frequency/Natural frequency F i g . l l R o t o r p e r f o r m a n c e u n d e r effects o f

the unsteady excitations with different frequencies on the tip clearance vortex Optimal rotor performance improvement can be acquired when the unsteady excitation has the natural frequency of the tip clearance vortex, so the unsteady flow behavior of tip clearance vortex under such excitation is investigated. Fig.12 shows the transient axial velocity coefficient contour with the excitation. Compared with the flow without the excitation as shown in Fig.2, it seems the excitation has no effects on the tip clearance vortex. However this is not true. The effects of the excitation on the tip clearance vortex can be observed by the static pressure RMS in the rotor tip region, given in Fig.13. It clearly shows that the excitation enhanced the unsteady characteristics of the tip clearance vortex according to the much stronger unsteady fluctuating amplitude with

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Journal of Thermal Science, Vol.14, No.3, 2005

C,,~U.,/U= -020

-0.15

-0.10 -0.05 0.00 0.06

0.11

0.16

0.21 0 . 2 6

0.31

0.36

0.41 0.46 0.51

16/40 T

Fig.12 Transient Axial velocity coefficient contour at 98% span in the rotor tip region with unsteady excitation /~Ms

II

1

[...i!:[~--

O.@U=*Umooo 003 006 6.09 0.13 0,16 0.19 622 0,25 0.28

characteristics for unsteady excitation with the frequency of 0.25, 0.8 and 1.9fn at monitor point T2 are shown. It can be found that the frequencies of tip clearance vortex hold at 1265 HZ all the time for the three different unsteady excitations, which implies that the periodic behavior of the tip clearance vortex is independent of the external unsteady excitation. 250 f

R ~ 0 ~ . ~2 5~ f n_]

20oo

O.8fn

Excitation = 0.25fn

Excitation = O.Sfn

(D

Without excitation

_,flll,fn = 1265 Hz e~

Fig.13 Time-averaged unsteady fluctuations

of static pressure at 98% span in rotor tip region for unsteady excitation the excitation than that without the excitation in the whole flow passage at the rotor tip region. The strongest unsteady fluctuating region moves upstream when the excitation is applied, which implies that the excitation undoubtedly changes the unsteady fluctuating manner of the tip clearance vortex. The enhanced unsteady tip clearance vortex can intensify the mixing between the tip clearance vortex and the mainstream to reduce the blockage at the endwall region so as to improve the rotor performance according to the experiment of Bae E161. However it is difficult to have a quantitative determination of the blockage of the tip clearance vortex in this paper. It still needs a further research of the mechanism leading to the improvement of rotor performance in the author's later work. The effect of the excitation on the frequency characteristic is also investigated as given in Fig.14. Only the frequency


0 Excitation= 1.9fn

200

0

500

1000 1500 Frequency / Hz

1.9fn

2000

2500

Fig.14 Frequency characteristic of tip clearance vortex for different unsteady excitation

Summary and Conclusions Effects of the operating conditions, tip clearance size and external unsteady excitation on the unsteady behavior of tip clearance flow in an isolated axial compressor rotor have been numerically studied. The following conclusions can be drawn through this study. 1. The unsteadiness of tip leakage flow in the rotor tip clearance region is clearly shown for the tip clearance

Hongwu ZHANG et al. Unsteady Tip Clearance Flow in an Isolated Axial Compressor Rotor

size of 3.4% chord at high loading operating condition. The transient reverse region of the tip clearance vortex appears periodically along the tip clearance vortex trajectory with the frequency of 0.5275 times the blade passing frequency. 2. Unsteady tip clearance vortex only can be found at higher loading operating conditions. With the decreasing of the flow coefficient, the unsteady fluctuation of the tip clearance vortex becomes stronger and the frequency becomes lower. The strongest fluctuation always occurs in the region at which tip clearance vortex interacts with the neighboring blade pressure surface. 3. With the tip clearance size increasing, the unsteady tip clearance vortex enhances, and its fluctuating frequency decreases at near stall operating condition. The reduced frequency of the tip clearance vortex for different clearance size is in the range of 0.6-0.9, which is in consistency with the recent results of other researches. 4. An optimal rotor performance of 0.2% increase in pressure rise and 0.6% decrease in loss can be acquired when an external unsteady excitation with a frequency equals to the natural frequency of the tip clearance vortex is specified at the rotor inlet boundary. The fluctuating frequency of the tip clearance vortex is independent of the influence of external unsteady excitation.

Acknowledgment This work was supported by National Natural Science Foundation of China with project No.50406027. The authors would like to thank Dr. Yifang Gong, Dr. Chaoqun Nie and Dr. Naixing Chen for their insightful discussions and suggestions.

References [1] Wisler, D C. Loss Reduction in Axial-Flow Compressors Through Low-Speed Model Testing. ASME J. Eng. Gas Turbines and Power, 1985, 107:354--363 [2] Howard, M A, Ivey, P C, Barton, J P, et al. Endwall Effects at Two Tip Clearances in a Multistage Axial Flow Compressor With Controlled Diffusion Blading. ASME J. Turbomachinery, 1994, 116:635--647 [3] Rains, D A. Tip Clearance Flows in Axial Flow Compressors and Pumps: [Report No.5]. USA: California Institute of Technology, Hydrodynamics and Mechanical Engineering Laboratories, 1954 [4] Lakshminarayana, B, Horlock, J. Leakage and Secondary Flow in Compressor Cascades. ARC R&M 3483, 1965 [5] Storer, J A, Cumpsty, N A. An Approximate Analysis and

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