numerical study on unsteadiness of tip clearance flow and ......low speed axial compressor. it was...

Journal of Mechanical Science and Technology 26 (5) (2012) 1379~1389

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0330-x

Numerical study on unsteadiness of tip clearance flow and performance

prediction of axial compressor† Yoojun Hwang* and Shin-Hyoung Kang

School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, 151-744, Korea

(Manuscript Received October 10, 2011; Revised February 28, 2012; Accepted February 28, 2012)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract Numerical calculations were performed to investigate unsteady features of tip clearance leakage flow in an axial compressor. The first

stage rotor of a low speed axial compressor with a large tip clearance was examined. It was confirmed that the numerically calculated performance data were in good agreement with the experimentally measured performance data. Using frequency analysis, the flow char-acteristic near the casing induced by tip clearance leakage flow was found to be not associated with the rotating speed of the rotor. This characteristic is called rotating instability or self-induced unsteadiness. We found that the circumferential length scale of the rotating instability of the compressor was longer than a pitch of a blade passage; therefore, a multi-blade passage was adopted to study the flow structure more precisely. The flow characteristic was described by the frequency, the circumferential length, and the phase velocity, and was changed by operating points toward stall. The behavior of the flow was characterized by circumferentially traveling waves. Hence, the mechanism governing the development of the unsteady feature was further examined in terms of the rotating wave pattern of the pressure distribution. Furthermore, the unsteady feature of the tip clearance leakage flow affected the prediction of compressor perform-ance by altering blockage, flow turning, and loss near the casing.

Keywords: Axial compressor; Numerical calculation; Tip clearance flow; Unsteadiness ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

Unsteady flows through the tip clearance in axial compres-sors have been investigated for decades. Mailach et al. [1] observed that rotating instabilities are responsible for the exci-tation of blade vibration and noise generation, and attributed this phenomenon to the fluctuating blade tip vortex. März et al. [2] conducted time-accurate numerical calculations for a full annulus of the rotor row to simulate the unsteady feature in a low speed axial compressor. It was found that a rotating insta-bility vortex from the tip clearance was induced by interac-tions among the tip leakage flow, the axially-reversed flow, and the incoming main flow. The rotating instabilities circum-ferentially rotated at nearly half the speed of the rotor. Kielb et al. [3] performed calculations for one-seventh of a rotor row and showed that non-synchronous vibration was a feature coupled to suction side vortex shedding and tip flow instabil-ity. In addition, Bae et al. [4] described the observed periodic unsteadiness in terms of trailing vortex instability theory

through measurements in a linear compressor cascade. Hah et al. [5] showed the same phenomenon in a transonic compres-sor rotor by simulating flows in the full-annulus of the rotor row.

This type of unsteady feature was recently referred to as self-induced unsteadiness by Du et al. [6]. They found that unsteadiness originated from interaction between the incom-ing flow and the tip leakage flow when the tip leakage flow was strong enough to alter the blade loading of the neighbor-ing blade. Moreover, Thomassin et al. [7] used jet core feed-back theory to explain the role of tip clearance flow in non-synchronous vibrations. This was numerically investigated by Drolet et al. [8] including blade vibratory motion using a mov-ing mesh.

It has been found that the unsteady feature of the tip leakage flow (TLF) is inherent in axial compressors. However, a mechanism of the unsteady feature has been shown only for a specific operating point, and the relation of the unsteady fea-ture to the flow condition has not been obvious. The main purpose of this study is to investigate characteristics of the unsteady tip leakage flow, and mechanisms of unsteadiness varying with the flow coefficient. Changes in performance prediction due to unsteadiness are also examined.

*Corresponding author. Tel.: +82 2 880 7118, Fax.: +82 2 883 0179 E-mail address: [email protected]

† This paper was presented at the AJK2011, Hamamatsu, Japan, July 2011. Rec-ommended by Guest Editor Hyon Kook Myong and Associate Editor Byeong Rog Shin.

© KSME & Springer 2012

1380 Y. Hwang and S.-H. Kang / Journal of Mechanical Science and Technology 26 (5) (2012) 1379~1389

2. Calculation models and methods Numerical calculations were executed for a low speed re-

search axial compressor (LSRC) previously studied by Wisler [9]. The LSRC has four identical stages following an inlet guide vane row (IGV). Each stage has a rotor row and a stator row. The numbers of blades for the IGV, rotor, and stator are 53, 54, and 74, respectively. The hub-to-tip ratio is 0.85. A configuration for the rotor tip clearance size of 2.8% of the blade height (which is relatively large) is under consideration since the aim of this study is to examine flow unsteadiness in tip leakage flow, as discussed in Ref. [1].

A commercial solver package, ANSYS-CFX 11.0, was used to solve unsteady three dimensional Reynolds-averaged Navier-Stokes equations for steady-state and unsteady calcula-tions. The standard k-ε model with the wall function was se-lected as a turbulence closure after the results of applying other turbulence models were compared for the purpose of reducing the calculation cost by adopting coarse grids. About 40,000 numerical cells per blade passage with a structured H-mesh were selected following several numerical uncertainty tests described by Kang [10]. A coarse grid was also used in the tip clearance gap since it has been shown that viscosity in the tip gap has little effect on the overall pattern of tip leakage flow [11].

The pressure rise characteristic of the four-stage LSRC was obtained to test the calculation method under steady-state as-sumptions. The inlet boundary conditions were the total tem-perature, total pressure, and flow direction, and the exit boundary condition was the mass flow rate. The mixing-plane interfaces between blade rows were used; thus, periodic boundary conditions in the circumferential direction were used for flows through the single blade passage for each blade row. Adiabatic and non-slip conditions were imposed on the solid walls.

The averaged stage performance from the steady-state cal-culations were compared with the measured data as shown in Fig. 1. The measured data were obtained from the results of Wisler [9]. The pressure coefficient and the flow coefficient are defined as

212

t

p

Uψ

ρ

Δ= , .x

t

cU

φ = (1)

The two characteristic curves have a similar trend around the design point. However, the calculation underestimates the pressure rise by 15% at the design point in comparison with the measured data. It seems that the mixing-plane assumption at the interfaces between the rotating and stationary domains causes this discrepancy. The beneficial effects of blade row interaction on rotor performance were studied by Valkov and Tan [12], Sirakov and Tan [13], and Graf et al. [14]. Valkov and Tan [12] showed that the upstream wake recovery in-creased the pressure rise in the downstream passage by 1 to 3%. Sirakov and Tan [13] explained that the upstream wake

suppressed double leakage of the tip clearance flow, thereby enhancing the pressure rise by about 2%. The effects of the downstream stator on the rotor are shown in Graf et al. [14]. The decrease of endwall loss and blockage of the rotor in-duced by the potential effect increased the pressure rise by up to 5%. This is also consistent with the results of Lucius and Brenner [15] who showed that the steady-state assumption resulted in 10% lower performance prediction than the un-steady calculation. However, even when the net effects of the blade interaction are considered, more than 5% of the pressure rise difference is still unresolved. It is suspected that there are more unsteady effects than just the blade interaction. The im-provement in rotor performance due to the unsteady feature of the tip leakage flow is described later in the present study. At low flow rates, it seems that the calculation predicts the stall line at a relatively high flow rate since it is suspected that the performance data at the lowest flow rate through the steady-state calculation is beyond the stall line due to the significant drop in the pressure coefficient. In the experiment, the first stage rotor had a casing treatment with circumferential grooves; this treatment was not considered in the calculations. It has been reported that an 8.2% improvement in the stall margin was achieved with no measurable change in the pres-sure rise characteristics [9].

Modification to the computational domain was required to examine the unsteady features of tip leakage flow since part of the annulus of the rotor row was chosen to be analyzed de-pending on the circumferential length scale of the unsteadiness, while representing the full annulus with periodic conditions in the circumferential direction. Fig. 2 shows the configuration of one-eighth of the annulus in the first stage rotor of the LSRC. The solidity was changed from 1.20 to 1.24 to include seven blades. Using steady-state calculations for a single blade pas-sage, it was found that little change in the pressure rise at the design point occurred due to the slight increase in solidity. However, the solidity change had little effect on the patterns of tip clearance flow as shown by Inoue and Kuroumaru [16]. For the IGV, a single blade passage was adopted with an addi-tional domain with the mixing-plane scheme on the interface

Fig. 1. Performance map of compressor through experiment and steady-state calculations.

Y. Hwang and S.-H. Kang / Journal of Mechanical Science and Technology 26 (5) (2012) 1379~1389 1381

between the two domains in front of the rotor row. This ex-cluded the wake effect of the IGV on the flow field in the rotor row while maintaining seemingly time-averaged values as obtained in the steady-state calculations. The boundary conditions for the unsteady calculations were the same as in the aforementioned steady-state calculations. The mass flow rate condition at the exit was reasonable as suggested by Hoy-ing et al. [17]. In their study, a constant throttle setting was used to simulate rotating stall inception for the same compres-sor rotor. The time-step for the unsteady calculation was one-tenth of the time period in which the rotor blade rotated one pitch. To record the static pressure signal during operation, a numerical probe was attached at a point near the casing corre-sponding to mid-gap between the rotor and the stator in the LSRC.

The unsteady result for the design point was obtained and was started from the steady-state result as initial values. The calculations were carried out until stable periodic pressure oscillation was observed at the monitoring point. By reducing the mass flow rate at the exit in a stepwise manner, the result for the next operating point was obtained. This process was continued until stable results were unable to be obtained.

3. Results

3.1 Unsteady feature of tip leakage flow

An unsteady calculation for a model with a single rotor blade passage was made to confirm that tip leakage flow had unsteady features. It was found that flow in the tip region os-cillated in time. Fig. 3 shows two instantaneous axial velocity distributions at the exit of the rotor at the design point. The blade wake and the tip leakage flow are seen as velocity defect. It seems that the flow region near the casing circumferentially rotated in time at this plane. The period of oscillation does not correspond to the blade passing time. To clarify the existence of the unsteadiness, a frequency analysis of the pressure signal recorded at the monitoring points near the casing was per-formed as shown in Fig. 4. A frequency spectrum of the signal

from the monitoring point rotating with the blade only shows the frequencies not related to the blade passing, as shown in Fig. 4(a), whereas a signal from the fixed monitoring point includes the blade passing frequency (BPF) and other fre-quencies, as shown in Fig. 4(b). It was found that the frequen-cies shown in Fig. 4(a) correspond to the rotating speed of the flow in the tip region shown in Fig 3. Therefore, this fre-quency can be considered to be related to the unsteady feature of the tip leakage flow. It is noted that the strength of the un-steadiness of the tip leakage flow is similar to that of the blade wake at this location, as shown in Fig. 4(b). The difference in the observed frequency of the tip leakage flow, depending on whether the monitoring point is located on the rotating frame or on the fixed frame, can be explained as shown in Fig. 5. The tip leakage flow appears to form a circumferential wave pattern near the casing. The wave length is a pitch distance. The phase velocity of the pattern is relative to the frame of reference. For this reason, each monitoring point observed different frequencies. This is called the Doppler shift effect in Ref. [3]. Consequently, the frequency obtained from the pres-

Fig. 3. Contour plots of instantaneous axial velocity at the exit of the rotor from unsteady calculation for single blade passage at the design point.

(a)

(b) Fig. 4. Frequency spectrum of the pressure signals of unsteady calcula-tion for single blade passage from: (a) rotating monitoring point; (b) fixed monitoring point.

Fig. 2. Computational geometry and grid for calculations.


sure signal is the same as the frequency observed from the change in the pattern of the tip leakage flow since the tip leak-age flow area had a lower static pressure.

Even though the unsteadiness of tip leakage flow was con-firmed, the unsteady flow was restrained within a single blade passage. Since the circumferential pattern of the tip leakage flow plays a key role in representing the unsteadiness as pre-viously mentioned, the length scale of the unsteady tip leakage flow must be examined. Therefore, unsteady calculations for multi-blade passages were performed including analysis of one-eighth and one-fourth annuli of the rotor row. The mass flow rate at the inlet of the calculation domain was monitored to check flow stability and periodicity as well as pressure sig-nals at the monitoring points. The flow structure in the rotor passage during the first two revolutions was the same as the flow structure result of the single blade passage. However, after 2.5 revolutions, the flow structure changed to the direc-tion that the mass flow rate at the inlet of the domain did not fluctuate as much. Fig. 6 shows the mass flow fluctuation for the one-eighth annulus calculation. This implies that the flow inside the passage became more stable due to the change in the flow structure. The main cause of the change was a flow pattern near the casing, as shown in Fig. 7. The circumferen-tial length scale of the tip leakage flow pattern became 1.4 times as long as in the single blade calculation. It was found that in terms of flow structure, the one-fourth annulus calcula-tion produced the same result as the one-eighth annulus calcu-lation. The frequency spectrums of the pressure signals at the rotating monitoring point show that the same unsteadiness existed in both cases, as shown in Fig. 8. Hence, the one-

eighth annulus model was chosen for the investigation of the unsteady features of the tip leakage flow.

The unsteady calculations for the one-eighth annulus model were performed with the flow rate decreasing from the design point. Figs. 9(a)-(c) show frequency spectrums of the pressure signal from the rotating monitoring point at the lower operat-ing points of φ = 0.387, φ = 0.366, and φ = 0.358, respectively. The tip leakage flow frequency decreased as the flow coeffi-cient decreased. A lower frequency than the tip leakage flow frequency was first observed at φ = 0.366 as the flow rate de-creased. It can be seen that the low frequency remained con-stant when the mass flow rate was decreased. Therefore, the flow structure in the rotor passage was examined to determine the cause of the low frequency. Fig. 10(a) shows the axial velocity distribution versus time at the exit of the rotor row at φ = 0.366 where the low frequency occurred for the first time. In contrast to the result at the design point, there was a circum-ferential disturbance in both the main flow region and the tip region. A rotating disturbance caused more blockage as repre-sented by negative axial velocities in the tip leakage flow. Consequently, the incoming flow near the casing was turned

Fig. 5. Schematic of the relation between relative and absolute phasevelocities for the tip leakage flow.

0 1 2 3 4-0.04

0.00

0.04

Flo

w r

ate

flu

ctu

atio

n [

%]

Revolution Fig. 6. Mass flow rate at the inlet of the calculation domain.

Fig. 7. Contour plots of instantaneous axial velocity at the exit of the rotor for multi-blade passages at the design point.

(a)

(b) Fig. 8. Frequency spectrums of the pressure signals of unsteady calcu-lation for multi-blade passage at the design point, φ = 0.407: (a) 1/8 annulus; (b) 1/4 annulus.


toward the hub due to the larger blockage, and the axial ve-locities of the main flow increased in that region. While the unsteadiness of the tip leakage flow was induced by the fluc-tuation of the low energy flow, this disturbance is related to the rotating distribution of pressure. For this reason, the fre-quency did not vary with the flow condition at low flow rates. The length scale of the disturbance or the wave length of the pattern is one-eighth of the circumference corresponding to the domain size. It can be seen that the rotating speed of the disturbance was nearly twice as fast as that of the tip leakage flow, which is consistent with the existence of almost half the tip leakage flow frequency.

Table 1 shows that the frequency and the relative phase ve-locity of the tip leakage flow varied with the operating points. The phase velocity was normalized with respect to the rotor tip speed. As the flow coefficient decreased, the relative phase velocity decreased as well as the frequency. As previously mentioned, the phase velocity of the tip leakage flow is related to the circumferential velocity of the flow near the casing. Therefore, the tangential velocity at the exit of the rotor row was examined. Fig. 11 shows distributions of pitch-averaged and time-averaged values from the hub to the casing at the four operating points. The relative tangential velocity de-creased at all span heights as the flow coefficient decreased. In particular, the amount of the decrease was larger in the tip region than in the rest of the span. The relative tangential ve-locity difference is the greatest, especially at the 90% span. Fig. 12 shows that there is a linear relation between the phase velocity and the averaged tangential velocity of the flow at the 90% span of the exit of the rotor row. Therefore, it is sug-

(a)

(b)

(c) Fig. 9. Frequency spectrums of the pressure signals of unsteady calcu-lation for 1/8 annulus passage at: (a) φ = 0.387; (b) φ = 0.366; (c) φ = 0.358.

(a)

(b)

Fig. 10. Contour plots of instantaneous axial velocity at the exit of therotor row at φ = 0.366 from: (a) unsteady calculation; (b) steady-state calculation.

Table 1. Effect of flow coefficient on unsteadiness of the tip leakage flow.

Flow coefficient (φ) 0.407 0.387 0.366 0.358

Frequency [Hz] 278 248 215 204 Relative phase velocity

normalized by Ut 0.521 0.465 0.403 0.382

0.0 0.5 1.00.0

0.5

1.0

Sp

an

φ = 0.407 φ = 0.387 φ = 0.366 φ = 0.358

/ tc Uθ Fig. 11. Spanwise distribution of pitch-averaged and time-averaged relative tangential velocity at the exit of the rotor row.


gested that the relative phase velocity of the tip leakage flow is proportional to the relative tangential velocity of the flow near the casing. Consequently, the frequency of the unsteadiness of the tip leakage flow is determined by the flow coefficient since the frequency is determined by the phase velocity and the wave length of the pattern. However, the determinant of the wave length, which is 1.4 times longer than a pitch of the rotor passage in this study, remains unresolved.

3.2 Mechanism of unsteady tip leakage flow

Mechanisms that are responsible for the unsteady feature of tip leakage flow have been studied by many researchers. Du et al. [6] referred to the phenomenon as self-induced unsteadi-ness. They suggested that by simulating the oscillation of the flow with a single rotor blade passage, pressure spots formed by the tip leakage flow periodically influence the pressure side of the neighboring blade and change the blade loading. Thus, the velocity of the tip leakage flow oscillates. On the other hand, based on experiment measurements, Mailach et al. [1] described the circumferential distribution and propagation of the tip leakage flow as rotating instabilities. The wavelength was about two rotor blade pitches. The consequence of the reversed flow of one blade tip vortex influencing the adjacent blade was proposed as a reason for the unsteady phenomenon. The unsteady feature of the tip leakage flow in our study is similar to the existence of rotating instabilities in terms of the circumferential length scale and propagation of the wave pat-tern.

Fig. 13(a) shows a mechanism of the unsteadiness of tip leakage flow at the design point used in this study. The static entropy difference is defined as

ln ln .pref ref

T ps C RT p

⎛ ⎞⎛ ⎞Δ = − ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

(2)

The reference values are the mean temperature and pressure at

the front of the rotor row. The high entropy region corre-sponds to tip leakage flow since loss is generated when flow crosses the tip gap. The entropy distributions on a 95% span plane are shown at four instants in time in Fig. 13(a). The interface between the tip leakage flow and the incoming flow shows a wave pattern near the leading edge region and varies with time. An interface formed by the leakage flow from the neighboring blade periodically impinges on the region be-tween the 30% and 70% chord from the leading edge on the pressure side of the blade. As a result, the blade loading is periodically changed since tip leakage flow has low pressure, thereby influencing the strength of the leakage flow from the tip gap of the blade. The mechanism is similar to that de-scribed in Ref. [6] in terms of the relation between unsteadi-ness time variation in the blade loading. However, there is a difference between the processes in Ref. [6] and those in this study in that the tip leakage flow originating from the leading edge goes across the blade passage in a different velocity. The entropy distribution on the same plane was obtained by steady-state calculation, as shown in Fig. 13(b). The flow structure is different, as expected. The interface between the incoming flow and the tip leakage flow, in particular, steadily impinges at 40% chord on the pressure side of the blade.

Similarly, the entropy distribution on the 95% span plane at the near-stall point, φ = 0.358, was examined as shown in Fig. 14(a). The behavior of the tip leakage flow near the leading edge was entirely different from that at the design point. The tip leakage flow periodically spilled over the leading edge plane. In Fig. 14(a), the flow indicated by (a) goes to the left in

0.2 0.3 0.4 0.5 0.60.2

0.3

0.4

0.5

0.6

V

rel /

Ut

wθ / Ut

Fig. 12. Relation between relative phase velocity of the tip leakageflow and pitch-averaged and time-averaged relative tangential velocityat 90% span of the exit of the rotor row.

(a)

(b)

Fig. 13. Contour plots of entropy at 95% span of the rotor row at the design point, φ = 0.407, from: (a) unsteady calculation; (b) steady-state calculation.


the direction to the neighboring blade at t0. When flow (a) met the leading edge one blade-passing duration later, it divided into two flows, (a1) and (a2). (a1) went to the next passage while (a2) was kept in the passage, flowing downstream on the pressure side of the blade. Subsequently, (a1) split into two flows: (a11), which was directed in the tangential direction, and (a12), which flowed on the suction side of the blade. (a12) grew by a large pressure difference between the pressure side and the suction side of the blade, whereas (a2) diminished in time. The result from our steady-state calculation shows that the interface between the incoming flow and the tip leakage flow formed at an upstream location of the leading edge plane, as shown in Fig. 14(b).

It is necessary to investigate the relation between the behav-ior of the tip leakage flow and the pressure distribution near the leading edge at the near-stall point in detail. Figs. 15(a) and (b) show the pressure distribution on the 95% span plane and the entropy distribution at the same instant, respectively. The high pressure areas indicated by solid circles and the low pressure areas indicated by dotted circles are induced by the tip leakage flow from the previous time step. Consequently, strong tip leakage is generated if the pressure difference at the leading edge between the pressure side and the suction side of the blade is large. The development of a weak tip leakage can be explained in the same manner. The intensification of the leakage flow on the suction side of the blade, (a12), is also due to change in blade loading. The solid circle in Fig. 15(b) indi-cates the high pressure area corresponding to the flow region downstream of the low entropy flow region, which means that the high pressure is induced by a stagnation effect in the low

entropy region since the axial velocity in the low entropy re-gion is greater than the rest. Therefore, the high pressure dif-ference causes the leakage flow to intensify. In contrast, the upstream area of the low entropy flow region indicated by the dotted circle shows that low pressure weakens the leakage flow.

3.3 Effect of unsteady tip leakage flow on performance pre-

diction

The calculated performance of the first stage rotor of the compressor is shown in Fig. 16. The results of the unsteady calculations for the one-eighth annulus model and the single blade model are compared with the result of the steady-state

(a)

(b)

Fig. 14. Contour plots of entropy at 95% span of the rotor row at the near-stall point, φ = 0.358, from: (a) unsteady calculation; (b) steady-state calculation.

(a)

(b)

(c)

Fig. 15. Instantaneous plots at the rotor row at the near-stall point, φ = 0.358: (a) pressure field at 95% span; (b) entropy at 95% span; (c) streamlines of the leakage flow.

0.30 0.35 0.40 0.450.0

0.1

0.2

0.3

0.4

ψ

φ

unsteady (1/8 annulus) unsteady (single blade) steady-state (mixing-plane)

Fig. 16. Performance map of the rotor through unsteady and steady-state calculations.


calculation with the mixing-plane scheme for the interfaces between the rotating and stationary frames. The pressure rise coefficient and the flow coefficient are defined in Eq. (1). For design point φ = 0.407, the steady-state calculation underesti-mates the pressure rise by 7% compared to the unsteady calcu-lation for the one-eighth annulus model. Even though the pressure rise from the unsteady calculation for the single blade model is higher than that of the state-state calculation, it is lower than that of the one-eighth annulus model by 1.4%. This implies that the difference in the calculated flow structure, as shown in Figs. 3 and 7, affects the performance prediction. Accordingly, the flow structures obtained from the unsteady and steady-state calculations are compared as shown in Fig. 17. Fig. 17(a) shows spanwise distribution of the pitch-

averaged and time-averaged axial velocity normalized by the rotor tip speed at the exit of the rotor row. The axial velocity midspan from the unsteady calculations was slightly smaller than that from the steady-state calculation; however, the axial velocity in the tip region from the unsteady calculations was higher than that from the steady-state calculation. This means that the unsteady feature of the tip leakage flow induced less blockage in the tip region and a more uniform spanwise distri-bution, thereby resulting in an increase in the pressure rise at this operating point. The difference of the blockage and the uniformity of the flow between the results from the one-eighth annulus model and the single blade model also gives a reason for the performance difference. Furthermore, examining the absolute tangential velocity distribution and the loss distribu-tion supports the underestimation of the steady-state calcula-tion. Fig. 17(b) shows absolute tangential velocity distribu-tions that represent flow turning in the rotor from the three calculations. It can be seen that flow turning midspan from the unsteady calculations was slightly greater than that from the steady-state calculations, which caused the increase in total enthalpy. On the contrary, flow turning in the tip region of the unsteady cases was smaller than that of the steady-state case. Nonetheless, this does not influence the performance predic-tion as much since the momentum of the flow near the casing was relatively small compared to that of the main flow. Fig. 17(c) shows the distribution of loss coefficient as

, ,1 ,

, , 1 1.t rel t rel

Rt rel

p pKp p

−=

− (3)

It is noted that the steady-state assumption for tip leakage flow predicts more loss in the tip region. This leads to a decrease in total pressure as predicted by the steady-state calculation.

As the mass flow rate was decreased from the design point, the difference between the unsteady and steady-state calcula-tions significantly grew as shown in Fig. 16. The pressure rise from the steady-state calculation rapidly decreased, whereas the pressure rise from the unsteady calculation peaked at the operating point of φ = 0.387 and slightly decreased toward the near-stall point. The difference in the predicted performances between the unsteady and steady-state calculations is ex-plained by the distribution of the axial velocity, the tangential velocity, and the loss coefficient. Fig. 18(a) shows that differ-ences in the blockage near the casing and the flow uniformity are more obvious than those at the design point. In addition, it is noted that the axial velocity near the tip has a negative value, which means that there is reversed flow near the trailing edge. Most of the difference in flow turning at the location midspan from the unsteady calculation accounts for the large difference in the performance prediction at this operating point, as shown in Fig. 18(b). Even the unsteady flow near the casing has large flow turning, which is different from the unsteady flow at the design point. Moreover, Fig. 18(c) shows that the loss in the tip region predicted under the steady-state assumption is up to three times greater than the loss from the unsteady calculation.

0.0 0.5 1.00.0

0.5

1.0

Sp

an

cx / Ut

unsteady (1/8 annulus) unsteady (single blade) steady-state (mixing-plane)

(a)

0.0 0.5 1.00.0

0.5

1.0

Sp

an

cθ / Ut

unsteady (1/8 annulus) unsteady (single-blade) steady-state (mixing-plane)

(b)

0.0 0.5 1.00.0

0.5

1.0

Sp

an

ΚR

unsteady (1/8 annulus) unsteady (single-blade) steady-state (mixing-plane)

(c)

Fig. 17. Spanwise distribution of pitch-averaged and time-averaged values at the exit of the rotor row at the design point, φ = 0.407: (a) axial velocity; (b) absolute tangential velocity; (c) loss coefficient.


Therefore, it is deduced that the unsteady flow structure en-hanced the prediction of the performance of the rotor.

4. Discussion

The results from the simulation of the unsteady feature of the tip leakage flow explain the underestimation of the perform-ance from the steady-state calculation. The net effects of the unsteady features, which are blade interactions from upstream and downstream blade rows and unsteady feature of tip leakage flow, on the pressure rise of the rotor may compensate for de-fects in the steady-state assumption. However, the effects of the unsteady feature of tip leakage flow from the rotor tip gap on the performance of the downstream stator have not yet been proven. Despite a report that there appeared to be no benefit

from the effects of blade interaction on the pressure rise of stator [18], the effects of tip leakage flow oscillation on the stator remains unresolved. Therefore, further study is needed.

A relatively long length scale circumferential disturbance was observed when the mass flow rate was decreased about 90% of the design point. The disturbance was different than the unsteady feature of the tip leakage flow: the disturbance showed a rotating characteristic of a pressure distribution. The wake-like pressure pattern in the tip region was formed by unsteady tip leakage flow since the leakage flow had a lower pressure than the incoming flow. A periodic spillage of the tip leakage flow at the leading edge plane near the casing and a periodic reversed flow at the trailing edge plane were observed as shown in Figs. 14 and 15. Vo et al. [19] suggested that the criteria for spike-type rotating stall inception are spillage of the leading edge and trailing edge backflow. From this perspective, it is considered that the circumferential disturbance of pressure found in this study is associated with rotating stall inception. However, the rotating speed is somewhat faster than that of the rotating stall inception. This is because, in general, stall incep-tion rotates at about 70% of the rotor speed in the direction opposite to the rotor rotation, while the pressure disturbance in this study is about 100% of the rotating speed. It might be ex-pected that this discrepancy can be corrected by calculating the full annulus of the rotor. Nevertheless, the findings are mean-ingful in that the pressure disturbance near the casing causes the tip leakage flow to periodically have an extremely reversed axial velocity, and thus may induce propagation of rotating stall cells represented by flow separation on the blade surfaces.

5. Conclusions

In this study, numerical calculations were performed for a low speed compressor. Even though only one-eighth of the annulus of the first stage of the rotor was considered, the be-havior of the tip leakage flow could still be investigated.

The tip leakage flow oscillated in a period of time that is not related to the blade passing or rotor rotation. The circumferen-tial length scale of the unsteady feature is not within a pitch of the rotor blade. The unsteadiness of the tip leakage flow corre-sponded to the results of a frequency analysis of the pressure signal. The frequency varied with the operating points since the flow speed in the rotor passage changed.

Mechanisms for the unsteadiness of the tip leakage flow for the design point and the near-stall point were proposed. Changes in blade loading influenced by the pressure distribu-tion that was induced by the tip leakage flow were responsible for the origin of the unsteady feature of the tip leakage flow. At the near-stall point, a strong fluctuation of the tip leakage flow was observed near the leading edge of the rotor. This is also explained by the resulting effect of the tip leakage flow in terms of pressure distribution.

The underestimation of the performance of the compressor by the steady-state calculation is explained by the existence of the unsteady feature of the tip leakage flow and by the blade interactions.

0.0 0.5 1.00.0

0.5

1.0

Sp

an

cx / Ut

unsteady (1/8 annulus) steady-state (mixing-plane)

(a)

0.0 0.5 1.00.0

0.5

1.0

Sp

an

cθ / Ut


(b)

0.0 0.5 1.00.0

0.5

1.0

Sp

an

ΚR


(c)

Fig. 18. Spanwise distribution of pitch-averaged and time-averaged values at the exit of the rotor row at the near-stall point, φ = 0.358: (a) axial velocity; (b) absolute tangential velocity; (c) loss coefficient.


In addition, it should be noted that the features indicating rotating stall inception were observed in this study in terms of the flow structure, although only part of the annulus of the rotor was simulated. This result provides insight into the de-velopment of the rotating disturbance and its relation to the unsteady tip leakage flow.

Acknowledgment

This work was supported by Brain Korea 21 project, Re-public of Korea.

Nomenclature------------------------------------------------------------------------

Cp : Constant pressure specific heat c : Absolute velocity of flow KR : Loss coefficient p : Static pressure R : Gas constant s : Static entropy T : Temperature t : Time t0 : Reference time Ut : Tip speed of rotor V : Phase velocity w : Relative velocity of flow ρ : Density Δ : Change in quantity τ : Blade passing period φ : Flow coefficient ψ : Pressure coefficient

Subscripts

1 : Rotor inlet abs : Absolute value x : Axial value rel : Relative value ref : Reference value t : Stagnation value θ : Tangential value

References

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Yoojun Hwang is currently a Ph.D Candidate in Mechanical and Aerospace Engineering at Seoul National Univer-sity. His research focuses on instability and unsteady phenomena in turbo-machinery, especially axial turbomachi-nes, by using numerical simulations.

Shin-Hyoung Kang is a professor of Mechanical and Aerospace Engineering at Seoul National University, Korea. He has over 40 year of experience in the field of turbomachinery in both industry and academia, previously serving as the Chairman of the KSME and SAREK. Currently, his research activities are

directed toward the optimization of turbomachinery perform-ance by using both CFD and experimental methods.

numerical study on unsteadiness of tip clearance flow and ......low speed axial compressor. it was...

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