Journal of Mechanical Science and Technology 28 (9) (2014) 3569~3581 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-014-0818-7

Stall inception and warning in a single-stage transonic axial compressor with axial skewed slot casing treatment† Byeung Jun Lim1,2, Tae Choon Park2 and Sejin Kwon1,* 1

Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, 21 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Korea 2 Engine Component Technology Team, Korea Aerospace Research Institute, 169-84 Gwahak-ro, Yuseong-gu, Daejeon, 305-806, Korea (Manuscript Received June 7, 2013; Revised April 28, 2014; Accepted May 13, 2014)

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Abstract Characteristic changes in the stall inception in a single-stage transonic axial compressor with an axial skewed slot casing treatment were investigated experimentally. A rotating stall occurred intermittently in a compressor with an axial skewed slot, whereas spike-type rotating stalls occurred in the case of smooth casing. The axial skewed slot suppressed stall cell growth and increased the operating range. A mild surge, the frequency of which is the Helmholtz frequency of the compressor system, occurred with the rotating stall. The irregularity in the pressure signals at the slot bottom increased decreasing flow rate. An autocorrelation-based stall warning method was applied to the measured pressure signals. Results estimate and warn against the stall margin in a compressor with an axial skewed slot. Keywords: Axial skewed slot; Casing treatment; Stall inception; Stall warning; Transonic axial compressor ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction Stalls and surges in compressors can cause engine failure. Given the unavailability of a reliable stall warning system, modern highly loaded compressors are still designed to have a wide and conservative stall margin. Compressors also exhibit high pressure ratios and isentropic efficiencies when operated close to the stall point. Therefore, many studies have been conducted to decrease the unnecessary stall margin. These studies detected stall precursors that appear prior to the occurrence of stall phenomena. These works mainly focused on the small flow perturbations involved in stall inceptions [1-3]. Two typical stall precursor flow patterns exist in axial flow compressors: a long-wavelength pattern called “modal oscillation” and a short-wavelength pattern, which is typically of the order of one or two blade passages and is called “spike” [3]. The former causes 2D flow instability in the compression system and rotates at a relatively low speed of approximately 50% of the shaft speed. This rotation builds up gradually and can be observed starting from several tens to hundreds of rotor revolutions prior to the stall. By contrast, a short-wavelength pattern propagates more quickly at speeds between 60% and 80% of the shaft speed. This pattern appears suddenly and grows directly into the stall cells soon after a few rotor revolutions. The rapid spike growth hinders currently available ac*

Corresponding author. Tel.: +82 42 350 3721, Fax.: +82 42 350 3710 E-mail address: [email protected] † Recommended by Associate Editor Yang Na © KSME & Springer 2014

tuation technologies from avoiding a stall, although the first spike inception is successfully detected. Many studies have indicated that the flow near the rotor tip is related to the spiketype stall inception in the compressor. Vo et al. [4] presented a tip-clearance flow mechanism to account for the inception of a spike-type stall, flow spillage near the leading compressor edge, and backflow on the trailing edge on the basis of a numerical simulation of subsonic compressors. Hah et al. [5] demonstrated a similar flow mechanism for the inception of a spike-type stall on the basis of the numerical simulation of a transonic compressor. An alternative approach to ensure an early stall warning of an axial compressor is to detect irregular signals in the internal flow of the compressor while it throttles toward a stall. Dhingra et al. [6] used an autocorrelation function to determine that the irregularity in pressure signals measured at the rotor tip increases as the compressor approaches a stall. Liu et al. [7] proposed a method for estimating the stall margin of a compressor on the basis of the abovementioned result. Tahara et al. [8] also proposed a stall warning method involving a similar autocorrelation technique, which measures pressure signals at the leading edge of the rotor of a single-stage axial compressor. The flow near the rotor tip in an axial compressor has a significant effect on the compressor stability. Therefore, manipulating the tip region through passive casing treatments has been studied for many years [9-12]. Two typical types of casing treatments exist. One type distributes multiple axial slots over the casing along the circumferential direction, whereas

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another type configures multiple circumferential grooves along the axial direction [13]. Most studies focus on minimizing the efficiency reduction because of casing treatments. Recently, studies on the effect of casing treatments on the inception of a stall were also performed. Houghton et al. [14] showed that circumferential grooves in a subsonic compressor could lead to a mode-type stall and modal activity before a stall could significantly decrease the groove effectiveness. Lim [15] showed that an axial skewed slot had the limitation of stall margin improvement when used in a subsonic axial compressor that exhibited modal-type stall inception. A study by Müller et al. [16] showed that although the inception of a typical spike-type stall occurred in the smooth casing of a single-stage transonic axial compressor, a part-span stall gradually developed into a full-span stall when circumferential grooves were employed. Their results also show that the mode-type phenomenon did not take place before the stall occurrence. Stall inception in a compressor can be changed using casing treatment as mentioned above. The operating range can also be extended using stall warning and active control methods by analyzing the flow characteristic changes as the compressor approaches the stall point. Therefore, the operating range can be further extended using an appropriate stall warning method, which considers the inception characteristics of a stall using casing treatment. The objectives of this paper are twofold: (1) to study the characteristic changes of the stall inception in a single-stage transonic axial compressor with an axial skewed slot, and (2) present a warning method against stalls. This study determines the inception characteristics of a stall in a single-stage transonic axial compressor with smooth casing and an axial skewed slot by experimentation to achieve these objectives. This study also applies an autocorrelation-based stall warning method to a compressor with an axial skewed slot and reviews the obtained results.

Table 1. Specifications of the single-stage transonic compressor designed at KARI. Parameters

Design point

Pressure ratio

1.6

Efficiency

86%

Mass flow rate

15.4 kg/s

Rotational speed

22000 rpm

Tip diameter

0.364 m

Rotor blade number

24

Rotor chord length at tip

54.98 mm

Projected axial rotor chord at tip

28.13 mm

Relative tip clearance (% of chord at tip)

0.91

Relative rotor tip inlet Mach number

1.38

Reynolds number

2.6 × 106

Fig. 1. Rotors and stators in the single-stage compressor designed at KARI.

2. Experimental facility and instrumentation Experimental investigation was performed on a single-stage transonic axial compressor. The compressor was designed for a low-pressure compressor in a 1500 lbf-class turbofan engine at the Korea Aerospace Research Institute (KARI) using multidisciplinary design optimization technology; this technology simultaneously considers the aerodynamic performance and structural stability [17]. The compressor primary specifications are listed in Table 1, whereas the rotor and stator shapes are shown in Fig. 1. The experiment was performed in a compressor test facility at the KARI. Fig. 2 shows the test facility layout. The facility is an open-flow type and is powered by a variable speed AC motor that offers maximum power of 2.25 MW. The facility consists of an air intake section, a test section, a driving section, and an exhaust section. For further test facility specifications, refer to Lee et al. [17].

Fig. 2. Test facility layout.

Fig. 3 shows that the test section consists of a rotor and stator. The rotor is mounted on the main shaft that is supported by a bearing carrier. The flows introduced through a bellmouth are compressed by the rotor and stator rows. The compressed air discharges into a collector in the exhaust section, and the flow rate is adjusted by throttle valves. The axial skewed slot used in this study was designed on the basis of the concept by Fujita [18]. The slot’s shape is shown in Fig. 4, and its specifications are listed in Table 2. The skewed angle of the slot is 60°, at which the maximum operating range is achieved by Fujita [18]. The starting point of the slot was located 5 mm upstream of the leading edge at the rotor tip.

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Table 2. Specifications of the single-stage transonic compressor designed at KARI. Parameters

Specifications

Skewed angle

60°

Height

35 mm

Width

4.38 mm

Land thickness

1.99 mm

Depth

7.3 mm

% of slot area

68.76 %

Number of slots

180

Fig. 3. Cross-section of the test compressor.

Fig. 5. Measurement locations of the Kulite sensor.

Fig. 4. Configuration of the axial skewed slot.

Wall static pressures on the compressor casing were measured with Kulite XCQ-062 fast-response pressure transducers to measure the transient flow phenomena that change rapidly over time. Each pressure transducer output was acquired at 100 kHz through an NI PXI-4495 data acquisition module and a PXIe-8108 controller. Eight Kulite sensors, which were evenly spaced around the annulus, were placed in front of the rotor (Fig. 5) to capture the stall inception characteristics and circumferential direction flow phenomena. The rotor inlet sensors were flush mounted on the casing. Eight fast-response pressure transducers were placed along the axial direction at the rotor tip with smooth casing and seven pressure transducers were placed at the slot bottom for detailed pressure-field observations.

3. Stall inception The compressor designed at the KARI had transonic characteristics of more than 70% of the design speed [19]. Thus, the experiment was performed at 80% (17600 rpm), 70% (15400 rpm), and 60% (13200 rpm) of the design speed to prevent mechanical damage because of a stall or surge. Unsteady pressures were measured by decreasing the mass flow

rate up to the point just prior to the stall inception at respective rotational speeds with throttling valves. The flow stabilized (within ± 1°C of the temperature variation in the collector) once the valves in the exhaust section were adjusted to a specific operating point. Unsteady pressure data were then sampled for 30 s. Starting from the last steady-state operating point to just prior to the stall inception, the valves were closed gradually and transient data were sampled continuously. 3.1 Stall inception of smooth casing Fig. 6 shows the propagation of a short length-scale disturbance at the spike-type stall inception at the rotational speed of N = 80%. This figure also shows traces of the casing wall pressure, which is measured with eight pressure transducers mounted at 13% of the axial chord upstream of the rotor tip at circumferentially equal intervals. The gray and red lines indicate raw data and low-pass filtered data at 1 kHz (approximately 14% of the blade passing frequency at N = 80%), respectively. The spike initially rotated at a speed equivalent to 74% of the shaft speed in the rotor rotational direction. The spike’s rotational speed decreased to 54% of the shaft speed within approximately five revolutions, which was followed by its development into a stall cell. Other signals such as modetype fluctuations were not observed before the spike occurrence. The inception of a spike-type stall was observed at N =

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Table 3. Stall characteristics in the case of a smooth casing.

compressor.

N

No. of stall cells

Stall frequency (f/frev)

ω/ωshaft spike

ω/ωshaft stall cell

80% 70% 60%

1 2-1 1

0.52 0.54 0.52

0.74 0.61 0.66

0.5 0.55 0.51

ω/ωshaft

0.74

0.75

3.2 Stall inception with axial skewed slot

0.54

0.56

8 7

1 kHz low pass filtered raw signal

Ps/(Ptin-Psin)

6 5 4 3 2

Spike

Circumferentail sensor location

5

1 -2

-1

0

1

2

3

4

5

6

7

Revolution

Fig. 6. Wall static pressure at the rotor inlet during the stall inception in the case of a smooth casing (N = 80%).

70% and N = 60% similar to N = 80%. The spike initially rotated at a speed of approximately 61%~66% of the shaft speed, and decreased to approximately 55%~51% when the stall cell developed completely. The stall initiated from two cells at the rotating speed of 70%, which then merged into a single cell, whereas a single-stall cell developed at other rotor speeds. Table 3 presents a summary of the stall inception characteristics in the case of a smooth casing. Fig. 7 shows the fast Fourier transform (FFT) results of the pressure signal at the rotor inlet at three different rotational speeds. Transient pressure signals were obtained as the valve throttled toward a stall. Figs. 7(a)-(c) show that a stall occurred suddenly without a clear degradation of the pressure ratio prior to the stall occurrence over the performance curves. Any peak frequency other than the shaft rotational frequency was not observed before the stall inception. Figs. 7(d)-(f) show that a stall abruptly occurred at point 6 in the cases of all three rotational speeds. The stall frequency in each case was approximately 50% of the respective rotational frequencies. A weak peak near the frequency of 17 Hz also appeared. The reason for the occurrence of this weak peak is discussed in Sec. 3.2. The compressor with a smooth casing experienced a spiketype stall inception at all three rotational speeds as mentioned above. The application of casing treatments seems reasonable in such compressor type because the spike-type stall inception is related to the rotor tip flow [4, 5]. Fig. 6 shows that the spike disturbance developed into a fully developed stall cell within a few revolutions. Therefore, a spike is unsuitable as a warning signal against a stall for active control in a high-speed

Fig. 8 shows the temporal evolution of the traces of the casing wall pressure at the rotor inlet of a compressor with an axial skewed slot at N = 80%. Pressure signals were low-pass filtered at the cut-off frequency of 1 kHz (approximately 14% of blade passing frequency at N = 80%). By contrast to the smooth casing, abrupt compressor instability was not observed (Fig. 8(a)). Interval 2 in Fig. 8(a) shows that with the flow rate decrease, a small pressure peak was detected but disappeared immediately. Fig. 8(b) shows the traces of casing wall pressure during the first rotating stall inception (section A of Fig. 8(a)). Pressure was measured with eight pressure transducers mounted at 13% upstream of the rotor tip and equally spaced in the circumferential direction. The stall cell rotated at a speed equivalent to 34% of the shaft speed in a rotational direction. The bigger pressure peaks occurred more frequently with throttling. Fig. 8(c) shows the eight pressure signals in section B of Fig. 8(a). The pressure signals show that the temporal pressure fluctuations are in phase irrespective of circumferential positions. A low-frequency sound was also distinctly detected in the moment of section B of Fig. 8(a). The circumferential propagation of the stall cells could not be identified from the traces of casing wall pressure at N = 60% and N = 70%. The stall cell was thus not fully developed. The stalling behavior of the compressor with an axial skewed slot showed that the rotating stall occurred intermittently. The stall cell of the axial skewed slot also had a smaller amplitude and lower rotating speed compared with that of the smooth casing. Once pressure is established for sufficient recirculation inside the slot, the fluid re-enters the main flow path with a velocity component against the direction of rotation. Fig. 9 illustrates the flow behavior inside the axial skewed slot and near the rotor tip region. This flow mechanism might suppress the stall cell growth and decrease its rotating speed. Fig. 10 shows the FFT results for the pressure signal at the rotor inlet of a compressor with an axial skewed slot at three rotational speeds. Two peaks appear clearly at all rotational speeds. One peak is related to the peak near 17 Hz as mentioned in the smooth casing, whereas the other peak is related to the rotating stall. The stall amplitudes were significantly less than those of the smooth casing. This result shows that the axial skewed slot successfully suppressed the stall that occurred at the rotor tip. The stall frequencies also decreased using casing treatment. Although the stall cell was not fully developed in the cases of N = 60% and N = 70%, the rotating stall frequencies could be found in the FFT results as shown in Figs. 10(e) and (f). One peak stood at approximately 17 Hz even with varying rotational speeds. Figs. 7(d)-(f) also show similar frequencies in smooth casing during the stall inception. These phenomena

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(a) Performance curve (N = 80%, SC)

(d) FFT results (N = 80%, SC)

(b) Performance curve (N = 70%, SC)

(e) FFT results (N = 70%, SC)

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(c) Performance curve (N = 60%, SC)

(f) FFT results (N = 60%, SC)

Fig. 7. Wall static pressure FFT at the rotor inlet with throttling in the case of a smooth casing.

(a) Wall static pressure – Ch1

(b) A

(c) B Fig. 8. Wall static pressure at the rotor inlet during instability inception in the case of an axial skewed slot (N = 80%).

can thus be assumed to be system characteristics. Surge can be classified according to the amplitude of the mass flow fluctuation. “Mild surge” refers to the condition where the annulus average mass flow oscillates but remains in forward flow at all times; the oscillation frequency is of the order of the Helmholtz resonance frequency [20], which can be defined as the following equation and determined according to the compressor system configuration. fH =

a 2p

AC VP LC

(1)

where a is the speed of sound, AC is the duct area of the com-

pressor, VP is the plenum volume, and LC is the effective duct length. The calculated Helmholtz frequency for the investigated compressor system was 16.8 Hz. The experimentally observed frequency of approximately 17 Hz was very close to the Helmholtz resonance frequency of the system. The observations related to sound, pressure fluctuation, and Helmholtz frequency suggest that the oscillation at approximately 17 Hz can be classified as the commonly known “mild surge” [21]. Day [22] stated that the Helmholtz wave amplitude is small and appears at the stall inception point. This condition agrees well with the smooth casing results. Greitzer [21] proposed the B-parameter of a 1D compressor

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Fig. 9. Illustration of flow behavior inside an axial skewed slot and near rotor tip region.

(a) Performance curve (N = 80%, AS)

(d) FFT results (N = 80%, AS)

(b) Performance curve (N = 70%, AS)

(e) FFT results (N = 70%, AS)

(c) Performance curve (N = 60%, AS)

(f) FFT results (N = 60%, AS)

Fig. 10. FFT of wall static pressure at the rotor inlet with throttling in the case of an axial skewed slot.

system to estimate the behavior of a compressor past the stall limit. Thus: B=

U 2a

VP AC LC

(2)

where U is the mean rotor speed, and other variables are the same as in Eq. (1). The B-parameter represents the ratio of stored energy to the work required to overcome inertial force. Greitzer [21] observed that the instability mode of a compressor changes from a rotating stall to a classic or deep surge when the B-parameter value is more than 0.8. A classic surge has larger amplitude and lower frequency than a mild surge. No flow reversal occurs in the both cases. A deep surge is more severe than the classic surge, and flow reversal is even possible [23]. Bparameter value of the investigated compressor was 0.52 at N = 80%, 0.46 at N = 70%, and 0.39 at N = 60%. Therefore, no classic or deep surge was observed in this compressor system and the experimental results were as expected. Warning against a stall in a compressor with an axial skewed slot was more difficult than that in a smooth casing.

The rotating stall amplitude, which appeared intermittently, was decreased using casing treatment. A mild surge signal related to the Helmholtz frequency was also observed after the rotating stall inception or along with the stall in the compressor system. The Helmholtz wave was also indirectly linked to the rotating stall inception or surge [22]. Therefore, the Helmholtz resonance might be useful in analyzing the dynamic behavior of a compressor system after the stall inception, but is unsuitable for warning against a stall. 3.3 Performance of casing treatments Fig. 11 shows that the performance curve for an axial skewed slot was compared with that of the smooth casing to evaluate the operating range expansion of the compressor using casing treatment. As shown in the following equation, the operating range was evaluated by determining the corrected mass flow rate at the operational point of the stall inception. é (m& ) - (m& c ) AS ù Dm& c = ê c SC ´ 100 ú [%] . & (mc ) SC ë û stall

(3)

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Fig. 11. Compressor performance curves in the cases of smooth casing and axial skewed slot.

(a) Smooth casing (N = 80%)

(d) Axial skewed slot (N = 80%)

(b) Smooth casing (N = 70%)

(e) Axial skewed slot (N = 70%)

(c) Smooth casing (N = 60%)

(f) Axial skewed slot (N = 60%)

Fig. 12. Span-wise total pressure ratio distributions in the cases of smooth casing and axial skewed slot.

A spike-type pressure disturbance developed into a stall cell within a short time span in the case of a smooth casing, whereas stalls and mild surges occurred intermittently and developed gradually in the case of an axial skewed slot. Therefore, the comparison was based on the mass flow rate at an operating point at which the first sign of instability was observed at each rotational speed. The axial skewed slot in-

creased the operating range by 2.5% at N = 80%, 12.3% at N = 70%, and 17% at N = 60%. The operating range increased in the case of N = 80%, but the pressure ratio decreased when the mass flow rate reached 11.3 kg/s. By contrast, the operating range expanded without any decrease in the pressure ratio at rotational speeds of 70% and 60%.

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Fig. 12 shows the span-wise total pressure ratio observed at the stator exit in all cases. Total pressures at the inlet were measured using three radial rakes in front of the rotor. Each radial rake had seven total pressure probes. Total pressures at the exit were also measured using five arc-type rakes at the stator exit. Each arc-type rake had six total pressure probes and was placed at five different radial heights. The distributions of the span-wise total pressure ratio far from the point of stall were compared with those near the stall point. Fig. 12 shows that all cases, except the case of the axial skewed slot at N = 80%, show similar pressure distributions. However, results for the axial skewed slot at N = 80% show a significant difference between two points (Fig. 12(d)). Total pressure ratios below the mid-span region significantly decreased near the stall point. The pressure drop from the hub region to the mid-span region explained the major cause for the decrease in the total pressure ratio of the axial skewed slot at N = 80%. A separation occurs between the hub and blade suction regions in most axial compressors. This separation is 3D, and the separation extent is insignificant in most cases. However, the separation size can grow significantly as the blade loading increases [24]. This separation is commonly known as “hubcorner stall” [25]. A compressor with an axial skewed slot can operate at a lower mass flow rate compared with that in the case of a smooth casing. The incidence angle of the incoming flow in the hub becomes higher than that at the tip at low mass flow rates. The increased incidence angle of the incoming flow causes the separation in the hub corner region to increase. The increase in the blockage area because of the separation growth in the hub region decreases the total pressure ratio for the axial skewed slot at N = 80%. The separation growth in the hub region is highly suppressed at lower rotational speeds because the compressor allows a somewhat higher incidence angle at a lower Mach number. Therefore, small reductions are observed in the total pressure from the hub region to the mid-span at lower rotational speeds as shown in Figs. 12(e) and (f). Danner et al. [26] presented similar results for the separation increase in the hub region of a transonic compressor with an axial skewed slot. The hub corner separation within the extended operating range became more critical for performance and stability than the tip clearance flow in the compressor with an axial skewed slot. Therefore, casing treatment should be considered as an integral part in the compressor stage design.

4. Stall warning An axial skewed slot in a transonic compressor complicates the detection of a stall occurrence because the stall cell amplitude is too small. No rapid reduction in the pressure ratio during the stall inception was also observed. Given such conditions, evaluating the stall margin in a transonic compressor using casing treatment became difficult. Providing prior warning against a stall for active control when such a compressor is

(a) Far from stall

(b) Near stall Fig. 13. Comparison between the static pressure irregularity at the rotor tip at operating points far from and near the stall (N = 80%, smooth casing).

used in actual aircraft engines is also difficult. Therefore, we sought a method to solve these challenges. 4.1 Irregularity of rotor tip pressure Many researchers have studied the phenomenon of the increasing irregularity in pressure signals measured at the rotor tip as a compressor approaches a stall. Biela et al. [27] showed that the tip leakage vortex moved to the leading edge of the adjacent rotor and it oscillated when a transonic axial compressor approached a stall. Thus, unsteadiness was observed at approximately 50% of the blade passing frequency (BPF). Tong et al. [28] presented a similar study applied to a lowspeed compressor. A comparison was made between the pressure signals of the rotor tip measured at the operating point far from the stall and those measured at the operating point near the smooth casing stall to verify the existence of the abovementioned phenomenon in our compressor. Fig. 13 shows that pressure irregularity is the difference between the pressure signals measured at the passage of the four blades and those at the same position one revolution earlier. The result shows an increase in irregularity near the stall operating point. Fig. 14 shows that the pressure irregularity at the bottom of the axial skewed slot also increased when the compressor operated close to the stall. Fig. 15 shows the FFT results for the pressure signals measured at the operating point far and near the stall at respective

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(a) N = 80%, x/cx,tip = 0.05

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(d) N = 80%, x/cx,tip = 0.22

(a) Far from stall

(b) N = 70%, x/cx,tip = 0.05

(e) N = 70%, x/cx,tip = 0.22

(c) N = 60%, x/cx,tip = 0.05

(f) N = 60%, x/cx,tip = 0.22

(b) Near stall Fig. 14. Comparison between the static pressure irregularity at the slot bottom at operating points far from and near the stall (N = 80%, axial skewed slot).

Fig. 16. Static pressure FFT at the slot bottom at operating points far from and near the stall in the case of an axial skewed slot.

(a) N = 80%, x/cx,tip = 0.05

(d) N = 80%, x/cx,tip = 0.22

(b) N = 70%, x/cx,tip = 0.05

(e) N = 70%, x/cx,tip = 0.22

(c) N = 60%, x/cx,tip = 0.05

(f) N = 60%, x/cx,tip = 0.22

Fig. 15. Static pressure FFT at the rotor tip at operating points far from and near the stall in the case of a smooth casing.

rotational speeds in the case of a smooth casing. The narrow peaks shown in the figure indicate the rotational shaft frequency and its harmonics. The results show that pressure unsteadiness increased significantly in approximately 50% of the BPF at the operating point near the stall at N = 60%. This result is similar to the results of previous studies [27, 28]. However, unsteadiness increased uniformly over the entire frequency domain at N = 70% and N = 80%. Young et al. [29] suggested that non-uniform tip clearance was the main cause of the pressure irregularity on the basis of the experimental results in a low-speed compressor. However, the reason for the increase in the pressure signal irregularity at the rotor tip is not yet understood clearly. Although our study results also do not reveal the cause of this phenomenon clearly, unsteadiness still increased as the compressor approached a stall. Fig. 16 shows a comparison between the FFT results for the pressure signals measured at the bottom of the axial skewed slot. Unsteadiness increased significantly between the BPF and its first harmonic at all rotational speeds. The results also show that the increase in pressure unsteadiness in the slot (x/cx,tip = 0.22) was higher than that near the leading edge of the rotor (x/cx,tip = 0.05). Further studies with numerical simulation are required to investigate the cause of the increase in

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irregularity with regard to the internal pressure of the axial slot. Although the reason for the increased unsteadiness of the pressure signal in the axial slot is unclear, the above results could be useful for warning against stalls in a high-speed compressor with an axial skewed slot. (a) Performance curve

4.2 Autocorrelation Different methods of stall warning were reviewed on the basis of the abovementioned results. Among the existing techniques, we used the autocorrelation function proposed by Dhingra et al. [6] and Tahara et al. [8] in our data analysis to evaluate the gradual development of instability. The autocorrelation technique is a method of determining the degree of irregularity by obtaining the autocorrelation between the pressure signals during a specific time window and those before one revolution in a same-sized window. Autocorrelation is defined as follows with reference to the results of existing studies:

R (t ) =

ò ( P(t ) - Pav,n )( P(t - t ) - Pav,n -1 )dt 2 2 ò ( P(t ) - Pav,n ) dt ò ( P(t - t ) - Pav,n -1 ) dt

(4)

where τ is the time period of one revolution of a rotor, P is the pressure, and Pav is the average pressure over a window. The integration is taken for the window. The window size can be varied between the pitch of one blade and that of one revolution. When the window size is too small, it is unsuitable for warning against a stall because autocorrelation is too sensitive to the signal unsteadiness. Autocorrelation could overlook valuable information when the window size is too large. Dhingra et al. [30] suggested that the window size should be two to four blades from their experience. The present study used a four-blade pitch window. Fig. 17 shows the autocorrelation results of the wall pressure measured at the rotor tip (x/cx,tip = 0.22) for one second as the flow rate decreased with smooth casing and those with an axial skewed slot at N = 80%. An autocorrelation close to one indicates high repeatability, whereas that close to zero indicates increasing irregularity. Autocorrelation was close to one at operating point S1 far from the stall in the case of a smooth casing. As the mass flow rate decreased, the mean value of autocorrelation decreased and its variation degree increased. Autocorrelation also decreased abruptly at operating point S3, indicating that a stall occurred. Similarly, the mean value of autocorrelation decreased as the mass flow rate decreased in the case of an axial skewed slot. The variation degree increased concurrently at points A1 and A2. Stall signals also appeared and then disappeared at point A3. Considering the inception characteristics of instability and referring to the results of a previous study [30], we compared the cumulative distribution function with autocorrelation. The cumulative distribution function was defined as follows:

(b) Smooth casing

(c) Axial skewed slot Fig. 17. Time variation in autocorrelation with throttling in cases of smooth casing and axial skewed slot (N = 80%).

(a) Axial skewed slot (N = 80%)

(b) Axial skewed slot (N = 70%)

(c) Axial skewed slot (N = 60%) Fig. 18. Distribution function variation of autocorrelation with throttling in the case of an axial skewed slot.

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rate reduction. This trend shows that the autocorrelation technique, which uses the pressure signals at the bottom of an axial skewed slot, can be used to estimate the stall margin by monitoring the occurrence rate of an event during compressor operation.

5. Conclusions (a) Axial skewed slot (N = 80%)

(b) Axial skewed slot (N = 70%)

(c) Axial skewed slot (N = 60%) Fig. 19. Variation in event rate with throttling in the case of an axial skewed slot.

F ( x) = P( X < x)

(5)

where X is a random variable, x is the specific value of the random variable, and P is the probability function. Fig. 18 shows the distribution function with regard to the autocorrelation of the pressure signals measured at the bottom of the axial skewed slot at x/cx,tip = 0.22. The results at all rotational speeds show that the autocorrelation distribution curve moved to the left and its slope became smaller with the flow rate decrease. This condition means that the mean value of the autocorrelation decreased and its variation increased as the flow rate decreased, respectively. Liu et al. [7] defined autocorrelation across a preset threshold value as an “event” and found that the occurrence rate of the event increased with the flow rate reduction as the stall neared. The stall margin can be predicted by counting the event number using this observation. Fig. 19 shows the event rate as the flow rate decreases in a compressor with an axial skewed slot. The threshold value was changed using the data measured for one second at x/cx,tip = 0.22 to count the number of event occurrences. The occurrence rate of the event at all three rotational speeds increased with the flow

Changes in the inception process of instability in a singlestage transonic axial compressor with an axial skewed slot, which is typically used in casing treatment, were investigated experimentally. The characteristics of increasing irregularity in the pressure inside an axial skewed slot as the compressor approaches the unstable operation point were also utilized to determine a warning method against stalls. (1) Spike-type rotating stalls occurred in the investigated single-stage transonic axial compressor in the case of a smooth casing. (2) Rotating stalls occurred and then disappeared intermittently in the investigated single-stage transonic axial compressor with an axial skewed slot. The rotating stall amplitude was significantly decreased by casing treatment. Mild surge, the frequency of which is the Helmholtz frequency of the compressor system, also occurred with the rotating stall. (3) The axial skewed slot increased the operating range by 2.5% at N = 80%, 12.3% at N = 70%, and 17% at N = 60%. The pressure ratio in the case of N = 80% decreased near the stall point because of the pressure decreases throughout the hub and mid-span regions. This result was caused by an increase in the blockage area led by separation in the hub. (4) Pressures measured at the rotor tip of the smooth casing and at the bottom of the axial skewed slot show that irregularity increased with the flow rate reduction. Unsteadiness increased significantly near 50% of the BPF at a low rotational speed of N = 60% in the case of a smooth casing. This result was similar to those of existing studies. Unsteadiness increased uniformly across the entire frequency domain at other rotational speeds. Unsteadiness also increased within the range between the BPF and its first harmonic at all rotational speeds in the case of an axial skewed slot. (5) Considering the characteristics of increasing irregularity of the pressure signals inside the axial skewed slot as the compressor approaches a stall, an autocorrelation technique was applied. This technique could be used to provide warnings against stalls and estimate their margins in compressors with an axial skewed slot.

Acknowledgment This work was supported by the Energy Technology Development Program (20131010101800) of the Korea Institute of Energy Technology Evaluation and Planning grant funded by the Korean Government Ministry of Trade, Industry, and Energy.

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Nomenclature-----------------------------------------------------------------------AC a cx,tip F fH frev LC m& c N Ps Psin Ptin PR R VP

w wrev x

: Duct area of compressor : Speed of sound : Projected axial rotor chord at tip : Cumulative distribution function : Helmholtz frequency : Shaft rotational frequency : Effective duct length : Corrected mass flow rate [kg/s] : Compressor rotational speed, % of design speed : Static pressure : Static pressure at rotor inlet : Total pressure at rotor inlet : Pressure ratio : Autocorrelation : Plenum volume : Spike or stall cell rotational speed : Shaft rotational speed : Axial length from rotor leading edge

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Byeung Jun Lim is a Ph.D. candidate in Aerospace Engineering at the Korea Advanced Institute of Science and Technology (KAIST). He received his B.S. degree from Inha University in 1996 and M.S. degree from Inha University in 1998. He has been working as a senior researcher at the Korea Aerospace Research Institute. His main research interests cover compressor instabilities, turbomachinery experiments, and aero gas turbine engine systems. Se Jin Kwon is a professor of Aerospace Engineering at KAIST. He received his B.S. degree from Seoul National University, M.S. degree from KAIST, and Ph.D. from the University of Michigan, Ann Arbor in 1982, 1984, and 1991, respectively. His research interests include satellite and spacecraft propulsion, MEMS technology, monopropellant systems, non-intrusive diagnostics of turbulent reacting flow, and propulsion systems.