Journal of Mechanical Science and Technology 25 (5) (2011) 1317~1324 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-011-0232-3

Experimental analysis about the magnitude of the shaft frequency growth near stall in the axial compressor† Hyung-Soo Lim1,*, Young-Cheon Lim1, Shin-Hyoung Kang1, Seung-Jin Song1, Soo-Seok Yang2 1

Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, 151-742, Korea 2 Propulsion Division, Korea Aerospace Research Institute, Daejeon 305-333, Korea (Manuscript Received June 10, 2010; Revised October 15, 2010; Accepted January 18, 2011)

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

Abstract The experimental study investigates the cause of prestall, which the magnitude increases of the shaft frequency near stall. This prestall phenomenon is related to the geometric non-uniformity of the axial compressor, which can be classified into blade non-uniformity and casing non-uniformity. The instant static pressure was decomposed into several signal components to investigate this phenomenon. To verify the blade non-uniformity, the dimensionless revolution aperiodic component (Ψ) distribution, which was measured at one arbitrary circumferential location, was analyzed, and to verify the casing non-uniformity, the amplitude of Ψ was analyzed at 8 equally spaced circumferential locations of the first stage. The measurements showed that the blade non-uniformity directly caused the increase of the magnitude of the shaft frequency near stall but that the casing non-uniformity induced the increase of the magnitude of the shaft frequency in the Seoul National University compressor. Keywords: Axial compressor; Non uniformity; Revolution aperiodic component; Shaft frequency; Signal decomposition ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction For high efficiency, the axial compressor should compress the intake air to a high pressure ratio. Thus, its operation point should be close to the surge line. A compressor operator wants to run the compressor as close as possible to the surge line for efficiency. However, if a compressor runs beyond the surge line, rotating stall or surge will occur and have a serious effect on performance and safe operation of the compressor. For decades, the mechanisms of stall onset and prestall were studied by experiment and theoretical work. Such efforts have provided full understanding of the prestall characteristic, allowing the operator to run the compressor with high efficiency. Prestall patterns can be classified by the shape of an unsteady signal distribution. All compressors have their own prestall characteristics, and a few types of prestall patterns were reported. Among them, prestall patterns like mode and spike were introduced in a few literatures. Camp et al. [1] investigated the detailed characteristics of mode and spike. They suggested the criteria for determining the pattern of a prestall by using a low speed axial compressor. Also, Inoue et al. [2], Vo et al. [3] and Hah et al. [4] researched the prestall †

This paper was recommended for publication in revised form by Associate Editor Jun Sang Park Corresponding author. Tel.: +82 2 880 8047, Fax.: +82 2 889 6205 E-mail address: [email protected] © KSME & Springer 2011 *

mechanism by the method of CFD and experiment. These days, with improved CFD technology, the prestall behavior of an axial compressor can be simulated more clearly and accurately. Another prestall pattern exists in which the magnitude of the shaft frequency ( f shaft ) increases near stall. f shaft is the shaft frequency which is mostly due to the non-uniformity of compressor geometry or inlet flow. Because of these nonuniformities, a signal which has a period for one revolution is generated repeatedly in every revolution, and f shaft represents the magnitude of f shaft . In the research of Tryfonidis et al. [5], Day et al. [6] and Hoss et al. [7], this phenomenon, in which f shaft increase near stall, occurred in a certain axial compressor, and it was analyzed with respect to the wave energy variation near stall. However, no practical reasons were mentioned about this phenomenon. In this research, the prestall phenomenon in which f shaft increases was investigated with the Seoul National University (SNU) compressor. f shaft variations were analyzed with instant pressure data, which were measured by a fast response pressure transducer. To investigate this phenomenon, an instant pressure signal was decomposed into some components. With signal decomposition, the actual cause for the increase of f shaft was determined, and this prestall phenomenon could be referenced to check the compressor geometric condition.

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Table 1. Specifications of test facility. Number of stages

4

Number of IGV / rotor / stator

53 / 54 / 74

System height [m]

3.89

Tip radius [m]

0.5

Hub/Tip ratio

0.85

Aspect ratio

1.2

Chord_rotor [mm]

62.5

Stagger_rotor [°]

51

DC motor [kW]

55

(a)

(b) Fig. 1. Schematic of test facility: (a) SNU (Seoul National University) compressor; (b) Fast response pressure transducer set up.

2. Test facility and measurement The schematic of 4-stage low speed axial compressor which was set up at Seoul National University (SNU compressor) is shown in Fig. 1(a). It is a low speed research compressor suitable for investigation of compressor unsteadiness like the rotating stall, and the SNU compressor is a scaled down General Electric (GE) low speed research compressor (LSRC) to 2 over 3. The axial compressor was set up vertically, such that the air came into the compressor from the top and compressed air was discharged through the bottom. A mesh screen was installed at the intake. The volume flow rate was controlled by the throttle valve. Fig. 1(b) illustrates the fast response pressure transducer setup for each stage. To analyze an instant signal variation and the progress of prestall, fast response pressure transducers (Kulite XCQ-062) were used. The sensors were installed 25% chord length upstream of the 1st stage rotor, and 16% chord length upstream of the 2nd ~ 4th stage rotor. Eight fast response pressure transducers were equally spaced at 45° in the circumferential direction. The specifications of the test facility are shown in Table 1. The blade consisted of 53 inlet guide vane (IGV), 54 rotor blades and 74 stator blades. The maximum rotation speed was

Fig. 2. Dimensionless performance curve at 650, 800 and 1000 rpm.

1200 rpm (revolutions per minute) by 55 kW DC motor and the design speed was 800 rpm. To verify the dimensionless performance of the compressor, the SNU compressor was operated at three different speeds (650, 800, 1000 rpm). In addition, at 800 rpm, the tip velocity was approximately 40 ms −1 . Measurements were taken at a fixed rotation speed. The compressor operating point could be varied by changing the location of the throttle valve. For data acquisition, a 16-bit resolution A/D board (NI 6251) was used and for signal decomposition, the instant static pressure was scanned at 18,000 Hz. The measurement uncertainties of Φ and Ψ were ± 0.35 % and ± 0.69 % of design point respectively for 95% confidence interval.

3. Dimensionless performance The dimensionless performance curves for three different rotation speeds are illustrated in Fig. 2. For flow coefficient (Φ), axial flow velocity (Cx) was calculated with circumferen tially averaged inlet total pressure and circumferentially averaged inlet static pressure. Inlet total and inlet static pressure probe are circumferentially spaced in 30° increments and positioned at two times of IGV true chord upstream from the lead-

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× 10−3

f shaft

2

Table 2. Instant pressure signal decomposition.

increasing

f

1

0.355 0.36

Φ

0.365 0.37

0.375

8

7

6

5

4

3

2

1

0

Rotational Freq. Shaft Freq.

Fig. 3. The increase of the magnitude of the shaft frequency near stall at 1st stage.

Revolution periodic [ ( Pjk ) RP ]

Revolution aperiodic [ ( Pj ) RA ]

Shaft unresolved component [ Pijk ' ]

0.5 0 0.345 0.35

Time average [ P ]

Shaft resolved component [ ( Pjk )ens ]

Instant pressure signal [ Pijk ]

1.5

near stall. In this research, we analyzed the same phenomenon by using the instant pressure signal decomposition method. With this method, we could obtain information related to the increase of f shaft near the stall.

5. Analysis of instant static pressure ing edge of IGV. For pressure coefficient (Ψ), circumferentially averaged inlet total pressure and circumferentially averaged 4th stage static pressure was used. The 4th stage static pressure probes are circumferentially spaced at 45° increments and positioned down stream of the 4th stage stator. The dimensionless performance curves coincided well during the whole operation range even with rotating stall. However, when the rotation speed is 650 rpm, because of the low Reynolds number, the dimensionless maximum pressure rise is 2% lower than the average one. As the flow rate decreases, compressor pressure rise increases to have the maximum value at Φ = 0.355(①) and rotating stall occurs at Φ = 0.347(②). When the compressor is forced to run beyond this stall limit by closing the throttle, the operation point suddenly dropped to another operation point (③) due to the occurrence of the rotating stall.

4. Magnitude of shaft frequency In the research of Tryfonidis et al. [5], Day et al. [6] and Hoss et al. [7], f shaft tended to increase when the compressor was run near stall. The analysis was focused on the wave energy variation, and they mentioned that not every compressor showed this phenomenon; only a certain compressor showed this prestall characteristic near stall. The SNU compressor showed the same prestall phenomenon, and the result is illustrated in Fig. 3. The static pressure signal which was measured by fast response pressure transducer was analyzed with Fast Fourier Transform, and the rotational frequency was calculated. The shaft frequency is a revolution frequency of the shaft. Thus, the ratio of rotational frequency and shaft frequency, in Fig. 3, means frequency distribution about the shaft frequency. f is dominant at the ratio of rotational frequency, and shaft frequency becomes 1. When the compressor was run near stall by slow closing the throttle, f shaft tended to grow. This means that when the compressor runs near stall, the strength of the shaft frequency increases. This result was analyzed by the frequency analysis method. However, this analysis method showed a limitation in its ability to investigate the actual cause of the increase of f shaft

5.1 Signal decomposition In this research, the prestall phenomenon of a compressor, in which f shaft increases, was analyzed by the signal decomposition method. The static pressure signal, which was measured at 8 equally-spaced locations of the 1st stage, was saved at 18,000 Hz sampling rate. About 200 revolutions phase locked data could be acquired. The blade passing frequency was 720 Hz at the design speed, so 25 discretization points were measured between blades. In the research of Suryavamshi et al. [8] and Kang et al. [9], the instant pressure signal was decomposed into a few components, which are listed in Table 2. The instant static pressure Pijk can be written as Pijk = ( Pjk )ens + Pijk ' .

(1)

( Pjk )ens is the shaft resolved component for 1 revolution and Pijk ' is the shaft unresolved component. ( Pjk )ens represents the average static pressure for one phase-locked revolution. It can be defined as

( Pjk )ens =

1 N rev

N rev

∑P n =1

ijk

.

(2)

As listed in Table 2, ( Pjk )ens can be decomposed into a time average component ( P ), a revolution aperiodic component ( ( Pj ) RA ) and a revolution periodic component ( ( Pjk ) RP ). The time average component P can be expressed as in Eq. (3). N

P=

N rev Nb pb 1 Pijk ∑∑∑ N rev × N b × N pb i =1 j =1 k =1

(3)

and it represents the time average value of Pijk . ( Pj ) RA is the revolution aperiodic component and can be defined as Eq. (4). It represents the size of ( Pjk )ens deviation about the time average component and is an averaged value for each blade pitch.

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Fig. 4(a) shows the instant static pressure distribution for 10 revolutions. With the instant pressure signal distribution, 10 repeated oscillations were observed for 10 revolutions. In this research, the oscillation for Φ = 0.37 was clearer than that for Φ = 0.53. All turbomachinery has its own periodic signal characteristics derived from the manufacturing and assembly conditions. Day et al. [6] mentioned this oscillation and called it shaft order perturbation. Fig. 4(b) illustrates the shaft resolved component, which was an average for about 200 revolutions. The abscissa represents 1 revolution (54 rotor blades) and the vertical axis represents the pressure value. Even though the flow rate is different, the distributions of the shaft resolved component seem similar. A sudden pressure rise or drop was detected at the same blade. For example, at both flow rates, abrupt pressure rise and drop were detected at blade 4 and blade 44, respectively. Fig. 4(c) illustrates the revolution aperiodic (RA) component. It represents the size of the deviation of the shaft resolved component from the time average component. When Φ = 0.37, the amplitude of the deviation increased by 50% from that when Φ = 0.54; this means that the size of the deviation grew at the low flow rate. With the RA component distribution, geometric non-uniformity could be analyzed and the practical meaning of the RA component distribution is discussed in the next section. Fig. 4(d) shows the revolution periodic component, which indicates the size of the pressure perturbation at each blade passing. This figure shows the highest pressure perturbation at the passing of blade 44, as given by Eq. (5).

(a)

(b)

(c)

5.2 Revolution aperiodic (RA) component distribution (d) Fig. 4. An example of pressure signal decomposition: (a) Instant static pressure signal; (b) Shaft resolved component; (c) Revolution aperiodic (RA) component; (d) Revolution periodic (RP) component. N ⎪⎧ 1 pb ⎪⎫ ( Pj ) RA = ⎨ (( Pjk )ens − P) ⎬ ∑ ⎩⎪ N pb k =1 ⎭⎪ j

(4)

( Pjk ) RP is the revolution periodic component and it is defined as Eq. (5). This component represents the size of the perturbation for each blade.

( Pjk ) RP = ⎡⎣( Pjk )ens − P − ( Pj ) RA ⎤⎦

(5)

An example of pressure signal decomposition is illustrated in Fig. 4. A pressure signal was measured at two different flow rates: one far from the stall condition (Φ = 0.53) and the other near the stall condition (Φ = 0.37). The decomposed signal components, which were measured at the different flow rates, were plotted together at the same time domain to compare their patterns of distribution.

If the blade is uniform, the casing is concentric and the inlet flow is also uniform, the distribution of the shaft resolved component would take the form of a sinusoidal wave, as shown in Fig. 5(a). In this case, the value of the RA component of each blade is uniform and almost zero. Such a value might be obtained under an ideal manufacturing and assembly condition. However, if the blade is non-uniform or the casing is eccentric, as in a real condition, the distribution of the shaft resolved component would take the form of an irregular sinusoidal wave, as shown in Fig. 5(b). The RA component represents the size of the signal deviation from the time average component, so the RA component can be expressed as shown in Fig. 5(b) for each blade. Thus, the RA component distribution can be used as an indication of geometric non-uniformity. Depending on the number of measurement locations, geometric non-uniformity can be classified into blade non-uniformity and casing non-uniformity. If the measurement is performed at one or more locations in the circumferential direction, blade non-uniformity can be analyzed. If the measurement is performed at more than one location in the annulus, casing nonuniformity can be analyzed.

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(a)

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(b)

Fig. 5. The schematic of RA component distribution: (a) Ideal condition; (b) Real condition.

Fig. 6. RA component distribution measured at 8 equally spaced locations of the 1st stage.

Fig. 6 illustrates the RA components distribution of the 1st stage. Eight fast response pressure transducers were equally spaced at 45° in the circumferential direction. The locations from 1 to 8 stand for the places where the measurements were carried out at two different flow rates. A and B represent the maximum RA component value for Φ = 0.54 and Φ = 0.36, respectively. C represents the minimum RA component value. The locations of A, B and C moved along the measured locations at the same rotation speed. This means that specific rotational elements led to the maximum or minimum RA value, and this element is the blade non-uniformity. The element of blade non-uniformity can not yet be determined. However, the existence of blade non-uniformity, which determines the RA component deviation, is verified by Fig. 6. 5.3 Ψ (dimensionless RA component) distribution Dimensionless RA component distributions (Ψ distribution)

for two different flow rates are illustrated in Fig. 7. To investigate the blade non-uniformity, Ψ was measured at one arbitrary location of the 1st stage (in this case, the data was measured at location 5). Fig. 7(a) illustrates the Ψ distribution at a condition far from stall (Φ = 0.54) and Fig. 7(b) at a condition near stall (Φ = 0.36). For both flow rates, even though the shaft speed is different, the distributions of Ψ match well. Especially, the magnitudes of A, B, C and their blade locations are almost conserved. Though the measured location is the same in Fig. 7(a) and (b), the reference blade locations of A and B (blade 4 for A and blade 17 for B) are different. However, the reference blade location of C (blade 45) is almost the same for the different flow rates. The reference blade location and the magnitudes of A, B, C were checked several times for both flow rates. Whenever they were checked, the same result, which was the conservation of the magnitudes of A, B, C and the disparity of the reference locations of A and B, was obtained.

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(a)

(a)

(b)

(b) Fig. 7. Ψ distribution about 1 revolution, which was measured at one arbitrary circumferential location (measured at Location 5): (a) Far from stall condition (Φ = 0.54); (b) Near stall condition (Φ = 0.36).

It is necessary to determine the actual cause for this result in future work. However, the existence of a specific Ψ distribution at every flow rate was obvious, and repeated measurements verified its existence. Thus, a Ψ distribution represents the blade non-uniformity. Additionally, the change of the location of the maximum Ψ (ie. from A to B) does not affect the increase of f shaft near stall because this change of the reference location still occurred during one revolution. The amplitude of Ψ is defined as ∆Ψ and expressed as Eq. (6). ∆Ψ = Ψ max − Ψ min

(6)

From Fig. 7, ∆Ψ at low flow rates is 50% greater than that at high flow rates. The increase of ∆Ψ leads to the increase of f shaft near stall, which will be discussed in the next section. 5.4 ∆Ψ (amplitude of Ψ) distribution To investigate the effect of casing non-uniformity, ∆Ψ was analyzed at 8 circumferential locations for two different flow rates. The result is illustrated in Fig. 8. Despite different rotation speeds, the ∆Ψ distributions matched well. However, the shape of the ∆Ψ distribution is different. At Φ = 0.54 (Fig. 8(a)), ∆Ψ distribution is almost flat along the circumferential

Fig. 8. ∆Ψ distribution about 1 revolution which measured equally spaced 8 circumferential locations: (a) Far from stall (Φ = 0.54), (b) Near stall (Φ = 0.36).

direction. This means that ∆Ψ is almost preserved along the circumferential direction at a position far from stall condition and this tendency is independent of rotation speed. However, the shape of the ∆Ψ distribution along the circumferential direction is sinusoidal at Φ = 0.36 (Fig. 8(b)). This means that ∆Ψ increases and decreases over the course of 1 revolution and there are specific circumferential locations where ∆Ψ varies. For the three different rotation speeds, ∆Ψ is the maximum near 180° of the reference circumferential location and it is the minimum near 45°. For this reason, ∆Ψ distribution represents casing non-uniformity. Frequency analysis of the data measured at the 8 circumferential locations showed that f shaft near the maximum ∆Ψ location (135°~225°) acts to increase f shaft of the whole annulus. The magnitude of ∆Ψ is related to the amplitude of the shaft resolved component and to the amplitude of the circumferential static pressure distribution. For this reason, the increase of f shaft near stall means the increase of the amplitude of the circumferential static pressure and the increasing instability of the pressure field condition. On the other hand, frequency analysis of the data measured near the minimum ∆Ψ location (315°~45°) showed that f shaft is not as high as that of the maximum ∆Ψ location. To sum up, the increase of f shaft near the maximum ∆Ψ is more dominant than the variation of f shaft near the mini-

H.-S. Lim et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1317~1324

(a)

(b) Fig. 9. The relation between ∆Ψ distribution and reference clearance: (a) ∆Ψ distribution at Φ = 0.36, (b) reference clearance.

mum ∆Ψ. As a result, f shaft increased near stall as shown in Fig. 3. When the SNU compressor was operated near the surge line, ∆Ψ distribution formed a sinusoidal pattern over the course of 1 revolution and its amplitude and phase were independent of the rotation speed. The existence of a sinusoidal ∆Ψ distribution that showed no relation with the rotation speed supports the existence of casing non-uniformity. ∆Ψ distribution was compared to the tip clearance and the result is illustrated in Fig. 9. The compressor casing radius was measured about the shaft axis, and the reference clearance size was acquired. Fig. 9(a) is the ∆Ψ distribution for one revolution, as shown in Fig. 8(b), and Fig. 9(b) illustrates the reference clearance distribution. Both ∆Ψ and the reference clearance are maximum near 180°. Also, the location of the minimum ∆Ψ is almost the same as that of the reference clearance. Even though the circumferential location for the distribution of ∆Ψ and reference clearance does not coincide exactly, the pattern of the ∆Ψ distribution is related to the reference clearance. The increase of f shaft is concomitant with the increase of Ψ amplitude, which is related to blade non-uniformity. For this reason, blade non-uniformity directly caused the increase of f shaft . However, ∆Ψ distribution verified that there was a certain location where the amplitude of Ψ increased at a low flow rate and as a result, f shaft grew. If there was no influence of casing non-uniformity on ∆Ψ distribution near stall, f shaft did not increase near stall. As a result, casing nonuniformity practically induces the increase of f shaft .

6. Conclusions In this paper, the dependency of prestall on the geometric feature of the compressor was analyzed and the results can be

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summarized as follows : (1) In the SNU compressor, a prestall phenomenon in which f shaft increases was detected. Instant static pressure was decomposed into pressure signal components. To explain the increase of f shaft at conditions near stall, this research focused on the variation of the RA component among these components. (2) The distribution of RA component represents blade nonuniformity and casing non-uniformity. The blade nonuniformity of the SNU compressor was analyzed by the Ψ distribution, which was measured at one arbitrary circumferential location, and the casing non-uniformity was analyzed by the ∆Ψ distribution, which was measured at 8 equally spaced circumferential locations. (3) Near stall condition, the distribution of ∆Ψ showed a sinusoidal pattern for one revolution period, and the static pressure signal, which was measured near the maximum ∆Ψ, acted to increase f shaft . However, far away from stall condition, no significant ∆Ψ distribution pattern was observed. By signal decomposition, blade non-uniformity was found to be the direct cause of the increase of f shaft near stall. However, in reality, casing non-uniformity induced the increase of f shaft in the SNU compressor. (4) To suggest the factors for blade non-uniformity and casing non-uniformity, a more in-depth verification is necessary. However, it was verified that the prestall in which f shaft is increased is related to the geometric non-uniformity of the compressor. Thus, this prestall phenomenon can be used as a tool to determine the geometric condition of an axial compressor.

Acknowledgment This study is financially supported by KATRA08 _A00133_ki 4 Program of the Aerospace Components Technology Development Project of the Ministry of Knowledge Economy. Also, support from the Institute of Advanced Machinery and Design and the BK21 Program of Seoul National University is gratefully acknowledged.

Nomenclature-----------------------------------------------------------------------Cx f f shaft

Nb Npb Nrev P U

ρ Ф Ψ ∆Ψ

: Axial flow velocity, m/s : Magnitude of the frequency : Magnitude of the shaft frequency : Number of blade : Number of discretization of a blade passage : Number of revolution : Pressure, Pa : Blade midspan velocity, m/s : Density : Flow coefficient (= Cx/ U ) 2 : Pressure coefficient (=(Ps-Pt)/(1/2ρ U )), Dimensionless RA component : Amplitude of Ψ (=Ψmax - Ψmin)

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Subscripts ens i j k s t RA RP

: Ensemble average : Index denoting revolution : Index denoting blade : Index denoting discretization : Static : Total : Revolution aperiodic : Revolution periodic

Overbar ―

: Time average

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distributions in a channel diffuser of centrifugal compressor, J. of Korea Fluid Machinery, 3 (2) (2000) 57-65. [10] E. M. Greitzer, Surge and rotating stall in axial flow Compressors PartⅠ, Ⅱ, J. of Engineering for Power (1976) 190-217. [11] F. K. Moore and E. M. Greitzer, A theory of post-stall transients in axial compression systems partⅠ, J. of Engineering for Gas Turbines and Power, 108 (1986) 68-76. [12] V. H. Garnier, A. H. Epstein and E. M. Greitzer, Rotating waves as a stall inception indication in axial compressors, J. of Turbomachinery, 113 (1991) 290-302. [13] I. J. Day, Stall inception in axial flow compressors, J. of Turbomachinery, 115 (1993) 1-9. [14] J. F. Escuret and V. Garnier, Stall inception measurements in a high-speed multistage compressor, J of Turbomachinery, 118 (1996) 690-696.

Hyung-Soo Lim received a MS in Mechanical engineering from Seoul National University in 2004. He has focused on the research of compressor stability issues including rotating stall inception and stability control. He currently works as a PhD course student in Seoul National University. Shin-Hyoung Kang is a professor of Mechanical and Aerospace Engineering at Seoul National University. He has over 40 years 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 performance by using both CFD and experimental methods. Seung-Jin Song is a professor of Mechanical and Aerospace Engineering at Seoul National University. His current research interests include aerodynamics and fluid-structure interactions in turbomachinery, analysis of propulsion / power generation systems, and related areas of fluid mechanics and renewable energy.