Article 正式发布 Versions 1 Vol 28 (5) : 862-874 2019
Application of Stall Warning Approach with Stall Precursor-Suppressed Casing Treatment on a Two-Stage Compressor 失速预警与先兆抑制型机匣处理结合的两级压气机扩稳控制
: 2019 - 09 - 05
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Abstract & Keywords
Abstract: A stall warning approach based on aero-acoustic theory is studied in this paper. For this stall warning approach, a parameter Rc is defined to measure the periodicity of the blade-passing signal. Signal simulation is used to investigate the mechanism of the stall warning approach. The results suggest that the value of Rc is influenced by the power of the perturbations. The experiments on a two-stage compressor indicate this stall warning approach can generate a warning signal several seconds before the stall. It is demonstrated in this paper that the stall warning approach can detect the distribution and evolution of stall precursors. According to the distribution of the stall precursors, the partial stall precursor-suppressed casing treatment is applied and realized a stabilization of compressor. 在对于压气机稳定性的主动控制研究中,如何在失速前及时有效地提供预警信号一直是备受关注的难题。传统预警方法对于模态波和spike波的检测往往只能提供几毫秒的预警时间。现有的控制手段无法在如此短暂的预警时间内对压气机进行有效的扩稳。在实际的压气机中,叶片信号具有一定的周期性,并且这一周期性会在接近失速边界时显著恶化。基于这一原理,因此本文研究了一种新的失速预警方法,这种方法通过检测压气机叶片信号的周期性变化实现预警。通过信号模拟的结果可以证明,压气机叶片信号的周期性受到流场内扰动能量大小的影响。本文的实验研究在一台两级低速轴流压气机上展开,实验结果表明这种失速预警可以在失速前3.7秒发出预警信号。并且根据在不同测点的预警结果可以分析出压气机内扰动的主要分布位置,并使用局部SPS机匣处理对扰动进行局部控制实现扩稳。
Keywords: axial compressor, stall warning, casing treatment
1. Introduction
Rotating stall and surge are two aerodynamic instabilities in aero-engines which restrict the perfor- mance of the compression system. To ensure that an engine could have a stable performance in a variety of working conditions such as inlet distortions, speed transients, and engine control tolerances, it is common to require the compressor to have about 20% stall margin at design operating point. In some cases, designs should sacrifice some efficiencies to achieve the stall margin requirement. If a reliable control system can enhance the compressor stability efficiently in advance of stall occurrence, the stall margin requirement may be reduced. Active control of compressor instabilities was originally proposed by Epstein et al. [1] in 1989. They advocated a strategy to suppress the onset of stall and surge by controlling the stall inception. Then Ffowcs Williams and Huang [2] first realized active surge suppression on a centrifugal compressor. Since then, plenty of investi- gations were conducted to detect the stall inception using relevant signal processing such as Fourier analysis [3-5] and wavelet techniques [6-8]. These techniques are very useful for analyzing the stall mechanism. Unfortunately, the moment that stall inception can be detected is only several rotor revolutions prior to the full developed rotating stall. It is too difficult for a control system to quickly respond and realize stall margin enhancement for practical. Thus, how to get a longer warning time ahead of rotating stall inception is a problem to be solved.
Inoue et al. [9] found that the pressure signal of passing blades is periodical and this periodicity will collapse near stall boundary. They used a parameter called similarity coefficient to describe the periodicity of the blade-passing signal. This similarity coefficient needs more than 200 rotor revolutions sampling data and thus it is not appropriate for transient condition. To measure the signal periodicity in time, Tahara et al. [10, 11] proposed the auto-correlation coefficient calculated from the pre- ssure signals of two contiguous rotor revolutions of the identical blades and studied the factors that had influen- ces on the value of the coefficient. The results show that this method has potential to generate a stall warning signal in advance of stall inception. Dhingra et al. [12,13] developed a stochastic model for the auto-correlation coefficient. They defined the auto-correlation coefficient dropping below a given threshold as an “event” and found time between events decreases as flow rate close to the stall boundary. Young et al. [14] did some further in- vestigations of the auto-correlation coefficient and found the value of the auto-correlation coefficient was strongly affected by both tip-clearance size and eccentricity.
a0Amplitude of blade-passing signalTsTime of one shaft period/s
aiAmplitude of perturbation signalGreek symbols
F (Rcth )Value of cumulative distribution functionFlow coefficient
fiPerturbation frequency/HzPressure rise coefficient
fsShaft frequency/HzSubscripts
P0Blade-passing signalNNumber of samples in one shaft-period
PiPerturbation signalsShaft
P (∙)ProbabilitythThreshold
A section of pressure signalSuperscript
RcA parameter to evaluate the periodicity of the signalnNumber of samples in one calculating window
RcthThreshold of Rc
All these researches above utilized the deterioration of blade-passing periodicity near stall but did not have enough theoretical analyzing for the mechanism behind this phenomenon. Li et al. [15] considered the collapse of periodicity could reflect the evolution of stall precursor. From this perspective, they explained the mechanism of this phenomenon by using aero-acoustic theory and vortex theory. Li considered that the evolution of stall precursor was always accompanied by complex vortex- like flow separation and vortex shedding on the blade. Those vortex flow which could influence the blade circulation caused the collapse of periodicity. Based on this theory, Dong et al. [16] applied this stall warning approach on a kind of stall precursor-suppressed (SPS) casing treatment to realize an online control. The mechanism of SPS casing treatment is to affect the evolution of the stall precursors in order to obtain stall margin improvement [17-19], and according to experi- mental results, this SPS casing treatment can enhance the compressor stall margin by 8%–18% [17, 18, 20]. The demonstration on a single-stage low-speed compressor showed that this online control method could effectively enlarge the working range of compressor [16].
It should be noticed that the study of this stall warning approach still remains on the single-stage compressor. When it comes to multi-stage compressor, flow structure becomes much more complicated, so in this paper we study how this stall warning technique performs in a multi-stage compressor and investigate the influence of transducer position on this technique. The paper is structured as below: firstly, the basic idea of the stall warning approach is introduced, and a series of sinu- soidal signals are chosen to simulate the blade signals and the stall warning approach is used to dispose these signals to study how different perturbations influence the results of this approach and to investigate the mechanism of the approach. Then this technique is implemented on a two-stage compressor to study the feature of the warning time. Next, sensors are installed on the different positions of the compressor to study the distribution and evolution of stall perturbations in the compressor. Then SPS casing treatment is used to realize a local control of precursor and enlarge the stable working range of the compressor.
2. Experimental Facilities
2.1   The two-stage compressor
The experiments were performed on a two-stage low- speed axial compressor with inlet guide vane. The two- stage compressor shown in Fig. 1 contains an inlet duct, an inlet guide vane (IGV), two rotor-stator stages, an outlet duct and a throttle comprising of a fixed cone and movable annular sleeve. The rotating speed of this com- pressor can be varied from 0 to 3000 r/min. The basic design parameters of the compressor are listed in Table 1.
2.2   Measurement system
In the experiments, the measurement system contains steady characteristic measurement and dynamic pressure measurement. The steady measurement consists of total pressure sensors in the inlet and outlet duct and the static pressure sensors placed on the casing wall of the inlet and outlet duct to get the characteristic parameters of the compressor (Fig. 1). High frequency Kulite pressure sensors are mounted on the casing and flushed with the inner wall, the measurements are adopted at the cross sections of leading edge of IGV, the first stage rotor and the second stage rotor respectively (as shown in Fig. 2) to capture the unsteady pressure signals of passing blades.

Fig. 1 Configuration of the two-stage compressor
Table 1 Design Parameters of the two-stage compressor
Geometrical parameters
IGV1st Rotor1st Stator2nd Rotor2nd Stator
Blade number3847454745
Established angle/°060106010
External diameter/mm600600600600600
Span-chord ratio1.691.691.691.691.69
Hub-tip ratio0.
Aerodynamic parameter
Design rotating speed3000 r/minMass flow6.8 kg·s-1
Total pressure ratio1.056Pressure rise4900 Pa

Fig. 2 Configuration of the transducers
The sampling rate of the transducers is 100 kHz. Considering the blade passing frequency (BPF) is approximately 2.4 kHz. This sampling rate can meet the requirement for unsteady pressure measurement. In the experiment, the phase-locking technique is also applied to help compare the blade passing signal of two contiguous revolutions. This technique uses a Hall sensor fixed on the shaft to give a pulse signal at a certain circumferential position in each revolution. The configuration of these transducers is displayed in Fig. 2.
3. Stall Warning Approach
In a compressor, it is clear that the blade-passing signals of two neighboring shaft periods are similar, and this similarity will degrade with the reducing of stall margin. Fig. 3 displays the time-pressure signals of the two-stage compressor sampled by the sensor located on the casing in front of the blades. The red and black curves are the signals of the current and previous shaft period, respectively. At the design point, the current signal is almost accordant with the signal one shaft period before. At the near stall point, because the flow separation and vortex shedding occur more frequently, the pressure signals of two contiguous revolutions are quite different from each other [15].

Fig. 3 Pressure signal of two neighboring shaft period
A parameter called Rc is used to evaluate the periodicity of the pressure signal, which can be calculated via the correlation measure as follows:
where Rc(j) is the value of Rc at present sample point j. The calculation process of the correlation measure is illustrated in Fig. 4. Vector is the blade-passing signal. The components of this vector can be written as, where is the discrete pressure signal collected by sensor. N is the number of samples in one shaft revolution and n equals to the number of samples in a calculating window. In this paper, n is set as the number of 3 blade samples. The reason for choosing 3 blades will be explained in the next section. By its mathematical definition, the range of Rc is from −1 to 1, and the closer this value is to one, the better the signal periodicity is.

Fig. 4 Calculation process of correlation measure
3.1   Signal simulation
According to the Fourier transform, a complicated signal can be represented by the sum of sinusoidal signals with different frequencies, so we select sinusoidal signals with some certain frequencies to simulate the blade signals of the two-stage compressor in order to investigate how different perturbations influence the result of correlation measure and explain the mechanism of this stall warning approach.
As mentioned above, the rotation frequency of the shaft (fs ) is 50 Hz, and the blade number of the first rotor is 47. Thus, the blade passing frequency (BPF) is 2350 Hz (47fs ). Ignoring the blade-to-blade difference, we describe the steady blade signal as:
In axial flow compressors, two typical low frequency perturbations appear before the stall occurs: “modal wave” and “spike”. The “modal wave” rotates at a relatively low speed below 50% of rotor speed (fs ), and “spike” propagates more quickly at speeds between 70% and 90% of the rotor speed (fs ). According to the rotating speed of the “modal wave” and “spike”, 0.5fs (25 Hz) and 0.9fs (45 Hz) signals are chosen to represent the low frequency perturbations in the compressor. Due to the interaction effect between two adjacent blade rows, there are some perturbations whose frequencies are close to multiples of the BPF, so the signals with frequencies of 94.5fs (4725 Hz) and 94.9fs (4745 Hz) are selected to stand for the high frequency perturbations in the compressor. Here, four signals whose frequencies are 0.5fs (25 Hz), 0.9fs (45 Hz), 94.5fs (4725 Hz) and 94.9fs (4745 Hz) are added into the steady blade signal to represent four different perturbations. The expressions of these four signals are
Compared with the steady blade-passing signal, the power of perturbations in a compressor is rather small, so the amplitude ai is set equal to 0.1a0 and 0.3a0 for each perturbation with different frequency.
Fig. 5 depicts the Rc value of the steady blade-passing signal. In Fig. 5, the value of Rc keeps at 1 from begin- ning to the end, which indicates a perfect periodicity of the blade-passing signal at the design point of the com- pressor. Figs. 6-9 depict the correlation measure results of the signal P0 with different perturbations P1 , P2 , P3 and P4 . The mean value of Rc for signals with each perturb- bation with different amplitude is detailed in Table 2.
It can be identified in Table 2 that, when the amplitude is 0.1a0 , the mean value of Rc for signals with different

Fig. 5Rc of blade-passing signal
Table 2 Mean value of Rc for signals with different perturbations
signalsai= 0.1a0ai= 0.3a0
perturbation is 0.980, 0.998, 0.980 and 0.998, and if the amplitude increases to 0.3a0 , it decreases to 0.841, 0.984, 0.835 and 0.984. This result indicates that for signals with a certain frequency perturbation if the amplitude is amplified, the mean value of Rc will decrease with verifying degrees.
As evident from Table 2, the correlation measure results of signal P0+P2 and P0+P4 are the same, and the mean values of Rc for signal P0+P1 and P0+P3 are also highly identical. It should be noticed that the frequency differences between P1 , P3 and P2 , P4 are both 4700 Hz. This suggests that two perturbations between which the

Fig. 6Rc of blade-passing signal with 25 Hz perturbation

Fig. 7Rc of blade-passing signal with 45 Hz perturbation

Fig. 8Rc of blade-passing signal with 4725 Hz perturbation

Fig. 9Rc of blade-passing signal with 4745 Hz perturbation
difference of frequency is a certain value may have a similar influence on the mean value of Rc. For a certain perturbation Pi , its frequency fi can be expressed as fi= (xi+yi )fs , xi ∈N, yi ∈[0,1). The correlation measure compares the blade-passing signals of two adjacent revolutions. The signal P0+Pi at present and one revolution before can be written as
Comparing two equations shows that xi has no influence to the difference between two signals, which indicates if the difference of frequency between two perturbations is equal to the integral multiple of shaft frequency this two perturbations will have an identical effect on the mean value of Rc. According to the periodicity property of sinusoidal signals, perturbation whose yi is close to 0 or 1 brings fewer differences to signals of two adjacent revolutions than perturbation of which the value of yi is near 0.5 does. This explains why the mean value of Rc for P0+P2 and P0+P4 is obviously higher than P0+P1 and P0+P3 .
Although the mean value of Rc for P0+P1 and P0+P3 is almost equal. The range of Rc in Fig. 6 is significantly larger than the Rc in Fig. 8. This difference in Rc range can be attributed to the short length of the calculating window. As can be seen in the Fig. 10, when the scale of calculating window is rather smaller than the perturb- bation wavelength, the influence that perturbation brings to the signal changes distinctly with time. In this figure, the Rc at j is lower than the Rc at time k. If the calculating window is extended from 3 blade pitches to 47 blade pitches (one revolution), the range of Rc for P0+P1 and P0+P3 is almost identical (Fig. 11). According to reference [15], in a compressor working at near stall point, the perturbations mainly consist of flow separation and vortex shedding on the blade. The scale of these flow phenomenon usually covers two to three blade pitches, so a calculating window covering three blade pitches is an appropriate choice. Hence, the distribution of Rc can be used to distinguish the low and high frequency perturb- bations for the range of Rc for signals with low frequency perturbations is large whereas for signals with high frequency perturbations it is small.

Fig. 10 Influence of perturbation at different time

Fig. 11Rc of signals with 25 Hz perturbation and 4725 Hz perturbation (ai= 0.3a0 )
Thus, the mechanism of this stall warning approach can be explained as below. Considering that the unstea- diness of flow separation and vortex shedding, the frequ- ency components of the perturbations are complicated and when the operating point of a compressor is slowly driven to stall boundary, the power of the perturbations will grow and the value of Rc will decrease.
3.2   Experimental validation
Based on the results of the signal simulation, we apply this stall warning approach on the two-stage compressor to validate whether this approach can provide sufficient warning time before the stall. Fig. 12 gives the pressure rise characteristics of the two-stage compressor at 100% design speed. The abscissa is flow coefficient (ϕ) and the ordinate represents for pressure rise coefficient (ψ). In this figure, three points A, B, and C represent three different operation points from a large flow rate to near stall flow rate. The time traces of Rc at three points are illustrated in Fig. 13. The time-pressure data used here is collected from the leading edge of the first rotor. When the flow coefficient is 0.26, the mean value of Rc is 0.827. Then the work point moves to B where the flow coefficient is 0.24 and the mean value of Rc becomes 0.759. With further throttling, the mean value of Rc drops to 0.645 at the flow coefficient of 0.22. According to Ref. [15], the cumulative distribution function can present the relationship between Rc and the stall margin more clearly. The cumulative distribution function of Rc can be expressed as
where Rcth is a given threshold of Rc and P(·) is the probability. It describes the probability of Rc when it is lower than or equal to Rcth . For instance, if a given sample of Rc spends 20% of its time below 0.9 (a setting threshold), the corresponding value of its distribution function F(0.9) would equal to 0.2. The distribution func- tion of Rc is displayed in Fig. 14. Each curve corresponds to a different flow coefficient of the compressor. In the figure, the distribution curves move left with the reduc- tion of flow coefficient, which indicates a declining trend of Rc with the reduction of stall margin. If Rcth is set at 0.6, F(0.6) at three operation points are 0.00675, 0.07231 and 0.3884. The change of F(Rcth ) with operation points has the potential to be used as a criterion of stall warning.

Fig. 12 Pressure rise characteristics of 2-stage compressor
Time pressure traces of Rc and F(Rcth ) during a continuing throttling process are given in Fig. 15. At the beginning of the throttling process, Rc stays at a relatively large level with some individual drops. As stall boundary comes closer, more and more sharp drops of Rc can be observed. The Rcth is set at 0.6 here. As shown in Fig. 15, the value of F(Rcth ) increases almost monoto- nically with the decreasing of stall margin. If a warning limit is set as 0.15, then this stall warning approach can generate a warning signal when the remain of stall margin is 5.5%. The time gap between generating a warning signal and stall point is 3.7 s (185 revolutions), which can provide sufficient time for modern devices to realize stability control for a compressor.

Fig. 13 Rc at different operation points
From the correlation measure results of signals during steady working points (Fig. 13) and throttling process (Fig. 15), it can be observed that at near stall point, the value of Rc is significantly lower and the range of Rc is relatively large. According to the results of signal simu- lation before, some low frequency perturbations may exist and the power of the low frequency perturbations are amplified near stall boundary. To verify this, spatial Fourier analysis of signals from eight sensors distributed on the first stage is applied and Fig. 16 depicts the time-resolved PSD results of the signals. The frequency here is normalized by the rotor speed and an evident low frequency perturbation can be identified in the figure. The perturbation emerges and grows several seconds before the stall. It appears that this perturbation may be responsible for the drop value of Rc.

Fig. 14 Distribution of Rc at different operation points

Fig. 15 Experimental results on two-stage compressor

Fig. 16 PSD results of stall evolution in the two-stage compressor
4. Application with SPS Casing Treatment
In most cases, the distribution of perturbations in a multistage compressor is not uniform. Since the Rc can reflect the intensity of perturbations near the sensor position, this stall warning approach may be used to analyze the distribution of perturbations by using several sensors located at the different position of the compressor. Then a local control of perturbations can be utilized to realize stabilization of the compressor. This research uses the stall precursor-suppressed (SPS) casing treatment as a perturbations control device.
4.1   SPS casing treatment
The scheme of SPS casing treatment is shown in Fig. 17, it is installed on the upstream side of the rotor blade with about one-half overlapped area on the blade tip region. The perforated ratio of this SPS casing treatment can be adjusted from 0 to 12%, and there is an annular back- chamber in 50 mm height, 100 mm length. This figure also briefly shows the mechanism of SPS casing treat- ment: the tip-region flow comes in and out the back- chamber generating some vortexes shedding at the slot edge, and these vortexes shedding can interact with the perturbation pressure waves in the main flow, and this interaction can be recognized as a soft boundary condition on this system. The detailed information of SPS casing treatment can be founded in Ref. [17].

Fig. 17 SPS casing treatment schematic and installing status
4.2   Results from different axial position
Firstly, the distribution of the perturbations at the different stage is analyzed. Fig. 18 shows the variance of Rc during the throttling process. The pressure data used in the Fig. 18 is collected from sensors located at the leading edge of IGV, the first stage rotor, and the second stage rotor respectively. A downtrend of Rc with the reduction of stall margin can be found at all three axial locations. This result indicates that regardless of the signal is collected from what stage of this compressor, the stall warning approach is effective and can provide a warning signal seconds before the stall occurs. The Rc in Fig. 18(a) and Fig. 18(c) is higher with a slight decline trend, whereas the Rc in Fig. 18(b) shows a noticeable decrease range near stall. It suggests that the intensity of pressure perturbation at the first stage is the most significant of all three axial locations. To evidence this, Fourier analysis is used here on the signals of the first stage and the second stage and the frequency characteristics of the signals are represented in Fig. 19. In this figure, some low frequency perturbations can be observed in both stages, and the amplitude of perturbations is much higher in the first stage than that in the second stage. Fig. 20 displays the time-resolved signals of both two stages during the stall process. The normalized no-dimensional static pressure signals of 16 channels are shown in the same time axis.

Fig. 18 Rc at different position of the compressor
Some oblique lines in this figure show the revolution of the rotating stall. It is clear that the stall onset can be firstly found in the first stage, and the stall signals detected in the second stage are from the first stage. All these results mean that the perturbations are firstly generated at the first stage and then propagated to the second stage. As to the sensor located at the leading edge of IGV, it is far from the rotor and the blade-passing signal decays rapidly with the increase of distance between sensor and rotor [16]. As a result, the perturb- bations in the blade-passing signal cannot have a significant influence on the signal before IGV, so the time-pressure signal here maintains a good periodicity before stall occurs.
According to the results above, the power of perturbations at the first stage is larger than the second stage, so if the SPS casing treatment is applied on the first stage, it will have a better effect on the compressor stability than on the second stage.
As evident in Fig. 21, when SPS casing treatment is installed at the first stage, the improvement of stall margin is noticeable and almost identical with the case that SPS casing treatment is installed on both stages.

Fig. 19 Frequency characteristics of stall evolution in the first stage and the second stage

Fig. 20 Dynamic static pressure signals of stall evolution

Fig. 21 Compressor performance lines of different casing conditions
However, if SPS casing treatment is only engaged on the second stage, it will not make a difference to stall margin compared with the solid casing. This is because the stall precursors emerged at first stage first, the SPS casing treatment at the first stage can suppress the growth of precursors and the SPS casing treatment at the second stage cannot influence the precursors at far field. The effects of stability enhancement of SPS casing treatment applied on the different stage are in good agreement with the distribution of the perturbations, which means the local control of perturbations is feasible in the multistage compressor.
4.3 Results from different circumferential positions
To investigate the circumferential distribution of per- turbbations in the compressor, we use 8 sensors mounted uniformly around the casing at the leading-edge of IGV (Fig. 2). Rc at different circumferential positions is presented in Fig. 22. Sensors 1 to 4 show the degradation

Fig. 22 Rc at different circumferential positions
of Rc at near stall point where Rc of sensors 5 to 8 still keep a high level until the stall occurs. To see the variation of Rc distribution more clearly, F(Rcth ) is calculated (Fig. 23). The value of Rcth is set as 0.75. Indices of sensor 1 to 4 increase several seconds before stall while indices of sensors 5 to 8 stay near zero and just rise after stall.
The results of the correlation measure at different circumferential positions indicate that the perturbations mainly exist near the location of sensors 1 to 4. It is mentioned that the perturbations are generated at the first stage. Based on this distribution of perturbations, part- circumference SPS casing treatment was applied on the first stage to verify the effect of this local control of the perturbations. The results of partial SPS casing treatment are provided in Fig. 24. The operating range of com- pressor with lower half SPS casing treatment is similar to the compressor with whole casing treatment and it seems that only installing upper half SPS casing treatment will not bring obvious benefit to the compressor stability.

Fig. 23 F (Rc) at different circumferential positions

Fig. 24 Compressor performance lines of different partial casing conditions
It can be concluded that in this two-stage compressor, perturbations mainly exist at the lower half of the first stage (area near the sensors 1 to 4) and this distribution of perturbations can be detected by the correlation measure of the pressure signal. Lower half SPS casing treatment can locally suppress the perturbations and extend the stable operating range of the compressor.
5. Conclusion
The main purpose of this study is to validate the effect of an acoustic-theory based stall warning approach and use this approach to detect the distribution of the perturbations in the compressor. Then based on the distribution of the perturbations, local control can be utilized with partial SPS casing treatment to extend the stable range of compressor. According to the results of signal simulation and experiments on the two-stage compressor, conclusions can be drawn as follows:
The degree of Rc degradation can reflect the power of perturbations such as flow separation and vortex shed- ding in the compressor. When the stall boundary is close, the growth of perturbations power will cause a decrease of Rc. This feature can be used for stall warning to provide sufficient time for stability control.
Considering the spatial scale of flow separation and vortex shedding on blades, a length of three blades is a proper choice for the calculating window. This length of the calculating window can also help distinguish high frequency and low frequency perturbations.
In the two-stage compressor, this stall warning app- roach can be applied to both stages and provides a warning signal seconds before the stall. It can also be used to detect the distribution of the perturbations in the compressor. Thus this stall warning approach can co- operate with other control devices such as casing treat- ment and air injection to realize a local control of com- pressor which can enhance the stability with lower cost.
Partial SPS casing treatment can be applied to the position where the power of perturbations is the most significant to suppress the perturbations regionally and enlarge the range of compressor effectively.
The research presented here is supported by China Academy of Launch vehicle Technology (No.51606223) and National Natural Science Foundation of China (Nos. 11661141020, 51576008, 51822601 and 51790514).
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Article and author information
Springer Link
XU Ruize
SUN Dakun
LI Fanyu
SUN Xiaofeng
LI Jia
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Published: Sept. 5, 2019 (Versions1
Journal of Thermal Science