Evolution of the flow instabilities in an axial compressor rotor with large tip clearance: An experimental and URANS study

Aerospace Science and Technology 96 (2020) 105557

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Evolution of the flow instabilities in an axial compressor rotor with large tip clearance: An experimental and URANS study Hao Wang a,∗ , Yadong Wu b,∗ , Yangang Wang a , Shuanghou Deng a a b

School of Power and Energy, Northwestern Polytechnical University, Xi’an, Shanxi 710072, People’s Republic of China School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 24 April 2019 Received in revised form 9 August 2019 Accepted 11 November 2019 Available online 22 November 2019

a b s t r a c t With modern engine designs trending toward smaller cores to increase propulsive efficiency, the gapto-span ratio in compressors is expected to increase, especially for the rear stages. Detailed knowledge of stronger tip clearance flow and its impact on compressor instability under large clearance condition become increasingly important. The present study is aiming for illuminating the instability evolution and the underlying flow physics in a large-tip-gap compressor, with the use of casing-mounted pressure transducers to acquire the unsteady nature of tip flow, and full-annulus URANS to obtain the threedimensional flow details related to instability generation. Results show that flow instability evolution of the compressor along speed-line experiences three stages: stable state, rotating instability, and rotating stall. Two critical behaviors of tip leakage vortex (TLV) are found to relate to the transition of instability pattern. As TLV moves to the adjacent blade trailing edge, it starts to oscillate under the interaction with the adjacent blade, leading to a short-length rotating disturbance, i.e. rotating instability. At nearstall condition, as the interface of TLV and main-flow exceeds the passage inlet plane, forward spillage occurs along with radial vortexes periodically shed from blade leading edge. The periodically generation, movement and decay of leading edge vortexes (LEVs) constitute an orderly propagating disturbance rather than evolve into a stall cell. However, as the compressor is further throttled, the orderly propagation of LEVs collapses due to their scattering, resulting in the generation of stall cells with local stronger blockage and higher entropy. © 2019 Elsevier Masson SAS. All rights reserved.

1. Introduction The low-flow-rate boundary of the operating range of axial compressors is strictly limited by aerodynamic instabilities, typically known as rotating stall and surge. The former is featured by a drastic reduction in pressure rise, while the latter by a violent oscillation of flow. It is generally known that rotating stall precedes complete disruption of compressor operation in the surge cycles. A great deal of research work has been devoted to obtain detailed knowledge on the flow physics of rotating stall cells, stall initiation process and a broad scope of pre-stall activities representing various routes to stalled flows. Understanding how pre-stall instabilities develop in the rotor passage and grow into a full-scale stall cell is important for exploiting theory to predict it and developing reliable stall warning technique.

*

Corresponding authors. E-mail addresses: [email protected] (H. Wang), [email protected] (Y. Wu). https://doi.org/10.1016/j.ast.2019.105557 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.

A significant amount of researches have revealed that the precursors to stall, also named as stall inception, are generally categorized into two types in compressors: the modal-type and the spike-type [1–3]. The modal type stall inception is through the growth of small-amplitude long-scale (of compressor circumference) disturbances, which can be detected 10 to even 100 rotor revolutions before stall onset [4,5]. The spike type stall inception is through transient disturbances with much shorter length (several blade pitches) and large amplitude, which transits from initial disturbance to fully developed stall cell within only three to four revolutions [6,7]. Further stepping back from the actual stalling process, pre-stall flow disturbances appear as the compressor is throttled towards stall. In the last two decades, researches on pre-stall activities have been mostly divided into tip flow unsteadiness [8] and stall warning [9]. Bergner [10] and Biela et al. [11] investigated the short-length-scale disturbance in a transonic compressor through unsteady pressure measurements. They observed unsteadiness of the pressure field in the rotor tip region at near stall condition, which was demonstrated to be caused by the oscillation of the

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Nomenclature Cp Dt f P Pt Q Ut

ρ ϕ ψ θi

γ2 ϕˆ ω

Pressure coefficient Rotor tip diameter Frequency Pressure Total pressure rise Volume flow rate Rotor tip velocity Air density Flow coefficient Total pressure coefficient Circumferential position Coherence function Phase angel of cross spectrum Angular frequency

leakage vortex. Hah et al. [12] conducted both casing unsteady pressure measurements and full-annulus large eddy simulations on a transonic rotor to investigate the tip clearance flow instability. They found that the movement of a instability vortex induced a rotating flow disturbance and contributed to the unsteadiness of tip clearance flow. With respect to the stall warning technique, the detection of disturbances in the tip flow field has been utilized for early stall warning as stall is approached, such as the work by Dhingra et al. [13]. They measured the repeatability of the blade passing pressure signature using a correlation function and found that as stall was approached this correlation function dropped. Liu et al. [14] found that the repeatability of blade passing signature ramped down rapidly due to the occurrence of unsteadiness in the rotor tip region, as the flow rate of compressor was reduced towards the stall point. By further applying a similar correlation technique as Dhingra, Christensen et al. [15] successfully developed a real engine control system, which was capable of warning the imminent stall in time for the engine operation to be adjusted away from danger. Contrary to the aforementioned findings, through the investigation on the effect of non-axisymmetric tip clearance, Young [16] pointed out the irregularity of blade passing signature rose in part of the annulus where the tip clearance was largest, while it decayed in the part with tight clearance. Their work showed the significant effect of tip clearance size and eccentricity on the feature of pre-stall flow disturbances, and questioned the effectiveness of the stall warning technique based on this approach to implement in an aero-engine compressor where concentricity and tip clearance change continually during the flight cycle and over the life of the compressor. Generally, compressors are designed and anticipated to run with nominal tip clearance size, however during actual engine operation tip clearance size has dynamic feature, which can increase under some conditions, such as rotor eccentricity, blade erosion and different thermal expansion between rotor and casing. Previous researches have revealed that increased rotor tip clearance results in a growth of the blockage associated with the recirculating tip leakage flow, which is a significant contributor to overall compressor loss [17–19]. As a result, the overall pressure rise capability of a compressor generally decreases with increased rotor tip clearance. With respects to the compressor flow instabilities, a rather particular pre-stall flow phenomenon has been widely observed by researchers within the compressor with large tip gap, known as “Rotating Instability” (RI). Though some controversy still remains on the subject of rotating instability regarding its termination and definition [20], it is typically identified by the broadband spectral hump arising at approximately half of the blade passing frequency (BPF). Marz et al. [21] investigated the rotating instabil-

a RMS SS TLV LEV RI RS IGV PT BPF NI PE NS SPL

Angular velocity Root mean square Stable State Tip leakage vortex Leading-edge vortex Rotating instability Rotating stall Inlet guide vane Pressure transducer Blade passing frequency Near instability inception Peak efficiency Near stall Sound pressure level

ity in a low speed compressor with experimental and numerical methods. Their results revealed that the movement of a radial vortex near blade leading edge plane was the cause of instability at near stall condition. Mailach et al. [22] conducted experiments on a four-stage compressor, with fast response pressure sensors installed both on the casing and rotor blades. They suggested that the periodic fluctuation of the tip clearance vortices and their interactions with the flow at the adjacent blade was responsible for the generation of a propagating flow disturbances with high mode orders, i.e. rotating instability. Through the studies on a lowpressure rise compressor, Inoue et al. [23] and Yamada et al. [24] observed short wavelength disturbance propagating circumferentially at near stall condition, which resulted in broadband excitation at about 1/4 BPF in pressure spectrum. They stated that this phenomenon was similar to rotating instability, and found that a tornado-like vortex was the source of rotating flow disturbance. Recently, Erk and Geist [25] studied the rotating instability in a low speed axial compressor and its potential as a stall indicator. They captured the multi-peak feature of rotating instability and attributed it to the leading edge radial vortex with varying number. The aforementioned works have gained some valuable understanding on flow physics of stalling mechanisms and pre-stall activities in compressors. However, various complex flow structures in the rotor tip region are strongly interdependent, leading to a very complex chain of cause and effect on compressor aerodynamic instabilities that is still part of ongoing research. While most of the previous researches primarily focused on the pre-stall activities within the narrow operating condition near the stall boundary, the pre-stall disturbance in a compressor rotor with large tip clearance may extend to a wider flow range far before the stall point. Thus, the current work attempts to illuminate the evolution characteristics of flow instabilities and uncovers the underlying flow physics over the whole flow range for a compressor with large tip gap. Detailed time-resolved pressure measurements by applying casing-mounted fast-response transducers have been carried out to analyze the transient flow events through time traces and frequency spectral. With the use of ensemble average and root-mean-square technique, the development of rotor tip flow and associated unsteadiness have been obtained. Also, a full-annulus URANS simulations have been conducted to clarify the details of the unsteady flow behavior during the instability evolution. 2. Test compressor and experimental setup The experimental investigations were conducted on a low speed single-stage axial compressor rig. Table 1 provides the pivotal design parameters of the compressor, meanwhile a schematic view of

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Fig. 1. Schematic of the compressor test rig.

Fig. 2. Setup schematic of time-resolved pressure measurements. Table 1 Key design parameters of the compressor. Parameters

Value

Duct diameter (mm) Hub-to-tip ratio Design Speed (rpm) Design mass flow rate (kg/s) IGV number Rotor blade number Rotor aspect ratio Rotor solidity Rotor tip clearance (% of span) Rotor tip clearance (% of blade chord at tip) Rotor tip velocity (m/s)

600 0.7 3000 4.9 13 21 1.41 1.598 2.2% 3.1% 93.62

the measuring setup and related instruments are shown in Fig. 1. The test bed is an open-flow wind tunnel with a bell-mouth at the inlet to provide evenly-distributed inflow and a throttling valve at the outlet to regulate the flow. The compressor rotor is driven by a motor installed in the hub. The speed of the motor-controlled shaft is 3000 rpm and the power is 20 kW. The rotor contains 21 NACA-65-series blades with a hub-to-tip ratio of 0.7. The chord length and staggered angle of the blade midspan profile are 60 mm and 35◦ respectively. The inlet guide vane (IGV) row consists of 13 blades, and the axial distance between the rotor and IGV at midspan is approximately 110% of rotor blade chord. The designed mass flow is 4.9 kg/s and the rotational speed is 3000 rpm. The compressor rotor is set with a relatively large tip gap configuration, 2.2% of blade height and 3.1% of blade chord at tip. The aerodynamic performance data were measured for design speed line by varying the throttle area downstream of the compressor. Near the duct inlet the total pressure and total temperature were measured by pneumatic probes, together with the inlet static pressure obtained by 8 circumferentially distributed pressure

taps imposed on the casing wall. The outflow condition of the rotor blade was measured by a five-hole probe traversing in the radial direction downstream of rotor. The time-resolved pressure measurements presented herein were collected using a chordwise array implementing 11 flushmounted fast-response pressure transducers (PT1-PT11, Kulite XCQ-093), as depicted in Fig. 2. Since the axial range of transducers installation was limited by the block of the flange closely upstream the rotor, the sensor array covered the distance from rotor leading edge to 0.25 axial chord length downstream the rotor. Additionally, an extra pressure transducer PT0 was positioned at the leading edge plane to verify the circumference propagating feature by correlating data with PT1. A NI PXI multichannel data acquisition system was used to record the casing unsteady pressure signals of 12 transducers synchronously. The recording lasted 20 s with a sampling frequency of 84 kHz. With a blade passing frequency of 1.05 kHz at design rotating speed, a resolution of 80 points per blade passage was achieved. 3. Numerical methodology Numerical simulations were carried out by the commercial CFD code Numeca FINE/TURBO, where the cell-centered control volume approach was used to compute 3-D Reynolds-averaged Navier-Stokes (RANS) equations. One equation turbulence model of Spalart-Allmaras was selected to compute the turbulent viscosity. Second-order upwind scheme was used to discretize the inviscid flux, and central differencing was used for the viscous terms. Steady Navier-Stokes equations were handled by a time-marching method using an explicit fourth-order Runge-Kutta procedure. Local time stepping, implicit residual smoothing and multigrid techniques were employed to speed up the convergence rate. Implicit dual-time stepping approach was used to perform unsteady sim-

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Fig. 3. Full-annulus calculated domain and rotor mesh details.

ulations, and every instantaneous flow solution was considered as a “pseudo-steady” problem, in which an explicit fourth-order Runge-Kutta scheme with local time step was performed. During the solving process, 64 physical time steps per blade passage and 60 inner iterations per time step were adopted when approaching convergence. After convergence, the solution kept on proceeding to extract data with halving both the outer and inner time steps, i.e. 32 physical time steps t ∗ per passage and 30 inner iterations. Full-annulus compressor rotor was modeled to precisely capture the circumferential propagating flow structures. The inlet guide vanes were removed, and exit flow angel of the IGV was given as the boundary condition of the rotor inlet. Structured multi-block meshes for the rotor passage were generated with Autogrid V5 using typical O4H topology for mainstream domain and H&O mesh for tip clearance region. The size of the first cell on solid surface was set to insure normalized wall distance y+ below 3. The sensitivity of grid dimension was evaluated based on 4 mesh solutions with different cell numbers. The chosen grid number of the single passage was 925,933, which consisted of 81 points in the spanwise direction including 25 points in the tip gap region, 121 points in the streamwise direction and 65 points in the pitchwise direction. The single passage was repeated to obtain the full annulus with a total grid number of approximately 19 × 106 . Fig. 3 represents a schematic view of the full annulus calculated domain and grid details of the rotor blades. The computational domain extended 1.5 duct radii upstream and downstream of the rotor blade row. Uniform total pressure, total temperature and spanwise distribution of flow angle according to the outflow angle of the IGV were used to determine the inlet conditions. And the turbulent viscosity of 1e−4 m2 /s was specified at the inlet boundary. Based on the measured data, the average static pressure at the exit boundary was given. The other dependent variables at the exit were deduced from the internal field, and the pressure distribution was transformed to ensure that the calculated average pressure was the given pressure. For all blade surfaces and solid walls, non-sliding and adiabatic boundaries were adopted. For steady-state simulation, the convergence criterion required that the residual be reduced to less than 10−4 and assured the monitoring flow rate, pressure and other related parameters remained unchanged. For unsteady simulations before stall, the convergence was verified by periodic fluctuation of pressure signals of monitor points and constant flow rate. For the unsteady simulations at stall condition, stabilized time-average of mass flow and fluctuating pressure signals were seen as the convergence of the solution. To achieve a converged unsteady simulation, the calculations need to proceed for almost 10 revolutions. Unsteady simulations have been performed at different operating conditions

with a small flow rate step to detect the onset of flow instabilities. Also in this way the unsteady results of one operating point could be set as the initial condition of the next smaller-flow-rate point, which was found to be more efficient to converge. Series of pressure monitoring point has been imposed on the rotor casing during the unsteady calculations. All the data process and results analysis were based on the monitored data after the convergence. 4. Results 4.1. Performance and flow instability characteristics The total pressure rise characteristic of the compressor has been captured at design rotating speed (3000 rpm) from large flow rate condition (throttle widely opening) to stall boundary, see Fig. 4. The total pressure coefficient ψ and flow coefficient ϕ are defined as ϕ = 4Q /π D t2 U t and ψ = 2P t /ρ U t2 respectively. Experimental results (black circle) are compared with steady simulations and unsteady simulations. Firstly, it can be observed from the figure that the steady results agree with the measured ones in the largeflow-rate range. As the compressor throttled, the curve of steady results begin to deviate from the experimental one from the operating condition ϕ = 0.168. After this condition, only the unsteady results can match the measured trend, which indicate that highly unsteady flow feature starts to become dominating in the rotor flow field. Indeed, both the measured pressure and URANS data have shown that the operating condition ϕ = 0.168 is the onset point of rotating instability, and that will be discussed detailedly in the following part. Additionally, in Fig. 4, the initial operating points of rotating instability and rotating stall are marked by grey strips (determined by measured pressure data) and black dotted lines (determined by URANS results). The detailed illustration on instability evolution characteristics based on transient pressure data are given afterwards. From the performance curve, the last stable condition before stall is at ϕ = 0.139, meanwhile the compressor reaches its maximum pressure rise of about ψ = 0.5. The further decrease of flow rate results in a sudden loss of the pressure rise at ϕ = 0.137, termed as RS (Rotating stall) condition. Fig. 5 provides the time traces and frequency spectra of measured unsteady pressure at the leading edge plane (PT1). At RS condition, the low-pass filtered pressure signal shown at the bottom of Fig. 5(a) (RS filtered) contains harmonic disturbance with a wavelength of about two rotor revolutions. Thus, the compressor rotor falls into stall with longscale disturbance. Whereas far from the stall boundary, at large flow condition of ϕ = 0.176, i.e. SS (Steady state) condition the pressure trace is featured as almost periodical fluctuations determined by the blade passing signature. Meanwhile, the pressure

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Fig. 4. Measured and predicted performance curve of compressor (marked with flow instability characteristics).

spectrum at SS condition shows only blade passing frequency and its harmonics with vacant turbulence background, which means that the flow field is dominated by the rotation of steady blade loading without other coherent disturbance. As flow rate reduces, at the operating condition of ϕ = 0.166, i.e. NI condition in Fig. 4 and 5, the enhance in blade passing signature irregularity is clearly seen in the pressure trace, along with a broadband hump below blade passing frequency in the pressure spectrum, indicating that flow disturbance occurs in the rotor flow field. As the compressor is further throttled, at PE (Peak efficiency) condition, the pressure trace is depicted as stronger irregularity in blade passing signature, meanwhile the broadband hump in pressure spectrum below blade passing frequency becomes stronger and comprises multiple peaks with nearly constant interval. This characteristic signature is a typical identification feature of a flow phenomenon termed as “Rotating Instability”, which has been considerably researched as a pre-stall activities [21,25]. Thus, the broadband hump below blade passing frequency in spectra is seen as the indication of occurrence of rotating instability. During the time-resolved pressure measurements, the compressor was being throttled with small steps to detect the occurrence of rotating instability. Yet, during the measuring campaign, the broadband frequency hump representing rotating instability gradually emerges as the flow rate decreases, that a certain flow rate point as the exact onset point of rotating instability can hardly be determined. The measured flow coefficient range of rotating instability emergence is approximately from 0.172 to 0.168, depicted as grey strip in Fig. 4. At the flow rate point below 0.168, the broadband frequency hump of rotating instability is doubtlessly observed in the spectra, thus the operating condition of ϕ = 0.166 is termed as the near instability inception (NI) condition. The most intense rotating instability appears at vicinity of PE condition, thereafter the level of broadband frequency hump gradually recede. At RS condition, local low pressure spikes, marked by the dotted blue circles, appear stochastically distributed near the rotor leading edge. These low pressure spikes are found to be induced by another pre-stall disturbance under vortex shedding mechanism, which is to be discussed in detail through the transient CFD results in the following section. Furthermore, till the rotating stall occurs, the rotating instability remains existence in the rotor flow field but its multi-peak feature disappears, replaced by a convex-type frequency band. Generally, rotating instabilities are defined as prestall flow activities, yet in present work the occurrence of rotating instability covers a wider flow range from flow rate larger than peak effi-

ciency point to stall condition. The similar results could also be found in the work of Kameier [26] and Pardowitz [27], which can be attributed to the larger rotor tip clearance inducing stronger tip leakage flow and stronger blockage of reverse flow. Some representative features of rotating instability can be observed at its intense condition, i.e. PE condition in Fig. 5b. In the measured pressure spectra rotating instability induces multiple frequency humps which located at RI, BPF-RI, BPF+RI and 2BPF-RI respectively. Previous investigations by Wang [28] have already demonstrated that these broadband humps representing rotating instability are caused by the interaction between propagating RI disturbance and rotation of steady rotor pressure field, which could be explained by the rotor-rotor interaction model [29]. Side-by-side peaks with almost constant interval are imposed on each of the broadband hump induced by RI. The measured pressure trace depicts an approximate two-passage periodicity which corresponds to the RI and BPF-RI broadband humps close to 1/2 BPF, and that can give some indication of the flow pattern in the rotor tip region under the disturbance of rotating instability. Coherence and phase spectra are used to analyze the propagating nature of RI disturbance based on the measured data of two circumferentially staggered sensors (PT0 and PT1 in Fig. 2). Fig. 6 provides the results for an condition with the most intense rotating instability (PE condition). In the figure, the frequency range of rotating instability is marked with grey background. The coherence function exhibits high amplitude within the frequency range of RI verifying the correlation between the pressure signals of these two circumferentially distributed sensors. Fig. 6 gives the phase angle of the cross spectra providing additional information about the relative phase of frequency components of two correlated signals. A linear phase shift (redrawn with red line) is observed within the frequency range of rotating instability, representing a circumferentially propagating nature of the aerodynamic source of the disturbance. As proposed by Liu [31], using the slope of the linear phase part and the angular distance between the two pressure sensors, the angular velocity of the rotating instability can be calculated by the following equation,

a=

θ dϕˆ /dω

(1)

where ϕˆ is the phase angle of the cross spectrum, and ω is the angular frequency, i.e. ω = 2π f . θ is the angular distance between

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Fig. 5. Time traces and frequency spectra of measured unsteady pressure at typical flow conditions. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

the two pressure sensors. Using the data from Fig. 6 and Equation (1), the calculated angular velocity of rotating instability is 194.5 rad/s, which is 61.9% of the angular speed of rotor’s rotation. To conclude, using the correlation analysis of spectral signature, rotating instability can now clearly be attributed to circumferential propagating flow disturbances. 4.2. Validation of CFD approach Again, see Fig. 4, the characteristic curve predicted by the steady calculations significantly deviates from the experimental one around a flow coefficient of 0.168. Referring to the associated flow field behavior, the monitored data from the URANS calculations show that pressure signals in the rotor tip region start to fluctuate from this operating condition to lower flow rate range, while they remain constant when flow rate is above this value. That is to say, in the CFD simulations, the appearance of flow disturbances in the rotor tip region has been captured from the operating condition of ϕ = 0.168, which is in accordance with the

aforementioned initial operating point of rotating instability determined by measured time-resolved pressure. Additionally, the comparison between predicted and measured frequency spectra obtained at equivalent position is provided for the operating condition with most intense rotating instability (PE) and rotating stall point (RS), see Fig. 7. It is seen that, for both PE and RS conditions, the predicted BPF coincides with the measured one, in both the frequency value and the peak amplitude. For PE condition, it is found that the broadband humps with side-by-side peaks arise in the same frequency range for the measured and predicted spectra. The predicted RI pattern shows higher frequency amplitude and lower frequency interval f than the measured ones. The broadband hump at approximately 0.8 BPF in the predicted spectrum represents the first higher harmonics of BPF-RI, which is not recognized in the measured one. That may be because in the experimental circumstance, the flow structure of rotating instability has lower fluctuating energy under the influence of other disturbances in the background turbulence. Thus, the amplitude of 2(BPF-RI) in the measured spectrum is much lower than that in the predicted one, then it is submerged below the turbulent

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Fig. 6. Spectra of frequency, coherence and phase angle of measured unsteady pressure at PE condition.

Fig. 7. Comparison of measured and predicted pressure spectra at PE and RS condition.

background noise. For RS condition, the measured and predicted results agree very well for the frequency signature of both rotating instability and rotating stall. Though there are some differences between the measured and predicted results regarding the amplitude of frequency components of rotating instability and rotating stall, the current computational method is capable to capture the predominating features of flow instabilities. Thus, the effectiveness of the current numerical approach to resolve the flow behavior under the instability evolution has, thus, been demonstrated. 4.3. Tip leakage flow trajectories and unsteadiness Data sampled from a large number of revolutions allow an analyzation of time-resolved pressure measurement applying sta-

tistical methods. Ensemble average and root-mean-square (RMS) unsteadiness are used to evaluate the measured unsteady pressure data, which are defined as follows

P (θi ) =

N 1 

N

[P (θi )]k

(2)

k =1

  N 1   2 P (θi ) − P (θi ) k P R M S (θi ) =  N

(3)

k =1

where θi corresponds to the ith phase position in a given revolution for N revolutions of data. The ensemble average of timeresolved pressure data collected from the casing-mounted array of

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transduces gives the time-averaged casing pressure distribution allowing the tip leakage flow to be tracked across the passage. The definition of rms provides the ability to identify regions of pressure unsteadiness associated with the tip leakage flow. The data processing of ensemble average and rms were performed over each revolution for at least 150 revolutions. Then the obtained pressure and rms distributions over the whole annulus were divided into 21 equal segments (one segments for each blade passage) and were averaged across these 21 segments. This calculation represents one average blade passing period neglecting the discrepancy between blades, thus the average result is repeated for different blade passage. The achieved distribution of ensemble average and rms pressure on one blade passage are given in Fig. 8 for four typical conditions, NI, PE, NS (near stall) and RS, comparing with the equivalent time-averaged pressure contours of simulation results. The tip leakage vortex trajectory is usually estimated by the center line through the pressure troughs of the static pressure distribution. By applying this approach, the time-averaged trajectory of the tip leakage vortex core is acquired through the timeaveraged pressure distribution from experimental and numerical results, as marked by black dotted line in Fig. 8a. It can be observed that the predicted and measured tip leakage vortex agree with each other enough well in both the initial position and the trajectory for different operating conditions. At NI condition, i.e. the initial occurring condition of rotating instability, the detected trajectory line depicts that the tip leakage vortex develops toward the trailing edge of the neighboring blade, indicating that the tip leakage vortex occupies the whole pitch-wise range of the blade passage outlet in the tip region from this condition. Therefore, a stronger blockage of the tip leakage vortex to the through flow can be expected. With the flow rate reduction, the tip leakage vortex gradually moves upstream toward the leading edge as a result of stronger tip leakage vortex due to the uploading of the blade row. At RS condition, the trajectory of the tip leakage vortex develops toward the leading edge of the neighboring blade. In Fig. 8b, the acquired tip leakage vortex trajectory based on the time-averaged pressure contour is superimposed on the RMS distribution. Again, a good agreement can be found between experimental and numerical results for RMS distribution. In the previous study by Yoon [30], the trajectory of tip leakage vortex corresponds to the locus of peak unsteadiness positions. However, that is not the case for present study. From the figure, the region with peak RMS locates upstream the tip leakage vortex core at the approximate position of interface of incoming flow and TLV. The RMS distribution associated with streamlines of tip leakage vortex, see Fig. 9, further supports this view. The peak RMS region locates at the interface of incoming flow and TLV rather than the trajectory of TLV core, indicating that, when TLV covers the whole transverse of the blade passage, the highest unsteadiness is induced by the interaction of TLV with incoming flow rather than the TLV itself. Additionally, two other local high RMS regions situate at the initial position of TLV and downstream the TLV trajectory representing the interface of TLV and downstream through flow. From the NS condition, the high RMS region corresponding to the interface of TLV and incoming flow exceeds the leading edge plane of the blade passages. Thus, forward spillage of tip clearance flow and associated stronger blockage can be anticipated at this condition. Especially, at RS condition, a local peak unsteadiness region exists closely upstream the blade leading edge, which is found to be caused by propagating vortex structures through the transient CFD analysis in the following section. The unsteady flow behaviors related to these observations are to be detailed interpreted through 3D flow structure visualization based on numerical results in the following part.

4.4. Flow behavior leading to instabilities In the above sections, the time traces and spectral analysis of unsteady pressure data provide a fundamental characteristics of flow instability evolution as compressor is throttled, meanwhile the ensemble averaged and RMS pressure distribution provide the evolving feature of tip leakage flow and associated unsteadiness. In the next step, a more detailed examination of the unsteady flow behavior based on the transient full-annulus numerical results is carried out to interpret the basic physics of instability evolution. In order to understand the generation mechanism of flow instability, i.e. rotating instability and rotating stall, the following analysis are mainly focused on three typical operating conditions, the initial condition of rotating instability (NI), the near stall condition (NS) and the rotating stall condition (RS). At the initial condition of rotating instability (NI), the timeaveraged pressure distribution has already shown that the trajectory of tip leakage vortex moves close to the trailing edge of the neighboring blade. The streamlines of tip leakage flow from numerical results, as depicted in Fig. 10, further demonstrate this view. Moreover, the associated RMS pressure distribution on blade surface shows a high unsteadiness region near the blade trailing edge close to the tip leakage vortex. Clearly, the fluctuation of the rotor tip flow field is significantly correlated to the behavior of tip leakage vortex, thus an interaction between the TLV and blade can be anticipated. To analyze the unsteady feature of tip leakage vortex and its interaction with rotor blades, the vortex structures visualized by λ2 criterion and static pressure on blade surface at different instants are presented in Fig. 11. A fluctuation of the rear part of the tip leakage vortex is clearly observed. Fig. 11 gives the instant results of φ/φ F = 0.00, 0.25, 0.50, 0.75 in one fluctuating period. It can be observed that the tip leakage vortex creates a local low pressure spot at the location where it impinges on the pressure surface of the adjacent blade, as marked by a black dashed circle in the figure. As the oscillation of the tip leakage vortex, this low pressure spot on blade suction surface gradually moves downstream. The low pressure spot created by the tip leakage vortex will impact on the pressure distribution on blade surface near rotor tip. Fig. 12 provides the blade pressure distribution at relative blade height of 98% for different instants at NI condition, along with the result of the nearest larger flow rate condition, i.e. the last stable condition ϕ = 0.168, for comparison. It is seen that the blade loading for condition ϕ = 0.168 locates almost at the averaged value of the blade loading of different instants for NI condition. In another words, the time-averaged blade loading in the tip region changes little from the last stable condition ϕ = 0.168 to initial condition of rotating instability (NI). Therefore, the fluctuation of the rotor tip flow field is mainly caused by the interaction between tip leakage flow and the rotor blades. The local enlarged view of the pressure distribution on blade suction surface near trailing edge clearly shows the local low pressure spot induced by the TLV gradually moves downstream with time. Furthermore, the variation of pressure distribution of neighboring blade impacts on the tip leakage velocity and the generation of tip leakage vortex in the next blade passage. This interaction process will propagate circumferentially along the rotor blade row, thus the balance of tip leakage vortex and blade loading is not able to maintain stable and the propagating flow disturbances, i.e. rotating instability, are triggered. To understand the pre-stall activities and its link to rotating stall, the particular flow mechanism at near stall condition (NS) is examined. The RMS pressure distribution (Fig. 8) has already shown that, at NS condition, the interface of TLV and incoming flow exceeds the leading edge plane of the blade passages, and forward spillage of tip clearance flow is anticipated. The bladeto-blade view of static pressure distribution associated with the

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Fig. 8. Ensemble averaged (EXP) and time averaged (CFD) static pressure and root-mean-square field over rotor for 4 typical conditions (TLF trajectories marked by black or white dotted lines).

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Fig. 9. Root-mean-square of static pressure field over rotor associated with tip leakage flow streamlines at PE condition.

Fig. 10. Root-mean-square static pressure on blade surface and tip leakage flow streamlines at NI condition.

velocity vector, see top in Fig. 13, further confirms this speculation. As the interface of clearance reversed flow and incoming flow exceeds the inlet plane, a variation of this interface can be observed from passage to passage, as marked by the blade dotted line in the figure. It is also seen that the forward spillage of tip clearance flow close to the blade leading edge induces a local low pressure spot. Further flow visualizations by λ2 criteria and streamlines, see bot-

tom middle and right in Fig. 13, show that it is caused by a vortex structure with deflected shape spanning between the casing and the suction side of the rotor blade, which is termed as “leading edge vortex (LEV)” herein. Time transients of the leading edge vortex dynamics are depicted in Fig. 14. After the LEV is generated near the blade leading edge (the right side blade in Fig. 14), the end of the vortex tube at the casing moves circumferentially, while the end on the suctionsurface convects downstream. As the end on the suction-surface passing the mid-chord of blade, the LEV gradually decays, and at the same time another new forward spillage of tip clearance flow occurs near the neighboring blade leading edge, B2 in the figure. Additionally, a highly coupling of the TLV oscillation and the LEV evolution can be observed from the transient dynamics of vortex structures. The dynamic period of the pulsation of these two vortex structures keeps the same. In brief, the LEVs create local low pressure spot on the casing, and they periodically generate, propagate circumferentially and decay inducing a circumferentially propagating flow disturbance, which is superimposed on the oscillation of TLV as the dynamics of rotating instability. Again, see Fig. 13, as the forward spillage occurs, LEV is generated near the leading edge (the case of B2 in Fig. 13). Then, the forepart of the blade tip is unloaded, leading to the maximum leakage position being pushed downstream and an attenuation of the clearance reversed flow. The LEV is found to be propagating along the inlet plane of the blade row after its generation. When the LEV transmits close to the midchord of the blade tip (the case of B1 in Fig. 13), the local low pressure region induced by the LEV uploads the blade tip, which is found to strengthen the clearance reversed flow. The blade-to-blade views of the flow field across the full annulus provide a holistic perspective on the propagating disturbances, as shown in Fig. 15 for static pressure and entropy distributions at NS condition. Through the low pressure spots near the leading edge plane, the LEVs can be identified, as pointed by the black triangles. A total of 30 LEVs have been found over the whole rotor circumference. Further, the entropy distribution downstream the rotor also shows the same periodicity (30) of flow disturbances as

Fig. 11. Instants of tip leakage vortex structure (λ2 criterion) and blade surface pressure at NI condition.

Fig. 12. Pressure distribution of blade surface at 98% relative blade height for different instants at NI condition.

H. Wang et al. / Aerospace Science and Technology 96 (2020) 105557

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Fig. 13. Forward spillage and generation of leading edge vortex at NS condition (depicted by blade-to-blade distribution of static pressure and velocity vector, and tip leakage vortex structure by λ2 criterion and streamlines).

Fig. 14. Time transient of leading edge vortex dynamics at NS condition.

the number of LEVs. Additionally, an approximately 3-period flow pattern has been observed across the annulus. The previous studies of Pullan et al. [7] and Inoue et al. [23] described that the generation of a similar vortical topology as LEV contributed to the formation of classical spike-type stall inception. Contrary to the previous findings, the present results show an almost evenly distribution of LEVs as they propagating circumferentially at NS condition, thus

inducing an kind of short-length flow non-uniformity with high circumferential periodicity rather than a stall cell. To summarize, at the NS condition, the generation of leading edge vortexes induces a orderly propagating short-length flow disturbance with a circumferential periodicity of 30, attributing to the dynamics of rotating instability, rather than evolving into a stall cell.

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H. Wang et al. / Aerospace Science and Technology 96 (2020) 105557

Fig. 15. Blade-to-blade distribution of static pressure and entropy across the whole annulus at NS condition.

Fig. 16. Blade-to-blade distribution of static pressure and entropy across the whole annulus at RS condition.

As the compressor is further throttled to RS condition, the orderly propagation of the LEVs has been disrupted, as is shown in blade-to-blade view of static pressure and entropy distributions in Fig. 16, where LEVs are also pointed out by the triangles. At RS condition, the number of LEV changes to 25, and two parts with scattering of LEVs have been observed, marked by the red triangles. Corresponding to the parts with scattered LEVs, two stall cells with high entropy have been found, thus inducing a flow disturbance with length-scale of rotor circumference. The reason for the stall cell generation can be interpreted as followed: The disruption of the orderly propagation of the LEVs results in the scattering of the LEVs. At the contiguous blade passages where the LEVs are scattered, they both move to the position near the blade midchord. As is found from above analysis on LEVs in Fig. 13, the LEV near the blade mid-chord would upload the blade tip and cause stronger clearance reversed flow. Thus, at the region where the LEVs are scattered, the adjacent several blades all suffer from an uploading of the blade tip and a strengthen of the clearance reversed flow, thus leading to the generation of stall cells with local stronger blockage and higher entropy. 5. Conclusion In present study, detailed time-resolved pressure measurements on a low speed axial compressor have been carried out to investigate the evolution features of flow instability as the compressor is throttled to stall limit. In addition, full-annulus URANS simulations contribute for a deeper understanding on the flow physics behind the instabilities transition. The following conclusions can be drawn: (1) For this compressor with large tip clearance, the occurrence of rotating instability, detected by both the broadband hump below BPF and the irregularity in blade passing pressure signature, has been captured in a wide operating range from the large-flow condition, even before the peak efficiency point, to the stall limit.

The experimental and numerical results agree well on both the evolution characteristics and the spectral pattern of flow instabilities (broadband hump with side-by-side peaks below BPF for RI, and low frequency peaks for RS). (2) Based on the measured spectra, along with the ensemble average and root mean square of pressure data, the rotating instability is found to appear when the trajectory of tip leakage flow moves to the trailing edge of the neighboring blade. The transient flow structures from the numerical results show that at this operating condition, the tip leakage vortex starts to oscillate under the interaction with the pressure surface of the neighboring blade, inducing a short-length scale propagating flow disturbance, i.e. rotating instability. (3) At near stall condition, the forward spillage occurring near the blade leading edge results in the generation of leading edge vortex. The periodically generation, movement and decay of the leading edge vortexes induce an orderly circumferentially propagating flow disturbance with short-length scale and high circumferential periodicity, which is superimposed on the disturbance caused by oscillation of tip leakage vortex as the dynamics of rotating instability, rather than evolves into a stall cell. (4) When LEV is generated near the leading edge, the forepart of the blade tip is unloaded, leading to the maximum leakage position being pushed downstream and an attenuation of the clearance reversed flow. When the LEV transmits close to the mid-chord of the blade tip, the LEV-induced local low pressure region uploads the blade tip, and strengthens the clearance reversed flow. (5) As the compressor is throttled to RS condition, the orderly propagation of the LEVs has been disrupted, resulting in the scattering of part of the LEVs. In the region with scattered LEVs, the contiguous several blades suffer from the uploading by LEVs, which causes stronger clearance reversed flow, and thus leads to the generation of stall cells with local stronger blockage and higher entropy.

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