Coherent Perturbations Research Articles

Flow–acoustic resonance mechanism in tandem deep cavities coupled with acoustic eigenmodes in turbulent shear layers

This study presents the interplay of flow and acoustics within tandem deep cavities, focusing on the resonance mechanism occurring between turbulent shear layers and acoustic eigenmodes. The arrangement inside the tandem deep cavities includes both close and remote configurations. A combined fully coupled and decoupled aeroacoustic simulation strategy was devised. Employing an advanced high-order spectral/hp element method in conjunction with implicit large eddy simulation, the nonlinear compressible Navier–Stokes equations were solved to acquire internal flow–acoustic resonant field. In parallel, the linearized Navier–Stokes equations were tackled to determine coherent shear layer perturbations with external acoustic forcing. Based on acoustic measurements, the mainstream Reynolds number approaches approximately $R{e_{in}} = {O}({10^5})$ , where we identified the presence of frequency lock-in and a resonance range. Aeroacoustic noise sources were examined by implementing spectral proper orthogonal decomposition to decompose the pressure fields into hydrodynamic and acoustic components. As feedback intensified, the flow characteristics by the acoustic forcing effect and the flow-interactive effect were categorized according to the development of concurrent turbulent shear layers. Subsequently, the alternating and synchronous behaviours of concurrent shear layers resonated with the out-of-phase and in-phase acoustic eigenmodes were identified, and the corresponding large-scale counter-rotating vortex pairs and co-rotating vortex structures at the cavity entrances were extracted. The acoustic power generated by the Coriolis force was calculated using Howe's vortex-sound analogy, and the aeroacoustic energy transfer mechanism between large-scale shear layer vortices with acoustic eigenmodes was further explored. Finally, a linear response of coherent perturbations of the concurrent shear layers by external acoustic forcing was established. The amplification of flow in the streamwise direction toward the main duct led to the formation of coherent vortex structures, accompanied by separation bubbles into the main duct.

Impact of density stratification and azimuthal velocity on the growth of coherent structures in a convectively unstable swirl flame

Large-scale coherent structures resulting from hydrodynamic instabilities can interact with turbulent swirl flames and lead to combustion instabilities. The present work investigates the impact of density stratification and azimuthal velocity on the growth of coherent structures in a convectively unstable swirl flame. Flame structure and flow field are measured by simultaneous hydroxyl planar laser-induced fluorescence and stereoscopic particle image velocimetry (S-PIV) at a repetition rate of 10 kHz and are analyzed by using the spectral proper orthogonal decomposition (SPOD) and spatial linear stability analysis (LSA). The SPOD reveals that the dominant symmetric and anti-symmetric modes are within the frequency range from 156 to 585 Hz, accounting for more than 25% of the turbulent kinetic energy. The spatial growths of these coherent structures are quantified by the LSA that predicts large growth rates near the nozzle exit with the corresponding frequency band matching well with the SPOD analysis. The LSA results show that both density stratification and azimuthal velocity have little effect on the instability frequencies of the most spatially unstable modes. However, the flame-induced density stratification suppresses the growth of the coherent structures by altering the pressure gradient and viscous diffusion, whereas the azimuthal velocity promotes flow instabilities through the changes in convection and production of the coherent perturbations. The results also suggest that the conventional PIV technique with two-component velocity measurement is inadequate for linear modeling of coherent structures, and the density stratification should also be taken into account in convectively unstable swirl flames.

Data-driven estimation of entropy production by large scale motions in an intermediate turbine duct

In modern gas turbines, the physics of three-dimensional inflow for aggressive intermediate turbine ducts are strongly associated with large-scale coherent motions, which contribute to the production of irreversible aerodynamic and thermodynamic energy losses. To address this problem, an extended data-driven approach for estimating the irreversible losses through viscosity dissipation and heat transfer in turbulent flows is proposed. An aggressive intermediate turbine duct connected to a high-pressure turbine is numerically investigated using the detached-eddy simulation framework. The influence of tip leakage vortices and rotor wakes on the aerodynamics in the duct is assessed through quadruple proper orthogonal decomposition analysis. The entropy production rate corresponding to the coherent structures is then identified, and the irreversible losses in the duct subject to unsteady flow motions are quantitatively evaluated. The results indicate that the coherent structures in the intermediate turbine duct are strongly associated with the upstream conditions, including the tip leakage flow and rotor wakes. Direct viscous dissipation accounts for the majority of the irreversible losses, with coherent perturbed dissipation contributing to 7.25% and 5.54% of the total for tip gap sizes of 1.5% and 3.5% span, respectively. The streamwise development of coherent perturbations is restricted compared with that in the mean structure, and the stochastic part contributes little to the viscous dissipation. The proposed method provides a systematic procedure for estimating the irreversible energy losses in unsteady turbulent flow, and highlights the significance of unsteady aero-thermodynamics in the design of turbomachinery.

A Multivariate Additive Inflation Approach to Improve Storm‐Scale Ensemble‐Based Data Assimilation and Forecasts: Methodology and Experiment With a Tornadic Supercell

AbstractEnsemble‐based convective‐scale radar data assimilation commonly suffers from an underdispersive background ensemble. This study introduces a multivariate additive‐inflation method to address such deficiency. The multivariate additive inflation (AI) approach generates coherent random perturbations drawn from a newly constructed convective‐scale static background error covariance matrix for all state variables including hydrometeors and vertical velocity. This method is compared with a previously proposed univariate AI approach, which perturbs each variable individually without cross‐variable coherency. Comparisons are performed on the analyses and forecasts of the 8 May 2003 Oklahoma City tornadic supercell. Within assimilation cycles, the multivariate approach is more efficient in increasing reflectivity spread and thus has a reduced spinup time than the univariate approach; the additional inclusion of hydrometeors and vertical velocity results in more background spread for both reflectivity and radial velocity. Significant differences among AI experiments also exist in the subsequent forecasts and are more pronounced for the forecasts initialized from the earlier assimilation cycles. The multivariate approach yields better forecasts of low‐level rotation, reflectivity distributions, and storm maintenance for most lead times. The additional inclusion of hydrometeor and vertical velocity in the multivariate method is beneficial in forecasts. Conversely, the additional inclusion of hydrometeor and vertical velocity in the univariate method poses negative impacts for the majority of forecast lead times.

Experimental study on laser propagation characteristics in local air turbulence disturbed by coherent acoustic waves

The existence of atmospheric turbulence seriously restricts the application of laser technology. However, the acoustic wave will affect the air density during the propagation process, change the original structure of the air turbulence, and then affect the propagation of the laser in the air turbulence. To study the effect of disturbance of atmospheric turbulence by acoustic waves on laser propagation, the propagation characteristics of lasers in local atmospheric turbulence under coherent acoustic wave perturbation are investigated experimentally. First, a coherent acoustic wave generator and a closed local air turbulence simulation device are designed. The propagation experiments of laser in a closed local air turbulence environment disturbed by coherent acoustic waves are carried out. It is found that the coherent acoustic wave will interfere with the wave reflected from the inner wall of the closed local air turbulence simulation device, and the sound pressure forms a regular standing wave intensity distribution pattern. Moreover, the variations of laser beam drift fluctuation variance, scintillation index, and beam diameter with coherent acoustic wave frequency, power, and sound source array position are studied. The results show that the original structure of air turbulence will be changed in the process of coherent acoustic wave propagation, which will affect the beam drift fluctuation variance, scintillation index, and beam diameter changes of laser propagation in air turbulence. The beam drift fluctuation variance, scintillation index, and beam diameter change regularly with the change of the frequency and power of the sound source. Changes of the fluctuations with frequency are relatively gentle, whereas changes with power are severe. This paper explores the influence of coherent acoustic waves disturbing air turbulence on laser propagation characteristics, and the research results provide a basis for improving or disturbing laser propagation performance in atmospheric turbulent environments.

Creating physically coherent and spatially correlated perturbations to initialize high‐resolution ensembles of simulated convection

AbstractThe use of ensembles for numerical weather prediction has become common during the last decade. For global models, the generation of initial‐condition perturbations has a number of well‐tested methodologies. In ensembles that predict convective storms explicitly (i.e., km), the generation of physically realistic perturbations is less well posed. This study introduces a technique to generate physically coherent and spatially correlated (PCSC) initial‐condition perturbations that are calibrated to the environment. Ensembles of idealized CM1 simulations, initialized with either PCSC perturbations (EXP_PCSC), spatially coherent random perturbations (EXP_3KM), or Gaussian white‐noise random perturbations (EXP_WHITE), are run for both a linear convective line of storms and a single “supercell” storm to demonstrate the utility of this new perturbation technique in diverse environments. PCSC perturbations are extracted from high‐resolution simulations of boundary‐layer turbulence and random perturbations are calibrated to be the same in magnitude as PCSC perturbations. EXP_PCSC simulations spawn turbulence fastest in this study. The simulated turbulence is more robust than in other experiments more than 1 hr into the simulation, because horizontal convective rolls enhance power at the largest scales. Random perturbations are slow to generate turbulence; this problem is exacerbated when the base model state flow is nonturbulent. Due to robust turbulence, EXP_PCSC ensemble spread increases fastest during the first simulation hour and remains largest throughout the remainder of the simulations. Although EXP_PCSC spread is the largest, the sensitivity of convection to the initial perturbations varies at different times in the storm life cycle. Storms appear more sensitive to perturbations added near the time of convective initiation.

On the scattering of entropy waves at sudden area expansions

In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. This is a canonical configuration representing internal flows with flow separation and stagnation pressure losses. The numerical approach is based on a triple decomposition of the flow variables into a steady mean, a small-amplitude coherent part, and a stochastic turbulent part. The coherent part contains acoustic, vortical, and entropy waves. The mean flow is obtained as the solution of the Reynolds-Averaged Navier–Stokes (RANS) equations. The equations governing the coherent perturbations are linearised and solved in the frequency domain. To account for the effect of turbulence on the coherent perturbations, a frozen eddy viscosity model is employed. When entropy fluctuations pass through the area expansion, the generated entropy noise behaves as a low-pass filter. The numerical predictions of the noise at low frequencies are compared to the predictions of compact, quasi-one-dimensional, and isentropic theory and large discrepancies are observed. An alternative model for the generated entropy noise tailored for area expansions is then proposed. Such model is based on the conservation of mass, momentum, and energy written in integral form. The model assumes zero frequency and the one-dimensionality of the flow variables far upstream and downstream of the expansion. The predictions of this model agree well with the numerical simulations across a range of finite subsonic Mach numbers including low, intermediate, and high Mach numbers. The contributions of this work are both numerical and theoretical. Numerically, a triple decomposition adapted to high-Mach-number, compressible flows is introduced for the first time in the context of acoustic simulations. From a theoretical point of view, the quasi-steady model proposed here correctly captures the low-frequency entropy noise generated at sudden area expansions, including at high subsonic Mach numbers.

Unsteady two-phase region evolution of SCO2 centrifugal compressor

In this study, unsteady numerical simulations of centrifugal compressors with and without volute were carried out. The unsteady two-phase region evolution in the centrifugal compressor is obtained. Large coherent perturbations were revealed by the decomposition of the transient flow data using the dynamic mode decomposition (DMD) approach. The results imply that because of the low static pressure strip LP1, the two-phase region presents a triangular distribution at the blade leading edge (LE) of the pressure surface (PS) side in one impeller rotation period for both a low flow rate and the design flow rate. At a high flow rate, the two-phase region displays a double triangle distribution on the PS side of the blade LE, which is correlated with the low static pressure strips LP1 and LP2. The maximum two-phase region on the PS side of the LE of the blade occurs downstream of the LP1 position. The two-phase region in the tip clearance is deflected along the LP1 trajectory. DMD analysis shows that there are four modes related to the two-phase region in the tip clearance: mean flow mode with a frequency of 0 Hz and three modes with frequencies of 0.5, 1.0, and 1.5 BPF respectively. Furthermore, the circumferential local perturbation region of these four modes has the same deflection trajectory as that of LP1.

Dynamical topological phase realized in a trapped-ion quantum simulator.

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders1-5. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase6, in a quasiperiodically driven array of ten 171Yb+ hyperfine qubits in Quantinuum's System Model H1 trapped-ion quantum processor7. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders8,9 that would enable error-resilient manipulation of quantum information.

Adaptative Perturbation Patterns: Realistic Adversarial Learning for Robust Intrusion Detection

Adversarial attacks pose a major threat to machine learning and to the systems that rely on it. In the cybersecurity domain, adversarial cyber-attack examples capable of evading detection are especially concerning. Nonetheless, an example generated for a domain with tabular data must be realistic within that domain. This work establishes the fundamental constraint levels required to achieve realism and introduces the adaptative perturbation pattern method (A2PM) to fulfill these constraints in a gray-box setting. A2PM relies on pattern sequences that are independently adapted to the characteristics of each class to create valid and coherent data perturbations. The proposed method was evaluated in a cybersecurity case study with two scenarios: Enterprise and Internet of Things (IoT) networks. Multilayer perceptron (MLP) and random forest (RF) classifiers were created with regular and adversarial training, using the CIC-IDS2017 and IoT-23 datasets. In each scenario, targeted and untargeted attacks were performed against the classifiers, and the generated examples were compared with the original network traffic flows to assess their realism. The obtained results demonstrate that A2PM provides a scalable generation of realistic adversarial examples, which can be advantageous for both adversarial training and attacks.

A polyfold proof of the Arnold conjecture

We give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds M via a direct Piunikhin–Salamon–Schwarz morphism. Our constructions are based on a coherent polyfold description for moduli spaces of pseudoholomorphic curves in a family of symplectic manifolds degenerating from {{mathbb {C}}{mathbb {P}}}^1times M to {{mathbb {C}}}^+ times M and {{mathbb {C}}}^-times M, as developed by Fish–Hofer–Wysocki–Zehnder as part of the Symplectic Field Theory package. To make the paper self-contained we include all polyfold assumptions, describe the coherent perturbation iteration in detail, and prove an abstract regularization theorem for moduli spaces with evaluation maps relative to a countable collection of submanifolds. The 2011 sketch of this proof was joint work with Peter Albers, Joel Fish.

Laser-Induced Cooperative Transition in Molecular Electronic Crystal.

The competing and non-equilibrium phase transitions, involving dynamic tunability of cooperative electronic and magnetic states in strongly correlated materials, show great promise in quantum sensing and information technology. To date, the stabilization of transient states is still in the preliminary stage, particularly with respect to molecular electronic solids. Here, a dynamic and cooperative phase in potassium-7,7,8,8-tetracyanoquinodimethane (K-TCNQ) with the control of pulsed electromagnetic excitation is demonstrated. Simultaneous dynamic and coherent lattice perturbation with 8 nspulsed laser (532nm, 15 MWcm-2 , 10 Hz)in such a molecular electronic crystal initiates a stable long-lived (over 400 days) conducting paramagnetic state (≈42 Ωcm), showing the charge-spin bistability over a broad temperature range from 2 to 360 K. Comprehensive noise spectroscopy, in situ high-pressure measurements, electron spin resonance (ESR), theoretical model, and scanning tunneling microscopy/spectroscopy (STM/STS) studies provide further evidence that such a transition is cooperative, requiring a dedicated charge-spin-lattice decoupling to activate and subsequently stabilize nonequilibrium phase. The cooperativity triggered by ultrahigh-strain-rate (above 106 s- 1 ) pulsed excitation offers a collective control toward the generation and stabilization of strongly correlated electronic and magnetic orders in molecular electronic solids and offers unique electro-magnetic phases with technological promises.

Tip Leakage Behavior and Large Coherent Perturbation Analysis of an Axial–Radial Combined Compressor With Outlet Distortion

Abstract Increasing performance requirements and compact structure design promote the generation of axial–radial combined compressors. However, its complex structure and asymmetrical outlet boundary cause difficulty to get an in-depth comprehension of the flow unsteadiness associated with spike-stall. In this work, unsteady full-annular simulations of an axial–radial combined compressor coupled with performance experiment validations were carried out. Based on the overall understanding of outlet distortion on each component, the general feature of tip leakage flow with asymmetrical outlet boundary was extracted. The temporal and spatial development of large coherent perturbations was revealed by the decomposition and reconstruction of the transient flow data with the dynamic mode decomposition approach. The results demonstrate that the outlet distortion can propagate reversely to the compressor inlet and the degree of distortion decreases gradually, which leads to the highest possibility for radial rotor to suffer from flow unsteadiness. In the circumferential location with distortion affected, the leakage momentum of the adjacent blade leading edge is enhanced by the secondary leakage, inducing the expansion of tip leakage vortex and causing flow instability. Besides organized perturbation structures related to mean flow and blade passing frequency, two large low-frequency stall perturbations approximately one-third and three-fourth rotor frequency was captured by the dynamic mode decomposition method, which is caused by volute potential effect and stator/rotor interference, respectively. The former occurs in the radial rotor and decays during its propagation, while the latter always exists owing to the multiple rotor/stator or stator/rotor interference in the axial–radial combined compressor.

Presence and absence of delocalization-localization transition in coherently perturbed disordered lattices.

A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few M frequencies a normal diffusion is realized, but the transition to a localized state always occurs as the perturbation strength is weakened below a critical value. The nature of the transition qualitatively follows the Anderson transition (AT) if the number of degrees of freedom M+1 is regarded as the spatial dimension d. However, the critical dimension is found to be d=M+1=3 and is not d=M+1=2, which should naturally be expected by the one-parameter scaling hypothesis.

Temporally coherent perturbation of neural dynamics during retention alters human multi-item working memory.

Temporarily storing a list of items in working memory (WM), a fundamental ability in cognition, has been posited to rely on the temporal dynamics of multi-item neural representations during retention. However, the causal evidence, particularly in human subjects, is still lacking, let alone WM manipulation. Here, we develop a novel "dynamic perturbation" approach to manipulate the relative memory strength of WM items held in human brain, by presenting temporally correlated luminance sequences during retention to interfere with the multi-item neural dynamics. Six experiments on more than 150 subjects confirm the effectiveness of this WM manipulation approach. A computational model combining continuous attractor neural network (CANN) and short-term synaptic plasticity (STP) principles further reproduces all the empirical findings. The model reveals that the "dynamic perturbation" modifies the synaptic efficacies of WM items through STP principles, eventually leading to changes in their relative memory strengths. Our results support the causal role of temporal dynamics of neural network in mediating multi-item WM, and offer a promising, purely bottom-up approach to manipulate WM.

Evidence for the predictability of changes in the stratospheric aerosol size following volcanic eruptions of diverse magnitudes using space-based instruments

Abstract. An analysis of multiwavelength stratospheric aerosol extinction coefficient data from the Stratospheric Aerosol and Gas Experiment II and III/ISS instruments is used to demonstrate a coherent relationship between the perturbation in extinction coefficient in an eruption's main aerosol layer and the wavelength dependence of that perturbation. This relationship spans multiple orders of magnitude in the aerosol extinction coefficient of stratospheric impact of volcanic events. The relationship is measurement-based and does not rely on assumptions about the aerosol size distribution. We note limitations on this analysis including that the presence of significant amounts of ash in the main sulfuric acid aerosol layer and other factors may significantly modulate these results. Despite these limitations, the findings suggest an avenue for improving aerosol extinction coefficient measurements from single-channel observations such as the Optical Spectrograph and Infrared Imager System as they rely on a prior assumptions about particle size. They may also represent a distinct avenue for the comparison of observations with interactive aerosol models used in global climate models and Earth system models.

Stability Analysis of Thermally Nonuniform Supersonic Jets

A computational investigation of the role of thermal nonuniformity on the development of instability modes in the shear-layer of a supersonic , jet is performed in this study. Cold fluid is injected at the axis of a heated jet to introduce radial nonuniformity and control the spatial development of shear layer. This is a companion investigation of an experimental study that observed a 2 dB reduction in peak narrowband sound pressure for centered injection. This investigation highlights the role of nozzle turbulence in changing the development of the noise-generating fluctuations by performing a separation of scales between boundary-layer turbulence and the coherent shear layer fluctuations. The mean flow is analyzed with an efficient Reynolds-averaged Navier–Stokes (RANS) approach. Different turbulence models are tested and compared with the experiments. The coherent perturbation is analyzed using linear parallel and parabolized stability equations (PSEs). PSEs agree with the experiments with regard to the small but consistent decrease in growth rate of forced modes with injection and identify the weakening of the first circumferential mode as the main contribution. Turbulence models for the base flow have a substantial effect on the perturbation development, and a compressibility correction of the RANS base flow is key to investigate jet-noise reduction strategies.

Observation of modulation instability and rogue breathers on stationary periodic waves

We present both theoretical description and experimental observation of the modulation instability process and related rogue breathers in the case of stationary periodic background waves, namely cnoidal and dnoidal envelopes. Despite being well-known solutions of the nonlinear Schrodinger equation, the stability of such background waves has remained unexplored experimentally until now, unlike the fundamental plane wave. By means of two experimental setups, namely, in nonlinear optics and hydrodynamics, we report on quantitative measurements of spontaneous modulation instability gain seeded by input random noise, as well as the formation of rogue breather solutions induced by a coherent perturbation. Our results confirm the generalization of modulation instability when more complex background waves are involved.

Numerical investigation of centrifugal compressor stall with compressed dynamic mode decomposition

Heightened interest in visualizing the flow structure under critical conditions for aero-engine led to further understanding of the underlying physical mechanism as well as to a better knowledge of the issues faced with their design and flow control. In this work, an unsteady full annular simulation of a centrifugal compressor coupled with experimental validations was presented. The diffuser stall was determined with various criterion principles and the wave-maker region under asymmetric flow field was investigated. Then, a dynamic mode decomposition (DMD) procedure concerning the whole domain and individual planes was applied to the numerical data so as to capture and visualize the dominating flow structure. With the purpose of improving calculation efficiency, a compressed DMD was adopted and validated against the standard DMD analysis results. Finally, the nonlinear development and spatial propagation between components of the coherent perturbations in diffuser and volute were reconstructed. The results indicate that the representative organized structure of flow instability can be captured with standard DMD approach. And by applying the compressed DMD approach, the flow mode can also be obtained with calculating time saving of 88.4% when the compression ratio is 1%. Considering the flow construction, four stall cells oscillating with little circumferential phase change are recovered during 6 rotor-cycles, indicating that the origin of the diffuser stall lies at the hub wall with fixed circumferential position near the diffuser outlet. The spatial propagation of stall mode except for the one near the volute tongue extends to the volute flow with a dumping effect of high-frequency perturbations.

Vortex trajectory prediction and mode analysis of compressor stall with strong non-uniformity

Given the heightened requirements of understanding the flow structure under critical condition and improving flow control technique for the turbocharger compressor, further insight into the unsteady behaviors of spike-stall inception associated with tip leakage flow was vital. In this work, an unsteady full annular simulation of a centrifugal compressor coupled with experimental validations was carried out by using the Reynolds averaged Navier–Stokes technique. A spike-type stall in the impeller was determined with multiple criterion principles. Then, a dynamic mode decomposition procedure was applied to the numerical data to capture and visualize the dominant flow structure in both absolute and relative coordinate. The temporal and spatial development of coherent perturbations was reconstructed. Finally, based on the results of mode decomposition, a modified prediction model of vortex trajectory concerning the asymmetrical flow, which can determine the circumferential location of spike-stall inception, was put forward. The results indicate that the low-frequency perturbation associated with stall inception can be captured by the DMD approach under both absolute and relative frames with the perturbation frequencies of 0.44 RF and 0.5 RF, respectively. Under absolute coordinate, the stall inception can be decomposed into three patterns: stationary stall cell in the mean flow, propagated stall cell in a certain region associated with BPF and oscillated stall cell in the origin place with the stall frequency of 0.44 RF. Considering the flow reconstruction, the flow instability in the impeller is relatively stationary stall inception without a significant phase shift and the stall perturbation occurs at 120∘ circumferential location. The specific location of stall inception is influenced by the blade leading edge, which can be predicted by the prediction model of the vortex trajectory accurately.