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In this paper, we introduce a new class of heterogeneous spatial autoregressive models (heterogeneous SAR models) where the variance parameters are modeled in terms of covariates. In order to estimate the model parameters, as well as their corresponding standard error estimates, we proposed a computational efficient MCMC method which combines the Gibbs sampler with Metropolis-Hastings algorithm. The proposed estimate method is illustrated through numerous simulations and is applied to the Boston housing data. [ABSTRACT FROM AUTHOR]

Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis–Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method. [ABSTRACT FROM AUTHOR]

Fine dust, represented by Fe-based fine particles and emitted from the production process of the iron and steel industry, is the primary factor causing many diseases represented by industrial pneumoconiosis, and ultra-low dust emission has always been a thorny problem to be solved urgently. To explore the magnetic coagulation effect of Fe-based fine particles in the magnetic field when removing them from industrial flue gas by the magnetic field effect in the iron and steel industry, using FLUENT software, magnetic dipole force was added between particles through user defined function (UDF) based on the computational fluid dynamics-discrete phase model (CFD-DPM) method so that the collision process of particles was then equivalent to their mutual trapping process. Next, the effects of particle size, particle volume fraction, external magnetic field strength, and particle magnetic susceptibility on the magnetic coagulation process were comprehensively studied. Meanwhile, the proton balance equation (PBE) was solved using the partition method on the basis of the computational fluid dynamics-population balance model (CFD-PBM) to compare the coagulation removal effect under random and aligned orientations of magnetic dipoles, respectively. The results showed that the magnetic coagulation strength under the random orientation of magnetic dipoles was greater than that under the aligned orientation. When the particle size of Fe-based fine particles increased from 0.5 μm to 1.5 μm, the magnetic coagulation coefficient decreased from 0.5414 to 0.2882, and the difference in the removal efficiency under the two different orientations of magnetic dipoles became smaller. When the particle volume fraction increased from 0.01 to 0.03, the magnetic coagulation coefficient increased from 0.2353 to 0.5061, and the difference in the removal efficiency under two orientations was enlarged. When the applied external magnetic field strength increased from 0.5 T to 1.0 T, the magnetic coagulation coefficient increased from 0.3940 to 0.5288, and the magnetic susceptibility increased from 0.0250 to 0.0500, the coagulation coefficient increased from 0.3940 to 0.5288, and the difference under two orientations basically stayed unchanged. [ABSTRACT FROM AUTHOR]

In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies. [ABSTRACT FROM AUTHOR]

Logistic mixed-effects models are widely used to study the relationship between the binary response and covariates for longitudinal data analysis, where the random effects are typically assumed to have a fully parametric distribution. As this assumption is likely limited or unreasonable in a multitude of practical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of binomial distribution logistic mixed-effects models, a general Bayesian framework is presented in which a semiparametric hierarchical modelling with an approximate truncated Dirichlet process prior distribution is specified for the random effects. The stick-breaking prior and the blocked Gibbs sampler using Pólya-Gamma mixture are employed to efficiently sample in the posterior analysis. Besides, a procedure calculating DIC for Bayesian model comparison is addressed. The methodology is demonstrated through simulation studies and a real example. [ABSTRACT FROM AUTHOR]

Dynamic crushing characteristics of coals are closely related with energy absorption and release of coals under certain strain rate. Hence, it is necessary to investigate energy dissipation laws of coal crushing under the impact loads with different strain rates. Based on the dynamic and static mechanical tests, crushing energy, total absorption energy, total releasable elastic latent energy, and relations between fractal feature of fragments, mean particle diameter and energy during crushing behaviors of outburst coal and nonoutburst coal were investigated. According to research results, crushing energy, total absorption energy, and releasable elastic latent energy of outburst coal and nonoutburst coal are related with strain rate, and they present exponential growths with the increase of the strain rate. However, the energy dissipation rate (ratio of crushing energy and incident energy) was basically constant at about 10%∼20%, that is, energy dissipation rate is a variable unrelated with strain rate. There is a good logarithmic relationship between the dynamic compressive strength of coals and the absorption energy density and elastic latent energy density, and dynamic comprehensive strength of coals has important impacts on energy absorption. The fractal features of coal fragments were obvious under dynamic impacts. The higher fractal dimension of fragment and the smaller mean particle diameter of experimental fragments bring the greater energy needed. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the influence of cavity width on the attenuation characteristic of gas explosion wave. Attenuation mechanism of gas explosion wave through cavity was obtained by numerical simulation. The gas explosion shock wave energy can be greatly attenuated through the cavity structure in five stages, namely, plane wave, expansion, oblique reflection, Mach reflection, and reflection stack, to ensure that it is eliminated. Cavities with various width sizes, namely, 500 ∗ 300 ∗ 200, 500 ∗ 500 ∗ 200, and 500 ∗ 800 ∗ 200 (length ∗ width ∗ height, unit: mm), were experimented to further investigate the attenuation characteristics through a self-established large-size pipe gas explosion experimental system with 200 mm diameter and 36 m length. Results showed an evident attenuation effect on flame duration light intensity (FDLI) and peak overpressure with increasing cavity width. Compared with 300 mm, the overall FDLI decreased by 83.0%, and the peak overpressure decreased by 71.2% when the cavity width was 800 mm. The fitting curves of the FDLI and peak overpressure attenuation factors to width-diameter demonstrated that the critical width-diameter was 2.19 when the FDLI attenuation factor was 1. The FDLI attenuation factor sharply decreased at the width-diameter ratio range from 1.5 to 2.5 and basically remained steady at 0.17 at the width-diameter ratio range from 2.7 to 4.0. The peak overpressure attenuation factor gradually decreased with the increase of width-diameter ratio and changed from 0.93 to 0.28 with width-diameter ratio from 1.5 to 4.0. The research results can serve as a good reference for the design of gas explosion wave-absorbing structures. [ABSTRACT FROM AUTHOR]

This paper presents the nonparametric quantile regression estimation for the regression function operator when the functional data with the responses missing at random are considered. Then, the large sample properties of the proposed estimator are established under some mild conditions. Finally, a simulation study is conducted to investigate the finite sample properties of the proposed method. [ABSTRACT FROM AUTHOR]

Handling data with the nonignorably missing mechanism is still a challenging problem in statistics. In this paper, we develop a fully Bayesian adaptive Lasso approach for quantile regression models with nonignorably missing response data, where the nonignorable missingness mechanism is specified by a logistic regression model. The proposed method extends the Bayesian Lasso by allowing different penalization parameters for different regression coefficients. Furthermore, a hybrid algorithm that combined the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simulate the parameters from posterior distributions, mainly including regression coefficients, shrinkage coefficients, parameters in the non-ignorable missing models. Finally, some simulation studies and a real example are used to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

The effect of rotor blade sweep on the flow stability of low-speed axial compressors is investigated by means of theoretical model, numerical simulations and experimental measurements. Four compressors with forward or backward swept rotors are carefully designed by modifying the tip element location of the baseline rotor. Steady simulation results show that the designed aerodynamic sweep in this work hardly changes the pressure rise and efficiency characteristics of the compressor, which ensures the comparability between these compressors regarding flow stability. The developed stall inception prediction model based on global linear stability analysis and eigenvalue theory is employed to evaluate the stall boundary of compressors after blade sweep designs, and results indicate that the forward sweep slightly improve the flow stability, while the backward sweep has significant deterioration effect. What's more, the circumferential propagation frequency of the perturbation wave at stall onset changes little after the sweep design. The steady and dynamic measurements in experiments for different rotor blades verifies the theoretical conclusions and the prediction accuracy of the theoretical model. Through steady and unsteady flow field analysis, it is found that the forward sweep reduces the diffusion factor, elementary work and blade loading at the rotor tip region, while the backward sweep has the opposite effect and enhances the interaction between the tip leakage flow and the primary flow, which is deemed the contributors to their effect on flow stability. [ABSTRACT FROM AUTHOR]

The development of optical temperature sensors is of fundamental and industrial importance for various applications. Despite the great advance in optical temperature-sensing techniques, challenges remain to search for novel sensing materials with low cost, easy fabrication and high sensitivity. Here, transparent glass ceramics (GC) embedded with cubic Sr 0.84 Lu 0.16 F 2.16 :Yb 3+ /Er 3+ nano-crystals were prepared via thermal annealing on the parent glass. The optical and structural properties were investigated. The enhanced emission intensity, obvious Stark splitting and prolonged lifetimes of Er 3+ confirm the enrichment of Er 3+ ions into formed Sr 0.84 Lu 0.16 F 2.16 nano-crystals. The temperature sensing performance of Yb 3+ /Er 3+ ions in Sr 0.84 Lu 0.16 F 2.16 GC were investigated based on up-conversion intensity ratio (FIR) from thermally coupled emitting states of Er 3+ . High energy difference ( Δ E  = 839 cm −1 ) and high absolute sensitivity (27.4 × 10 −4  K −1 at 606 K) are obtained. Our results reveal Sr 0.84 Lu 0.16 F 2.16 GC are excellent host for rare earth ions doping and potential candidate for optical thermometry. [ABSTRACT FROM AUTHOR]

A regression model with skew-normal errors provides a useful extension for ordinary normal regression models when the dataset under consideration involves asymmetric outcomes. In this article, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis for joint location and scale nonlinear models with skew-normal errors, which relax the normality assumption and include the normal one as a special case. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of MCMC methods to simulate samples from the joint posterior distribution. Finally, simulation studies and a real example are used to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

A stability model for axial compressors with inlet circumferential distortion is proposed in the present work. Based on the small perturbation theory, the compressor is divided into several inter-blade volumes containing two-dimensional primary flows. The volumes are connected by the actuator disks that includes the work and loss of the blade rows. The final equations are closed with the inlet boundary condition of no input perturbation and outlet boundary condition of no reflected perturbation. The rate of perturbation increase is then determined by the eigenfrequency, and hence the compressor stability is predicted. The model is verified on a low-speed single-stage compressor (TA36) which is numerically simulated and experimentally measured at uniform inlet condition and circumferentially distorted inlet condition. By comparing the stall onsets predicted by this model and classic Hynes-Greitzer (HG) model with experimental results, the reliability and ability of the present model are proved. Finally, a fast stability model to predict the stall onset under inlet circumferential distortion in the design stage is established based on the small perturbation theory and the idea of parallel compressor, which could provide a reference for the compressor stability. [ABSTRACT FROM AUTHOR]

In this paper, we consider inference aspects of skew-normal semiparametric varying coefficient models which provide a useful extension of the normal regression models. The maximum likelihood estimation based on B-spline is proposed. Further, we discuss the score test for homogeneity of the variance in skew-normal semiparametric varying coefficient models. Their asymptotical properties are investigated. Some simulated examples are used to examine our proposed methods. [ABSTRACT FROM AUTHOR]

The stall inception prediction method based on eigenvalue theory is established to analyze the effect of rotor blade loading distribution on the flow stability of transonic compressors. The parameterization is implemented to describe the blade geometry with a number of control parameters. Four designs with different blade loading distributions are achieved by modifying the maximum thickness position of each element profile. The steady simulations show that the variation of rotor blade loading distribution leads to significant change of the steady performance incorporating pressure ratio and efficiency at all mass flow conditions. When the blade loading is located further downstream, the pressure rise curve moves towards smaller mass flow and higher pressure ratio, while there exists an optimal blade loading distribution that maximizes the rotor peak efficiency. According to the theoretical prediction, moving the blade loading downstream leads to a smaller stall inception mass flow rate. The rotor work, entropy generation and diffusion factor of the four rotors are analyzed to explain the performance difference. And the relative positions of passage shock and unsteady tip clearance flow at design and near-stall operating conditions are compared in detail to explain the stall onset distinction. [ABSTRACT FROM AUTHOR]

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. If misspecification occurs, it may lead to inefficient or biased estimators of parameters in the mean. One of the most commonly used methods for handling the covariance matrix is based on simultaneous modeling of the Cholesky decomposition. Therefore, in this paper, we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a fully Bayesian inference for joint mean and covariance models based on this decomposition. A computational efficient Markov chain Monte Carlo method which combines the Gibbs sampler and Metropolis–Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard deviation estimates. Finally, several simulation studies and a real example are presented to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Three compressors with fore-loaded, uniformly loaded and aft-loaded rotor blades are designed via streamline curvature method coupled with blade generation that uses arbitrary camber lines so as to study the effect mechanism of rotor axial blade loading distributions on compressor performance. The rotor blade loading design is achieved by modifying the flow circulation in the rotor region on the basis of ensuring the total rotor work unchanged during the through-flow solving. Based on global linear stability analysis, a stall inception prediction model is established and integrated into the compressor design process as an assessment tool of flow stability. The predicted stall inception of the fore-loaded compressor validates the model precision by comparing with experimental measurements. Steady numerical simulations show that the pressure rise and efficiency of aft-loaded compressor are the best at the mass flow rates less than design point, followed by the uniformly loaded compressor, and those of the fore-loaded compressor are the worst. Steady blade loading analysis indicates that the peak loading positions of the three types of rotors move towards the leading edge accompanying with the throttling process. The comparison of predicted stall inception points among the three compressors presents that the fore-loaded compressor is the first to enter instability state, followed by the uniformly loaded compressor, while the aft-loaded compressor is the last. The steady and unsteady flow fields show that the maximum tip loading of rotor and stator blades becomes larger at the near-stall point as the rotor becomes more fore-loaded. This finding combined with the unsteady tip clearance flow explains the flow stability distinction of the three compressors to some extent. [ABSTRACT FROM AUTHOR]

A stall inception prediction model considering radial inlet distortions is established in this paper in order to quickly and accurately predict the stall limit of a compressor at radially distorted inlet flow conditions. Furthermore, the quantitative effect of the radial inlet distortion on compressor stability is investigated on a low-speed single-stage axial-flow compressor which is named TA36 and located in Beijing University of Aeronautics and Astronautics. Two kinds of distortion intensities are achieved by two radial inlet distortion generators in experiments. By utilizing the developed stability model, the predicted stall limits of TA36 at clean, 10% and 20% radially distorted inlet flow conditions all agree well with the experimental data only with relative errors of −0.74%, 1.28%, and 0.53% respectively. These relative errors less than 1.50% validate the ability of the developed stability model to predict the stall onset of a compressor with clean inlet or radial inlet distortions. Moreover, the predicted results confirm that radial inlet distortions deteriorate the compressor stability, and the adverse effect becomes more severe with the increase of distortion intensity, which can also be concluded from the experimental data. After comparing the load distribution on the rotor blade at the three inlet conditions, the increase of the maximum load at the tip region at distorted inlet conditions is considered to be a critical factor contributing to the negative effect of radial inlet distortions on compressor stability. [ABSTRACT FROM AUTHOR]

• The main content of this study is to investigate the coupled effects of blade sweep and radial distortion on flow stability. • Steady numerical simulations, theoretical model predictions, and experimental validations were conducted. • The use of a linear flow stability model based on small disturbance theory predicted the stall inceptions with high accuracy. • Higher intensities of distortion lead to worse flow stability. Under radially distorted inlet conditions, forward sweep enhances flow stability whereas backward sweep further worsens it. The stability enhancement of forward sweep cannot fully counteract the adverse impact of radial distortion on flow stability. • Elevated rotor tip loading was identified as the primary cause of instability under tip total pressure distorted inlet conditions. Forward sweep can slightly reduce this loading, whereas backward sweep has the opposite effect. Furthermore, the impact of rotor sweep on rotor tip loading intensifies with increasing distortion intensity. Flow stability enhancement for axial flow compressors under radially distorted inlet conditions through rotor sweep design is an important issue for designers. To investigate the couped effect of rotor swept and radial inlet distortion on flow stability, steady numerical simulations, theoretical model predictions, and experimental validations were conducted for a low-speed, single-stage axial compressor (TA36) under various intensities of tip total pressure distorted inlet conditions with different swept rotor configurations. The steady pressure rise significantly decreases as the intensity of the distortion increases, whereas the rotor sweep has little effect on the pressure rise characteristic. The maximum error via model prediction is 1.25 %, while for steady numerical calculation, it is 3.89 %. Higher intensities of distortion lead to worse flow stability. Under radially distorted inlet conditions, forward sweep enhances flow stability whereas backward sweep further worsens it. What's more, quantitative analysis shows that the stability enhancement of forward sweep cannot fully counteract the adverse impact of radial distortion on flow stability. Elevated rotor tip loading was identified as the primary cause of instability under tip total pressure distorted inlet conditions. Forward sweep can slightly reduce this loading, whereas backward sweep has the opposite effect. Furthermore, the impact of rotor sweep on rotor tip loading intensifies with increasing distortion intensity. Unsteady flow field analysis was conducted. Which shows that radial distortion and blade sweep both affect flow stability by altering the intensity of tip leakage flow. [ABSTRACT FROM AUTHOR]

Heteroscedasticity is often encountered in spatial-data analysis, so a new class of heterogeneous spatial autoregressive models is introduced in this paper, where the variance parameters are allowed to depend on some explanatory variables. Here, we are interested in the problem of parameter estimation and the variable selection for both the mean and variance models. Then, a unified procedure via double-penalized quasi-maximum likelihood is proposed, to simultaneously select important variables. Under certain regular conditions, the consistency and oracle property of the resulting estimators are established. Finally, both simulation studies and a real data analysis of the Boston housing data are carried to illustrate the developed methodology. [ABSTRACT FROM AUTHOR]

The essence of both rockburst and coal and gas outburst lies in fast energy release. In order to explore the energy action mechanism of coal and gas outburst induced by rockburst in rockburst and coal and gas outburst combined mines, the split Hopkinson pressure bar (SHPB) experimental device was firstly used to conduct uniaxial impact failure test of coal specimens prone to outburst under different strain rates, and their energy dissipation laws under impact loading were obtained. Next, under the engineering background of coal and gas dynamic phenomena induced by rockburst with different intensities in Xinyi Coal Mine and Pingdingshan Coal Group No. 12 Colliery in Henan Province and Dingji Coal Mine of Huainan Mining Group in Anhui Province, experimental study results were combined with numerical simulation analysis to discuss the energy mechanism of coal and gas outburst induced by rockburst. The study results show that the outburst can be divided into two different processes—critical outburst and outburst—according to the evolution law of outburst energy, and the critical energy conditions for coal and gas outburst are proposed. The minimum destructive energy range for the critical outburst of coal mass is obtained as (5–10) × 104 J/m3. Under some low gas, high stress, or strong disturbance conditions, applied loads can become the main energy sources causing critical failure and even crushing and throwing of coal mass. The coal mass will present an interval splitting structure under dynamic loading, which is obviously different from the failure mode of coal mass under static actions. [ABSTRACT FROM AUTHOR]

In this article, we develop estimation procedures for partially linear quantile regression models, where some of the responses are censored by another random variable. The nonparametric function is estimated by basis function approximations. The estimation procedure is easy to implement through existing weighted quantile regression, and it requires no specification of the error distributions. We show the largesample properties of the resulting estimates, the proposed estimator of the regression parameter is root-n consistent and asymptotically normal and the estimator of the functional component achieves the optimal convergence rate of the nonparametric function. The proposed method is studied via simulations and illustrated with the analysis of a primary biliary cirrhosis (BPC) data. [ABSTRACT FROM AUTHOR]

Abstract: The development of scintillators is of fundamental and industrial meaning for their diverse applications. Despite the great advance in scintillating mono‐crystals, challenge remains to search for novel scintillating materials with low cost, large volume, and high efficiency. Here, Tb3+‐doped glass ceramics (GC) with crystallized Lu6O5F8 nano‐crystals were prepared and characterized as potential X‐ray scintillators. Their structural, optical, and luminescent properties were explored systematically. After thermal treatment, X‐ray excited luminescence (XEL) intensity from Lu6O5F8:Tb3+ GC is greatly increased and the relative intensity is about 64% of commercial BGO scintillator, benefiting from preferential enrichment of Tb3+ ions into Lu6O5F8 nano‐crystals with low phonon energy. Moreover, unusual decay behaviors of Tb3+ emissions in GC sample are observed and discussed. Our results indicate that rare earth doped GC may offer a novel platform for designing and fabricating new scintillating materials in the future. [ABSTRACT FROM AUTHOR]

The development of optical temperature sensors is of fundamental and industrial importance for various applications. Despite the great advance in optical temperature-sensing techniques, challenges remain to search for novel sensing materials with low cost, easy fabrication, high sensitivity and wide temperature-sensing range. Here, bulk KLu 2 F 7 :Yb 3+ /Er 3+ glass ceramics (GC), prepared by simple conversional melt-quenching method with subsequent heat-treatment, are carefully characterized for potential temperature sensor using fluorescence intensity ratio (FIR) technique. The structural and luminescent properties of KLu 2 F 7 :Yb 3+ /Er 3+ GC are systematically investigated by XRD, TEM, up-conversion and lifetime measurement. Compared to other reported typical Er 3+ -doped temperature-sensing materials, Er 3+ ions in KLu 2 F 7 GC present wide temperature-sensing range (300–773 K), large energy gap (861 cm −1 ) and high absolute sensitivity (47.3 × 10 −4 K −1 at 620 K). Our results indicate that KLu 2 F 7 :Yb 3+ /Er 3+ GC are promising temperature sensing materials for designing highly sensitive FIR-based optical thermometers. [ABSTRACT FROM AUTHOR]

Abstract A batch of Bi3+/Eu3+ single and co-doped BaGd 2 O 4 phosphors were elaborated by traditional high temperature solid-state method. Their structural and photoluminescent properties were methodically studied by X-ray diffraction (XRD), scanning electron microscope (SEM), excitation spectra, emission spectra, decay curves as well as temperature dependent emission spectra. Under ultraviolet (UV) excitation, via a high-efficiency energy transfer process, the prepared Bi3+/Eu3+ co-doped BaGd 2 O 4 phosphors reveal both blue wide emission from Bi3+ ions and characteristic red sharp emission from Eu3+ ions. The energy transfer mechanism, energy transfer efficiency and luminescence chromaticity coordinates were procured. Our results indicate that BaGd 2 O 4 :Bi3+, y Eu3+ phosphors may act as promising candidate to boost the photosynthesis of plant. [ABSTRACT FROM AUTHOR]

Bi-Global stability analysis (BGSA) is employed to assess the flow separation (FS) in two-dimensional compressor cascades, aiming to investigate the unstable phenomena and underlying mechanisms. The prediction results are correlated with the separation bubble (SPB) on suction surface (SS) or the trailing edge vortex (TEV) and exhibit good agreement with the unsteady numerical simulation (UNS), thereby confirming the instability of these two flow structures. Meanwhile, the prediction results can also partially reflect the initiation of unsteady blade loading. The perturbation distributions obtained from the eigenvectors corresponding to the physically meaningful eigenvalue, reveal two primary unstable regions: one located in the wake region and another coinciding with the SPB. With the increase of incidence angle (IA), the growth rate (GR) of small perturbations transitions from negative to positive, corresponding to the flow state shifting from stable to unstable. Additionally, the inception position of eigenmodes on SS moves upstream until it reaches the leading edge (LE) of the blade. The velocity magnitude distributions in the circumferential direction were further analyzed, demonstrating good agreement with predicted perturbation distributions, and suggesting that the K-H instability mechanism contributes to unstable phenomena. In the analysis of a two-passage flow domain, it is further observed that there exists a time delay in the vortex shedding within the wake, which is not evident at the single-passage condition. [ABSTRACT FROM AUTHOR]

Bi-Global stability analysis (BGSA) is employed to assess the flow separation (FS) in two-dimensional compressor cascades, aiming to investigate the unstable phenomena and underlying mechanisms. The prediction results are correlated with the separation bubble (SPB) on suction surface (SS) or the trailing edge vortex (TEV) and exhibit good agreement with the unsteady numerical simulation (UNS), thereby confirming the instability of these two flow structures. Meanwhile, the prediction results can also partially reflect the initiation of unsteady blade loading. The perturbation distributions obtained from the eigenvectors corresponding to the physically meaningful eigenvalue, reveal two primary unstable regions: one located in the wake region and another coinciding with the SPB. With the increase of incidence angle (IA), the growth rate (GR) of small perturbations transitions from negative to positive, corresponding to the flow state shifting from stable to unstable. Additionally, the inception position of eigenmodes on SS moves upstream until it reaches the leading edge (LE) of the blade. The velocity magnitude distributions in the circumferential direction were further analyzed, demonstrating good agreement with predicted perturbation distributions, and suggesting that the K-H instability mechanism contributes to unstable phenomena. In the analysis of a two-passage flow domain, it is further observed that there exists a time delay in the vortex shedding within the wake, which is not evident at the single-passage condition. [ABSTRACT FROM AUTHOR]