Dynamic Mode Research Articles

Exploring the Performance of Alkaline Water Electrolyzers Under Dynamic Operational Conditions

Green hydrogen, produced through water electrolysis driven by Renewable Energy Sources (RES), is a compelling solution for storing renewable energy. Directly coupling RES with water electrolyzers enhances system efficiency and cost-effectiveness. Alkaline water electrolysis, a mature and cost-effective technology, faces challenges operating under fluctuating RES conditions using AC/DC convertor , which supply rippled DC. A comprehensive understanding of electrolyzer performance in dynamic conditions is crucial for developing durable, efficient systems.In the present experimental study, we extensively explored the performance of alkaline water electrolyzers and the key factors influencing it under dynamic operational conditions. The electrolytic cell was constructed using a zero-gap configuration, comprising a NiCoOx-based anode deposited on a Ni-mesh and an Ln-doped RuOx cathode deposited on a fine mesh of Ni metal. The Zirfon Perl UTP500 membrane served as a separator between the two cell compartments [1]. A 7.0 Molar KOH electrolyte at a room temperature of approximately 30°C was employed. The cell underwent dynamic operational mode through the application of a square wave cell voltage, shown in Fig.1 (a), utilizing the NF BP4620 power supply. Square waves with different frequencies, specifically 1, 100, 1000, and 3000 Hz, were employed. Steady-state operations were conducted while applying various DC voltages, serving as a reference study. The resulting current and the actual cell voltage waveforms were monitored and recorded using a high-resolution oscilloscope (YOKOGAWA DL850E). The flow of H2 gas was measured using a film flow meter (HORIBA STEC, SF series VP-3). The apparent power, real power, and reactive power components were calculated using formulas from a previously published report [2]. Subsequently, the specific energy consumption was determined for each condition.The applied cell voltages were categorized into two groups. In the first category, the maximum cell voltage (Vmax) was set at 2.0 V, a value sufficiently high and suitable for industrial cell operation when applied in a DC mode. Within this category, the minimum cell voltage (Vmin) took various values, namely 1.8, 1.6, and 1.4 V. In the second category, the average cell voltage was maintained at a constant 2.0 V, while the amplitude of the waveform was adjusted to 0.2 and 0.4 V by modifying both Vmax and Vmin. Figure 1(b) depicts the resulting current of the voltage waveform at 100 Hz, illustrating three different Vmin values. The figure reveals that at a high Vmin of 1.8V, the current consistently maintained positive values during the voltage cycle, indicating that the double-layer capacitance remained charged throughout the operational period. However, with Vmin set at 1.6V, a relatively small capacitive current emerged, suggesting partial discharge of the double-layer capacitance. Moreover, at a lower Vmin of 1.4V, the cell voltage became insufficient to drive water electrolysis in the current cell. Consequently, a relatively large negative (capacitive) current manifested during the Vmin period, denoting a deep discharge of the double-layer capacitance.The obtained results revealed a profound influence of the charge and discharge status of the double-layer capacitance on the AWE cell's performance throughout the voltage cycles. Notably, when the double-layer capacitor remained fully charged during the voltage cycles, minimal impact of the frequency was observed on key performance parameters, including H2 flow rate that shown in figure 1 (c), specific energy consumption that shown in figure 1 (d), and power factor. However, under conditions of partial discharge within the cell voltage cycles, a noticeable correlation between the size and frequency of the voltage waveform and the AWE cell's performance emerged. Deep discharge of the double-layer capacitance led to a frequency-dependent reduction in H2 flow rate, attributed to incomplete charge/discharge cycles. Hence, the critical factor influencing the performance of the electrolytic cell during dynamic operation is the condition (charging/discharging) of the double-layer capacitance. These findings offer valuable insights into optimizing the dynamic operation of AWE cells for enhanced efficiency and performance. Acknowledgments: This research was partially supported by New Energy and Industrial Technology Development Organization (NEDO).

Characteristic value decomposition: A unifying paradigm for data-driven modal analysis

Data-driven modal analysis is an indispensable means to understand the dynamic behavior of engineered structures and natural systems. It effectively captures active dynamic behavior and embeds them in a set of identified linear modal subspaces, unveiling complex dynamic behavior via the superposition of simpler hierarchical spatiotemporal dynamics. Despite the existence of many methods, there is no unified perspective connecting these modal analysis techniques. This paper proposes a new modal decomposition method, the characteristic value decomposition (CVD), that provides a unifying paradigm for data-driven modal analysis. CVD identifies identical spatial modes and temporal coordinates from two measurement data matrices. The modal parameters are identified through an eigendecomposition to a quotient of auto-covariance and cross-covariance matrices of the two data matrices. This paper shows that several data-driven modal analysis methods, namely, the state-variable decomposition, the dynamic mode decomposition, the Ibrahim time domain method, and the eigensystem realization algorithm, are special cases of CVD when the two data matrices are appropriately selected. Moreover, the CVD identifies the modal parameters with higher accuracy and is robust to added noise compared to established methods, as demonstrated using numerical experiments. It is also shown that the CVD flexibly utilizes data from multiple experiments and undersampled data sets to unveil system dynamics.

Abstract Tu110: CD36-Mediated Transendothelial Fatty Acid Transport Determines Cardiomyocyte Uptake and is Critical to Limiting a Lipotoxic Ceramide Profile and Supporting Cardiac Function during Pathological Stress.

The heart primarily relies on long chain fatty acid oxidation (LCFA) to meet ATP demand. CD36, is a transmembrane glycoprotein transferase for LCFA uptake widely expressed in several cell types including endothelial cells (ECs), cardiomyocytes (CMs), skeletal myocytes, adipocytes, and monocyte/macrophages. Notably, genetic deficiency of CD36 in humans is associated with hypertrophic cardiomyopathy. The role of CD36 in transendothelial LCFA delivery to CMs under physiologic vs pathologic conditions is unknown. We explored consequences of EC-specific CD36 deletion (EC-CD36 KO mice) on the cardiac response to pressure overload. Lack of EC-CD36 increased severity of left ventricular hypertrophy (LVH), and systolic and diastolic dysfunction at 8 weeks of pressure overload via transverse aortic constriction (TAC), with increases in HW:TL ratio, LV mass by echo, reduced EF (p<0.05), and elevated E/E’ in EC-CD36-KO vs. flox/flox littermate controls (f/f) (p<0.5) (Fig 1). Dynamic mode 13 C NMR revealed delayed 13 C LCFA uptake kinetics (time constant, τ) in CMs of isolated, sham and TAC EC-CD36 KO hearts provided 13 C palmitate + 13 C oleate (0.02 mM each) + 10 mM glucose + 1 mM lactate (Fig 2). 13 C LCFA esterification into triglyceride (TG) was also reduced in EC-CD36-KO vs f/f controls, but without evidence for an additional effect of TAC. The contribution of 13 C LCFA to acetyl CoA entry into oxidation via the TCA cycle, was reduced by lack of EC-CD36 in sham and TAC hearts (p<0.0001) (Fig 2). Consistent with diminished LCFA oxidation, phosphocreatine (PCr) to ATP ratio was also compromised in EC-CD36-KO-TAC hearts (p<0.05). Lack of EC-CD36 during TAC increased 13 C LCFA trafficking to lipotoxic C16 ceramide in EC-CD36 KO hearts (Fig 3). CD36 in ECs is critical to LCFA delivery to CMs during pathological stress on the heart. The imbalance in intramyocellular LCFA dynamics due to restricted transendothelial delivery of LCFA to CMs increased lipotoxic ceramide formation. Thus, EC CD36 is critical to the adaptive cardiac response to pathological stress, and the absence of EC CD36-dependent delivery of LCFA to CMs exacerbates reduced energy potential, adverse cardiac remodeling, and dysfunction during afterload stress.

Experimental investigation on the dynamic response of vent plate under methane-air mixtures explosion load

The dynamic response study of explosion venting components is of great significance for the assessment of explosion disasters and the determination of damage. Based on the self-developed rectangular explosion venting device, a series of experimental investigations on the dynamic response and failure mode of calcium silicate vent plates under the methane explosion loads induced by a detonator were conducted. The results show that the vent plate mainly exhibits brittleness and presents a plastic hinge failure mode under the blasting loads. When the gas concentration is closer to the stoichiometric concentration, P2 (the peak overpressure generated by the vent plate rupture) and its pressure rise rate dP2/dt are higher. Conversely, when the methane concentration is closer to the upper or lower limits of the explosion, the explosion load tends to be static, the yield line of the vent plate is shorter, and there are fewer fragments generated by the failure of the plate. The pressure-displacement curve and the correlation diagram of failure modes proposed provide a reference for predicting the failure mode of light and fragile explosion venting components.

Estimation of Carleman operator from a univariate time series.

Reconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable. In this work, the techniques for Carleman linearization, phase-space embedding, and dynamic mode decomposition are integrated to rebuild an optimal dynamical system from time series for one specific variable. Using the Takens theorem, the embedding dimension is determined, which is adopted as the dynamical system's dimension. The Carleman linearization is then used to transform this finite nonlinear system into an infinite linear system, which is further truncated into a finite linear system using the dynamic mode decomposition technique. We illustrate the performance of this integrated technique using data generated by the well-known Lorenz model, the Duffing oscillator, and empirical records of electrocardiogram, electroencephalogram, and measles outbreaks. The results show that this solution accurately estimates the operators of the nonlinear dynamical systems. This work provides a new data-driven method to estimate the Carleman operator of nonlinear dynamical systems.

Elastoviscoplastic flows past a cylinder: Fluid-mechanical aspects and dynamic mode decomposition analysis

Elastoviscoplastic flows past a cylinder: Fluid-mechanical aspects and dynamic mode decomposition analysis

Identifying optimal location for control of thermoacoustic instability through statistical analysis of saddle point trajectories.

We propose a framework of Lagrangian Coherent Structures (LCSs) to enable passive open-loop control of tonal sound generated during thermoacoustic instability. Experiments were performed in a laboratory-scale bluff-body stabilized turbulent combustor in the state of thermoacoustic instability. We use dynamic mode decomposition on the flow-field to identify dynamical regions where the acoustic frequency is dominant. We find that the separating shear layer from the backward-facing step of the combustor envelops a cylindrical vortex in the outer recirculation zone, which eventually impinges on the top wall of the combustor during thermoacoustic instability. We track the saddle points in this shear layer emerging from the backward-facing step over several acoustic cycles. A passive control strategy is then developed by injecting a steady stream of secondary air targeting the identified optimal location where the saddle points spend a majority of their time in a statistical sense. After implementing the control action, the resultant flow-field is also analyzed using LCS to understand the key differences in flow dynamics. We find that the shear layer emerging from the dump plane is deflected in a direction almost parallel to the axis of the combustor after the control action. This deflection, in turn, prevents the shear layer from enveloping the vortex and impinging on the combustor walls, resulting in a drastic reduction in the amplitude of the sound produced.

Near-field hydrodynamic interactions determine travelling wave directions of collectively beating cilia.

Cilia can beat collectively in the form of a metachronal wave, and we investigate how near-field hydrodynamic interactions between cilia can influence the collective response of the beating cilia. Based on the theoretical framework developed in the work of Meng et al. (Meng et al. 2021 Proc. Natl Acad. Sci. USA 118, e2102828118), we find that the first harmonic mode in the driving force acting on each individual cilium can determine the direction of the metachronal wave after considering the finite size of the beating trajectories, which is confirmed by our agent-based numerical simulations. The stable wave patterns, e.g. the travelling direction, can be controlled by the driving forces acting on the cilia, based on which one can change the flow field generated by the cilia. This work can not only help to understand the role of the hydrodynamic interactions in the collective behaviours of cilia, but can also guide future designs of artificial cilia beating in the desired dynamic mode.

Approximation of translation invariant Koopman operators for coupled non-linear systems.

Many physical systems exhibit translational invariance, meaning that the underlying physical laws are independent of the position in space. Data driven approximations of the infinite dimensional but linear Koopman operator of non-linear dynamical systems need to be physically informed in order to respect such physical symmetries. In the current work, we introduce a translation invariant extended dynamic mode decomposition (tieDMD) for coupled non-linear systems on periodic domains. This is achieved by exploiting a block-diagonal structure of the Koopman operator in Fourier space. Variants of tieDMD are applied to data obtained on one-dimensional periodic domains from the non-linear phase-diffusion equation, the Burgers equation, the Korteweg-de Vries equation, and a coupled FitzHugh-Nagumo system of partial differential equations. The reconstruction capability of tieDMD is compared to existing linear and non-linear variants of the dynamic mode decomposition applied to the same data. For the regarded data, tieDMD consistently shows superior capabilities in data reconstruction.

Effect of jet splitting using passive strut on the performance and thermoacoustic characteristics of a scramjet combustor

A scramjet engine offers a potential route to achieve supersonic speeds using airbreathing engines. Achieving proper mixing and combustion poses a challenge due to the supersonic inflow of air. Researchers have explored multi-strut configurations to tackle this issue. However, multiple struts supplying fuel inefficiently can lead to fuel loss and reduced efficiency. Alternatively, utilizing a multi-strut setup passively could enhance combustion and mixing efficiency. In this study, two types of jet splitting passive strut configurations were investigated computationally with the improved delayed detached-eddy simulation turbulence model. Implementation of passive strut altered vortical structures, influencing mixing and combustion performance. The splitting of the jet introduces large-scale vortices downstream. Strategically placing the passive strut in the wake of the combustion zone was found to improve both mixing and combustion efficiency. Acoustic loading was seen to increase with the introduction of passive strut. It was observed that the diamond-shaped passive strut has the highest combustion efficiency; however, it suffers from higher acoustic loading. The dynamic mode decomposition analysis revealed the coupling frequency of fluctuating pressure and heat release rate, which causes thermoacoustic loading. Overall, passive strut placement significantly influenced combustion, mixing, and thermoacoustic properties, highlighting the importance of considering passive strut configurations in design optimization for scramjet engines.

Soft Sensors for Industrial Processes Using Multi-Step-Ahead Hankel Dynamic Mode Decomposition with Control

In this paper, a novel data-driven approach for the development of soft sensors (SSs) for multi-step-ahead prediction of industrial process variables is proposed. This method is based on the recent developments in Koopman operator theory and dynamic mode decomposition (DMD). It is derived from Hankel DMD with control (HDMDc) to deal with highly nonlinear dynamics using augmented linear models, exploiting input and output regressors. The proposed multi-step-ahead HDMDc (MSA-HDMDc) is designed to perform multi-step prediction and capture complex dynamics with a linear approximation for a highly nonlinear system. This enables the construction of SSs capable of estimating the output of a process over a long period of time and/or using the developed SSs for model predictive control purposes. Hyperparameter tuning and model order reduction are specifically designed to perform multi-step-ahead predictions. Two real-world case studies consisting of a sulfur recovery unit and a debutanizer column, which are widely used as benchmarks in the SS field, are used to validate the proposed methodology. Data covering multiple system operating points are used for identification. The proposed MSA-HDMDc outperforms currently adopted methods in the SSs domain, such as autoregressive models with exogenous inputs and finite impulse response models, and proves to be robust to the variability of systems operating points.

Direct numerical simulation of laminar boundary layer interaction with a wall-mounted circular cylinder at low-Reynolds number

In our current study, we employ direct numerical simulation to investigate the interaction between a laminar boundary layer flow and a wall-mounted circular cylinder with an aspect ratio of 4 and a Reynolds number of 750, based on the cylinder diameter and free-stream velocity. As highlighted in recent works by Morton et al. [Int. J. Heat Fluid Flow 72, 109–122 (2018)] and Crane et al. [J. Fluid Mech. 931, R1 (2022)], understanding of flow at low-Reynolds number around wall-mounted circular cylinders remains limited, motivating our study to contribute to this knowledge gap. Our objectives include exploring flow topology, analyzing first- and second-order statistics to characterize the turbulent wake flow, and investigate turbulent kinetic energy transport budgets to comprehend energy transfer mechanisms behind the cylinder. Our spectral analysis of velocity content reveals a low-frequency peak, consistent with recently published literature. However, we observe certain discrepancies between our findings and those of similar studies conducted at lower Reynolds numbers, particularly regarding the frequency content of the wake region. We employ dynamic mode decomposition to unravel the flow dynamics associated with the highest-amplitude mode. Our results indicate that the low-frequency mode reported in the above-mentioned references primarily correlates with the incoming boundary layer and is prominently evident in the lateral force coefficient, in contrast to scenarios at higher Reynolds numbers.

Unravelling spatiotemporal patterns in global sea surface temperatures with dynamic mode decomposition

AbstractExtracting global sea surface temperature (SST) patterns is essential for understanding climate variability in both regional and global perspective. Traditional methods, limited by assumptions of orthogonality, hinder our ability to fully capture the dynamics of global SST, particularly in the complex Pacific basin. This study introduces dynamic mode decomposition (DMD), a powerful method from fluid dynamics, to extract global SST patterns since 1900. Our analysis shows that DMD successfully captures well‐known patterns like global warming and the Atlantic Multidecadal Oscillation (AMO). More importantly, it reveals three Pacific SST modes that are spatially non‐orthogonal but exhibit distinct characteristics. Spectral analysis shows that these Pacific modes have distinct periodicities: Pacific Multi‐decadal Mode (PMDM, ~50 years), Quasi‐decadal Mode (PQDM, 8–16 years) and Interannual Mode (PIAM, 2–8 years). This highlights DMD's strength in not only capturing known patterns but also separating modes with similar spatial features but unique dynamics. Further analysis reveals significant differences in their impacts on global air temperature. During positive phases, all three modes induce tropical warming, with PIAM exerting the strongest influence and PMDM the weakest. In the Northern Hemisphere, both PQDM and PIAM drive mid‐latitude cooling and high‐latitude warming, with a more pronounced effect from PQDM. PMDM, in contrast, triggers widespread cooling across the Northern extratropics. In the Southern Hemisphere, PMDM's influence on temperature exhibits a distinct latitudinal banding pattern. PIAM and PQDM, on the other hand, exhibit a regionalized impact, primarily concentrated in the Amundsen and Ross Seas, with PQDM's influence extending to the Antarctic continent.

Numerical analysis of tulip flame by dynamic mode decomposition

Inversion of a premixed flame front to the shape of a tulip flower during the last stage of its propagation in a channel or tube of aspect ratio (AR) greater than two has intrigued the scientific community for decades. In the present work, the tulip inversion of hydrogen-air premixed flame is simulated numerically in two dimensional domains of AR 7.32, and 3.66. Dynamic Mode Decomposition is carried out on the two-dimensional pressure distribution obtained from the numerical simulation to understand the reasons behind the flame inversion. A plot of real and imaginary components of the eigenvalues over a unit circle clearly showed the presence of unstable acoustic modes during the tulip inversion for the domain of AR 7.32. The tulip inversion is not observed for the domain of AR 3.66. The distribution of the power and frequency of various modes are also plotted to identify the unstable modes. The present study shows generation of additional pressure waves during the tulip inversion process, which in term creates a velocity field that facilitates the flame inversion process.

Free Vibration analysis of C/SiC blisk based on modified global mode method

The bladed disk is the core component which is under load in aero-engine, rocket engine and gas turbine. In recent years, the bladed disk has developed towards the direction of integrated bladed disk (blisk) and being applied with ceramic matrix composites. However, there is no accurate semi-analytical dynamic model to describe the dynamic characteristic of ceramic matrix composite blisk. In this paper, a new semi-analytical method, modified global mode method (MGMM) is proposed to model the 2D C/SiC laminated blisk. In proposed method, Chebyshev polynomials series are used to expand the displacements of the blades and disk, constraints between blades and disk is strictly satisfied by multi-modal transformation and integrated into governing equation, and high-order shear deformation theory is combined to establish the dynamic model of the blisk of 2D C/SiC laminated composite material. The proposed method avoids the matrix singular problem appearing in traditional global mode method when modeling of combined structure and makes the system perform dynamic analysis and mode prediction without mode extraction and reconstruction. Then, amplitude frequency response and modal experiment are carried out to verify the correctness and convergence of the proposed method. Finally, under the framework of proposed method, the effects of material parameters and geometric parameters on the modal characteristics of the blisk are analyzed. The results show that compared with the geometric parameters, the material parameters have less influence on the modal characteristics of blisk, additionally, a series of modal steering is observed. The work in this paper can provide theoretical guidance for the dynamic design of composite blisk.

Effect of the combustion chamber length in combustion instability of low-toxic hypergolic thruster

In this study, the effect of combustion chamber length on the hypergolic combustion instability of hydrogen peroxide-based propellants was investigated. Twenty-four hot-firing tests were conducted using a combination of 95 wt.% hydrogen peroxide and amine-based fuel with a drop test ignition delay of 5.65 ms and an adjustable length hypergolic thruster. When the chamber length was changed from 80 mm to 120 mm, the root mean square (RMS) combustion instability decreased drastically from 24 % to 9 %. The measured high-frequency instability was considerably consistent with the longitudinal resonance mode of each combustion chamber geometry. Low-frequency instability, that is, the rate of popping, occurred predominantly in all hot-firing tests. Within the 245–418 Hz range, its frequency increased as the chamber length decreased or the chamber pressure increased. The high-speed camera image of the exhaust plume coincided with the period of low-frequency instability, which was confirmed by the periodic popping of the propellant. Combustion instability was analyzed in depth by performing power spectral density (PSD), wavelet synchro squeezed transform (WSST), dynamic mode decomposition (DMD), and image intensity analyses using the chamber pressure and exhaust plume images. DMD decomposed the plume behavior into one expansion mode and three plume decay modes, and it also matched the low-frequency instability of the chamber pressure with an error of less than 5 %.

Experimental investigation on aerodynamic noise of a small-scale multi-blade centrifugal fan

In this study, the aerodynamic noise of a small-scale centrifugal fan was experimentally investigated using acoustic testing techniques and time-resolved stereoscopic particle image velocimetry (SPIV). During the acoustic experiments, both far-field noise and near-field pressure fluctuations of the test fan were measured. The overall far-field noise towards the fan inlet side was found to be higher than that of the back side. The pressure fluctuations on the fan upper casing exceeded those on the side wall due to the uncontracted volute tongue, indicating pronounced flow-to-wall interactions. Moreover, based on a simultaneous measurement, the coherence between the near-field pressure fluctuations and far-field noise highlighted the significant contributions of impeller rotation to noise radiation. SPIV measurements uncovered the time-averaged and transient flow fields at the fan's inlet and outlet. The time-averaged results demonstrated the concentrated inlet flow and outlet flow separation, leading to high flow unsteadiness. Transient flow fields displayed an asymmetric jet-wake region characterized by both quasi-steady flow and rotational flow behaviours. The instantaneous flow results were analyzed using the dynamic mode decomposition (DMD) method, which clearly recognized the jet-wake patterns with frequencies corresponding to the rotational frequency. The observed consistency in frequency characteristics among noise, pressure fluctuations, and unsteady flow affirms that flow dynamics are crucial to the primary noise mechanisms.

Numerical comprehensive evaluation of the flow control effect on a circular cylinder with a control rod

The drag reduction of the single circular cylinder is achieved by changing the position of an additional control rod in the present work. In order to look for where to place the control rod will help the drag force exerted on the main cylinder surface as little as possible, the additional control rod is arranged at various positions in the downstream region, the upstream region, and the middle region of the single circular cylinder, respectively. The numerical results show that the maximum drag reduction rate of the single circular cylinder can be up to 21.68%. While the additional control rod is located at some specific positions in the flow field, the drag of the single circular cylinder will increase. However, if two bluff bodies (the main circular cylinder and the control rod) are considered as a whole system, due to the extra drag contribution of the control rod, the maximum drag reduction effect of the system is 8.65%. Additionally, the lift exerted on the main cylinder and the control rod has changed a lot due to the interaction between two bluff bodies. Furthermore, the Dynamic Mode Decomposition analysis method is employed to probe the mechanism of drag variation employing the dominant flow modes.

Investigation of Reynolds number effects on flow stability of a transonic compressor using a dynamic mode decomposition method

With the continuous increase in aircraft flight altitude, low Reynolds number effects in high-altitude environments significantly impact the stability of compressor operation. In this study, dynamic mode decomposition (DMD) of the flow field at various time instances near stall conditions in a transonic compressor was performed to investigate the influence of Reynolds number (Re) effects on critical flow characteristics and instability mechanisms. The results indicate that under different Reynolds number index (RNI) conditions near stall conditions, the frequency of tip leakage flow varies. Under high RNI condition, the influence of tip leakage flow is concentrated mainly from the leading edge to the mid-chord. The stall mode is primarily caused by the interaction of shock with the Tip Leakage Vortex, resulting in the breakdown of the vortex. The development of vortex structures inside the passage leads to a delay in the flow field response to blade passing. Under low RNI condition, the tip clearance leakage flow is stronger, with a relatively reduced influence from the leading edge to the mid-chord and an increased impact from the mid-chord to the trailing edge. The main cause of the stall mode is the circumferential movement of vortex structures, causing secondary leakage over adjacent blade tip clearances. The blockage formed by vortex structures within the passage is weaker, and the flow field response to blade passing remains consistent with the blade passing frequency. However, as stall develops further, the flow field response significantly decreases.

Large dynamic scissoring mode displacements coupled to band gap opening in the cubic phase of the methylammonium lead halide perovskites

Hybrid perovskites are a rapidly growing research area, having reached photovoltaic power conversion efficiencies of over 25%. There is a increasing consensus that the structures of these materials, and hence their electronic structures, cannot be understood purely from the time and space averaged crystal structures observable by conventional methods. We apply a symmetry-motivated analysis method to analyse x-ray pair distribution function data of the cubic phases of the hybrid perovskites MAPbX 3 (X = I, Br, Cl). We demonstrate that, even in the cubic phase, the local structure of the inorganic components of MAPbX 3 (X = I, Br, Cl), are dominated by scissoring type deformations of the PbX 6 octahedra. We find these modes to have a larger amplitude than equivalent distortions in the A-site deficient perovskite ScF3 and demonstrate that they show a significant departure from the harmonic approximation. Calculations performed on an inorganic perovskite analogue, FrPbBr3, show that the large amplitudes of the scissoring modes are coupled to a dynamic opening of the electronic band gap. Finally, we use density functional theory calculations to show that the organic MA cations reorientate to accommodate the large amplitude scissoring modes.