Modal Coefficients Research Articles

Experimental exploration of methane-coal dust explosion suppression by expandable graphite: From the point of view of pressure, flame, spectrum, and flow field

Expandable graphite (EG) has been proposed as a more efficient material for suppressing methane-coal dust explosions. The suppression effect was evaluated based on pressure, flame, spectrum, and flow field. The influence of particle size, expansion ratio, and suppressant concentration on the suppression effect was considered, and the suppression mechanism was analyzed. The explosion characteristics and OH* emission spectrum indicated that EG effectively suppressed methane-coal dust explosions. Higher concentrations, smaller particle sizes, and higher expansion ratios resulted in a stronger suppression effect. The influence of EG parameters on suppression effectiveness was ranked from highest to lowest in terms of the concentration, particle size, and expansion ratio. Schlieren imaging showed that EG can partially suppress the initial flame. However, the significant suppression effect occurs during the pressure-increase stage. The flow field was also analyzed using proper orthogonal decomposition. The results showed that EG suppressed flow-field fluctuations, with the mode coefficient trends aligned closely with the pressure-change curve.

Spatiotemporal coupling deep neural network for time-resolved flow field reconstruction around a circular cylinder

We propose a spatiotemporal coupling deep neural network approach for time-resolved reconstruction of the velocity field around a circular cylinder. The neural network leverages two distinct data types: (1) non-time-resolved velocity field around the cylinder, consisting of fixed frequency sampling and variable frequency sampling velocity field, and (2) the time-resolved surface pressure sequence around the cylinder. The deep neural network comprises two sub-networks: a convolutional autoencoder (CAE) for nonlinear mode extraction and a Transformer for sequence-to-sequence learning. We refer to this architecture as CTNet (CAE-Transformer Network). The encoder in the CAE maps non-time-resolved velocity field to a latent vector, enabling the extraction of nonlinear modal coefficients. An appropriate time window length for the surface pressure sequence is then selected to establish a Transformer sequence learning model, using the chosen sequence as input to predict the corresponding nonlinear modal coefficients. Once the Transformer is well trained, the time-resolved nonlinear modal coefficients of velocity field can be achieved. Along with the well-trained decoder in the CAE, the time-resolved velocity field can be reconstructed from the output of the Transformer. We verify the performance of CTNet by a simulated dataset at a representative Reynolds number of 3900. The results show a relative reconstruction error of just 6.3% for the time-resolved velocity field, demonstrating high reliability in the reconstruction. We further compare the reconstructed velocity field obtained with and without the utilization of variable frequency sampling velocity field. Notably, the inclusion of variable frequency sampling velocity field significantly improves the reconstruction quality.

Complex flow field analysis in Multi-Shaft stirred Reactors: Dynamics of Wave-Vortex coupling revealed by POD and DMD methods

Insufficient understanding of complex flow structures in multi-shaft stirred reactors hinders industrial adoption. In this work, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) methods were used to analyze the Large-Eddy Simulation (LES) results of the stationary and rotating zones for three types of stirred reactors, including multi-shaft configurations. The results indicate that the flexible spatial distribution of the impellers in multi-shaft stirred reactors enhances fluid interactions, leading to the superior performance in energy cascading, flow field self-regulation, and wave-vortex coupling. Frequency analysis of single modes underscores DMD’s efficacy in interpreting complex flow phenomena. Based on this, the DMD modal coefficients were fitted to equations, clarifying the development process of wave-vortex coupling within the stirred reactors. Additionally, by integrating fundamental fluid mechanics equations with the outcomes of the DMD method, a wave-vortex coupling model was developed, which is anticipated to yield a more accurate representation of the flow field.

The broad study of blade cascade under controlled torsional flutter: Dynamics of the flow and stability analysis

The experimental and numerical investigation of the flow instabilities acting on rigid blades and vice versa was conducted for both compressor and turbine configuration. The blade cascade consisted of five rectangular NACA 0010 blades, with three middle blades capable of performing harmonic motion with one degree of freedom (pitching) using force excitation. The base case (all blades fixed) and excited regime were examined. The influence of various angles of attack, harmonic frequency values, amplitude values, inter-blade phase angles and Reynolds numbers (Re) were tested. The mean flow properties as well as the fluid - structure interaction (FSI) were studied using Particle Image Velocimetry (PIV), Reynolds-averaged Navier-Stokes (RANS) CFD methods and using force measurement. Additionally, two different approaches, namely traveling wave mode (TWM) and aerodynamic influence coefficient (AIC), were adopted to estimate the aeroelastic stability of the blade cascade, and the results were compared. The results show significant aeroelastic coupling between the blades in both compressor and turbine configuration. However, the aerodynamic coupling effect for torsional flutter is more prominent in turbine configuration.

DMD-based spatiotemporal superresolution measurement of a supersonic jet using dual planar PIV and acoustic data

The present study applies a framework of the spatiotemporal superresolution measurement based on the total-least-squares dynamic mode decomposition, the Kalman filter and the Rauch-Tung-Striebel smoother to an axisymmetric underexpanded supersonic jet of a jet Mach number of 1.35. Dual planar particle image velocimetry was utilized, and paired velocity fields of the flow with a short time interval were obtained at a temporal resolution of 5000 Hz. High-frequency acoustic data of 200,000 Hz were simultaneously obtained. Then, the time-resolved velocity fields of the supersonic jet were reconstructed at a temporal resolution of 200,000 Hz. Also, time coefficients of dynamic modes in high temporal resolution were calculated. The correlation between time coefficients implies that the mixing promotion by screech tone causes the lift-up of the high-velocity fluid from the jet center and accelerates at the downstream side.

Global prediction and analysis for helicopter noise footprint based on acoustic modes.

Aiming to address the significant external noise produced by helicopter rotors, an integrated process based on acoustic modes has been developed for predicting the global noise footprint. The proposed method has the advantages of global prediction, analysis, and low computational costs. The key steps involve constructing an acoustic modal database and efficient prediction of noise footprint. First, the global noise model is utilized to map the time-domain sound pressure to amplitudes and coefficients in the acoustic modal domain. Acoustic mode coefficients representing various flight states are systematically cataloged in the database. Subsequently, the coefficients are extracted based on the characteristic parameters of trajectory elements, allowing for the evaluation of noise radiation in the acoustic modal domain. To investigate the impact of descent angle and advance ratio on the noise footprint, a simulation study is conducted in the forward and approach flight with an AS350 helicopter. Results indicated that, for a region with 1800 observers, the computational time of the developed approach requires only one-fifth of the time compared to the traditional Rotorcraft Noise Model method. This remarkable reduction in computation time, along with the global predictive capability, supports the practicality of efficient noise footprint assessment in both military and civilian contexts.

Experimental Investigations on Aeroelastic Stability of Combined Plunge-Pitch Mode Shapes in a Linear Compressor Cascade

Abstract The effect of mode shape and reduced frequency on the flutter stability of a linear low-speed compressor cascade was investigated experimentally, employing the aerodynamic influence coefficient (AIC) approach. This paper describes in detail the methodology, experimental setup, and measurement techniques. The paper presents experimentally determined influence coefficients, and discusses the findings with regard to the aeroelastic design parameter “plunge-to-twist incidence ratio” (PTIR), which combines reduced frequency and torsion axis setback in an attempt a design variable reduction. The influence of the vibrating blade on itself was always stabilizing, while other blades, mainly the first pressure side neighbor, vibrating at forward-traveling, low nodal diameter inter-blade phase angles (IBPAs), can destabilize the reference blade. As PTIR is increased, the phase of the complex modal force coefficients (AICs) of all blades is decreased, increasing the stabilizing effect of the vibrating blade on itself and overall cascade stability. Within the considered parameter range, the impact of reduced frequency is eliminated to a large extent if the incidence ratio is kept constant, requiring the torsion axis setback to be adjusted accordingly. The findings show that the plunge-to-twist incidence ratio is a meaningful aeroelastic design parameter that can explain the global effect of mode shape on flutter stability and should be considered early in the aeromechanical blade design process to ensure flutter-free blading.

Bridge the gap between simulated and real-world data in optical fiber mode decomposition for accuracy improvement: A deep learning-based co-learning framework with visual similarity-based matching

In the area of optical fiber mode decomposition (MD), data-driven deep-learning (DL) algorithms have achieved remarkable strides with unlimited theoretically synthetic data, but the differences between theoretical and real-world data in the DL context are rarely investigated. The two differences, namely the information bottleneck and the domain discrepancy, between the simulation and realistic domain remain significant obstacles that limit the practical deployment of DL-based MD approaches in real-world optical systems. The paper aims to mitigate their influence on the accuracy limitation and the accuracy degradation of DL-based MD. First, we present a DL-based co-learning framework for MD for the first time. With the co-learning process, the knowledge of the teacher model learned from rich input information sources (near-field, far-field, and phase-distribution optical images) is transferred to the student model with the only near-field input source, which breaks the information bottleneck by allowing the student model to learn more knowledge in a simulation context. Furthermore, to settle the domain discrepancy between ideal data and practical observation, we propose a visual similarity-based matching to assign real values of modal coefficients to the practical optical images whose ground truth values cannot be easily acquired, which enables the transfer learning from the synthetic data to the real-world data for accuracy enhancement. Simulated and experimental results show that the proposed co-learning framework with visual similarity-based matching has realized high precision and robustness in MD simulated and practical tasks. By bridging the gap between theoretical and practical data, our study offers novel perspectives on DL-based MD practice.

Second register production on the clarinet: Nonlinear losses in the register hole as a decisive physical phenomenon.

This study investigates the role of localized nonlinear losses in the register hole of a clarinet in producing second-register notes. First, an experiment is conducted to study the ability of the opening of a register hole to trigger a jump in oscillatory regime from the first to the second register. A cylindrical tube is drilled with holes of increasing diameter: five at the register hole level and five at the thumb hole level of a B-flat clarinet. Clarinetists are asked to play with constant parameters, blindfolded, beginning with all holes closed. The operator randomly opens one of the ten holes, noting the resulting register. The experiment is replicated numerically by time integration of two different models. The first is the model from Taillard, Silva, Guillemain, and Kergomard [(2018). Appl. Acoust. 141, 271-280] based on the modal decomposition of the input impedance. The second accounts for localized nonlinear losses in the register hole, through the model from Dalmont, Nederveen, Dubos, Ollivier, Méserette, and Sligte [(2002). Acta Acust. united Ac. 88, 567-575]. These losses are handled through variable modal coefficients. For the first model, simulations never produce the second register for any of the open holes. For the second, the proportion of second-register production is close to the experiment for upstream holes, but remains at zero for downstream holes.

OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws

Suppressing spurious oscillations is crucial for designing reliable high-order numerical schemes for hyperbolic conservation laws, yet it has been a challenge actively investigated over the past several decades. This paper proposes a novel, robust, and efficient oscillation-eliminating discontinuous Galerkin (OEDG) method on general meshes, motivated by the damping technique (see J. Lu, Y. Liu, and C. W. Shu [SIAM J. Numer. Anal. 59 (2021), pp. 1299–1324]). The OEDG method incorporates an oscillation-eliminating (OE) procedure after each Runge–Kutta stage, and it is devised by alternately evolving the conventional semidiscrete discontinuous Galerkin (DG) scheme and a damping equation. A novel damping operator is carefully designed to possess both scale-invariant and evolution-invariant properties. We rigorously prove the optimal error estimates of the fully discrete OEDG method for smooth solutions of linear scalar conservation laws. This might be the first generic fully discrete error estimate for nonlinear DG schemes with an automatic oscillation control mechanism. The OEDG method exhibits many notable advantages. It effectively eliminates spurious oscillations for challenging problems spanning various scales and wave speeds, without necessitating problem-specific parameters for all the tested cases. It also obviates the need for characteristic decomposition in hyperbolic systems. Furthermore, it retains the key properties of the conventional DG method, such as local conservation, optimal convergence rates, and superconvergence. Moreover, the OEDG method maintains stability under the normal Courant–Friedrichs–Lewy (CFL) condition, even in the presence of strong shocks associated with highly stiff damping terms. The OE procedure is nonintrusive, facilitating seamless integration into existing DG codes as an independent module. Its implementation is straightforward and efficient, involving only simple multiplications of modal coefficients by scalars. The OEDG approach provides new insights into the damping mechanism for oscillation control. It reveals the role of the damping operator as a modal filter, establishing close relations between the damping technique and spectral viscosity techniques. Extensive numerical results validate the theoretical analysis and confirm the effectiveness and advantages of the OEDG method.

The reduced order model for creep using dynamic mode decomposition

Given the computational challenges associated with finite element methods in analyzing creep behavior in high-temperature components, this work presents an advanced method for modeling thermal creep in complex structures through a reduced order model (ROM) developed via dynamic mode decomposition (DMD). The results indicate that the ROM using DMD can predict long-term structural responses related to creep based on short-term data with high accuracy, enhancing significantly computational efficiency. The application of ROM allows for the rapid estimation of creep effects in complex structures, like monoliths in the MegaPower reactor, thereby improving the design efficiency. The eigenvalues of the creep related ROM all fall in the unit circle on the complex plane, indicating that creep is a stable development process. The DMD with improved time mode coefficient can reconstruct strain-rate related plastic deformation and cyclic visco-plastic deformation process. Additionally, we derive the necessary stress updating algorithm and consistent tangent operator matrix for the 316H unified visco-plastic constitutive equation in 2023 edition ASME code, ensuring accurate modeling of material creep behavior under high temperatures in this paper. This work provides a valuable tool for the safe design and operation of critical components in nuclear engineering and other high-temperature applications.

A novel model order reduction technique for solving horizontal refraction equations in the modeling of three-dimensional underwater acoustic propagation

Modeling three-dimensional (3D) underwater acoustic propagation is vital for underwater detection, localization, and navigation. This article introduces a novel model order reduction (MOR) technique to solve horizontal refraction equations (HREs) in the modeling of 3D underwater acoustic propagation. This approach relies on an adiabatic approximation of the 3D sound field, representing the field as a combination of local vertical modes with their modal coefficients governed by a system of two-dimensional (2D) HREs. Inspired by normal mode theory, the coefficients in the expansion over vertical modes are determined by projecting them onto a lower-dimensional, orthogonal space defined by their transverse eigenfunctions. By artificially truncating the horizontal domain in the transverse directions using two perfectly matched layers (PMLs), the eigenproblem associated with the transverse eigenfunctions of the modal coefficients is closed and thus can be solved through a modal projection method. The modal projection method enables fast computation of modal coefficients in a longitudinally invariant environment within seconds, offering a naturally wide-angle solution covering ±90°. The MOR method is extended to encompass fully 3D cases by introducing an admittance matrix, a memory-saving strategy that prevents numerical overflow when the longitudinal range is large. Moreover, the fact that the outer boundaries of the PMLs are range-independent allows the proposed MOR technique to perform well on a coarse grid when employing the Magnus scheme, significantly saving the numerical cost for the fully 3D simulation. Numerical simulations are provided for both longitudinally invariant and fully 3D scenarios, demonstrating the high accuracy and efficiency of the proposed MOR technique in solving HREs.

On the prediction of the turbulent flow behind cylinder arrays via echo state networks

This study aims at the prediction of the turbulent flow behind cylinder arrays by the application of Echo State Networks (ESN). Three different arrangements of arrays of seven cylinders are chosen for the current study. These represent different flow regimes: single bluff body flow, transient flow, and co-shedding flow. This allows the investigation of turbulent flows that fundamentally originate from wake flows yet exhibit highly diverse dynamics. The data is reduced by Proper Orthogonal Decomposition (POD) which is optimal in terms of kinetic energy. The Time Coefficients of the POD Modes (TCPM) are predicted by the ESN. The network architecture is optimized with respect to its three main hyperparameters, Input Scaling (INS), Spectral Radius (SR), and Leaking Rate (LR), in order to produce the best predictions in terms of Weighted Prediction Score (WPS), a metric leveling statistic and deterministic prediction. In general, the ESN is capable of imitating the complex dynamics of turbulent flows even for longer periods of several vortex shedding cycles. Furthermore, the mutual interdependencies of the TCPM are well preserved. However, optimal hyperparameters depend strongly on the flow characteristics. Generally, as flow dynamics become faster and more intermittent, larger LR and INS values result in better predictions, whereas less clear trends for SR are observable.

The measurement of complex modal coefficients of a superposed vortex beam based on intensity sampling methods

In recent years, extracting information from superposed vortex beams has been a topic of intense study. In this paper, complex coefficients of various superpositions are measured in both simulation and experiment by proposing and implementing four different sampling methods. Superposed vortex beams are experimentally generated using a digital micromirror device, and recorded on a 2 f optical imaging setup. To extract both amplitude and phase values of modal coefficients, a single intensity frame of the beam is sampled in the form of concentric circles, sectors, random circles, and random squares. Considering just specified parts of the intensity instead of the whole to sample the pattern increases the speed of the modal coefficient extraction. Besides, a linear set of coherent equations is solved, and achievements are compared together. As a consequence, measuring both the amplitude and phase values of coefficients simultaneously can pave the way to enable high-capacity optical communication which is carried out in this research with better than 99% and 96% accuracy, respectively.

Моделирование КВ-радиотрасс на основе волноводного подхода

We present a scheme for modeling HF radio signal characteristics along paths of different lengths, which is based on the waveguide approach — the normal mode method. We use a representation of the recorded signal field in the form of Green function products of the angular operator, excitation coefficients, and reception coefficients of individual normal modes. Algorithms have been developed for calculating distance-frequency, frequency-angular, and amplitude characteristics of signals in large spatial regions through analysis and numerical summation of normal mode series. We have implemented a complex algorithm for simulating propagation conditions of HF radio signals, which includes a medium model, algorithms for calculating signal characteristics, and operational diagnostics of radio channel. We have compared the results of the HF signal propagation characteristic modeling and the experimental oblique sounding data obtained along paths of different lengths and orientation. To analyze experimental ionograms, determine the maximum usable frequencies for propagation modes along radio paths, we employ the method of automatic processing and interpretation of oblique sounding ionograms.

HF radio path modeling by waveguide approach

We present a scheme for modeling HF radio signal characteristics along paths of different lengths, which is based on the waveguide approach — the normal mode method. We use a representation of the recorded signal field in the form of Green function products of the angular operator, excitation coefficients, and reception coefficients of individual normal modes. Algorithms have been developed for calculating distance-frequency, frequency-angular, and amplitude characteristics of signals in large spatial regions through analysis and numerical summation of normal mode series. We have implemented a complex algorithm for simulating propagation conditions of HF radio signals, which includes a medium model, algorithms for calculating signal characteristics, and operational diagnostics of radio channel. We have compared the results of the HF signal propagation characteristic modeling and the experimental oblique sounding data obtained along paths of different lengths and orientation. To analyze experimental ionograms, determine the maximum usable frequencies for propagation modes along radio paths, we employ the method of automatic processing and interpretation of oblique sounding ionograms.

Asymptotic analysis of fluid thermodynamic behaviors in the near-critical region under highly variable physical properties

Asymptotic analysis based on the fluids governing equations with the exponential model of thermophysical properties is introduced to quantify the influence of each property on the heat and mass transfer behavior of the near-critical fluid. The one-dimensional asymptotic model finds the different behavior in boundary layers and bulk regions controlled by the diffusion and wave mode, respectively. From the asymptotic model, three characteristic parameters are found: nondimensional wave velocity for wave mode, nondimensional diffusion coefficient for diffusion mode, and nondimensional mass transport coefficient for the coupling in between. Larger thermal conductivity, fluid compressibility, and lower specific heat are found to enhance the thermal wave. However, the efficiency of heat transfer by thermal waves is irrelevant to the thermal diffusivity but related to the fluid compressibility. From the calculation of the asymptotic model for supercritical carbon dioxide (sCO2), such efficiency is 0.150, which indicates that most of the thermal energy is accumulated in the boundary layers.

Study on Spatial-Temporal Evolution, Decoupling Effect and Influencing Factors of Tourism Transportation Carbon Emissions: Taking North China as an Example

As global warming intensifies, reducing carbon emissions has become a global common mission. Tourism transportation is one of the important sources of carbon emissions, and reducing its carbon emissions is a key part of achieving China’s carbon reduction goals. Based on the panel data of various provinces and cities in North China from 2000 to 2022, this paper calculates the carbon emissions of tourism transportation by using the carbon emission coefficients of different transportation modes in different segments. Moreover, the temporal and spatial evolution of the tourism economy is systematically analyzed. The Tapio decoupling model and LMDI addition decomposition model are used to analyze the relationship between carbon emissions and tourism economic growth and the effects of 11 influencing factors on carbon emissions. The results show that: ① The carbon emission of tourism transportation in North China has experienced four stages: a steady growth period, a transitional adaptation period, a stable equilibrium period, and a drastic decline period. The overall carbon emission level of tourism transportation is as follows: Hebei Province > Shanxi Province > Inner Mongolia Autonomous Region > Beijing City > Tianjin City. ② The decoupling coefficient between tourism traffic carbon emissions and economic development fluctuates but mainly shows a weak decoupling state. ③ In terms of influencing factors, passenger size and passenger density have the greatest impact on the carbon emissions of tourism transportation.

Research on modal combination coefficients considering the spectral characteristics of strong ground motion

To address the limitations of traditional complete quadratic combination (CQC) modal combination coefficients in calculating ground motions with narrow bandwidth and long periods, a revised methodology is proposed. The new CQC modal combination coefficients are formulated by considering the spectral characteristics of strong ground motion, taking the modified Kanai-Tajimi spectrum model as a prerequisite, and applying random vibration theory. Simultaneously, a random phase simple harmonic process model for a single harmonic component is established, and corresponding combination coefficients are provided. The necessity and rationality of considering the spectral characteristics of strong ground motion are demonstrated from three perspectives: differences in power spectral models, variations in combination coefficients, and the inherent combination mechanism. As an illustrative example, the layer shear model is analyzed and compared with the results of the structure's modal combination taking different combination coefficients. This comparison is conducted under the influence of long-period simple harmonic waves, four natural seismic waves in the basin, and the 50 natural ground motions suggested by ATC-63, respectively. The results indicate that the modal combination coefficients developed by considering the spectral characteristics of strong ground motions are more reasonable and can serve as a viable replacement for traditional CQC combination rules. This is especially advantageous when dealing with ground motion inputs characterized by narrow bandwidth and long periods, providing significant benefits in such scenarios.

Adjustable effective electromechanical coupling of Lamb wave resonator using AlN/Sc0.096Al0.904N composite films

With the rapid development of fifth-generation communication technology, there are more and more 5 G frequency bands and their bandwidths differ. Therefore, many researchers devote themselves to the study of resonators with adjustable electromechanical coupling coefficient. In this paper, we apply composite films to the Lamb wave resonator with a double-IDT configuration to achieve adjustable effective electromechanical coupling coefficient (Keff 2) of the first symmetric mode. The experimental results show that with the increase of the thickness ratio, the series resonant frequency ( fs ) of the resonator decreases from 2.567 GHz to 2.333 GHz; and the parallel resonant frequency ( fp ) of the resonator decreases from 2.608 GHz to 2.396 GHz. The Keff 2 is adjusted from 3.82% to 6.32% and the Δf ( fp−fs ) is adjusted from 41 to 63 MHz by using the AlN/Sc0.096Al0.904N composite films with different thickness ratios. This method may be an efficient way to adjust the bandwidth of the filter to meet the needs of different frequency bands.