Numerical Approaches Research Articles

A universal application of the general integral transform: New technique for the analysis of nonlinear oscillator systems

The wide applicability of a nonlinear oscillator is the main reason why it has gained so much attention from mathematicians and scientists, while it is difficult to be solved both numerically and theoretically. Variational iteration method is one of the numerical approaches which are used to investigate these nonlinear systems. In this paper, we present a nonlinear oscillator arising in a micro-electromechanical system as an example and derive its analytical solution by He’s frequency formula method and variational iteration method coupled with a new general integral transformation. The Lagrange multiplier is formulated and the new iterative format for the correction functional of the variational iteration method is given by the general integral transformation. The approximate nonlinear frequencies are achieved by this new technique and compared with the numerical ones obtained by the Runge–Kutta method. The new general integral transformation has the same essential qualities as those for Laplace and Fourier transform, and it becomes a promising tool to nonlinear problems when coupled with the variational iteration method.

Secondary Resonances of Asymmetric Gyroscopic Spinning Composite Box Beams

A comprehensive theoretical investigation on the occurrence of secondary resonances in parametrically excited unbalanced spinning composite beams under the stretching effects is conducted numerically and analytically. Based on an optimal stacking sequence and Rayleigh’s beam theory, the governing equations of the system are derived using extended Hamilton’s principle. The system’s partial differential equations are then discretized using the Galerkin method. Numerical (Runge–Kutta technique) and analytical (multiple scales method) approaches are exploited to solve the reduced-order equations, and their results are compared and verified accordingly. Comparison and convergence investigations are performed to guarantee the validity of the outcomes. Stability and bifurcation analyses are accomplished, and resonance effects are thoroughly studied utilizing frequency-response diagrams, phase portraits, Poincaré maps and time-history responses. It is observed that among the various types of secondary resonance, only a combination resonance can be observed in the system dynamics. The outputs reveal that, in this resonance, the gyroscopic coupling results in the steady-state time response consisting of three main frequencies. By examining the effects of damping, eccentricity, and beam length, it is exhibited that this resonance does not occur in the system’s dynamics for any combination of these parameters. Therefore, these parameters can be adjusted in the design of asymmetric beams to prevent this type of resonance.

Optimization of polarization spectroscopy signal for laser-frequency stabilization

Abstract We experimentally generate polarization spectroscopy (error) signals corresponding to the D2-line hyperfine transitions, F g = 2 → F e = 1 , 2 , 3 of 87Rb, and F g = 3 → F e = 2 , 3 , 4 of 85Rb, and show that the strongest error signals correspond to the closed hyperfine transitions (oscillator strength ∼ 0.7 ), F g = 2 → F e = 3 and F g = 3 → F e = 4 , respectively. We make the generated error signal robust to fluctuations in external parameters by finding optimum values for the vapor cell temperature and pump-probe intensities at two different beam diameters. We further employ these optimized error signals to directly (without the need for frequency/phase modulation) lock the laser frequency—reducing the rms drift/linewidth from ∼ 10 MHz to < 500 kHz, when measured over a ∼ 60 min duration. In addition, by comparing theoretically calculated and experimentally measured error signals for the pump intensities ranging from ∼ 0.1 I sat 0 − 10 I sat 0 (where, I sat 0 ∼ 1.6 mW cm−2 is the two-level saturation intensity for the Rb D2-line transitions), we discuss the applicability and limitations of existing numerical and analytical approaches based on a full multi-level rate equation model for polarization spectroscopy.

Stability optimization of energetic particle driven modes in nuclear fusion devices: the FAR3d gyro-fluid code

The development of reduced models provide efficient methods that can be used to perform short term experimental data analysis or narrow down the parametric range of more sophisticated numerical approaches. Reduced models are derived by simplifying the physics description with the goal of retaining only the essential ingredients required to reproduce the phenomena under study. This is the role of the gyro-fluid code FAR3d, dedicated to analyze the linear and nonlinear stability of Alfvén Eigenmodes (AE), Energetic Particle Modes (EPM) and magnetic-hydrodynamic modes as pressure gradient driven mode (PGDM) and current driven modes (CDM) in nuclear fusion devices. Such analysis is valuable for improving the plasma heating efficiency and confinement; this can enhance the overall device performance. The present review is dedicated to a description of the most important contributions of the FAR3d code in the field of energetic particles (EP) and AE/EPM stability. FAR3d is used to model and characterize the AE/EPM activity measured in fusion devices as LHD, JET, DIII-D, EAST, TJ-II and Heliotron J. In addition, the computational efficiency of FAR3d facilitates performing massive parametric studies leading to the identification of optimization trends with respect to the AE/EPM stability. This can aid in identifying operational regimes where AE/EPM activity is avoided or minimized. This technique is applied to the analysis of optimized configurations with respect to the thermal plasma parameters, magnetic field configuration, external actuators and the effect of multiple EP populations. In addition, the AE/EPM saturation phase is analyzed, taking into account both steady-state phases and bursting activity observed in LHD and DIII-D devices. The nonlinear calculations provide: the induced EP transport, the generation of zonal structures as well as the energy transfer towards the thermal plasma and between different toroidal/helical families. Finally, FAR3d is used to forecast the AE/EPM stability in operational scenarios of future devices as ITER, CFETR, JT60SA and CFQS as well as possible approaches to optimization with respect to variations in the most important plasma parameters.

Energy absorption properties of origami‐based re‐entrant honeycomb sandwich structures with CFRP subjected to low‐velocity impact

AbstractThis paper investigates a honeycomb sandwich structure that draws inspiration from the craft of origami. A specific folding pattern was applied to the honeycomb to create the origami‐based re‐entrant honeycomb (ORH), aimed at improving the energy absorption properties of the sandwich structure. The study on the energy absorption properties of structures under low‐velocity impact (LVI) utilized both experimental and numerical approaches. The energy absorption properties of the sandwich structure were examined by conducting LVI tests with different impact energy and then compared to the mechanical properties of the traditional re‐entrant honeycomb sandwich structures (TRHSS). Additionally, a refined finite element model has been established and its accuracy verified. Numerical studies were conducted to explore the effects of structural parameters on the energy absorption properties of ORH sandwich structure (ORHSS). The results show that the ORHSS exhibited a significant reduction in peak force when subjected to LVI, in contrast to the TRHSS. Furthermore, the ORHSS exhibit significant efficiency in energy absorption. Enhancing the wall thickness or folding angle can significantly improve the energy absorption properties of the ORHSS, thereby boosting the honeycomb's contribution to this process. This optimization results in an improved absorptive effect of the structure. The findings offer new recommendations for developing lightweight absorbent materials with potential applications across various industries.Highlights A novel composite sandwich structure serves as an efficient device for absorbing energy. This sandwich structure exhibits excellent cushioning and energy absorption capabilities. Changing geometric parameters can enhance the impact performance of the structure. A larger folding angle makes the core more prone to deformation. The greater the forward length of the ORH, the lower specific energy absorption (SEA) of the ORHSS.

Analytical and Numerical Approaches via Quadratic Integral Equations

Analytical and Numerical Approaches via Quadratic Integral Equations

Geometric tunability of interlaminar resistance

The inherent weakness and variability in the interlaminar properties of composites and associated delamination pose significant challenges, compromising the performance of composite structures. This study investigates a strategy to tailor the apparent interlaminar resistance by altering the geometry of the interface to control crack propagation. We have developed analytical models, which propose a formulation that links the geometry, i.e. the interface width change rate and shape factor of the crack growth plane, with the reaction force–displacement curve. The results obtained, a family of power law relations followed during interlaminar crack growth, indicate that the analytical formulation is valid for all geometries tested, including those with significant width change rates; however, it may not always be easy to use or interpret. An approximated solution, constrained to slowly varying geometries, is also proposed. The limits of using this model are presented and discussed. The final validation of the models is performed using numerical and experimental approaches, considering the delamination of carbon fiber laminates. This work offers new insights into the design of composites and the fracture process in general, featuring unique shapes and improved crack resistance. It also addresses practical issues, e.g., related to composite repairs, which can enhance the performance and longevity of composite structures. Specifically, the proposed formulations can be easily adopted to obtain optimized patch geometries.

Two highly accurate and efficient numerical methods for solving the fractional Liénard’s equation arising in oscillating circuits

In this paper, we investigate the fractional model of the Liénard and Duffing equations with the Liouville-Caputo fractional derivative. These equations grow with the evolution of radio and vacuum tube technology, which describe oscillating circuits and generalize the spring–mass device equation. We compare two numerical approaches, namely Jacobi and Haar wavelet collocation methods. The given approaches are used to discretize and transform the equation into a system of algebraic equations, and the Broyden-Quasi Newton algorithm is applied to solve the resulting nonlinear system of equations. A complete error analysis and convergence rates for different grid sizes are derived for both methods, which are used to compare the accuracy and efficiency of the two approaches. While both approaches produce correct solutions, according to the numerical findings, the Jacobi collocation method is more efficient and accurate than the Haar wavelet collocation method.

Effect of rotation speed fluctuation on rotor noise generation: A numerical and experimental study

The practical operations of rotors for unmanned aircraft systems can undergo time-varying rotation speeds due to various uncertainty factors. This work investigates the aeroacoustic effect of the rotor’s rotation speed fluctuation using both numerical and experimental approaches. The measured real-time angular speed signal reveals that a hovering rotor experiences highly deterministic rotation speed variations in one revolution, which are closely related to the motor property. Delayed detached eddy simulations are performed, and the fluctuating rotation speed is realized by controlling the mesh displacement at each time step. The results suggest that significant additional tones are produced at the excitation frequency and neighbour frequencies, even though the amplitudes of the rotation speed fluctuations at the dominant frequencies are much smaller than the mean rotation speed. By comparing the full signal to individual harmonic components, it is found that the phase difference between each mode is unimportant. Therefore, the total aeroacoustic effect can be regarded as a linear superposition of different harmonic components. Aeroacoustic source analysis is also performed to isolate the contribution of various source types and correlate the far-field noise with the near-field source distribution. The results show that the extra tonal noise is mostly dominated by the loading noise, with a weaker contribution from the thickness noise. The agreement between the experiments and the simulations indicates that the rotation speed fluctuation is likely responsible for the generation of middle-frequency tonal noise at harmonics of the blade passing frequency.

Physics-informed convolutional neural network for microgrid economic dispatch

The variability of renewable energy generation and the unpredictability of electricity demand create a need for real-time economic dispatch (ED) of assets in microgrids. However, solving numerical optimization problems in real-time can be incredibly challenging. This study proposes using a convolutional neural network (CNN) based on deep learning to address these challenges. Compared to traditional methods, CNN is more efficient, delivers more dependable results, and has a shorter response time when dealing with uncertainties. While CNN has shown promising results, it does not extract explainable knowledge from the data. To address this limitation, a physics-inspired CNN model is developed by incorporating constraints of the ED problem into the CNN training to ensure that the model follows physical laws while fitting the data. The proposed method can significantly accelerate real-time economic dispatch of microgrids without compromising the accuracy of numerical optimization techniques. The effectiveness of the proposed data-driven approach for optimal allocation of microgrid resources in real-time is verified through a comprehensive comparison with conventional numerical optimization approaches.

Understanding Unsteady Vortex Structure and Shedding Frequency of Cylindrical Hole Film Cooling: Insights From Experimental and Numerical Approaches

Abstract To enhance film cooling effectiveness and reduce mixing loss, it is imperative to understand the dynamics of the unsteady vortex system and its interaction with the mainstream flow. In this study, a comprehensive experimental investigation was conducted to assess the film cooling effectiveness of a flat-plate cylindrical hole, along with the structure of the vortex system and the frequency of vortex shedding. This was achieved using a variety of techniques including pressure-sensitive paint (PSP), particle image velocimetry (PIV), hot-wire anemometry, and dynamic pressure sensors. To complement the experimental findings, a detailed analysis of the evolution mechanisms of unsteady coherent vortices was performed using the detached eddy simulation (DES) numerical method. The findings of the study revealed that the Kelvin–Helmholtz (K–H) shear vortex patterns on the windward side undergo a transition from clockwise to counterclockwise rotation with increasing blowing ratios. Large-scale vortex sheds from the K–H shear vortices, ultimately evolving into the hairpin vortex in the downstream region. Additionally, the study proposed two evolution models for the vortex systems in the film cooling flow field at different blowing ratios and elucidated the evolution mechanisms of counter-rotating vortex pair (CRVP). The results of the spectral analysis revealed a notable discrepancy in the slopes of the eigenfrequencies, which could be attributed to variations in the evolution patterns of the vortex systems.

Progressive Dies for L-hanger Ducting (L-HD) Utilizing Low-Carbon Steel SPCC-SD Material: An Experimental and Numerical Analysis

Industrial developments, especially in the manufacturing and construction sectors, recognize L-hanger ducting as a critical component in HVAC (heating ventilation and air conditioning) ducting systems, which play a role in supporting and stabilizing air ducts. The L-Hanger ducting manufacturing process involves a series of stages, such as shearing, blanking, piercing, trimming, and bending processes. This research focuses on the design and simulation of dies and punches for piercing, blanking, and bending processes using 1.6 mm-thick SPCC-SD material. The aim of this research is to design and analyze progressive dies in order to increase the efficiency of the production process. A comprehensive calculation of the forces involved in the shearing, blanking, piercing, trimming, and bending processes is required in order to predict press machine tonnage requirements to support the production process. This research applies theoretical and numerical validation approaches. Theoretical analysis is used to calculate the overall forces, which are then compared with numerical results and verified through an experimental approach. By understanding and optimizing the design of progressive dies, it is hoped that we can increase the production efficiency of L-hanger Ducting and expand knowledge in the field of metal forming, contributing to the metal forming industry and supporting the development of science.

Interrelationship between Wall and Beach Erosion in Loc An, Vietnam: Remote Sensing and Numerical Modeling Approaches

Beach erosion and coastal protection are complex and interconnected phenomena that have a substantial impact on coastal environments worldwide. Among the various coastal protection measures, seawalls have been widely implemented to mitigate erosion and protect coastal assets. However, the interrelationship between beach erosion and seawalls remains a critical topic for investigation to ensure effective and sustainable coastal management strategies. Seawalls impact the shoreline, particularly through the “end effect”, where the seawall functions similarly to a groin, causing erosion on the downdrift side relative to the direction of wave approach. This study provides a detailed analysis of the interplay between beach erosion and seawall structures in Loc An, Vietnam, employing both remote sensing and numerical approaches. Sentinel-2 images were employed together with an analytical solution to observe the shoreline change at the Loc An sand spit and to determine input values for the numerical model. Based on the shoreline dynamics, a numerical scheme was employed to study the shoreline evolution after the construction of a seawall. Our findings show that the shoreline evolution can be divided into three stages: (1) The first stage corresponds to the elongation of the sand spit without interference from coastal structures. (2) The second stage shows the effect of jetties on the shoreline, as signaled by the buildup of sand updrift of the jetties. (3) The third stage shows the effectiveness of the seawall, where the shoreline reaches its equilibrium condition. The study provides a quick and simple method for estimating shoreline diffusivity (ε) in situations where measured data is scarce.

Numerical Investigation of Wake Characteristics for Scaled 20 kW Wind Turbine Models with Various Size Factors

Wind energy is essential for sustainable energy development, providing a clean and reliable energy source through the wind turbine. However, the vortices and turbulence generated as wind passes through turbines reduce wind speed and increase turbulence, leading to significant power losses for downstream turbines in wind farms. This study investigates wake characteristics in wind turbines by examining the effects of different scale ratios on wake dynamics, using both experimental and numerical approaches, utilizing scaled-down models of the Aeolos H-20 kW turbine at scales of 1:33, 1:50, and 1:67. The experimental component involved wind tunnel tests in an open-circuit tunnel with adjustable wind speeds and controlled turbulence intensity. Additionally, Computational Fluid Dynamics (CFD) simulations were conducted using STAR-CCM+ (Version 15.06.02) to numerically analyze the wake characteristics. Prior to the simulation, a convergence test was performed by varying grid density and y+ values to establish optimized simulation settings essential for accurately capturing wake dynamics. The results were validated against experimental data, reinforcing the reliability of the simulations. Despite minor inconsistencies in areas affected by tower and nacelle interference, the overall results strongly support the methodology’s effectiveness. The discrepancies between the experimental results and CFD simulations underscore the limitations of the rigid body assumption, which does not fully account for the deformation observed in the experiment.

An Innovative Dual-Level Energy Dissipation System with Friction/Yielding Dampers: Numerical and Theoretical Approaches

An Innovative Dual-Level Energy Dissipation System with Friction/Yielding Dampers: Numerical and Theoretical Approaches

Comparing Large-Eddy Simulation and Gaussian Plume Model to Sensor Measurements of an Urban Smoke Plume

The fast prediction of the extent and impact of accidental air pollution releases is important to enable a quick and informed response, especially in cities. Despite this importance, only a small number of case studies are available studying the dispersion of air pollutants from fires in a short distance (O(1 km)) in urban areas. While monitoring pollution levels in Southampton, UK, using low-cost sensors, a fire broke out from an outbuilding containing roughly 3000 reels of highly flammable cine nitrate film and movie equipment, which resulted in high values of PM2.5 being measured by the sensors approximately 1500 m downstream of the fire site. This provided a unique opportunity to evaluate urban air pollution dispersion models using observed data for PM2.5 and the meteorological conditions. Two numerical approaches were used to simulate the plume from the transient fire: a high-fidelity computational fluid dynamics model with large-eddy simulation (LES) embedded in the open-source package OpenFOAM, and a lower-fidelity Gaussian plume model implemented in a commercial software package: the Atmospheric Dispersion Modeling System (ADMS). Both numerical models were able to quantitatively reproduce consistent spatial and temporal profiles of the PM2.5 concentration at approximately 1500 m downstream of the fire site. Considering the unavoidable large uncertainties, a comparison between the sensor measurements and the numerical predictions was carried out, leading to an approximate estimation of the emission rate, temperature, and the start and duration of the fire. The estimation of the fire start time was consistent with the local authority report. The LES data showed that the fire lasted for at least 80 min at an emission rate of 50 g/s of PM2.5. The emission was significantly greater than a ‘normal’ house fire reported in the literature, suggesting the crucial importance of the emission estimation and monitoring of PM2.5 concentration in such incidents. Finally, we discuss the advantages and limitations of the two numerical approaches, aiming to suggest the selection of fast-response numerical models at various compromised levels of accuracy, efficiency and cost.

The Advanced Analysis of Deep Drawing Processes for 1-Inch Diameter Dop-Pipe Caps: Simulation and Experimental Insights

This article investigates the challenges and solutions within the deep drawing process, focusing on issues like cracks and deviations from standard thickness dimensions. Utilizing both experimental methods with a 40-ton power press machine and numerical simulations via ABAQUS software, the study uses SPCC-SD steel to produce a Dop-pipe 1-inch diameter pipe cap. Key findings reveal significant correlations in elements E-90 and E-91, with minimal disparities of around 4.5% between experimental and numerical approaches, showcasing the accuracy of numerical predictions. Notably, the numerical simulations identify potential issues such as increased thickness due to higher axial forces, providing valuable insights for process optimization and defect reduction. By advancing the deep drawing process and extending its applicability to broader material-forming applications, this research contributes significantly to enhancing production efficiency and improving manufacturing practices, emphasizing the importance of simulation-driven approaches in achieving precision and quality enhancement in complex manufacturing processes.

Numerical implementation and comparison study on simulating thermo-elastic fracture using adaptive phase-field method combined with BFGS algorithm and AM algorithm

In this paper, the computational performance of alternate minimization (AM) and Broyden–Fletcher–Goldfarb–Shanno (BFGS) to solve the coupled partial differential equations arising within the framework of the phase field method is numerically studied. Both the numerical approaches are employed on an adaptive phase field method. In the case of BFGS, a double-loop recursive algorithm in combination with a line search is implemented. The local refinement is based on a pre-defined threshold on the damage variable and element size. The incompatible nodes due to adaptive refinement are handled by variable-node elements. The performance of the solution algorithm is numerically studied for a few problems with different loading conditions, viz., pure mechanical, pure thermal and combined thermo-mechanical. From the study, it is opined that the BFGS algorithm is 2∼5 times faster than the AM approach, which is typically used for adaptive phase field framework. In addition, the detailed numerical implementation is presented.

Application of a UV-vis spectrometer to investigate the effect of dissolution media on the diffusivity of small molecules and proteins

To date, the commonly used methods for diffusion coefficient measurements have some hurdles that prevent them from being widely applied in pharmaceutical laboratories. This study aimed to modify a method developed by di Cagno et al. based on the use of a UV-Vis spectrometer and apply the method to investigate the effect of dissolution media on the diffusivity of small molecules and proteins. A total of five small molecules and two proteins in different aqueous media and polymer solutions were investigated in this study. By attaching a 3D-printed cover with an open slit to a standard UV-Vis cuvette, the incident UV light could only pass through the open slit to measure the local drug concentration. During the diffusion experiment, drug molecules diffused from the cuvette bottom to the slit. According to the concentration measured as a function of time, diffusion coefficient was calculated based on Fick's law of diffusion using the analytical and numerical approaches. As a result, diffusion coefficients could be accurately measured with high reproducibility. The results also suggested that different media could affect the diffusion coefficients of small molecules by < 10% and proteins by < 15%. Since the UV-Vis spectrometer is a routine instrument, this method can potentially be employed by many pharmaceutical laboratories for diffusion coefficient measurements.

A simple analytical method to estimate runoff generation and accumulation

The study of runoff formation in semiarid regions relies generally on the solution of Richards equations using numerical approaches such as those provided by Hydrus-1D. We demonstrate here that a Simple Analytical Method (SAM) could be easily applied to estimate areas under flooding risk, under different soil and rainfall conditions, without the need to run burdensome numerical models. The impact of antecedent soil moisture condition was expressed quantitatively, conferring to SAM a predictive capability based on a-priori information on soil properties, rainfall characteristics, and initial conditions. The SAM was applied to the Shikma catchment, in the center of Israel, to illustrate its capability to estimate the spatial distribution of time of runoff occurrence and runoff coefficient for a prescribed rainfall event. The results suggest that SAM can be used as part of early warning systems of flood risks. Radars, carried by satellites and drones, can be used to provide refined data on rainfall intensity and soil surface initial conditions. SAM could be then coupled with these remotely sensed data to improve runoff initiation and accumulation estimates, thus reducing the time interval required to reach operational decisions regarding potential floods and inundations, and related water erosion hazards.