3D Finite Element Method Model Research Articles

Early detection of deep-seated smouldering fires in wood waste storage using ERT

Incidents of waste and biofuel fires are common at all stages of the waste recycling chain and have grave implications for business, employees, firefighters, society, and environment. An early detection of waste and biofuel fires in the smouldering stage could save precious lives, resources, and our environment. Existing fire detection methodologies e.g. handheld temperature sensors, IR cameras, gas sensors, and video and satellite-based monitoring techniques have inherent limitations to efficiently detect smouldering fires. An attempt was made to explore the potential of electrical resistivity tomography (ERT) as an alternate tool to address the problem. In the experiments an externally powered resistive wire was employed to initiate the smouldering fire inside the test material (wood pellets, wood shavings, wood fines). Time series of ERT that followed the initiation and development of smouldering were recorded using an automated monitoring instrument setup. The actual geometry of the experimental sample container and electrode setup was integrated in the 3D finite element method (FEM) model grid to perform inverse numerical modelling (inversion) and to develop resistivity tomographic images. The study shows a sharp increase in ratio of resistivity (R/Ro ≥ 50 %) in the test material in the region of smouldering hotspot and demonstrates the potential use of ERT technique for the detection of smouldering hotspots in silos and pile storage of organic material such as wood-based fuels, wood waste, coal, municipal solid waste (MSW), recyclables etc. More research is however required for enabling the use of this technique at the practical scale for different storage conditions.

Numerical Simulation of Cathode Nodule Local Effects

As one of the main factors decreasing current efficiency and product quality, the growth of nodules deserves attention in the copper electrorefining process. Three-dimensional (3D) Finite Element Method models combining tertiary current distribution and fluid flow were established in this study to investigate the details of the growth of columnar nodules, including the electrolyte flow around the nodule and its effects. Compared with an inert nodule, a significant impact of the electrochemical reaction of an active nodule has been observed on the fluid flow, which may be one of the reasons for the formation of small nodule clusters on the cathode. Furthermore, the local current density is not even on the nodule surface under the comprehensive influence of local electrolyte flow, local overvoltage, and the angle with the anode surface. Thus, the head of an active nodule grows faster than the root, and the upper parts grow faster than the lower parts, leading to asymmetric growth of the nodules.

Operational Analysis of an Axial and Solid Double-Pole Configuration in a Permanent Magnet Flux-Switching Generator

There are two main beneficial characteristics that doubly salient permanent magnet (PM) electrical machines present for aircraft applications: armature windings and PMs excitation sources placed on the stator side (maintenance and thermal management), and having a clear-cut rotor without PMs or excitation windings (vulnerable at high speeds due to associated centripetal mechanical stresses). Within this framework, a doubly salient permanent magnet (DSPM) generator was conceived by optimizing the stator size and rotor structure to minimize the torque ripple and maximize the root-mean-square (RMS) voltage value per turn of each generator phase. Firstly, a comparison between the 2D and 3D finite element method (FEM) models is made considering the results of 3D finite element analysis (FEA) as our benchmark in order to understand the accuracy of the 2D results against our benchmark model, the 3D one. A multi-objective design strategy based on a 2D FEA is made, it is set to have characteristics closest to optimal for a Boeing 767 turbine, that is, the necessary electromotive force for a required power of 90 kW at 3000 rpm, feeding a simplified Boeing 767 electrical power distribution system. The results show that the machine could not deliver the required power at 3000 rpm since the 2D FEA demonstrates that the 2D model gives optimistic results when compared with the 3D FEM model. However, with a 3D FEA of the machine feeding the aircraft load, it was seen that the machine’s efficiency is 92%, suggesting that this machine can be a plausible solution.

Influence of modelling hypotheses on strength assessment of CFRP stepped repairs

Composite stepped repairs can achieve high strength recovery without the addition of bolts or fasteners to the structure. They are therefore a major issue in the field of aerospace composite structure damage repair. However, there is no standardized method to design this type of repairs. Many analytical, semi-analytical and finite element models were proposed throughout the years to predict the strength of stepped repairs, using various hypotheses and simplifications. The aim of this paper is to investigate the influence of modelling hypotheses on stress distribution and strength prediction of composite stepped repairs. Five simplified stepped joint models using macro-element (ME) modelling and finite element method (FE) are compared to a full 3D FE model of a stepped repaired panel. The influence of step length and adhesive fracture toughness was investigated to determine the field of validity of each model. Among FE models, it was shown that modelling the equivalent joint under 2D generalized plain strain gives a very close strength prediction to the 3D stepped repair model while saving computation time. Simplified macro-element models under bar or beam hypotheses are fairly close to the results of FE modelling, but the deviation between those and FE is sensitive to step length and adhesive fracture toughness.

Study of the demagnetization behavior of no-insulation persistent-current mode HTS coils under external AC fields by 3D FEM simulation

The no-insulation (NI) winding technique is promising for applications in the persistent-current mode (PCM) operation of high-temperature superconducting (HTS) coils. To produce an NI PCM coil, it is essential to understand its demagnetization behavior (i.e. decay of persistent DC current) under an external AC field, which occurs in maglev trains, electric machines and other dynamic magnet systems. For this purpose, a 3D finite-element method (FEM) model, capturing the full electromagnetic properties of NI HTS coils is established. This work studied three kinds of AC fields, observing the impact of turn-to-turn contact resistivity on demagnetization rates, which is attributed to current distribution modulations. Under a transverse AC field, the lower contact resistivity attracts more transport current to flow in the radial pathway to bypass the ‘dynamic resistance’ generated in the superconductor, leading to slower demagnetization. Under an axial AC field, the demagnetization rate exhibits a non-monotonic relation with the contact resistivity: (1) the initial decrease in contact resistivity leads to a concentration of induced AC current on the outer turns, which accelerates the demagnetization; (2) the further decrease in contact resistivity makes the current smartly redistribute to avoid flowing through the loss-concentrated outer turns, thus slowing down the demagnetization. Under a rotating DC field, a hybrid of transverse and axial fields, the impact of contact resistivity on the demagnetization rate exhibits combined characteristics of the transverse and axial components. Additionally, quantitative prediction of the demagnetization rate of NI PCM coil under external AC field is instructive for practical designs and operations, which is tested by this 3D FEM model, and a comparison with experimental results is conducted.

Mechanism of hydraulic fracture vertical propagation in deep shale formation based on elastic–plastic model

Deep shale reservoirs exhibit strong plasticity, and the simulation results from previous fracturing simulations based on elastic models may not adequately account for the effects of plastic. Therefore, the research objective is to develop a 3D finite element method (FEM) model of hydraulic fracture vertical propagation in multilayer reservoirs. The model simultaneously considering Drucker-Prager elastic–plastic rock model and bedding plane. To investigate the impact of various parameters on the vertical propagation pattern of fracture, it is crucial to consider factors such as friction angle, yield strength, interlayer strength, and vertical stress. This study quantitatively characterizes the mechanical parameters such as ground stress, matrix strength, and interface strength on hydraulic fracture morphology. Additionally, a new integrated control diagram is established to provide a comprehensive understanding of these effects. The results indicate that rocks with high friction angles and low yield strength are more resistant to cracking, and hydraulic fractures tend to have narrower fractures. Fracturing from high-strength and high-stress zones to lower zones promotes vertical fracture propagation. The high vertical stress plays a crucial role in preventing the fracturing fluid from entering the interface. Moreover, the strength of the formation interface greatly influences the vertical extension of hydraulic fractures. The bedding plane interface with a high cementation level can enhance the possibility of fracture vertical connection with multiple reservoirs. Conversely, breaking through low strength cemented interfaces in the formation can pose challenges for hydraulic fractures. The present simulation conditions determine that the fracture's ability to cross the layer depends on the ratio of interface strength to matrix strength, which should be between 0.25 and 0.5. These findings offer valuable theoretical guidance on the vertical propagation of fractures in deep multilayer fracturing.

The homogeneity effects of magnetic flux density distribution on the detection of railhead surface defects via the magnetic flux leakage method

Magnetic flux leakage (MFL) is a non-destructive testing method used to detect railhead surface defects. For effective MFL testing, the homogeneity of the magnetic flux density distribution (MFDD) within the railhead is crucial. Inhomogeneous formation of the MFDD within the railhead reduces the efficiency of the MFL testing. The homogeneity of the MFDD depends on the distance between poles (DBP) of the MFL testing system. According to the literature, as the DBP parameter increases, the MFDD becomes more homogeneous. In this study, four different homogeneity levels of the MFDD are introduced based on the DBP parameter. 3D finite element method (FEM) modelling simulation is conducted to obtain MFL testing analyses. The analyses are performed on a rail that contains rectangular surface defects of varying depth and length. The results of this study are evaluated using characteristic features of the MFL signal BX component, namely the slope of the baseline, the bottom value and the peak-to-peak value. The results show that if the homogeneity level of the MFDD within the railhead is higher, the bottom value and slope of the baseline decrease and the peak-to-peak value increases. This indicates that higher homogeneity of the MFDD enhances the detection efficiency of the MFL testing. Eventually, it is found that with the formation of nearly 100% homogeneous MFDD in the railhead, the slope of the baseline, the bottom value and the peak-to-peak value are enhanced by up to 83%, 77% and 12%, respectively.

Combining finite element and reinforcement learning methods to design superconducting coils of saturated iron-core superconducting fault current limiter in the DC power system.

A saturated iron-core type superconducting fault current limiter (SI-SFCL) can effectively restrict the magnitude of the fault current and alleviate the strain on circuit breakers in DC power systems. Design of a superconducting coil (SC), which is one of the key tasks in the SI-SFCL design, requires guaranteeing a sufficient magnetic field, ensuring optimization of the shape and size, minimizing the wire cost, and satisfying the safety and stability of operation. Generally, finite element method (FEM) is used to calculate and evaluate the operating characteristics of SCs, from which it is possible to determine their optimal design parameters. When the coil is complex and large, the simulation time may range from hours to days, and if input parameters change even slightly, the simulations have to be redone from scratch. Recent advances in deep learning represent the ability to be effective for modeling and optimizing complex problems from training data or in real-time. In this paper, we presented a combination of the FEM simulation and deep Q-network (DQN) algorithm to optimize the SC design of a lab-scale SI-SFCL for a DC power system. The detailed design process and options for the SC of SI-SFCL were proposed. In order to analyze the characteristics related to the electromagnetic properties and operational features of the SC, a 3D FEM model was developed. Then, a DQN model was constructed and integrated with the FEM simulation for training and optimizing the design parameters of the SC in real-time. The obtained results of this study have the potential to effectively optimize the design parameters of large-scale SI-SFCL development for high-voltage DC power systems.

Evaluation of segmental lining response during shield tunnel construction based on field measurements and 3D FEM simulation

Lining safety can be threatened more severely at the construction stage than at the service stage, because the loads at the construction stage are larger. This study presents an in-situ experiment for measuring the loads acting on the lining and the internal forces of the lining to investigate the lining response during both the construction and service stages. A three-dimensional (3D) finite element method (FEM) model that could simulate the main relevant components of the shield tunnel construction process was employed to gain further insight into the mechanisms of the lining response. The influences of the key segment position and assembly sequence on the lining behavior were examined through a comprehensive parametric analysis. The results showed that during the assembly stage, the insertion of a key segment resulted in the most significant increase in the axial force, followed by the assembly of an adjacent segment. The lining responses were significantly influenced by the key segment, particularly during the construction stage, whereas the assembly sequence had a limited effect on the lining responses. During the construction stage, the closer the key segment to the tunnel invert, the greater was the axial force and the smaller was the bending moment of the lining. During the construction stage, the closer the key segment to the tunnel invert, the smaller was the axial force of the tunnel lining and the greater was the bending moment. The circumferential compressive stress reached its maximum value at the joint interfaces. Finally, the jack thrust force was the greatest at the tunnel invert. The key segment should not be placed at this location.

A computational framework for the lifetime prediction of vertical-axis wind turbines: CFD simulations and high-cycle fatigue modeling

A novel computational framework is presented for the lifetime prediction of vertical-axis wind turbines (VAWTs). The framework uses high-fidelity computational fluid dynamics (CFD) simulations for the accurate determination of the aerodynamic loading on the wind turbine, and includes these loading characteristics in a detailed 3D finite element method (FEM) model to predict fatigue cracking in the structure with a fatigue interface damage model. The fatigue interface damage model allows to simulate high-cycle fatigue cracking processes in the wind turbine in an accurate and robust fashion at manageable computational cost. The FEM analyses show that the blade-strut connection is the most critical structural part for the fatigue life of the VAWT, particularly when it is carried out as an adhesive connection (instead of a welded connection). The sensitivity of the fatigue response of the VAWT to specific static and fatigue modeling parameters and to the presence of a structural flaw is analyzed. Depending on the flaw size and flaw location, the fatigue life of the VAWT can decrease by 25%. Additionally, the decrease of the fatigue resistance of the VAWT appears to be mainly characterized by the monotonic reduction of the tensile strength of the adhesive blade-strut connection, rather than by the reduction of its mode I toughness, such that fatigue cracking develops in a brittle fashion under a relatively small crack opening. It is emphasized that the present computational framework is generic; it can also be applied for analyzing the fatigue performance of other rotating machinery subjected to fluid–structure interaction, such as horizontal-axis wind turbines, steam turbine generators and multistage pumps and compressors.

Laser shock peening induced mechanical properties enhancement of 50CrVA alloy

Laser shock peening (LSP) was implemented to treat aircraft landing gear 50CrVA alloy to improve mechanical properties. The sensitivity investigations of time step and mesh size were used to benchmark the 3D finite element method (FEM) model. Based on the established FEM model, the dynamic propagation characteristics of the shock wave inside the sample were predicted. The influence of laser energy and spot diameter on the residual stress field was further investigated. The numerical results indicate that regulating two critical LSP parameters can effectively improve the compressive residual stress (CRS) of metals, and the spot diameter has a greater effect than the laser energy in improving the uniformity of the CRS distribution. After that, the influences of LSP on the CRS field, microstructure, and mechanical properties were experimentally studied. After LSP treatment, the surface CRS reached 494.8 ± 31.8 MPa with an affected depth of about 400 μm. The phase composition was not changed by LSP treatment, but it weakened texture strength and refines grains. Under the impact of grain refinement and CRS, the average surface microhardness of the 50CrVA alloy reached 355 HV, indicating an increase up to 5.3 %. The ultimate tensile strength and yield strength were increased by 11.3 % and 14.5 %, respectively, which were in contrast to the unchanged elongation. This work verifies the feasibility of mechanical properties enhancement of 50CrVA alloy by LSP.

A 2D FEM Model for Impedance and Loss Calculation of Armored Three-Core Cables With Inclusion of 3D Pitching Effects

A method is introduced for impedance and loss calculation of three-core power cables with steel armoring, based on 2D finite element method (FEM) computations. The pitching effect of the cores and armor wires is taken into account by 1) enforcing identical net current on the wires, and by 2) introducing a fictitious non-conductive material between the wires having a complex-valued permeability. The permeability is obtained by considering the effect of the pitching on the total energy in a volume slab around each wire, which involves the solving of a small 2D FEM problem in an optimization loop. The method permits to calculate the positive-sequence and zero-sequence impedance on cables, induced sheath currents, and losses in cores, sheaths, and armor. The method is validated against published results using a full 3D FEM model. The calculations are fast, requiring only a few seconds of computation time. The procedure is simplified by use of pre-calculated look-up tables for the fictitious material permeability value.

Prediction of 2G HTS Tape Quench Behavior by Random Forest Model Trained on 2-D FEM Simulations

Detailed Finite Element Method (FEM) based simulations for 2 G HTS tapes return high quality results, but the computation takes a long time due to the non-linearity of superconducting properties and they needed high mesh density. This work describes a method for prediction of quench behavior in a long 2 G HTS tape based on a series of 2D FEM model simulations for short length of tape in many different conditions. The random forest model is trained by the set of results from the short-pieces FEM calculations. Subsequently the model can be applied to any length of HTS tape with similar thermal characteristics. Comparison of quench simulation in 10 cm long HTS tape between a detailed FEM model and a fully trained random forest model show that the predicted temperatures are within 0.68 %, while the computation time is significantly faster: The random forest model ran in less than 1 s, while the run time of the FEM model was 5:30 min.

Predicting fretting-fatigue endurance of rotating bending shrink-fitted assemblies using a sequential RUIZ-SWT approach: The effect of entrapped debris layer

Fretting-fatigue damage often appears in shaft shrink-fitted assemblies submitted to rotating bending. This paper focuses on the influence of the sleeve edge geometry on such damage. Rotating bending tests have been performed and broken and unbroken specimens have been expertized confirming fretting-fatigue phenomena. A 3D finite element method model was developed to evaluate the sliding and opening lengths. A sequential tribological - fatigue stress analysis strategy allowed the prediction of the maximum crack location ( Ruiz criterion) then the estimation of the fatigue endurance of the assembly using the SWT criterion. The last step of this σSWTXΓmaxapproach considers the presence of a debris layer within the contact to improve the consistency of the service life prediction.

Linear extrapolation method based on multiple equiproportional models for thermal performance prediction of ultra-large array.

Strong demand for developing the photothermal (PT) and electrothermal devices with ultra-large array is increasing. Thermal performance prediction is vital to optimize the key properties of the devices with ultra-large array. Finite element method (FEM) provides a powerful numerical approach for solving complex thermophysics issues. However, for calculating the performance of devices with ultra-large array, it is very memory-consuming and time-consuming to build an equal scale three-dimensional (3D) FEM model. For an ultra-large periodic array irradiated with a local heating source, the use of periodic boundary conditions could lead to considerable errors. To solve this problem, a linear extrapolation method based on multiple equiproportional models (LEM-MEM) is proposed in this paper. The proposed method builds several reduced-size FEM models to carry out simulation and extrapolation, which avoids dealing with the ultra-large arrays directly and greatly reduces the computation consumption. To verify the accuracy of LEM-MEM, a PT transducer with beyond 4000 × 4000 pixels is proposed, fabricated, tested and compared with the prediction results. Four different pixel patterns are designed and fabricated to test their steady thermal properties. The experimental results demonstrate that LEM-MEM has great predictability, and the maximum percentage error of average temperature is within 5.22% in four different pixel patterns. In addition, the measured response time of the proposed PT transducer is within 2 ms. The proposed LEM-MEM not only provides design guidance for optimizing PT transducers, but is also very useful for other thermal engineering problems in ultra-large array that requires facile and efficient prediction strategy.

Examination of the Partial Discharge Behaviour Within a Spherical Cavity in Insulation Paper of Transformer

This paper investigates the behaviour of partial discharge (PD) in transformer insulation paper based on the Finite Element Method (FEM). The three-dimensional (3D) FEM model consists of conductor and insulation paper, representing part of a transformer’s high voltage winding. The conductor’s width, height, and length used in this study were 2.4 mm, 11.5 mm, and 16 mm. An insulation paper thickness of 1 mm was modelled around the conductor. An internal cavity with a diameter of 0.5 mm cavity was introduced within the insulation paper. This study introduced two locations of the spherical cavities at the centre and left corner of the insulation paper: Location 1 (L1) and Location 2 (L2). An AC voltage of 33 kV, 50 Hz, was applied to the conductor while the bottom of the insulation paper was grounded. The model was used to study the electric field distribution within the insulation paper and its effect on PD current and charge magnitude. The influence of cavity location on the charge magnitude was also examined. It is found that the electric field distribution is influenced by the conductor configuration as well as the location of the cavity. The electric field in the cavity is the highest at L1 compared to L2. The first PD occurs faster for the cavity with a high electric field. Due to the PD occurrence at the same inception field, the real PD current and charge magnitude is similar at different locations. The apparent PD current and charge magnitude induced at the ground electrode is slightly higher at L1 than at L2.

Simulation Time Reduction with 2.5D FEM Analysis for Axial Flux Machines

Abstract In this paper, an approach for a two-and-half-dimensional (2.5D) finite element method (FEM)-based analysis, or quasi-three-dimensional (3D) FEM analysis, of an axial flux machine is discussed. By cutting the 3D model laterally and thereby creating cylindrical surface cuts, the 3D model can be split into several cylindrical surfaces. Transforming those cylindrical cuts into planes leads to a layer-based two-dimensional (2D) model with different radii for each layer. By integrating over all lateral surface cuts, the results for the entire axial flux machine can be determined. In comparison to the simulation of a full 3D FEM model, the simulation of the proposed 2.5D model is much faster. To validate the approach, the two main types of axial flux machines are simulated with both 3D-FEM-based model and 2.5D-FEM-based approach, and the results are presented in this paper.

3D deformation modeling of CrAlN coated tool steel compound during nanoindentation

The finite element method (FEM) nanoindentation simulations of nitride hard coatings are either focused on the coating only or contain an axisymmetric model of the coated compound with isotropic material behavior. Moreover, the material model parameters are optimized at only one particular indentation load. The current work aims to develop a 3D FEM model for studying deformation behavior of a CrAlN PVD coated HS6-5-2C tool steel compound during nanoindentation at varying indentation loads. A machine learning (ML)-based algorithm was used to characterize the coating microstructure. This information allowed to set up a 3D FEM model containing a digital clone of the compound microstructure along with the local orientations of the grains embedded into a larger elastically modelled frame. The material model parameters such as Young's modulus E, yield stress Y, strain hardening coefficient B and strain hardening exponent n for coating, interlayer and substrate were determined by fitting the simulated force-displacement curves to the experimental ones through an iterative optimization approach at four different indentation loads. An overall good agreement between the simulated and experimental force-displacement curves along with physically reasonable material model parameters was achieved. The obtained yield stress of CrAlN coating was comparable to ceramics. Moreover, elastic-plastic deformation in interlayer and elastic deformation in substrate at indentation depth below 10 % of the coating thickness was observed. This necessitates the interlayer and substrate consideration for FEM nanoindentation simulations of PVD coated compounds as in the present study. Therefore, the used modeling approach, based on orthotropic elastic material law for the coating combined with 3D digital clone of the compound microstructure, was successfully implemented and validated for low as well as high indentation loads.

Analytical approximations for the self-field distribution of a superconducting tape between iron cores

Magnetic switches apply AC magnetic fields to DC current-carrying high temperature superconducting (HTS) tapes to generate DC voltages and are commonly used in the persistent current switches (PCSs) and flux pumps to charge HTS-coated conductor magnets. Normally, they are made of copper field coils and iron cores with narrow air gaps for the HTS tape to pass through. However, the perpendicular components of the self-field of the HTS tape in the air gap can be enhanced by the iron cores and cause a critical current reduction of up to 40% to the tape. If ignored, this reduction, rather than the magnets themselves, will limit the current carrying capability of the HTS magnets. To tackle this problem, we present analytical approximations to calculate the self-field distribution of a superconducting tape between iron cores. The approximate solutions are based on the method of images in electromagnetics to simplify the derivation and are then verified by the experiments and 3D finite element method models using the T–A formulation. The solutions are universal and can be applied to almost all the magnetic switches currently in use. A case study of typical magnetic switches shows that the solutions can be used to determine the critical current reduction quickly and accurately, analyse the influence of different parameters, and simplify the design process of magnetic switches. The results can significantly benefit the design and optimisation of PCSs and flux pumps for HTS magnet charging systems in the future.

Study on the Optimal Cross-Sectional Shapes of the PEMFC Endplates by Using a Moment of Inertia and 3D FEM Models

The deflection of the endplate under the clamping force has a vital effect on fuel cell performance. An optimal cross-sectional shape with a high moment of inertia of the endplate is significant to maximize the bending stiffness of the fuel cell stack. Five cross-sectional shapes (rectangular, round, parabolic, rectangular + round, and rectangular + parabolic) of the typical endplates are proposed. An analytical study on the moments of inertia of the endplates is introduced and analyzed. The maximum moments of inertia of the cross-sections are obtained and displayed in a matrix in thickness and length. The statistical results show that the “rectangular + parabolic” cross-section has the advantage of wide dimensional size while maintaining a high moment of inertia. Finally, the analytical studies are validated by a finite element method (FEM) and the corresponding trends are highly agreed upon. The maximum moment of inertia of the parabolic endplate is 85.71% higher than the rectangular endplate with a thickness of 80 mm, and the corresponding contact pressure variance is 6.15% less than the rectangular endplate. The presented analytical study is significant and effective to optimize the cross-sectional shape of the endplate and provide an endplate design direction for a large fuel cell stack.