Grid Boundary Research Articles

Loss and Thermal Analysis of a High-Power-Density Permanent Magnet Starter/Generator

Reducing heat and improving the overall operation stability of the motor play a key role in the design of a starting engine. This paper focuses on the loss and thermal analysis of a permanent magnet (PM) brushless machine used in starter generators. The loss of the starter generator was calculated through a combination of theoretical analysis and the finite element method. A thermal analysis model was established based on the division of the fluid domain, boundary grid, heat source setting, and so on. The temperature fields of the whole motor and the main components were calculated and analyzed. The main factors affecting the air cooling effect were analyzed, including air flow rate, air temperature, and motor speed. A prototype experimental platform of the SG motor was built. The efficiency and temperature rise in the motor were tested. The temperature values were compared with the calculated values. The experimental results show that the performance of the motor is excellent, and the error between the temperature and the design calculation is less than 10% under each load torque. The accuracy of the thermal analysis method is verified. The correctness of the motor transient model was also confirmed through a temperature rise experiment under rated conditions, providing a research basis for improving operation efficiency.

Acanthus ornament generation using layout subdivisions with parameterized motifs

AbstractAcanthus ornaments frequently adorn Western architectural designs. The placement of these motifs varies according to the decorative object, with some having motifs arranged in a grid pattern. In this study, we propose a procedural modeling system aimed at generating acanthus ornaments on a planar surface. The proposed approach initially establishes the layout of boundary grids for acanthus motifs by subdividing the target surface into nonuniform grids. Subsequently, the medial axis line of the acanthus motif is generated to optimally conform to each boundary grid, employing a parameterized representation of deformable motifs. The three‐dimensional motif shapes are ultimately constructed from the medial axis, with the shape parameters adjusted to improve aesthetic appeal. The proposed system generates various acanthus ornaments through rule‐based layout subdivisions, offering users the option to select their preferred design while adjusting the motif shapes with a few manual parameters.

An Efficient Progressive Grid Generation Method Considering Internal Quality and Boundary Grid Adjustment

Due to its elegant appearance and high structural efficiency, free-form grid structures are increasingly adopted in architectural design. However, it is a challenging task for engineers to generate a uniform and well-shaped grid on a free-form surface while considering the processing of both interior and boundary of grid, especially for composite surfaces. To generate well-shaped grids with uniform rods, regular cells and smooth visual effects over free-form surfaces, this paper develops an innovative triangular grid generation method capable of automatically managing grid boundary with extending initial surface. In the method, nodes of grid structure are considered to be zero mass particles and are progressively added to the extended surface from geometric center to the boundary of surface. A boundary-processing algorithm is then established to evenly distribute nodes on initial boundary curve, while ensuring that grid cells at the boundary do not exhibit elongation. A mechanical simulation system based on spring-mass model is improved to optimize spatial grid structure, rods of grid are regarded as linear springs, a surface attraction force and an anchoring force are performed on grid nodes. Moreover, the proposed method allows architects change grid direction and rods length easily, which can greatly improve the efficiency of design. Several case studies show that the method can effectively avoid distortion of grids and generate well-shaped grids that can meet aesthetic requirements.

Flow Analysis of Centrifugal Compressor using ANSYS

Abstract: The aerodynamic and structural designs of the impeller are vital to the functioning of the entire compressor stage in centrifugal compressors. In contrast to previous years, there has been a greater demand for industrial centrifugal compressors to operate with greater efficiency and operational range. Although the efficiency of low-pressure-ratio centrifugal compressors has nearly achieved its maximum, intermediate and high-pressure ratio machines still lag behind the state-of-the-art in terms of efficiency. Maintaining maximum efficiency while extending the working range is a challenging task in centrifugal compressor design. Furthermore, a single design must be usable globally due to product globalisation, even in the face of technological disparities and variances in electricity frequency of up to 10 percent in some nations. Often operating at different rotational speeds, centrifugal compressors add another layer of complexity to the impeller structural design. A full-3D impeller design that is optimised for both structural integrity and aerodynamic performance is shown in this study .For air conditioning systems of the future, centrifugal compressor performance must be improved. This research focusses on systematic numerical simulation, a computationally efficient method of optimising centrifugal compressor performance. ANSYS simulations are used in conjunction with a thorough literature review on the aerodynamic behaviour of materials used in centrifugal compressors. For the purpose of performing flow simulations under subsonic circumstances with suitable boundary conditions and grid independence checks, geometric modelling was completed using CATIAV5R22 and imported into ANSYS. Tests were conducted using various aluminium materials and mass flow rates, and enhanced efficiency findings were confirmed by comparison with experimental data. Materials Processing and Characterisations is in charge of peer review.

Imbalanced data sampling design based on grid boundary domain for big data

Imbalanced data sampling design based on grid boundary domain for big data

An Optimal Numerical Strategy for Intake in Crosswind Conditions

Abstract Crosswind can reduce the operability of an aeroengine significantly at static or near static operating conditions. Computational fluid dynamics predictions of the flow at crosswind conditions will play an important part in future designs, however, accurate numerical predictions of the flow within the intake remain challenging even for simulations of cases with intake only. The main objective of this paper is to demonstrate the importance of numerical setup and to determine an optimal computational model for crosswind investigations that can be used by other researchers. By considering the flow to be inherently unsteady, the influence of inlet and exit boundary conditions, and grid sensitivity is studied by using unsteady Reynolds-average Navier–Stokes (URANS) simulations. Numerical predictions of the time-averaged intake pressure recovery (IPR) and the motion of the vortex on the ground are compared against the existing experimental data. The results show that for an intake under crosswind, the ground vortex that forms under the intake and the in-duct separation, when present, exhibit unsteady behavior that become stronger as the crosswind velocity is increased. The steady-state simulation is only representative at lower crosswinds. The intake flow separation and ground vortex predictions are influenced by the inlet boundary layer profiles. Moreover, acoustic reflection was observed at the intake exit boundary which propagates upstream, creating artificial unsteady frequencies in IPR. The reflection is generated from the use of uniform boundary conditions at the intake exit and is not dissipated in the grid due to the long wavelength; this can be mitigated by using a choked nozzle at the intake exit. Acoustic reflection was also observed at the far-field exit boundary. These reflections are caused from interaction of trailing vortex and far-field boundary.

Numerical implications of including drifts in SOLPS-ITER simulations of EAST

The inclusion of drifts in plasma edge codes like SOLPS-ITER is required to match simulation data with experimental profiles. However, this remains numerically challenging. In this paper, the effect of some numerical factors on the final plasma solution is investigated. This study is performed on three EAST simulations in the upper single null configuration: an attached purely deuterium case, an attached case with limited Ne-seeding, and a detached Ne-seeded case. The effects of the anomalous conductivity and anomalous thermo-electric coefficient on the plasma potential are investigated. Next, the effect of the employed grids is shown. In order to investigate these effects, accurate drift simulations are needed. Therefore, the employed time step and numerical parameters are discussed for the three studied simulations. For all presented simulations, it is verified that the restriction of the grid to the first flux surface tangent to the main chamber wall is sufficient within the context of non-extended simulations. This means that the main power dissipation takes place inside the simulated domain, and only a small fraction of the power is leaving the B2.5 grid through the grid boundary closest to the first wall. Finally, the effect of drifts on the asymmetry between the inner and outer target for EAST simulations is demonstrated.

Improved Head and Data Augmentation to Reduce Artifacts at Grid Boundaries in Object Detection

Improved Head and Data Augmentation to Reduce Artifacts at Grid Boundaries in Object Detection

Fine scale simulation of sea salt aerosol under strong wind: WRF sensitivity test on PBL schemes and LES under Typhoon Hagibis

Identifying which factors among the planetary boundary layer (PBL) scheme, grid resolution, and source or sink terms dominantly influence the sea salt aerosol (SSA) spatial distribution is necessary. The dependence of SSA transport on PBL processes was investigated using a numerical weather prediction (NWP) model with a grid scale of ∼143 m. Size-segregated SSA transport during Typhoon Hagibis, which made landfall in Japan in 2019, was simulated using the Weather Research and Forecasting (WRF) model. The PBL schemes of Yonsei University (YSU), scale-aware YSU (Shin and Hong, 2015's scheme, SH) and Mellor-Yamada Nakanishi-Niino (MYNN), and large-eddy simulation (LES) subjected to turbulence transition enhancement via a cell perturbation method were tested to evaluate the reproducibility of observed values of wind speed, surface pressure, relative humidity, and temperature at meteorology masts. The results showed that wind speed was most influenced by the selection of the PBL scheme and LES. The distance from the coastline, as determined by the wind direction during the most intense typhoon stage, was correlated with a decrease in the time averaged SSA concentration when the storm moved inland. Despite the simulated SSA emission scheme's high sensitivity to wind speed (nearly 3rd power), the near-surface average concentration was less sensitive to the PBL schemes and LES selection than wind speed. However, the maximum arrival of the SSA differed by ∼20 % during the most vigorous stage of the typhoon. Budget analysis of the SSA transport equation highlighted that the advection term and gravity settling were most dependent on the PBL schemes and LES. The impacts of both factors on SSA transport were not limited to near-surface tendencies but were in a broader range over the atmosphere, up to 1–2 km. These results indicated that the vertical structure of the SSA field over the boundary layer depended on the PBL schemes and LES, thereby modulating the inland arrival of the SSA.

Topology optimization for reducing stress shielding in cancellous bone scaffold

In this paper, a topology optimization method is proposed to design bone scaffold structures that match the anisotropic elasticity tensors of cancellous bone. Grid point density and boundary error are introduced in the optimization model to achieve smooth boundaries of scaffold topology and control the distribution of intermediate elements. Combined with finite element analysis, the effects of scaffolds with different levels of elasticity tensors on the stress transfer and distribution of the scaffold-cancellous bone structure are investigated. It is found that scaffolds with the same or slightly lower elastic properties (0.9 times) than cancellous bone transmitted more uniform stresses into the cancellous bone. Finally, we demonstrate that optimized scaffolds can be fabricated by Stereolithography (SLA).

Numerical study of liquid jet and shock wave induced by two-bubble collapse in open field

The shock waves and high-speed jets induced by the violent collapse of bubbles can cause serious damage to nearby structures. To fully understand the shock wave and jet characteristics induced by bubble-bubble interaction, we developed a diffuse-interface method for the simulation of compressible two-phase flow, which combined interface compression technique with interface sharpening technique to keep the sharpness of the shock wave and phase interface. The thermodynamically consistent five-equation model was improved using interface compression technique to maintain a constant thickness of the phase interface. To further suppress numerical dissipation, the high-order scheme WENO (Weighted Essentially Non-Oscillatory) and interface sharpening function THINC (Tangent of Hyperbola for INterface Capturing) were used for the flux reconstruction at the grid boundary to ensure that the total variation at the cell boundary was minimized (Boundary Variation Diminishing, BVD), thus the spatial reconstruction scheme, named WENO-THINC-BVD, was developed. Moreover, we extended the present method to a block-structured adaptive mesh refinement framework to improve grid resolution and save computing resources. Numerical results of several benchmark tests fully demonstrated the advantages of the present method in simulating complex compressible flows containing shock-shock and shock-interface interactions. Based on the present high-fidelity numerical methods, we investigated the shock wave and liquid jet induced by the two-bubble interaction in an open space. A phase diagram of the liquid jet propagation direction as a function of the initial bubble pressure and the inter-bubble distance was summarized. Finally, according to the bubble-bubble interaction process, an empirical formula for the collapse strength and another for the attenuation of shock waves were developed.

Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods

For many application problems that are modeled by partial differential equations (PDEs), not only it is important to obtain accurate approximations to the solutions, but also accurate approximations to the derivatives of the solutions. In this study, some new high order compact (HOC) finite difference schemes are derived to approximate the first and second derivatives of the solution to some elliptic PDEs using the numerical solution obtained from a HOC scheme applied to the same PDE. Convergence analysis for the computed derivatives is also presented to show that the order of the convergence is the same as that of the solution. The new HOC schemes for computing partial derivatives at both interior and boundary grid points take into account of the partial differential equations including the source term and/or the boundary conditions (Dirichlet, Neumann, or Robin). Fourth order accurate compact finite difference formulas with pre-computed coefficients and weights are developed for Poisson/Helmholtz PDEs, and code generated coefficients for diffusion-advection equations with constant coefficients. One important application is a new fourth-order compact scheme for solving incompressible Stokes equations with periodic boundary conditions.

Generalized neural closure models with interpretability

Improving the predictive capability and computational cost of dynamical models is often at the heart of augmenting computational physics with machine learning (ML). However, most learning results are limited in interpretability and generalization over different computational grid resolutions, initial and boundary conditions, domain geometries, and physical or problem-specific parameters. In the present study, we simultaneously address all these challenges by developing the novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. The melding of the existing models with NNs in the continuous spatiotemporal space followed by numerical discretization automatically allows for the desired generalizability. The Markovian term is designed to enable extraction of its analytical form and thus provides interpretability. The non-Markovian terms allow accounting for inherently missing time delays needed to represent the real world. Our flexible modeling framework provides full autonomy for the design of the unknown closure terms such as using any linear-, shallow-, or deep-NN architectures, selecting the span of the input function libraries, and using either or both Markovian and non-Markovian closure terms, all in accord with prior knowledge. We obtain adjoint PDEs in the continuous form, thus enabling direct implementation across differentiable and non-differentiable computational physics codes, different ML frameworks, and treatment of nonuniformly-spaced spatiotemporal training data. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models. Our learned gnCMs discover missing physics, find leading numerical error terms, discriminate among candidate functional forms in an interpretable fashion, achieve generalization, and compensate for the lack of complexity in simpler models. Finally, we analyze the computational advantages of our new framework.

Self-nested large-eddy simulations in PALM model system v21.10 for offshore wind prediction under different atmospheric stability conditions

Abstract. Large-eddy simulation (LES) resolves large-scale turbulence directly and parametrizes small-scale turbulence. Resolving micro-scale turbulence, e.g., in wind turbine wakes, requires both a sufficiently small grid spacing and a domain large enough to develop turbulent flow. Refining a grid locally via a nesting interface effectively decreases the required computational time compared to the global grid refinement. However, interpolating the flow between nested grid boundaries introduces another source of uncertainty. Previous studies reviewed nesting effects for a buoyancy-driven flow and observed a secondary circulation in the two-way nested area. Using a nesting interface with a shear-driven flow in LES, therefore, requires additional verification. We use PALM model system 21.10 to simulate a boundary layer in a cascading self-nested domain under neutral, convective, and stable conditions and verify the results based on the wind speed measurements taken at the FINO1 platform in the North Sea. We show that the feedback between parent and child domains in a two-way nested simulation of a non-neutral boundary layer alters the circulation in the nested area, despite spectral characteristics following the reference measurements. Unlike the pure buoyancy-driven flow, a non-neutral shear-driven flow slows down in a two-way nested area and accelerates after exiting the child domain. We also briefly review the nesting effect on the velocity profiles and turbulence anisotropy.

General Exact Schemes for Second-Order Linear Differential Equations Using the Concept of Local Green Functions

In this paper, we introduce a special system of linear equations with a symmetric, tridiagonal matrix, whose solution vector contains the values of the analytical solution of the original ordinary differential equation (ODE) in grid points. Further, we present the derivation of an exact scheme for an arbitrary mesh grid and prove that its application can completely avoid other errors in discretization and numerical methods. The presented method is constructed on the basis of special local green functions, whose special properties provide the possibility to invert the differential operator of the ODE. Thus, the newly obtained results provide a general, exact solution method for the second-order ODE, which is also effective for obtaining the arbitrary grid, Dirichlet, and/or Neumann boundary conditions. Both the results obtained and the short case study confirm that the use of the exact scheme is efficient and straightforward even for ODEs with discontinuity functions.

A Modified Gray Wolf Optimizer-Based Negative Selection Algorithm for Network Anomaly Detection

Intrusion detection systems are crucial in fighting against various network attacks. By monitoring the network behavior in real time, possible attack attempts can be detected and acted upon. However, with the development of openness and flexibility of networks, artificial immunity-based network anomaly detection methods lack continuous adaptability and hence have poor detection performance. Thus, a novel framework for network anomaly detection with adaptive regulation is built in this paper. First, a heuristic dimensionality reduction algorithm based on unsupervised clustering is proposed. This algorithm uses the correlation between features to select the best subset. Then, a hybrid partitioning strategy is introduced in the negative selection algorithm (NSA), which divides the feature space into a grid based on the sample distribution density and generates specific candidate detectors in the boundary grid to effectively mitigate the holes caused by boundary diversity. Finally, the NSA is improved by self-set clustering and a novel gray wolf optimizer to achieve adaptive adjustment of the detector radius and position. The results show that the proposed NSA algorithm based on mixed hierarchical division and gray wolf optimization (MDGWO-NSA) achieves a higher detection rate, lower false alarm rate, and better generation quality than other network anomaly detection algorithms.

Extended B‐spline‐based implicit material point method enhanced by F‐bar projection method to suppress pressure oscillation

SummaryAn enhancement of the extended B‐spline‐based implicit material point method (EBS‐MPM) is developed to avoid pressure oscillation and volumetric locking. The EBS‐MPM is a stable implicit MPM that enables the imposition of arbitrary boundary conditions thanks to the higher‐order EBS basis functions and the help of Nitsche's method. In particular, by means of the higher‐order EBS basis functions, the EBS‐MPM can suppress the cell‐crossing errors caused by material points crossing the background grid boundaries and can avoid both the stress oscillations arising from inaccurate numerical integration and the ill‐conditioning of the resulting tangent matrices. Although the higher‐order EBS basis functions are known to avoid volumetric locking, the problem of pressure oscillation has not yet been resolved. Therefore, to suppress pressure oscillation due to quasi‐incompressibility, we propose the incorporation of the F‐bar projection method into the EBS‐MPM, which is compatible with the higher‐order EBS basis functions. Three representative numerical examples are presented to demonstrate the capability of the proposed method in suppressing both the pressure oscillation and volumetric locking. The results of the proposed method are compared to those of the finite element method with F‐bar elements and those of isogeometric analysis with quadratic NURBS elements.

Transient Dynamics and Propagation of Voltage and Frequency Fluctuations in Transmission Grids

The energy transition towards increased electric power production from renewable energy (RE) resources creates new challenges to ensure the stability of power grids. In conventional power grids voltage fluctuations can be controlled locally. Here, it is explored whether this may be changed by the energy transition. It is well established that the increase of RE resources in power grids increases the amplitude of frequency deviations and the velocity with which these deviations spread throughout the power grid. However, its effect on voltage dynamics and propagation has not been systematically studied. Here, a systematic study is carried out of the transients of voltage amplitude, phase and frequency deviations due to local contingencies in dependence on system inertia, heterogeneity and topology. The 3rd order dynamic power grid model is studied numerically and analytically and compared with real grid simulations for the Nigerian (330 kV) power grid and other grid models, using DigSILENT PowerFactory software. A quantitative analysis of the parametric dependence of the velocity with which a disturbance propagates throughout the grid and of the period of oscillations of the frequency and voltage transients is provided. Beating patterns are found in the transients and are identified as footprints of the location of the fault bus, as caused by multiple reflections of propagating disturbances from the grid boundary. These may result in interarea oscillations. It is confirmed that voltage deviations remain local for realistic ranges of parameters, but that it can propagate by literally surfing on the frequency deviation wave. However, it is found that this no longer holds true when the electrical power in the grid approaches its critical value beyond which no stationary solution exists. Furthermore, time dependent second moments of the geodesic distance weighted with frequency deviations <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\delta \omega }(t)$ </tex-math></inline-formula> and voltage deviations <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\delta V}(t)$ </tex-math></inline-formula> , respectively are evaluated, confirming a ballistic disturbance propagation in homogeneous model grids. However, in real grid simulations, a linear time dependence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S(t)$ </tex-math></inline-formula> is observed, indicating a diffusive propagation due to multiple scattering from the inhomogeneities in these power grids.

Local Compatibility Boundary Conditions for High-Order Accurate Finite-Difference Approximations of PDEs

We describe a new approach to derive numerical approximations of boundary conditions for high-order accurate finite-difference approximations. The approach, called the Local Compatibility Boundary Condition (LCBC) method, uses boundary conditions and compatibility boundary conditions derived from the governing equations, as well as interior and boundary grid values, to construct a local polynomial, whose degree matches the order of accuracy of the interior scheme, centered at each boundary point. The local polynomial is then used to derive a discrete formula for each ghost point in terms of the data. This approach leads to centered approximations that are generally more accurate and stable than one-sided approximations. Moreover, the stencil approximations are local since they do not couple to neighboring ghost-point values which can occur with traditional compatibility conditions. The local polynomial is derived using continuous operators and derivatives which enables the automatic construction of stencil approximations at different orders of accuracy. The LCBC method is developed here for problems governed by second-order partial differential equations, and it is verified for a wide range of sample problems, both time-dependent and time-independent, in two space dimensions and for schemes up to sixth-order accuracy.

Taylor particle-in-cell transfer and kernel correction for material point method

The material point method (MPM) has been extensively used to solve problems involving large displacements and deformations. The standard MPM formulation, which adopts fluid-implicit-particle (FLIP) transfer, is less dissipative but also less stable than particle-in-cell (PIC) transfer. The affine PIC (APIC) transfer introduces the affine velocity and was developed to realize stable simulations while overcoming dissipations of the angular momentum in PIC. This paper presents Taylor-PIC (TPIC) transfer, which is a type of APIC transfer that combines the affine velocity based on the first-order Taylor series approximation and PIC transfer. TPIC is simple (only the particle velocity gradient is required) and inherits the key advantages of the original APIC, such as less dissipation and stability. Although TPIC does not conserve angular momentum, in contrast to APIC, the velocity gradient is preserved in the transfer between particles and the grid. This velocity gradient contains the angular information in its skew-symmetric component, which allows TPIC to adequately describe angular motion, similar to APIC.Furthermore, the MPM can cause stress oscillations near boundaries when boundary conditions are explicitly imposed, e.g., when the boundary grid velocity (or momentum) is set to zero. When affine-type transfers are used, this instability is exacerbated, and simulations can easily fail. Therefore, we propose a kernel correction method based on the weighted least squares for particles near boundaries. The proposed TPIC transfer and kernel correction are validated through five types of simulations, each using a different material—linear elastic, von Mises, Newtonian fluid, and Drucker–Prager. In the simulations, incorrect results due to stress oscillations are observed even for small deformations. Applying the corrected kernels successfully removes these spurious oscillations, and the results are consistent with the analytical solutions. Moreover, the numerical results confirm the accuracy and robustness of the proposed TPIC transfer.