Improving the boundary efficiency of a compact finite difference scheme through optimising its composite template

This paper presents efforts to improve the boundary efficiency and accuracy of a compact finite difference scheme, based on its composite template. Unlike precursory attempts the current methodology is unique in its quantification of dispersion and dissipation errors, which are only evaluated after the matrix system of equations has been rearranged for the derivative. This results in a more accurate prediction of the boundary performance, since the analysis is directly based on how the derivative is represented in simulations. A genetic algorithm acts as a comprehensive method for the optimisation of the boundary coefficients, incorporating an eigenvalue constraint for the linear stability of the matrix system of equations. The performance of the optimised composite template is tested on one-dimensional linear wave convection and two-dimensional inviscid vortex convection problems, with uniform and curvilinear grids. In all cases, it yields substantial accuracy and efficiency improvements while maintaining stable solutions and fourth-order accuracy

Analysis of radiation pressure and aerodynamic forces acting on powder grains in powder-based additive manufacturing

Selection of process parameters is an important step in Powder-Based Additive Manufacturing (PBAM) of metals. In order to achieve an optimal parameter set, current literature is mainly focused on the understanding of powder dynamics by analysing the aerodynamic forces. In this letter, however, we show the importance of the laser induced force (radiation pressure) on the powder dynamics. Generalised Lorenz-Mie theory has been employed to accurately estimate the radiation pressure and it is shown that its magnitude is significant in comparison to various aerodynamic forces and the grains weight, hence, can significantly contribute to denudation and spatter observed in the manufacturing process. Furthermore, the importance of compressibility and rarefaction effects on the magnitude of drag and lift forces that a particle experiences is demonstrated by estimating the Ma and Kn numbers under process conditions, which directly impact the powder dynamics

Strongly coupled peridynamic and lattice Boltzmann models using immersed boundary method for flow-induced structural deformation and fracture

To simulate the dynamics of structural deformation and fracture caused by fluid-structure interactions accurately and efficiently, a strong coupling between the peridynamic model and the lattice Boltzmann method using the immersed boundary method is developed here. In this novel method, the peridynamic model predicts structural deformation and fracture, the cascaded lattice Boltzmann method serves as the flow solver, and the immersed boundary method is to enforce a no-slip boundary condition on the fluid-solid interface. The strong coupling is achieved by adding velocity corrections for the fluid and solid phases simultaneously at each time step, which are calculated by solving a linear system of equations derived from an implicit velocity correction immersed boundary scheme. Therefore, this new scheme based on the immersed boundary method eliminates the need to iteratively solve the dynamics of the fluid and solid phases at each time step. The proposed method is rigorously validated considering the plate with a pre-existing crack under velocity boundary conditions, the sedimentation of an elastic disk, the cross-flow over a flexible beam, and the flow-induced deformation of an elastic beam attached to a rigid cylinder. More importantly, the structural deformation, crack formation, and fracture due to interaction with the fluid flow are captured innovatively

A multi-physics peridynamics-DEM-IB-CLBM framework for the prediction of erosive impact of solid particles in viscous fluids

In this paper, a new fully-resolved framework capable of capturing the fundamental physics of particle–fluid interactions, the collision of particles with solid surfaces, and the resulting damage is proposed. A coupled DEM-IB-CLBM, consisting of a discrete element method (DEM), an immersed boundary (IB) method, and a cascaded lattice Boltzmann method (CLBM), is used to fully resolve the interaction of the particles with the surrounding viscous fluid. The peridynamics theory is then implemented and used to predict the impact damage to the target material. This framework is validated by comparing the trajectory of a particle–wall collision event in a viscous fluid with the previous results in the literature. Furthermore, the variation of the restitution coefficient with the impact velocity is in a good agreement with the available experimental results. The influence of multiple impacts and the resulting surface damage on the fluid dynamics of the system is investigated. It is demonstrated that the method correctly predicts the expected effects of multiple collisions and impact angle variations on the surface damage

Force-Chain Finder: A software tool for the recursive detection of force-chains in granular materials via minor principal stress

Force transmission in granular media occurs through an inhomogeneous network of inter-particle contacts referred to as force-chains. A thorough understanding of the structure of these chains is indispensable for a better comprehension of the macroscopic signatures they generate. This paper introduces Force-Chain Finder (FCF), an open-source software tool designed for detecting force-chains in granular materials. Leveraging the stress tensor computed for each particle based on its interactions with neighboring particles, the tool effectively identifies the magnitude and direction of the most compressive principal stress. Through a recursive traversal of particles and their neighbours, force-chains are robustly detected based on the alignment of the principal stress directions, which is decided by a parameter α (an angle in radians). The software provides a comprehensive suite of post-processing features, including the exportation of results in different formats, enabling detailed analysis of specific regions and dynamic phenomena. Additionally, the software facilitates the computation of statistical measures pertaining to chain size and population. By streamlining the identification and characterization of force-chains within discrete element method (DEM) simulations, this tool significantly enhances the efficiency and accuracy of force-chain analysis. Thus, the software promotes deeper insights into the behaviour of granular materials by enabling researchers to effortlessly detect and analyse force-chains

Hybrid PD-DEM approach for modeling surface erosion by particles impact

Peridynamics (PD) theory is a promising technique for modeling solids with discontinuities. Short-range repulsive force models are commonly employed in PD impact event simulations. Despite their extensive usage, short-range force models do not take damping, friction, and tangential force components into account and hence are unable to effectively describe energy dissipation, leading to uncertainty in the calculation of contact forces. However, the accuracy of impact simulations using alternate contact models has not been extensively investigated in the context of PD impact simulations. The Discrete Element Method (DEM) has been proven to be the most reliable and effective approach to model collision processes between distinct solid objects. This work presents, a particle-based hybrid PD-DEM model to accurately predict the particle impact forces and the resulting damage to the target material. The present model brings together the unique capabilities of PD and DEM and has the potential to make use of the various DEM contact laws, which allow the development and adjustment of relevant contact forces in the normal and tangential directions. Furthermore, damping effects, friction, and intra-particle stiffness are incorporated into the simulations through DEM. The proposed method has been used for modeling material failure after being validated and verified for the contact parameters during the impact process. The predicted damage patterns and resulting material loss demonstrate good agreement with the experimental results reported in the literature

On the impact of powder cohesion on the bulk properties of a powder bed in Additive Manufacturing using Discrete Element Method (DEM) simulations

In powder based Additive Manufacturing (AM) a uniform and compact spread of particles is required which can then be accurately fused layer by layer to form final products. As powders are spread, several parameters control the quality of the final powder bed layer; namely, spreader type, powder grain shape, powder characteristics and ambient manufacturing conditions. Utilising discrete element method (DEM) simulations this paper investigates the effect of cohesion on the quality of the powder bed post spreading. However, only cohesion due to the formation of liquid bridges as a result of moisture content of the powder is considered in this work. Simulations are run with a realistic spreader (geometry of which was created from data points from manufacturing equipment used within industry), alongside realistic particle shapes created via Multi-Sphere Approximations (MSA) of models derived from powder X-ray microtomography images, see Figure 1. A random selection of powder particles is chosen and used within simulations, with the resolution of these particles being controlled via a surface smoothing factor [1] to ensure an acceptable balance of accuracy and computational cost. Simulations are run with an appropriate subset of the total number of particles to yield a statistically accurate representation of the grain population to identify the effects of cohesion on the final quality of the powder bed layer. In this paper for the first time, the relationship between the moisture content and powder bed quality is investigated and the simulation results indicate that the cohesion has a strong effect on the powder bed quality which is quantified via a surface roughness parameter and powder's bulk density

Determination of Trace Amounts of Lead Using the Flotation-spectrophotometric method

The present study describes a simple and highly selective method for separation, preconcentration and spectrophotometric determination of extremely low concentrations of lead. It is based on flotation of a complex of Pb2+ ions and Alizarin yellow between aqueous and n-hexane interface at pH = 6. The proposed procedure is also applied for determination of lead in both tap water and prepared sea water samples. Beer’s Law was obeyed over the concentration range of 3.86 × 10−8 To 8.20 × 10−7 molL−1 (8–170 ngmL−1) with an apparent molar absorptivity of 1.33 × 106 molL−1 cm−1 for a 100 mL aliquot of the water sample. The detection limit (n = 10) was 8.7 × 10−9 molL−1 (1.0 ngmL−1) and the Relative standard deviation (R.S.D), (n = 10) for 7.2 × 10−7 molL−1 (150 ngmL−1) of Pb (II) was 4.36%. A notable advantage of the method is that the determination of Pb (II) is free from the interference of almost all cations and ions found in the environment and waste water samples. The determination of Pb (II) in tap and synthetic seawater samples was also carried out by the present method. The results were satisfactorily comparable so that the applicability of the proposed method was confirmed to the real samples