Search Results (6)

Securing the power grid is of extreme concern to many nations as power infrastructure has become integral to modern life and society. A high-altitude electromagnetic pulse (HEMP) is generated by a nuclear detonation high in the atmosphere, producing a powerful electromagnetic field that can damage or destroy electronic devices over a wide area. Protecting against HEMP attacks (insults) requires knowledge of the problem’s bounds before the problem can be appropriately solved. This paper presents a collection of analyses to determine the basic requirements for controller placements on a power grid. Two primary analyses are conducted. The first is an inverted controllability analysis in which the HEMP event is treated as an unbounded control input to the system. Considering the HEMP insult as a controller, we can break down controllability to reduce its influence on the system. The analysis indicates that either all but one neutral path to ground must be protected or that all transmission lines should be secured. However, further exploration of the controllability definition suggests that fewer blocking devices are sufficient for effective HEMP mitigation. The second analysis involves observability to identify the minimum number of sensors needed for full-state feedback. The results show that only one state sensor is required to achieve full-state feedback for the system. These requirements suggest that there is room to optimize controller design and placement to minimize total controller count on a power grid to ensure HEMP mitigation. As an example, the Horton et al. system model with 15 transformers and 15 transmission lines is used to provide a baseline comparison for future optimization studies by running all permutations of neutral and transmission line blocking cases. The minimum number of neutral controllers is 8, which is approximately half of the bounding solution of 14. The minimum number of transmission line controllers is 3, which is one-fifth of the bounding solution of 15 and less than half of the required neutral controllers. Full article

The motion of air bubbles within a liquid plays a crucial role in various aspects including heat transfer and material quality. In the context of non-Newtonian fluids, such as elastoviscoplastic fluids, the presence of air bubbles significantly influences the viscosity of the liquid. This study presents the development of an interface-capturing method for multiphase viscoelastic fluid flow simulations. The proposed algorithm utilizes a geometric volume of fluid (isoAdvector) approach and incorporates a reconstructed distance function (RDF) to determine interface curvature instead of relying on volume fraction gradients. Additionally, a piecewise linear interface construction (PLIC) scheme is employed in conjunction with the RDF-based interface reconstruction for improved accuracy and robustness. The validation of the multiphase viscoelastic PLIC-RDF isoAdvector (MVP-RIA) algorithm involved simulations of the buoyancy-driven rise of a bubble in fluids with varying degrees of rheological complexity. First, the newly developed algorithm was applied to investigate the buoyancy-driven rise of a bubble in a Newtonian fluid on an unbounded domain. The results show excellent agreement with experimental and theoretical findings, capturing the bubble shape and velocity accurately. Next, the algorithm was extended to simulate the buoyancy-driven rise of a bubble in a viscoelastic shear-thinning fluid described by the Giesekus constitutive model. As the influence of normal stress surpasses surface tension, the bubble shape undergoes a transition to a prolate or teardrop shape, often exhibiting a cusp at the bubble tail. This is in contrast to the spherical, ellipsoidal, or spherical-cap shapes observed in the first case study with a bubble in a Newtonian fluid. Lastly, the algorithm was employed to study the buoyancy-driven rise of a bubble in an unbounded elastoviscoplastic medium, modeled using the Saramito–Herschel–Bulkley constitutive equation. It was observed that in very small air bubbles within the elastoviscoplastic fluid, the dominance of elasticity and capillary forces restricts the degree of bubble deformation. As the bubble volume increases, lateral stretching becomes prominent, resulting in the emergence of two tails. Ultimately, a highly elongated bubble shape with sharper tails is observed. The results show that by applying the newly developed MVP-RIA algorithm, with a tangible coarser grid compared to the algebraic VOF method, an accurate solution is achieved. This will open doors to plenty of applications such as bubble columns in reactors, oil and gas mixtures, 3D printing, polymer processing, etc. Full article

Finite difference operators were applied on a Delaunay mesh. This way it is possible to discretize a radial boundary that is used to perform a Kelvin mapping of an additional outer domain to virtually extend the computation domain to infinity. With an example two-wire problem, the performance of this approach is shown in comparison with a conventional calculation domain and with the analytical solution, respectively. The presented implementation delivers a more precise approximation to the real values and at the same time requires a smaller system of equations—i.e., allows for faster computations. Full article

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method. Full article

Grounding systems are essential parts of substations and power generation stations. The evaluation of transferred potentials from an active grounding system to other passive ones or to any near conductors is an important aspect to be considered, because transferred potentials may cause serious and fatal events. Moreover, it is an intrinsic issue of the Smart Grid where the ground systems of the power and ICT systems could be close to each other. Therefore, the estimation of the transferred potential is necessary at grounding system design stage for people safety and electric components safeguard. Numerical methods are the best choice to perform a truthful estimation, especially when large and complex grounding systems have to be designed. However, this task is complicated by the “unbounded” nature of the electromagnetic field and by the presence of components of extremely different size in the analysis domain. In this paper, an efficient hybrid finite element method is applied for the accurate and fast computation of transferred earth potentials from grounding systems. Moreover, the small dimensions of the components in the analysis domain are taken into account by the use of one-dimensional finite elements inserted in the tetrahedral mesh. It is worth mentioning the additional advantage of obtaining the electric potential on the earth surface without any post-processing operation. Full article

Chris Langton proposed a model of an artificial life that he named “ant”: an agent- called ant- that is over a square of a grid moves by turning to the left (or right) accordingly to black (or white) color of the square where it is heading, and the square then reverses its color. Bunimovich and Troubetzkoy proved that an ant’s trajectory is always unbounded, or equivalently, there exists no repeatable configuration of the ant’s system. On the other hand, by introducing a new type of color where the ant goes straight ahead and the color never changes, repeatable configurations are known to exist. In this paper, we prove that determining whether a given finite configuration of generalized Langton’s ant is repeatable or not is PSPACE-hard. We also prove the PSPACE-hardness of the ant’s problem on a hexagonal grid. Full article