Arc Flow Research Articles

Design of ION Thruster

Ion thrusters represent a significant advancement in electric propulsion, enhancing fuel efficiency by accelerating ions for thrust generation. These systems, demonstrated in missions such as Deep Space 1 and Dawn, facilitate substantial velocity changes with minimal propellant, making them suitable for long-duration space missions. This paper outlines the design of an ion thruster aimed at achieving a thrust of 0.2 Newton, focusing on the use of xenon as the propellant and employing highvoltage grids for ion acceleration. Key design aspects include an efficient power supply delivering at least 26 W, effective thermal management, and the integration of control systems. Performance metrics target a specific impulse of 3,000 seconds and a thrust-to-power efficiency ratio greater than 0.5. Through detailed calculations, including arc distance, flow configuration and velocity analyses and testing using different materials, this study identifies optimal configurations for thrust generation. The developed ion thruster is tailored for small satellites (700-800 kg) to enhance trajectory control and station-keeping, underscoring the importance of ion propulsion in modern space exploration

Influence of Mixed Cathode Emissivity on Generated Plasma Flow in Vacuum Arc with Heated Cathode

Influence of Mixed Cathode Emissivity on Generated Plasma Flow in Vacuum Arc with Heated Cathode

Fleet repositioning in the tramp ship routing and scheduling problem with bunker optimization: A matheuristic solution approach

This paper investigates an important planning problem faced by dry bulk shipping operators, referred to as the Tramp Ship Routing and Scheduling Problem with Bunker Optimization (TSRSPBO). The problem is to maximize the overall profit of a fleet of vessels by selecting cargoes and determining ship routes and schedules. We consider this problem under a set of practically relevant features such as flexibility in cargo quantities, as well as bunkering decisions on where to procure fuel and how much. As a particularly novel feature, we address the regional allocation of vessels at the end of the planning period to be well prepared for meeting (uncertain) future demand. To incorporate this, we consider the TSRSPBO as a two-stage stochastic programming problem, where cargo selection, routing, and bunkering decisions are solved in the first-stage problem, and the recourse cost of fleet repositioning is considered in the second stage. We present arc flow and path flow formulations, where the latter employs a priori generation of feasible routes as input. For solving realistically sized instances, we propose a matheuristic based on an Adaptive Large Neighborhood Search (ALNS) framework that iteratively generates columns and solves the path flow model. Computational experiments based on real data show that this matheuristic finds high-quality solutions for large test instances with 120 cargoes, 30 vessels, and ten bunker ports in less than one hour. Also, considering the TSRSPBO as a two-stage stochastic problem achieves the highest profits and is solved almost as quickly as the deterministic problem variant.

Features of Network Flow Systems for Decision Making with Motivation Accounting

The present work investigates the problem of considering the influence of motivation in discrete network flow decision-making systems. Motivation is the primary factor that drives people to achieve their goals and plays a key role in decision-making systems. A method is proposed by which this influence is accounted for using the arc flow function amplification or attenuation coefficients. These operations are in the class of generalized network flows (flows with gains and losses). Methods to determine both the maximal and minimal value of the generalized network flow with consideration of the motivation are proposed A numerical example of a decision-making system based on a generalized network flow with motivation accounting is described, which confirms the obtained theoretical results.

An exact algorithm for simultaneous pickup and delivery problem with split demand and time windows

This study introduces a new variant of the vehicle routing problem (VRP) called the simultaneous pickup and delivery problem with split demand and time windows (SPDP-SDTW). The motivation behind this study stems from real-life urban and rural delivery scenarios, encompassing features such as split demand, simultaneous pickup and delivery, many-to-many pickup and delivery, and time windows. The study thoroughly investigates the properties of the optimal solution for the SPDP-SDTW. Based on these properties, an arc flow model is developed for the SPDP-SDTW. Dantzig Wolfe (DW) decomposition techniques are employed to obtain the master problem and the pricing subproblem. In order to effectively address the SPDP-SDTW, an improved branch and price (I-BP) algorithm is proposed, incorporating a tailored column generation (CG) algorithm, branching strategies, and dual stabilization strategies. The proposed CG algorithm provides a framework that combines the improved adaptive degree heuristic (I-AGH) algorithm and the solver Gurobi. This integration substantially mitigates the computational burden involved in solving the subproblem. Extensive computational experiments conducted on datasets of varying sizes, including small, medium, and large instances, consistently demonstrate that the I-BP algorithm performs the best in both solution quality and computational efficiency when compared to existing exact and heuristic algorithms.

Stable set reformulations for the degree preserving spanning tree problem

Let G=(V,E) be a connected undirected graph and assume that a spanning tree is available for it. Any vertex in this tree is called degree preserving if it has the same degree in the graph and in the tree. Building upon this concept, the Degree Preserving Spanning Tree Problem (DPSTP) asks for a spanning tree of G with as many degree preserving vertices as possible. DPSTP is very much intertwined with the most important application for it, so far, i.e., the online monitoring of arc flows in a water distribution network, what serves us as an additional motivation for our investigation. We show that degree preserving vertices correspond to a stable set of a properly defined DPSTP conflict graph. This, in turn, allows us to use valid inequalities for the Stable Set Polytope (SSP) and thus strengthen the DPSTP formulations previously suggested in the literature. In doing so, the Branch-and-cut and Benders Decomposition algorithms suggested for these formulations are greatly enhanced. Additionally, as a further contribution, we also introduce a new and very challenging set of DPSTP test instances, given by graphs that closely resemble water distribution networks. For these instances, the new algorithms very clearly outperform all previous DPSTP algorithms. They not only run faster than their competitors but are also less dependent on good initial DPSTP primal bounds. For previous DPSTP test sets, the new algorithms lag behind the best existing algorithm for them, which is based on Lagrangian relaxation. However, as compared to additional DPSTP previous algorithms that do not benefit from SSP inequalities, the new ones come much closer to the Lagrangian relaxation one.

Information Flow Management regarding the Functioning of Public Authorities in Crisis Situations

For the management of information flow, the use of the functional modelling methodology is proposed, as part of the graph theory for describing the functioning of systems, such as public authorities as organizational-management structures. The methodology is based on concepts such as functional block and interface arc (flow). In organizational-management structures, one of the functional blocks is the manager, and the others are managed. Each of the blocks is a source of information and generates information flows, transferring information to a managed functional block or several ones. For the implementation and management of information exchange by the public authorities in crisis management, processing and protection of data flow, when working in a group environment, it is proposed to build an adequate communication and information system using the methodology of functional modelling.

Managementul fluxului de informații privind funcționarea autorităților publice în situații de criză

For the management of information flow, the use of the functional modelling methodology is proposed, as part of the graph theory for describing the functioning of systems, such as public authorities as organizational-management structures. The methodology is based on concepts such as functional block and interface arc (flow). In organizational-management structures, one of the functional blocks is the manager, and the others are managed. Each of the blocks is a source of information and generates information flows, transferring information to a managed functional block or several ones. For the implementation and management of information exchange by the public authorities in crisis management, processing and protection of data flow, when working in a group environment, it is proposed to build an adequate communication and information system using the methodology of functional modelling.

Two-temperature modeling of lamellar cathode arc

A three-dimensional, two-temperature (2T) model of a lamellar cathode arc is constructed, drawing upon the conservation equations for mass, momentum, electron energy, and heavy particle energy, in addition to Maxwell’s equations. The model aims to elucidate how the physical properties of electrons and heavy particles affect heat transfer and fluid flow in a lamellar cathode arc. This is achieved by solving and comparing the fields of electron temperature, heavy particle temperature, fluid flow, current density, and Lorentz force distribution under varying welding currents. The results show that the guiding effect of the lamellar cathode on current density, the inertial drag effect of moving arc, and the attraction effect of Lorentz force at the lamellar cathode tip primarily govern the distribution of the arc’s physical fields. The guiding effect localizes the current density to the front end of the lamellar cathode, particularly where the discharge gap is minimal. Both the inertial drag effect and the attraction effect of Lorentz force direct arc flow toward its periphery. Under the influence of the aforementioned factors, the physical fields of the lamellar cathode arc undergo expansion and shift counter to the arc’s direction of motion. A reduction in welding current substantially weakens the guiding effect, causing the arc’s physical fields to deviate further in the direction opposite to the arc motion. In comparison with a cylindrical cathode arc, the physical fields of the lamellar cathode arc are markedly expanded, leading to a reduction in current density, electron temperature, heavy particle temperature, cathode jet flow velocity, and Lorentz force.

An enhanced exact algorithm for the multi-trip vehicle routing problem with time windows and capacitated unloading station

This paper introduces a vehicle routing problem that simultaneously considers multiple trips, time windows, and a capacitated unloading station. This problem is a generalization of the multi-trip vehicle routing problem with time windows, which determines a set of least-cost vehicle routes to fulfill all customer demands while respecting the constraints of vehicle capacity and time windows. Due to restricted resources (e.g., equipment and labor force) at the depot, vehicles may need to wait in a queue for being unloaded when they arrive. This unloading capacity constraint significantly complicates the problem, as it causes a trip to involve three stages—traveling, waiting, and unloading. We formulate this problem as an arc flow model and a trip-based set partitioning model, where the latter is solved by a branch-price-and-cut (BPC) algorithm. To improve the computational aspect of the BPC framework, a two-phase column generation (CG) algorithm is designed. First, a bidirectional labeling algorithm is tailored to solve the pricing problem, where two accelerating strategies are employed to speed up the resolution process. Meanwhile, k-path inequalities and limited-memory subset row inequalities are utilized to tighten the linear relaxation of the master problem. Computational results based on the instances adapted from the well-known Solomon’s benchmark show that the developed BPC algorithm can solve most instances within 50 customers to optimality in a short time frame and some instances of 100 customers to optimality within a 3-hour time limit. Moreover, our BPC algorithm performs better than exact algorithms in the literature for similar problem variants in both solution quality and computing time.

A Numerical Study on the Influence of External Magnetic field on Hydrogen Electric Arc Flow

We present a 3D numerical model capable of simulating hydrogen electric arc. The numerical model couples the electromagnetic field with hydrogen plasma arc dynamics (flow and heat transfer). Electric arc operates under the conditions of atmospheric pressure using direct current (DC) in the presence of external magnetic field. It is found that arc instabilities emerge spontaneously near the cathode before propagating downwards along the arc jet. Also, spontaneous splitting into several arcs is observed before merging again into one arc. The horizontal magnetic field induces arc skewing and directional flow perpendicular to the applied magnetic field. However, the axial magnetic field induces a rotational flow and arc swirling.

Complex heat transfer in a bath under arcs of high-power arc steel-melting furnaces. Part II. Conversion of radiant arc flows into convection and heat conduction flows in the bath

Complex heat transfer in a bath under arcs of high-power arc steel-melting furnaces. Part II. Conversion of radiant arc flows into convection and heat conduction flows in the bath

Mathematical models and exact algorithms for the Colored Bin Packing Problem

This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the same color can appear consecutively in the same bin. To simplify modeling, we present a characterization of any feasible packing of this problem in a way that does not depend on its ordering. This allows us to describe the problem with a simple mathematical model. Furthermore, we present four exact algorithms for the CBPP. First, we propose a generalization of Valério de Carvalho’s arc flow formulation for the CBPP using a graph with multiple layers, each representing a color. Second, we present an improved arc flow formulation that uses a more compact graph and has the same linear relaxation bound as the first formulation. And finally, we design two exponential set-partition models based on reductions to a generalized vehicle routing problem, which are solved by a branch-cut-and-price algorithm through VRPSolver. To compare the proposed algorithms, a varied benchmark set with 574 instances of the CBPP is presented. Experimental results show that our best model, the improved arc flow formulation, was able to solve instances of up to 500 items and 37 colors. The set-partition models are also shown to exceed their arc flow counterparts in instances with a very small number of colors.

Design and Structural Optimization of Electrically Controlled Throttle Valve Core for Stratified Injection

In order to solve the problems of poor regulation of throttling pressure drop and excessive viscous friction in electrically controlled throttle valves in stratified injection, a new valve core structure that can efficiently regulate pressure drop and reduce viscous friction is designed. An effective valve core simulation model is established, and the model is divided into grids for fluid dynamics simulation. The pressure drop and shear rate of three commonly used valve and throttle structures are compared comprehensively based on the simulation results. The optimal circular arc flow channel structure is selected, and the influence of the length of the circular arc structure on the shear rate is simulated. Compared with 20mm, 25mm and 30mm, the best effect was obtained when the valve joint length is 30mm.The experimental results show that the average viscosity of the optimized valve core is less than 11%, which reduces the viscosity loss.which provided theoretical support for the optimization of layered injection tool.

Valid inequalities for the non-unit demand capacitated minimum spanning tree problem with arc time windows and flow costs

In this paper, we introduce the non-unit demand capacitated minimum spanning tree problem with arc time windows and flow costs. The problem is a variant of the capacitated minimum spanning tree problem with arc time windows (CMSTP_ATW). We devise a mixed integer programming (MIP) formulation to model the problem and solve it using CPLEX. Furthermore, we propose three sets of inequalities, and we prove that they are valid. These valid inequalities tighten the model and lead to better lower bounds. To examine the quality of the solutions obtained, we convert the original data sets of Solomon (1987, “Algorithms for the Vehicle Routing and Scheduling Problem with Time Window Constraints.” Operations Research 35 (2): 254–265. https://doi.org/10.1287/opre.35.2.254) to approximate the non-unit demand CMSTP_ATW instances and provide results for the problems with 100 nodes. We execute extensive computational experiments, and the results show the positive effect of the inclusion of valid inequalities in the MIP.

Plasma-Arc-Flow Technology for Sustainable Treatment of High-Impact Fluid Waste: A Graphene-Based Material for Industrial-Wastewater Purification

The research presented aimed to address the treatment of fluid waste with significant environmental impact by utilizing plasma technology, specifically plasma arc flow (PAF). The goal was to develop a novel purification material based on graphene for industrial applications and to optimize the treatment process. Analysis and monitoring of a submerged arc plasma reactor were the main goals of this research. This entailed a careful examination of the incoming wastewater that needed to be treated with the goal of identifying its precise composition characteristics with the relative tolerances needed for the reactions that were to follow in the reactor. The focus of the analysis was on input-parameter optimization, production of characteristic curves, and analysis of the factors affecting hydrogen evolution in syngas. Additionally, the study investigated how to determine the best viscosity for a particular input matrix by carrying out an evaluation study. The effects of this parameter were thought to be reduced by preheating the incoming wastewater through heat recovery. The long-term objective of the research is to create filters that can purify the water used and produced in gasification processes as well as to characterize the fixed reside from the gasifier for potential conversion into graphene-based material. In addition, this work acknowledges that additional experiments are required to validate its purifying capacity on wastewater produced by various industrial processes. Moreover, the inclusion of plans to model the evolution of hydrogen in PAF using the CHEMCAD software® and defining guidelines for optimizing parameters for enhanced energy efficiency showcased the research’s ambition to expand and refine its scope. Finding the best plant solutions that can significantly reduce electricity consumption is the ultimate goal. In summary, the study demonstrated significant advancement in the analysis and optimization of fluid-waste treatment with high environmental impact through the use of plasma technology, specifically PAF. A thorough and forward-looking approach was demonstrated by the use of modeling software, experimental studies, and plans for future research. The potential creation of graphene-based filters and the use of the fixed residue as a useful material further highlight the innovativeness of this research.

Modeling and Performance Analysis of Municipal Solid Waste Treatment in Plasma Torch Reactor

Thermal plasma has emerged as a technology with tremendous promise for municipal wastes that should be disposed of sustainably. A numerical simulation of a symmetric turbulent plasma jet from a thermal air plasma torch was developed using COMSOL Multiphysics®5.4 engineering simulation software. The velocities, temperature, arc root motion, and joule heating of the plasma jet were examined under the impact of the gas mass flow rate and current. Moreover, the electrical power required for the municipal solid waste (MSW) processing was estimated. The enthalpy and the effectiveness of the plasma torch were analyzed and discussed. Subsequently an investigation was conducted into the gasification characteristics of MSW using air and steam gases. The torch’s power and efficiency could be enhanced with a higher mass flow rate and temperature. Three operating modes were identified from the current–arc flow combination. Among the plasma gas considered, the air gas plasma torch guarantees an acceptable thermal efficiency and a low anode erosion rate. Plasma gasification produces cleaner syngas with higher efficiency (84%) than the conventional process due to the elevated temperature used during the process that breaks down all the char, dioxins, and tars.

Boosted Arc Flow Formulation Using Graph Compression for the Two-Dimensional Strip Cutting Problem

Since the requirement for a material cutting process occurs in a wide variety of applied contemporary manufacturing, the cutting stock problem plays a critical role in optimizing the amount of raw material utilized in everyday production operations. In this paper, we address the two-dimension strip-cutting problem and implement the graph compression technique to improve the performance of the arc-flow formulation. The number of variables of the obtained mathematical model are substantially reduced. A comparative study on a large set of benchmark instances shows that our compressed model yields very good results for the non-unitary item demand case in contrast to the state-of-the-art mathematical models. Moreover, improved bounds are provided for 24 unsolved benchmark instances, among which 8 have been solved to optimality.

Physical mechanism of material flow and temperature distribution in keyhole plasma arc welding at initial unstable stage

The initial unstable stage associated with keyhole plasma arc welding affects the stability and quality heavily, especially in the non-vertical welding position, which is difficult to control and restricts the process development and application. This work clarifies the temperature distribution and flow behavior of the process from the digging keyhole stage to the keyhole stable movement stage via an infrared thermography system and high-speed camera system. The experimental results showed that the molten metal on the rear side of the keyhole gradually accumulates and solidifies on the exit side and rear wall of the keyhole. When enough molten metal accumulates on the keyhole rear sidewall, it closes under the action of surface tension. The angle (86°–90°) of the keyhole rear sidewall formation can be used to determine whether the keyhole rear side is closed and reached the keyhole stable movement stage. Simultaneously, the influence of the shifting direction of gravity on the temperature distribution, flow behavior, and solidification morphology of the keyhole weld pool was investigated, which further revealed the initial unstable stage of the welding process. In the flat position, at this stage, the high-temperature area within the keyhole rear sidewall surface gradually accumulates close to the exit side of the weld pool. More molten metal flows to the keyhole exit side by gravity and shear forces, which causes a separation area on the keyhole rear side that is nearer to the exit side of the weld pool. This makes it harder to close the keyhole wall when it is in a flat position during the initial unstable stage. Furthermore, the temperature distribution and flow behavior of the keyhole rear side can be used as another factor to characterize the flow state of the weld pool in all positions and stages of welding.

Solving Unsplittable Network Flow Problems with Decision Diagrams

In unsplittable network flow problems, certain nodes must satisfy a combinatorial requirement that the incoming arc flows cannot be split or merged when routed through outgoing arcs. This so-called no-split no-merge requirement arises in unit train scheduling where train consists should remain intact at stations that lack necessary equipment and manpower to attach/detach them. Solving the unsplittable network flow problems with standard mixed-integer programming formulations is computationally difficult due to the large number of binary variables needed to determine matching pairs between incoming and outgoing arcs of nodes with no-split no-merge constraint. In this paper, we study a stochastic variant of the unit train scheduling problem where the demand is uncertain. We develop a novel decision diagram (DD)-based framework that decomposes the underlying two-stage formulation into a master problem that contains the combinatorial requirements and a subproblem that models a continuous network flow problem. The master problem is modeled by a DD in a transformed space of variables with a smaller dimension, leading to a substantial improvement in solution time. Similar to the Benders decomposition technique, the subproblems output cutting planes that are used to refine the master DD. Computational experiments show a significant improvement in solution time of the DD framework compared with that of standard methods. Funding: This work was supported by the Iowa Energy Center [Grant 20IEC005]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1194 .