Search results for: gravitational pseudo-tensor

Authors: Ali Ateş, Ansar B. Mwimbo, Ali H. Abdulkarim

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General transport equation has a wide range of application in Fluid Mechanics and Heat Transfer problems. In this equation, generally when φ variable which represents a flow property is used to represent fluid velocity component, general transport equation turns into momentum equations or with its well known name Navier-Stokes equations. In these non-linear differential equations instead of seeking for analytic solutions, preferring numerical solutions is a more frequently used procedure. Finite difference method is a commonly used numerical solution method. In these equations using velocity and pressure gradients instead of stress tensors decreases the number of unknowns. Also, continuity equation, by integrating the system, number of equations is obtained as number of unknowns. In this situation, velocity and pressure components emerge as two important parameters. In the solution of differential equation system, velocities and pressures must be solved together. However, in the considered grid system, when pressure and velocity values are jointly solved for the same nodal points some problems confront us. To overcome this problem, using staggered grid system is a referred solution method. For the computerized solutions of the staggered grid system various algorithms were developed. From these, two most commonly used are SIMPLE and SIMPLER algorithms. In this study Navier-Stokes equations were numerically solved for Newtonian flow, whose mass or gravitational forces were neglected, for incompressible and laminar fluid, as a hydro dynamically fully developed region and in two dimensional cartesian coordinate system. Finite difference method was chosen as the solution method. This is a parametric study in which varying values of velocity components, pressure and Reynolds numbers were used. Differential equations were discritized using central difference and hybrid scheme. The discritized equation system was solved by Gauss-Siedel iteration method. SIMPLE and SIMPLER were used as solution algorithms. The obtained results, were compared for central difference and hybrid as discritization methods. Also, as solution algorithm, SIMPLE algorithm and SIMPLER algorithm were compared to each other. As a result, it was observed that hybrid discritization method gave better results over a larger area. Furthermore, as computer solution algorithm, besides some disadvantages, it can be said that SIMPLER algorithm is more practical and gave result in short time. For this study, a code was developed in DELPHI programming language. The values obtained in a computer program were converted into graphs and discussed. During sketching, the quality of the graph was increased by adding intermediate values to the obtained result values using Lagrange interpolation formula. For the solution of the system, number of grid and node was found as an estimated. At the same time, to indicate that the obtained results are satisfactory enough, by doing independent analysis from the grid (GCI analysis) for coarse, medium and fine grid system solution domain was obtained. It was observed that when graphs and program outputs were compared with similar studies highly satisfactory results were achieved.

Keywords: finite difference method, GCI analysis, numerical solution of the Navier-Stokes equations, SIMPLE and SIMPLER algoritms

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Authors: Sara Scolari, Davide Mombelli, Gianluca Dall'Osto, Jasna Kastivnik, Gašper Tavčar, Carlo Mapelli

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The EIT Raw Materials RIS-DustRec-II project aims to transform Electric Arc Furnace Dust (EAFD) into a valuable resource by overcoming the challenges associated with traditional recycling approaches. EAFD, a zinc-rich industrial by-product typically recycled by the Waelz process, contains complex oxides such as franklinite (ZnFe₂O₄), which hinder the efficient extraction of zinc, by also introducing other valuable elements (Fe, Ni, Cr, Cu, …) in the slag. The project aims to develop a multistage multidisciplinary approach to separate EAFD into two streams: a magnetic and non-magnetic one. In this paper the production of self-reducing briquettes from the magnetic stream of EAFD with a reducing agent, aiming to drive carbothermic reduction and recover iron as a usable alloy, was investigated. Research was focused on optimizing the magnetic and subsequent gravimetric separation (MGS) processes, followed by high-temperature smelting to evaluate reduction efficiency and phase separation. The characterization of selected two different raw EAFD samples and their magnetic-gravitational separation to isolate zinc- and iron-rich fractions was performed by X-ray diffraction and scanning electron microscope. The iron-enriched concentrates were then agglomerated into self-reducing briquettes by mixing them with either biochar (olive pomace pyrolyzed at 350 and 750°C and wood chips pyrolyzed at 750 °C) and a Cupola Furnace dust as reducing agents, combined with gelatinized corn starch as a binder. Cylindrical briquettes were produced and cured for 14 days to ensure structural integrity during subsequent thermal treatments. Smelting tests were carried out at 1400 °C in an inert argon atmosphere to assess the metallization efficiency and the separation between metal and slag phases. A carbon/oxides mass ratio of 0.262 (C/(ZnO+Fe₂O₃)) was used in these tests to maintain continuity with previous studies and to standardize reduction conditions. The magnetic and gravimetric separations effectively isolated zinc- and iron-enriched fractions, particularly for one of the two EAFD, where the concentration of Zn in the concentration fraction was reduced by 8 wt.% while Fe reached 45 wt.%. The reduction tests conducted at 1400 °C showed that the chosen carbon/oxides ratio was sufficient for the smelting of the reducible oxides within the briquettes. However, an important limitation became apparent: the amount of carbon, exceeding the stochiometric value, proved to be excessive for the effective coalescence of metal droplets, preventing clear metal-slag separation. To address this, further smelting tests were carried out in an air atmosphere rather than inert conditions to burn off excess carbon. This paper demonstrates the potential of controlled carbothermic reduction for EAFD recycling. By carefully optimizing the C/(ZnO+Fe₂O₃) ratio, the process can maximize metal recovery while achieving better separation of the metal and slag phases. This approach offers a promising alternative to traditional EAFD recycling methods, with further studies recommended to refine the parameters for industrial application.

Keywords: biochars, electrical arc furnace dust, metallization, smelting

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Authors: K. C. Apil, Keshab Sharma, Bigul Pokharel

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Kathmandu Valley, capital city of Nepal houses numerous historical monuments as well as religious structures which are as old as from the 4th century A.D. The city alone is home to seven UNESCO’s world heritage sites including various public squares and religious sanctums which are often regarded as living heritages by various historians and archeological explorers. Recently on April 25, 2015, the capital city including other nearby locations was struck with Gorkha earthquake of moment magnitude (Mw) 7.8, followed by the strongest aftershock of moment magnitude (Mw) 7.3 on May 12. This study reports structural failures and collapse of heritage structures in Kathmandu Valley during the earthquake and presents preliminary findings as to the causes of failures and collapses. Field reconnaissance was carried immediately after the main shock and the aftershock, in major heritage sites: UNESCO world heritage sites, a number of temples and historic buildings in Kathmandu Durbar Square, Patan Durbar Square, and Bhaktapur Durbar Square. Despite such catastrophe, a significant number of heritage structures stood high, performing very well during the earthquake. Preliminary reports from archeological department suggest that 721 of such structures were severely affected, whereas numbers within the valley only were 444 including 76 structures which were completely collapsed. This study presents recorded accelerograms and geology of Kathmandu Valley. Structural typology and architecture of the heritage structures in Kathmandu Valley are briefly described. Case histories of damaged heritage structures, the patterns, and the failure mechanisms are also discussed in this paper. It was observed that performance of heritage structures was influenced by the multiple factors such as structural and architecture typology, configuration, and structural deficiency, local ground site effects and ground motion characteristics, age and maintenance level, material quality etc. Most of such heritage structures are of masonry type using bricks and earth-mortar as a bonding agent. The walls' resistance is mainly compressive, thus capable of withstanding vertical static gravitational load but not horizontal dynamic seismic load. There was no definitive pattern of damage to heritage structures as most of them behaved as a composite structure. Some structures were extensively damaged in some locations, while structures with similar configuration at nearby location had little or no damage. Out of major heritage structures, Dome, Pagoda (2, 3 or 5 tiered temples) and Shikhara structures were studied with similar variables. Studying varying degrees of damages in such structures, it was found that Shikhara structures were most vulnerable one where Dome structures were found to be the most stable one, followed by Pagoda structures. The seismic performance of the masonry-timber and stone masonry structures were slightly better than that of the masonry structures. Regular maintenance and periodic seismic retrofitting seems to have played pivotal role in strengthening seismic performance of the structure. The study also recommends some key functions to strengthen the seismic performance of such structures through study based on structural analysis, building material behavior and retrofitting details. The result also recognises the importance of documentation of traditional knowledge and its revised transformation in modern technology.

Keywords: Gorkha earthquake, field observation, heritage structure, seismic performance, masonry building

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Authors: Anne Schattel, Mitja Echim, Christof Büskens

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Trajectory planning for deep space missions has become a recent topic of great interest. Flying to space objects like asteroids provides two main challenges. One is to find rare earth elements, the other to gain scientific knowledge of the origin of the world. Due to the enormous spatial distances such explorer missions have to be performed unmanned and autonomously. The mathematical field of optimization and optimal control can be used to realize autonomous missions while protecting recourses and making them safer. The resulting algorithms may be applied to other, earth-bound applications like e.g. deep sea navigation and autonomous driving as well. The project KaNaRiA ('Kognitionsbasierte, autonome Navigation am Beispiel des Ressourcenabbaus im All') investigates the possibilities of cognitive autonomous navigation on the example of an asteroid mining mission, including the cruise phase and approach as well as the asteroid rendezvous, landing and surface exploration. To verify and test all methods an interactive, real-time capable simulation using virtual reality is developed under KaNaRiA. This paper focuses on the specific challenge of the guidance during the cruise phase of the spacecraft, i.e. trajectory optimization and optimal control, including first solutions and results. In principle there exist two ways to solve optimal control problems (OCPs), the so called indirect and direct methods. The indirect methods are being studied since several decades and their usage needs advanced skills regarding optimal control theory. The main idea of direct approaches, also known as transcription techniques, is to transform the infinite-dimensional OCP into a finite-dimensional non-linear optimization problem (NLP) via discretization of states and controls. These direct methods are applied in this paper. The resulting high dimensional NLP with constraints can be solved efficiently by special NLP methods, e.g. sequential quadratic programming (SQP) or interior point methods (IP). The movement of the spacecraft due to gravitational influences of the sun and other planets, as well as the thrust commands, is described through ordinary differential equations (ODEs). The competitive mission aims like short flight times and low energy consumption are considered by using a multi-criteria objective function. The resulting non-linear high-dimensional optimization problems are solved by using the software package WORHP ('We Optimize Really Huge Problems'), a software routine combining SQP at an outer level and IP to solve underlying quadratic subproblems. An application-adapted model of impulsive thrusting, as well as a model of an electrically powered spacecraft propulsion system, is introduced. Different priorities and possibilities of a space mission regarding energy cost and flight time duration are investigated by choosing different weighting factors for the multi-criteria objective function. Varying mission trajectories are analyzed and compared, both aiming at different destination asteroids and using different propulsion systems. For the transcription, the robust method of full discretization is used. The results strengthen the need for trajectory optimization as a foundation for autonomous decision making during deep space missions. Simultaneously they show the enormous increase in possibilities for flight maneuvers by being able to consider different and opposite mission objectives.

Keywords: deep space navigation, guidance, multi-objective, non-linear optimization, optimal control, trajectory planning.

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Authors: Tehrrie Konig, Cassiano Bortolozo, Daniel Metodiev, Rodolfo Mendes, Marcio Andrade, Marcio Moraes

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Gravitational mass movements are recurrent events in Brazil, usually triggered by intense rainfall. When these events occur in urban areas, they end up becoming disasters due to the economic damage, social impact, and loss of human life. To identify the landslide-susceptible areas, it is important to know the geotechnical parameters of the soil, such as cohesion, internal friction angle, unit weight, hydraulic conductivity, and hydraulic diffusivity. The measurement of these parameters is made by collecting soil samples to analyze in the laboratory and by using geophysical methodologies, such as Vertical Electrical Survey (VES). The geophysical surveys analyze the soil properties with minimal impact in its initial structure. Statistical analysis and mathematical models of physical basis are used to model and calculate the Factor of Safety for steep slope areas. In general, such mathematical models work from the combination of slope stability models and hydrological models. One example is the mathematical model TRIGRS (Transient Rainfall Infiltration and Grid-based Regional Slope- Stability Model) which calculates the variation of the Factor of Safety of a determined study area. The model relies on changes in pore-pressure and soil moisture during a rainfall event. TRIGRS was written in the Fortran programming language and associates the hydrological model, which is based on the Richards Equation, with the stability model based on the principle of equilibrium limit. Therefore, the aims of this work are modeling the slope stability of Campos do Jordão with TRIGRS, using geotechnical and geophysical methodologies to acquire the soil properties. The study area is located at southern-east of Sao Paulo State in the Mantiqueira Mountains and has a historic landslide register. During the fieldwork, soil samples were collected, and the VES method applied. These procedures provide the soil properties, which were used as input data in the TRIGRS model. The hydrological data (infiltration rate and initial water table height) and rainfall duration and intensity, were acquired from the eight rain gauges installed by Cemaden in the study area. A very high spatial resolution digital terrain model was used to identify the slopes declivity. The analyzed period is from March 6th to March 8th of 2017. As results, the TRIGRS model calculates the variation of the Factor of Safety within a 72-hour period in which two heavy rainfall events stroke the area and six landslides were registered. After each rainfall, the Factor of Safety declined, as expected. The landslides happened in areas identified by the model with low values of Factor of Safety, proving its efficiency on the identification of landslides susceptible areas. This study presents a critical threshold for landslides, in which an accumulated rainfall higher than 80mm/m² in 72 hours might trigger landslides in urban and natural slopes. The geotechnical and geophysics methods are shown to be very useful to identify the soil properties and provide the geological characteristics of the area. Therefore, the combine geotechnical and geophysical methods for soil characterization and the modeling of landslides susceptible areas with TRIGRS are useful for urban planning. Furthermore, early warning systems can be developed by combining the TRIGRS model and weather forecast, to prevent disasters in urban slopes.

Keywords: landslides, susceptibility, TRIGRS, vertical electrical survey

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

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This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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