Search results for: Lagrange multipliers

Authors: Adefarati Oloruntoba, Yongmin Zhang, Hongliang Xiao

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An annular fluidized bed (AFB) is gaining extensive application in the process industry due to its efficient gas-solids contacting. But a direct evaluation of its reaction performance is still lacking. In this paper, comparative 3D Euler–Lagrange multiphase-particle-in-cell (MP-PIC) computations are performed to assess the reaction performance of AFB relative to a bubbling fluidized bed (BFB) in an FCC regeneration process. By using the energy-minimization multi-scale (EMMS) drag model with a suitable heterogeneity index, the MP-PIC simulation predicts the typical fountain region in AFB and solids holdup of BFB, which is consistent with an experiment. Coke combustion rate, flue gas and temperature profile are utilized as the performance indicators, while related bed hydrodynamics are explored to account for the different performance under varying superficial gas velocities (0.5 m/s, 0.6 m/s, and 0.7 m/s). Simulation results indicate that the burning rates of coke and its species are relatively the same in both beds, albeit marginal increase in BFB. Similarly, the shape and evolution time of flue gas (CO, CO₂, H₂O and O₂) curves are indistinguishable but match the coke combustion rates. However, AFB has high proclivity to high temperature-gradient as higher gas and solids temperatures are predicted in the freeboard. Moreover, for both beds, the effect of superficial gas velocity is only conspicuous on the temperature but negligible on combustion efficiency and effluent gas emissions due to constant gas volumetric flow rate and bed loading criteria. Cross-flow of solids from the annulus to the spout region as well as the high primary gas in the AFB directly assume the underlying mechanisms for its unique gas-solids hydrodynamics (pressure, solids holdup, velocity, mass flux) and local spatial homogeneity, which in turn influence the reactor performance. Overall, the study portrays AFB as a cheap alternative reactor to BFB for catalyst regeneration.

Keywords: annular fluidized bed, bubbling fluidized bed, coke combustion, flue gas, fountaining, CFD, MP-PIC, hydrodynamics, FCC regeneration

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Authors: M. Abuziarov

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The designed complex is intended for the numerical simulation of fast dynamic processes of interaction of heterogeneous environments susceptible to the significant formability. The main challenges in solving such problems are associated with the construction of the numerical meshes. Currently, there are two basic approaches to solve this problem. One is using of Lagrangian or Lagrangian Eulerian grid associated with the boundaries of media and the second is associated with the fixed Eulerian mesh, boundary cells of which cut boundaries of the environment medium and requires the calculation of these cut volumes. Both approaches require the complex grid generators and significant time for preparing the code’s data for simulation. In this codes these problems are solved using two grids, regular fixed and mobile local Euler Lagrange - Eulerian (ALE approach) accompanying the contact and free boundaries, the surfaces of shock waves and phase transitions, and other possible features of solutions, with mutual interpolation of integrated parameters. For modeling of both liquids and gases, and deformable solids the Godunov scheme of increased accuracy is used in Lagrangian - Eulerian variables, the same for the Euler equations and for the Euler- Cauchy, describing the deformation of the solid. The increased accuracy of the scheme is achieved by using 3D spatial time dependent solution of the discontinuity problem (3D space time dependent Riemann's Problem solver). The same solution is used to calculate the interaction at the liquid-solid surface (Fluid Structure Interaction problem). The codes does not require complex 3D mesh generators, only the surfaces of the calculating objects as the STL files created by means of engineering graphics are given by the user, which greatly simplifies the preparing the task and makes it convenient to use directly by the designer at the design stage. The results of the test solutions and applications related to the generation and extension of the detonation and shock waves, loading the constructions are presented.

Keywords: fluid structure interaction, Riemann's solver, Euler variables, 3D codes

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Authors: Piret Pernik

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Based on strategic, operational, and technical analysis of the ongoing armed conflict in Ukraine, this paper will examine the opportunities and risks of using small commercial drones (dual-use unmanned aerial vehicles, UAV) for military purposes. The paper discusses the opportunities and risks in the information domain, encompassing both cyber and electromagnetic interference and attacks. The paper will draw conclusions on a possible strategic impact to the battlefield outcomes in the modern armed conflicts by the widespread use of dual-use UAVs. This article will contribute to filling the gap in the literature by examining based on empirical data cyberattacks and electromagnetic interference. Today, more than one hundred states and non-state actors possess UAVs ranging from low cost commodity models, widely are dual-use, available and affordable to anyone, to high-cost combat UAVs (UCAV) with lethal kinetic strike capabilities, which can be enhanced with Artificial Intelligence (AI) and Machine Learning (ML). Dual-use UAVs have been used by various actors for intelligence, reconnaissance, surveillance, situational awareness, geolocation, and kinetic targeting. Thus they function as force multipliers enabling kinetic and electronic warfare attacks and provide comparative and asymmetric operational and tactical advances. Some go as far as argue that automated (or semi-automated) systems can change the character of warfare, while others observe that the use of small drones has not changed the balance of power or battlefield outcomes. UAVs give considerable opportunities for commanders, for example, because they can be operated without GPS navigation, makes them less vulnerable and dependent on satellite communications. They can and have been used to conduct cyberattacks, electromagnetic interference, and kinetic attacks. However, they are highly vulnerable to those attacks themselves. So far, strategic studies, literature, and expert commentary have overlooked cybersecurity and electronic interference dimension of the use of dual use UAVs. The studies that link technical analysis of opportunities and risks with strategic battlefield outcomes is missing. It is expected that dual use commercial UAV proliferation in armed and hybrid conflicts will continue and accelerate in the future. Therefore, it is important to understand specific opportunities and risks related to the crowdsourced use of dual-use UAVs, which can have kinetic effects. Technical countermeasures to protect UAVs differ depending on a type of UAV (small, midsize, large, stealth combat), and this paper will offer a unique analysis of small UAVs both from the view of opportunities and risks for commanders and other actors in armed conflict.

Keywords: dual-use technology, cyber attacks, electromagnetic warfare, case studies of cyberattacks in armed conflicts

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Authors: Thomas Arink, Isam Janajreh

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The petroleum industry generates significant amounts of waste in the form of drill cuttings, contaminated soil and oily sludge. Drill cuttings are a product of the off-shore drilling rigs, containing wet soil and total petroleum hydrocarbons (TPH). Contaminated soil comes from different on-shore sites and also contains TPH. The oily sludge is mainly residue or tank bottom sludge from storage tanks. The two main treatment methods currently used are incineration and thermal desorption (TD). Thermal desorption is a method where the waste material is heated to 450ºC in an anaerobic environment to release volatiles, the condensed volatiles can be used as a liquid fuel. For the thermal desorption unit dry contaminated soil is mixed with moist drill cuttings to generate a suitable mixture. By thermo gravimetric analysis (TGA) of the TD feedstock it was found that less than 50% of the TPH are released, the discharged material is stored in landfill. This study proposes co-gasification of petroleum waste with waste tires as an alternative to thermal desorption. Co-gasification with a high-calorific material is necessary since the petroleum waste consists of more than 60 wt% ash (soil/sand), causing its calorific value to be too low for gasification. Since the gasification process occurs at 900ºC and higher, close to 100% of the TPH can be released, according to the TGA. This work consists of three parts: 1. a mathematical gasification model, 2. a reactive flow CFD model and 3. experimental work on a drop tube reactor. Extensive material characterization was done by means of proximate analysis (TGA), ultimate analysis (CHNOS flash analysis) and calorific value measurements (Bomb calorimeter) for the input parameters of the mathematical and CFD model. The mathematical model is a zero dimensional model based on Gibbs energy minimization together with Lagrange multiplier; it is used to find the product species composition (molar fractions of CO, H2, CH4 etc.) for different tire/petroleum feedstock mixtures and equivalence ratios. The results of the mathematical model act as a reference for the CFD model of the drop-tube reactor. With the CFD model the efficiency and product species composition can be predicted for different mixtures and particle sizes. Finally both models are verified by experiments on a drop tube reactor (1540 mm long, 66 mm inner diameter, 1400 K maximum temperature).

Keywords: computational fluid dynamics (CFD), drop tube reactor, gasification, Gibbs energy minimization, petroleum waste, waste tires

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Authors: Zeinab Yazdanfar, Dilan Robert, Daniel Lester, S. Setunge

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Scour has been identified as the most common threat to bridge stability worldwide. Traditionally, scour around bridge piers is calculated using the empirical approaches that have considerable limitations and are difficult to generalize. The multi-physic nature of scouring which involves turbulent flow, soil mechanics and solid-fluid interactions cannot be captured by simple empirical equations developed based on limited laboratory data. These limitations can be overcome by direct numerical modeling of coupled hydro-mechanical scour process that provides a robust prediction of bridge scour and valuable insights into the scour process. Several numerical models have been proposed in the literature for bridge scour estimation including Eulerian flow models and coupled Euler-Lagrange models incorporating an empirical sediment transport description. However, the contact forces between particles and the flow-particle interaction haven’t been taken into consideration. Incorporating collisional and frictional forces between soil particles as well as the effect of flow-driven forces on particles will facilitate accurate modeling of the complex nature of scour. In this study, a coupled Computational Fluid Dynamics and Discrete Element Model (CFD-DEM) has been developed to simulate the scour process that directly models the hydro-mechanical interactions between the sediment particles and the flowing water. This approach obviates the need for an empirical description as the fundamental fluid-particle, and particle-particle interactions are fully resolved. The sediment bed is simulated as a dense pack of particles and the frictional and collisional forces between particles are calculated, whilst the turbulent fluid flow is modeled using a Reynolds Averaged Navier Stocks (RANS) approach. The CFD-DEM model is validated against experimental data in order to assess the reliability of the CFD-DEM model. The modeling results reveal the criticality of particle impact on the assessment of scour depth which, to the authors’ best knowledge, hasn’t been considered in previous studies. The results of this study open new perspectives to the scour depth and time assessment which is the key to manage the failure risk of bridge infrastructures.

Keywords: bridge scour, discrete element method, CFD-DEM model, multi-phase model

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Authors: Gaurav Gupta, Jitendra Mahakud

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This study focuses on the significance of internal financing constraints on the determination of corporate fixed investments in the case of Indian manufacturing companies. Financing constraints companies which have less internal fund or retained earnings face more transaction and borrowing costs due to imperfections in the capital market. The period of study is 1999-2000 to 2013-2014 and we consider 618 manufacturing companies for which the continuous data is available throughout the study period. The data is collected from PROWESS data base maintained by Centre for Monitoring Indian Economy Pvt. Ltd. Panel data methods like fixed effect and random effect methods are used for the analysis. The Likelihood Ratio test, Lagrange Multiplier test, and Hausman test results conclude the suitability of the fixed effect model for the estimation. The cash flow and liquidity of the company have been used as the proxies for the internal financial constraints. In accordance with various theories of corporate investments, we consider other firm specific variable like firm age, firm size, profitability, sales and leverage as the control variables in the model. From the econometric analysis, we find internal cash flow and liquidity have the significant and positive impact on the corporate investments. The variables like cost of capital, sales growth and growth opportunities are found to be significantly determining the corporate investments in India, which is consistent with the neoclassical, accelerator and Tobin’s q theory of corporate investment. To check the robustness of results, we divided the sample on the basis of cash flow and liquidity. Firms having cash flow greater than zero are put under one group, and firms with cash flow less than zero are put under another group. Also, the firms are divided on the basis of liquidity following the same approach. We find that the results are robust to both types of companies having positive and negative cash flow and liquidity. The results for other variables are also in the same line as we find for the whole sample. These findings confirm that internal financing constraints play a significant role for determination of corporate investment in India. The findings of this study have the implications for the corporate managers to focus on the projects having higher expected cash inflows to avoid the financing constraints. Apart from that, they should also maintain adequate liquidity to minimize the external financing costs.

Keywords: cash flow, corporate investment, financing constraints, panel data method

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Authors: Anwar Beg, Sireetorn Kuharat, Rashid Mehmood, Rabil Tabassum, Meisam Babaie

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Nano-polymeric solar paints and sol-gels have emerged as a major new development in solar cell/collector coatings offering significant improvements in durability, anti-corrosion and thermal efficiency. They also exhibit substantial viscosity variation with temperature which can be exploited in solar collector designs. Modern manufacturing processes for such nano-rheological materials frequently employ stagnation flow dynamics under high temperature which invokes radiative heat transfer. Motivated by elaborating in further detail the nanoscale heat, mass and momentum characteristics of such sol gels, the present article presents a mathematical and computational study of the steady, two-dimensional, non-aligned thermo-fluid boundary layer transport of copper metal-doped water-based nano-polymeric sol gels under radiative heat flux. To simulate real nano-polymer boundary interface dynamics, thermal slip is analysed at the wall. A temperature-dependent viscosity is also considered. The Tiwari-Das nanofluid model is deployed which features a volume fraction for the nanoparticle concentration. This approach also features a Maxwell-Garnet model for the nanofluid thermal conductivity. The conservation equations for mass, normal and tangential momentum and energy (heat) are normalized via appropriate transformations to generate a multi-degree, ordinary differential, non-linear, coupled boundary value problem. Numerical solutions are obtained via the stable, efficient Runge-Kutta-Fehlberg scheme with shooting quadrature in MATLAB symbolic software. Validation of solutions is achieved with a Variational Iterative Method (VIM) utilizing Langrangian multipliers. The impact of key emerging dimensionless parameters i.e. obliqueness parameter, radiation-conduction Rosseland number (Rd), thermal slip parameter (α), viscosity parameter (m), nanoparticles volume fraction (ϕ) on non-dimensional normal and tangential velocity components, temperature, wall shear stress, local heat flux and streamline distributions is visualized graphically. Shear stress and temperature are boosted with increasing radiative effect whereas local heat flux is reduced. Increasing wall thermal slip parameter depletes temperatures. With greater volume fraction of copper nanoparticles temperature and thermal boundary layer thickness is elevated. Streamlines are found to be skewed markedly towards the left with positive obliqueness parameter.

Keywords: non-orthogonal stagnation-point heat transfer, solar nano-polymer coating, MATLAB numerical quadrature, Variational Iterative Method (VIM)

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Authors: Hussain Bohra, Pradyuman Sharma

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This study highlights the significance of Balance Sheet Indicators on the corporate performance in the case of Indian manufacturing companies. Balance sheet indicators show the actual financial health of the company and it helps to the external investors to choose the right company for their investment and it also help to external financing agency to give easy finance to the manufacturing companies. The period of study is 2000 to 2014 for 813 manufacturing companies for which the continuous data is available throughout the study period. The data is collected from PROWESS data base maintained by Centre for Monitoring Indian Economy Pvt. Ltd. Panel data methods like fixed effect and random effect methods are used for the analysis. The Likelihood Ratio test, Lagrange Multiplier test and Hausman test results proof the suitability of the fixed effect model for the estimation. Return on assets (ROA) is used as the proxy to measure corporate performance. ROA is the best proxy to measure corporate performance as it already used by the most of the authors who worked on the corporate performance. ROA shows return on long term investment projects of firms. Different ratios like Current Ratio, Debt-equity ratio, Receivable turnover ratio, solvency ratio have been used as the proxies for the Balance Sheet Indicators. Other firm specific variable like firm size, and sales as the control variables in the model. From the empirical analysis, it was found that all selected financial ratios have significant and positive impact on the corporate performance. Firm sales and firm size also found significant and positive impact on the corporate performance. To check the robustness of results, the sample was divided on the basis of different ratio like firm having high debt equity ratio and low debt equity ratio, firms having high current ratio and low current ratio, firms having high receivable turnover and low receivable ratio and solvency ratio in the form of firms having high solving ratio and low solvency ratio. We find that the results are robust to all types of companies having different form of selected balance sheet indicators ratio. The results for other variables are also in the same line as for the whole sample. These findings confirm that Balance sheet indicators play as significant role on the corporate performance in India. The findings of this study have the implications for the corporate managers to focus different ratio to maintain the minimum expected level of performance. Apart from that, they should also maintain adequate sales and total assets to improve corporate performance.

Keywords: balance sheet, corporate performance, current ratio, panel data method

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Authors: Boguslaw Schreyer

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During the wheeled robot’s braking process, the extra dynamic vertical forces act on all wheels: left, right, front or rear. Those forces are directed downward on the front wheels while directed upward on the rear wheels. In order to maximize the deceleration, therefore, minimize the braking time and braking distance, we need to calculate a correct torque distribution: the front braking torque should be increased, and rear torque should be decreased. At the same time, we need to provide better transversal stability. In a simple case of all adhesion coefficients being the same under all wheels, the torque distribution may secure the optimal (maximal) control of the robot braking process, securing the minimum braking distance and a minimum braking time. At the same time, the transversal stability is relatively good. At any time, we control the transversal acceleration. In the case of the transversal movement, we stop the braking process and re-apply braking torque after a defined period of time. If we correctly calculate the value of the torques, we may secure the traction coefficient under the front and rear wheels close to its maximum. Also, in order to provide an optimum braking control, we need to calculate the timing of the braking torque application and the timing of its release. The braking torques should be released shortly after the wheels passed a maximum traction coefficient (while a wheels’ slip increases) and applied again after the wheels pass a maximum of traction coefficient (while the slip decreases). The correct braking torque distribution secures the front and rear wheels, passing this maximum at the same time. It guarantees an optimum deceleration control, therefore, minimum braking time. In order to calculate a correct torque distribution, a control unit should receive the input signals of a rear torque value (which changes independently), the robot’s deceleration, and values of the vertical front and rear forces. In order to calculate the timing of torque application and torque release, more signals are needed: speed of the robot: angular speed, and angular deceleration of the wheels. In case of different adhesion coefficients under the left and right wheels, but the same under each pair of wheels- the same under right wheels and the same under left wheels, the Select-Low (SL) and select high (SH) methods are applied. The SL method is suggested if transversal stability is more important than braking efficiency. Often in the case of the robot, more important is braking efficiency; therefore, the SH method is applied with some control of the transversal stability. In the case that all adhesion coefficients are different under all wheels, the front-rear torque distribution is maintained as in all previous cases. However, the timing of the braking torque application and release is controlled by the rear wheels’ lowest adhesion coefficient. The Lagrange equations have been used to describe robot dynamics. Matlab has been used in order to simulate the process of wheeled robot braking, and in conclusion, the braking methods have been selected.

Keywords: wheeled robots, braking, traction coefficient, asymmetric

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Authors: Ahmad Almajid

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The idea of unifying quantum mechanics with general relativity is still a dream for many researchers, as physics has only two paths, no more. Einstein's path, which is mainly based on particle mechanics, and the path of Paul Dirac and others, which is based on wave mechanics, the incompatibility of the two approaches is due to the radical difference in the initial assumptions and the mathematical nature of each approach. Logical thinking in modern physics leads us to two problems: - In quantum mechanics, despite its success, the problem of measurement and the problem of wave function interpretation is still obscure. - In special relativity, despite the success of the equivalence of rest-mass and energy, but at the speed of light, the fact that the energy becomes infinite is contrary to logic because the speed of light is not infinite, and the mass of the particle is not infinite too. These contradictions arise from the overlap of relativistic and quantum mechanics in the neighborhood of the speed of light, and in order to solve these problems, one must understand well how to move from relativistic mechanics to quantum mechanics, or rather, to unify them in a way different from Dirac's method, in order to go along with God or Nature, since, as Einstein said, "God doesn't play dice." From De Broglie's hypothesis about wave-particle duality, Léon Brillouin's definition of the new proper time was deduced, and thus the quantum Lorentz factor was obtained. Finally, using the Euler-Lagrange equation, we come up with new equations in quantum mechanics. In this paper, the two problems in modern physics mentioned above are solved; it can be said that this new approach to quantum mechanics will enable us to unify it with general relativity quite simply. If the experiments prove the validity of the results of this research, we will be able in the future to transport the matter at speed close to the speed of light. Finally, this research yielded three important results: 1- Lorentz quantum factor. 2- Planck energy is a limited case of Einstein energy. 3- Real quantum mechanics, in which new equations for quantum mechanics match and exceed Dirac's equations, these equations have been reached in a completely different way from Dirac's method. These equations show that quantum mechanics is a limited case of relativistic mechanics. At the Solvay Conference in 1927, the debate about quantum mechanics between Bohr, Einstein, and others reached its climax, while Bohr suggested that if particles are not observed, they are in a probabilistic state, then Einstein said his famous claim ("God does not play dice"). Thus, Einstein was right, especially when he didn't accept the principle of indeterminacy in quantum theory, although experiments support quantum mechanics. However, the results of our research indicate that God really does not play dice; when the electron disappears, it turns into amicable particles or an elastic medium, according to the above obvious equations. Likewise, Bohr was right also, when he indicated that there must be a science like quantum mechanics to monitor and study the motion of subatomic particles, but the picture in front of him was blurry and not clear, so he resorted to the probabilistic interpretation.

Keywords: lorentz quantum factor, new, planck’s energy as a limiting case of einstein’s energy, real quantum mechanics, new equations for quantum mechanics

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Authors: Bashar Mahmoud, Lee Mortimer, Michael Fairweather

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New methods have recently been introduced to improve the thermal property values of molten nitrate salts (a binary mixture of NaNO3:KNO3in 60:40 wt. %), by doping them with minute concentration of nanoparticles in the range of 0.5 to 1.5 wt. % to form the so-called: Nano-heat-transfer-fluid, apt for thermal energy transfer and storage applications. The present study aims to assess the stability of these nanofluids using the advanced computational modelling technique, Lagrangian particle tracking. A multi-phase solid-liquid model is used, where the motion of embedded nanoparticles in the suspended fluid is treated by an Euler-Lagrange hybrid scheme with fixed time stepping. This technique enables measurements of various multi-scale forces whose characteristic (length and timescales) are quite different. Two systems are considered, both consisting of 50 nm Al2O3 ceramic nanoparticles suspended in fluids of different density ratios. This includes both water (5 to 95 °C) and molten nitrate salt (220 to 500 °C) at various volume fractions ranging between 1% to 5%. Dynamic properties of both phases are coupled to the ambient temperature of the fluid suspension. The three-dimensional computational region consists of a 1μm cube and particles are homogeneously distributed across the domain. Periodic boundary conditions are enforced. The particle equations of motion are integrated using the fourth order Runge-Kutta algorithm with a very small time-step, Δts, set at 10-11 s. The implemented technique demonstrates the key dynamics of aggregated nanoparticles and this involves: Brownian motion, soft-sphere particle-particle collisions, and Derjaguin, Landau, Vervey, and Overbeek (DLVO) forces. These mechanisms are responsible for the predictive model of aggregation of nano-suspensions. An energy transport-based method of predicting the thermal conductivity of the nanofluids is also used to determine thermal properties of the suspension. The simulation results confirms the effectiveness of the technique. The values are in excellent agreement with the theoretical and experimental data obtained from similar studies. The predictions indicates the role of Brownian motion and DLVO force (represented by both the repulsive electric double layer and an attractive Van der Waals) and its influence in the level of nanoparticles agglomeration. As to the nano-aggregates formed that was found to play a key role in governing the thermal behavior of nanofluids at various particle concentration. The presentation will include a quantitative assessment of these forces and mechanisms, which would lead to conclusions about nanofluids, heat transfer performance and thermal characteristics and its potential application in solar thermal energy plants.

Keywords: thermal energy storage, molten salt, nano-fluids, multi-scale computational modelling

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Authors: Kamyar Tolouei, Ehsan Moosavi

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In open-pit mines, the long-term production scheduling optimization problem (LTPSOP) is a complicated problem that contains constraints, large datasets, and uncertainties. Uncertainty in the output is caused by several geological, economic, or technical factors. Due to its dimensions and NP-hard nature, it is usually difficult to find an ideal solution to the LTPSOP. The optimal schedule generally restricts the ore, metal, and waste tonnages, average grades, and cash flows of each period. Past decades have witnessed important measurements of long-term production scheduling and optimal algorithms since researchers have become highly cognizant of the issue. In fact, it is not possible to consider LTPSOP as a well-solved problem. Traditional production scheduling methods in open-pit mines apply an estimated orebody model to produce optimal schedules. The smoothing result of some geostatistical estimation procedures causes most of the mine schedules and production predictions to be unrealistic and imperfect. With the expansion of simulation procedures, the risks from grade uncertainty in ore reserves can be evaluated and organized through a set of equally probable orebody realizations. In this paper, to synthesize grade uncertainty into the strategic mine schedule, a stochastic integer programming framework is presented to LTPSOP. The objective function of the model is to maximize the net present value and minimize the risk of deviation from the production targets considering grade uncertainty simultaneously while satisfying all technical constraints and operational requirements. Instead of applying one estimated orebody model as input to optimize the production schedule, a set of equally probable orebody realizations are applied to synthesize grade uncertainty in the strategic mine schedule and to produce a more profitable and risk-based production schedule. A mixture of metaheuristic procedures and mathematical methods paves the way to achieve an appropriate solution. This paper introduced a hybrid model between the augmented Lagrangian relaxation (ALR) method and the metaheuristic algorithm, the Harris Hawks optimization (HHO), to solve the LTPSOP under grade uncertainty conditions. In this study, the HHO is experienced to update Lagrange coefficients. Besides, a machine learning method called Random Forest is applied to estimate gold grade in a mineral deposit. The Monte Carlo method is used as the simulation method with 20 realizations. The results specify that the progressive versions have been considerably developed in comparison with the traditional methods. The outcomes were also compared with the ALR-genetic algorithm and ALR-sub-gradient. To indicate the applicability of the model, a case study on an open-pit gold mining operation is implemented. The framework displays the capability to minimize risk and improvement in the expected net present value and financial profitability for LTPSOP. The framework could control geological risk more effectively than the traditional procedure considering grade uncertainty in the hybrid model framework.

Keywords: grade uncertainty, metaheuristic algorithms, open-pit mine, production scheduling optimization

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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: Manuel Alejandro Taborda Ceballos, Martin Sommerfeld

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Transport phenomena and dispersion of non-spherical particle in turbulent flows are found everywhere in industrial application and processes. Powder handling, pollution control, pneumatic transport, particle separation are just some examples where the particle encountered are not only spherical. These types of multiphase flows are wall bounded and mostly highly turbulent. The particles found in these processes are rarely spherical but may have various shapes (e.g., fibers, and rods). Although research related to the behavior of regular non-spherical particles in turbulent flows has been carried out for many years, it is still necessary to refine models, especially near walls where the interaction fiber-wall changes completely its behavior. Imaging-based experimental studies on dispersed particle-laden flows have been applied for many decades for a detailed experimental analysis. These techniques have the advantages that they provide field information in two or three dimensions, but have a lower temporal resolution compared to point-wise techniques such as PDA (phase-Doppler anemometry) and derivations therefrom. The applied imaging techniques in dispersed two-phase flows are extensions from classical PIV (particle image velocimetry) and PTV (particle tracking velocimetry) and the main emphasis was simultaneous measurement of the velocity fields of both phases. In a similar way, such data should also provide adequate information for validating the proposed models. Available experimental studies on the behavior of non-spherical particles are uncommon and mostly based on planar light-sheet measurements. Especially for elongated non-spherical particles, however, three-dimensional measurements are needed to fully describe their motion and to provide sufficient information for validation of numerical computations. For further providing detailed experimental results allowing a validation of numerical calculations of non-spherical particle dispersion in turbulent flows, a water channel test facility was built around a horizontal closed water channel. Into this horizontal main flow, a small cross-jet laden with fiber-like particles was injected, which was also solely driven by gravity. The dispersion of the fibers was measured by applying imaging techniques based on a LED array for backlighting and high-speed cameras. For obtaining the fluid velocity fields, almost neutrally buoyant tracer was used. The discrimination between tracer and fibers was done based on image size which was also the basis to determine fiber orientation with respect to the inertial coordinate system. The synchronous measurement of fluid velocity and fiber properties also allow the collection of statistics of fiber orientation, velocity fields of tracer and fibers, the angular velocity of the fibers and the orientation between fiber and instantaneous relative velocity. Consequently, an experimental study the behavior of elongated non-spherical particles in wall bounded turbulent flows was achieved. The development of a comprehensive analysis was succeeded, especially near the wall region, where exists hydrodynamic wall interaction effects (e.g., collision or lubrication) and abrupt changes of particle rotational velocity. This allowed us to predict numerically afterwards the behavior of non-spherical particles within the frame of the Euler/Lagrange approach, where the particles are therein treated as “point-particles”.

Keywords: crossflow, non-spherical particles, particle tracking velocimetry, PIV

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

Abstract:

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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