Search results for: Euler equations
1166 Deriving Generic Transformation Matrices for Multi-Axis Milling Machine
Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin
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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.Keywords: CAM, multi-axis milling machining, transformation matrix, rotation angles
Procedia PDF Downloads 4691165 Electromagnetic Simulation Based on Drift and Diffusion Currents for Real-Time Systems
Authors: Alexander Norbach
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The script in this paper describes the use of advanced simulation environment using electronic systems (Microcontroller, Operational Amplifiers, and FPGA). The simulation may be used for all dynamic systems with the diffusion and the ionisation behaviour also. By additionally required observer structure, the system works with parallel real-time simulation based on diffusion model and the state-space representation for other dynamics. The proposed deposited model may be used for electrodynamic effects, including ionising effects and eddy current distribution also. With the script and proposed method, it is possible to calculate the spatial distribution of the electromagnetic fields in real-time. For further purpose, the spatial temperature distribution may be used also. With upon system, the uncertainties, unknown initial states and disturbances may be determined. This provides the estimation of the more precise system states for the required system, and additionally, the estimation of the ionising disturbances that occur due to radiation effects. The results have shown that a system can be also developed and adopted specifically for space systems with the real-time calculation of the radiation effects only. Electronic systems can take damage caused by impacts with charged particle flux in space or radiation environment. In order to be able to react to these processes, it must be calculated within a shorter time that ionising radiation and dose is present. All available sensors shall be used to observe the spatial distributions. By measured value of size and known location of the sensors, the entire distribution can be calculated retroactively or more accurately. With the formation, the type of ionisation and the direct effect to the systems and thus possible prevent processes can be activated up to the shutdown. The results show possibilities to perform more qualitative and faster simulations independent of kind of systems space-systems and radiation environment also. The paper gives additionally an overview of the diffusion effects and their mechanisms. For the modelling and derivation of equations, the extended current equation is used. The size K represents the proposed charge density drifting vector. The extended diffusion equation was derived and shows the quantising character and has similar law like the Klein-Gordon equation. These kinds of PDE's (Partial Differential Equations) are analytically solvable by giving initial distribution conditions (Cauchy problem) and boundary conditions (Dirichlet boundary condition). For a simpler structure, a transfer function for B- and E- fields was analytically calculated. With known discretised responses g₁(k·Ts) and g₂(k·Ts), the electric current or voltage may be calculated using a convolution; g₁ is the direct function and g₂ is a recursive function. The analytical results are good enough for calculation of fields with diffusion effects. Within the scope of this work, a proposed model of the consideration of the electromagnetic diffusion effects of arbitrary current 'waveforms' has been developed. The advantage of the proposed calculation of diffusion is the real-time capability, which is not really possible with the FEM programs available today. It makes sense in the further course of research to use these methods and to investigate them thoroughly.Keywords: advanced observer, electrodynamics, systems, diffusion, partial differential equations, solver
Procedia PDF Downloads 1231164 A Mathematical Model for Studying Landing Dynamics of a Typical Lunar Soft Lander
Authors: Johns Paul, Santhosh J. Nalluveettil, P. Purushothaman, M. Premdas
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Lunar landing is one of the most critical phases of lunar mission. The lander is provided with a soft landing system to prevent structural damage of lunar module by absorbing the landing shock and also assure stability during landing. Presently available software are not capable to simulate the rigid body dynamics coupled with contact simulation and elastic/plastic deformation analysis. Hence a separate mathematical model has been generated for studying the dynamics of a typical lunar soft lander. Parameters used in the analysis includes lunar surface slope, coefficient of friction, initial touchdown velocity (vertical and horizontal), mass and moment of inertia of lander, crushing force due to energy absorbing material in the legs, number of legs and geometry of lander. The mathematical model is capable to simulate plastic and elastic deformation of honey comb, frictional force between landing leg and lunar soil, surface contact simulation, lunar gravitational force, rigid body dynamics and linkage dynamics of inverted tripod landing gear. The non linear differential equations generated for studying the dynamics of lunar lander is solved by numerical method. Matlab programme has been used as a computer tool for solving the numerical equations. The position of each kinematic joint is defined by mathematical equations for the generation of equation of motion. All hinged locations are defined by position vectors with respect to body fixed coordinate. The vehicle rigid body rotations and motions about body coordinate are only due to the external forces and moments arise from footpad reaction force due to impact, footpad frictional force and weight of vehicle. All these force are mathematically simulated for the generation of equation of motion. The validation of mathematical model is done by two different phases. First phase is the validation of plastic deformation of crushable elements by employing conservation of energy principle. The second phase is the validation of rigid body dynamics of model by simulating a lander model in ADAMS software after replacing the crushable elements to elastic spring element. Simulation of plastic deformation along with rigid body dynamics and contact force cannot be modeled in ADAMS. Hence plastic element of primary strut is replaced with a spring element and analysis is carried out in ADAMS software. The same analysis is also carried out using the mathematical model where the simulation of honeycomb crushing is replaced by elastic spring deformation and compared the results with ADAMS analysis. The rotational motion of linkages and 6 degree of freedom motion of lunar Lander about its CG can be validated by ADAMS software by replacing crushing element to spring element. The model is also validated by the drop test results of 4 leg lunar lander. This paper presents the details of mathematical model generated and its validation.Keywords: honeycomb, landing leg tripod, lunar lander, primary link, secondary link
Procedia PDF Downloads 3371163 Soliton Solutions in (3+1)-Dimensions
Authors: Magdy G. Asaad
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Solitons are among the most beneficial solutions for science and technology for their applicability in physical applications including plasma, energy transport along protein molecules, wave transport along poly-acetylene molecules, ocean waves, constructing optical communication systems, transmission of information through optical fibers and Josephson junctions. In this talk, we will apply the bilinear technique to generate a class of soliton solutions to the (3+1)-dimensional nonlinear soliton equation of Jimbo-Miwa type. Examples of the resulting soliton solutions are computed and a few solutions are plotted.Keywords: Pfaffian solutions, N-soliton solutions, soliton equations, Jimbo-Miwa
Procedia PDF Downloads 4411162 Chebyshev Polynomials Relad with Fibonacci and Lucas Polynomials
Authors: Vandana N. Purav
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Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials. Procedia PDF Downloads 3581161 Four-Electron Auger Process for Hollow Ions
Authors: Shahin A. Abdel-Naby, James P. Colgan, Michael S. Pindzola
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A time-dependent close-coupling method is developed to calculate a total, double and triple autoionization rates for hollow atomic ions of four-electron systems. This work was motivated by recent observations of the four-electron Auger process in near K-edge photoionization of C+ ions. The time-dependent close-coupled equations are solved using lattice techniques to obtain a discrete representation of radial wave functions and all operators on a four-dimensional grid with uniform spacing. Initial excited states are obtained by relaxation of the Schrodinger equation in imaginary time using a Schmidt orthogonalization method involving interior subshells. The radial wave function grids are partitioned over the cores on a massively parallel computer, which is essential due to the large memory requirements needed to store the coupled-wave functions and the long run times needed to reach the convergence of the ionization process. Total, double, and triple autoionization rates are obtained by the propagation of the time-dependent close-coupled equations in real-time using integration over bound and continuum single-particle states. These states are generated by matrix diagonalization of one-electron Hamiltonians. The total autoionization rates for each L excited state is found to be slightly above the single autoionization rate for the excited configuration using configuration-average distorted-wave theory. As expected, we find the double and triple autoionization rates to be much smaller than the total autoionization rates. Future work can be extended to study electron-impact triple ionization of atoms or ions. The work was supported in part by grants from the American University of Sharjah and the US Department of Energy. Computational work was carried out at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, California, USA.Keywords: hollow atoms, autoionization, auger rates, time-dependent close-coupling method
Procedia PDF Downloads 1471160 Simulation of Reflectometry in Alborz Tokamak
Authors: S. Kohestani, R. Amrollahi, P. Daryabor
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Microwave diagnostics such as reflectometry are receiving growing attention in magnetic confinement fusionresearch. In order to obtain the better understanding of plasma confinement physics, more detailed measurements on density profile and its fluctuations might be required. A 2D full-wave simulation of ordinary mode propagation has been written in an effort to model effects seen in reflectometry experiment. The code uses the finite-difference-time-domain method with a perfectly-matched-layer absorption boundary to solve Maxwell’s equations.The code has been used to simulate the reflectometer measurement in Alborz Tokamak.Keywords: reflectometry, simulation, ordinary mode, tokamak
Procedia PDF Downloads 4131159 Exponential Stabilization of a Flexible Structure via a Delayed Boundary Control
Authors: N. Smaoui, B. Chentouf
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The boundary stabilization problem of the rotating disk-beam system is a topic of interest in research studies. This system involves a flexible beam attached to the center of a disk, and the control and stabilization of this system have been extensively studied. This research focuses on the case where the center of mass is fixed in an inertial frame, and the rotation of the center is non-uniform. The system is represented by a set of nonlinear coupled partial differential equations and ordinary differential equations. The boundary stabilization problem of this system via a delayed boundary control is considered. We assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. The aim of this research is threefold: First, we demonstrate that the rotating disk-beam system is well-posed in an appropriate functional space. Then, we establish the exponential stability property of the system. Finally, we provide numerical simulations that illustrate the theoretical findings. The research utilizes the semigroup theory to establish the well-posedness of the system. The resolvent method is then employed to prove the exponential stability property. Finally, the finite element method is used to demonstrate the theoretical results through numerical simulations. The research findings indicate that the rotating disk-beam system can be stabilized using a boundary control with a time delay. The proof of stability is based on the resolvent method and a variation of constants formula. The numerical simulations further illustrate the theoretical results. The findings have potential implications for the design and implementation of control strategies in similar systems. In conclusion, this research demonstrates that the rotating disk-beam system can be stabilized using a boundary control with time delay. The well-posedness and exponential stability properties are established through theoretical analysis, and these findings are further supported by numerical simulations. The research contributes to the understanding and practical application of control strategies for flexible structures, providing insights into the stability of rotating disk-beam systems.Keywords: rotating disk-beam, delayed force control, delayed moment control, torque control, exponential stability
Procedia PDF Downloads 671158 Electromagnetic Tuned Mass Damper Approach for Regenerative Suspension
Authors: S. Kopylov, C. Z. Bo
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This study is aimed at exploring the possibility of energy recovery through the suppression of vibrations. The article describes design of electromagnetic dynamic damper. The magnetic part of the device performs the function of a tuned mass damper, thereby providing both energy regeneration and damping properties to the protected mass. According to the theory of tuned mass damper, equations of mathematical models were obtained. Then, under given properties of current system, amplitude frequency response was investigated. Therefore, main ideas and methods for further research were defined.Keywords: electromagnetic damper, oscillations with two degrees of freedom, regeneration systems, tuned mass damper
Procedia PDF Downloads 2031157 Enhanced Tensor Tomographic Reconstruction: Integrating Absorption, Refraction and Temporal Effects
Authors: Lukas Vierus, Thomas Schuster
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A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions
Procedia PDF Downloads 381156 Multivalued Behavior for a Two-Level System Using Homotopy Analysis Method
Authors: Angelo I. Aquino, Luis Ma. T. Bo-ot
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We use the Homotopy Analysis Method (HAM) to solve the system of equations modeling the two-level system and extract results which will pinpoint to turbulent behavior. We look at multi-valued solutions as indicative of turbulence or turbulent-like behavior. We take dierent specic cases which result in multi-valued velocities. The solutions are in series form and application of HAM ensures convergence in some region.Keywords: multivalued solutions, homotopy analysis method, two-level system, equation
Procedia PDF Downloads 5891155 Analysis of the Inverse Kinematics for 5 DOF Robot Arm Using D-H Parameters
Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale
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This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories
Procedia PDF Downloads 1901154 Comparative Numerical Simulations of Reaction-Coupled Annular and Free-Bubbling Fluidized Beds Performance
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
Procedia PDF Downloads 1501153 Chaos in a Stadium-Shaped 2-D Quantum Dot
Authors: Roger Yu
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A numerical scheme has been developed to solve wave equations for chaotic systems such as stadium-shaped cavity. The same numerical method can also be used for finding wave properties of rectangle cavities with randomly placed obstacles. About 30k eigenvalues have been obtained accurately on a normal circumstance. For comparison, we also initiated an experimental study which determines both eigenfrequencies and eigenfunctions of a stadium-shaped cavity using pulse and normal mode analyzing techniques. The acoustic cavity was made adjustable so that the transition from nonchaotic (circle) to chaotic (stadium) waves can be investigated.Keywords: quantum dot, chaos, numerical method, eigenvalues
Procedia PDF Downloads 1121152 Multidimensional Integral and Discrete Opial–Type Inequalities
Authors: Maja Andrić, Josip Pečarić
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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality
Procedia PDF Downloads 4251151 Exploring Solutions in Extended Horava-Lifshitz Gravity
Authors: Aziza Altaibayeva, Ertan Güdekli, Ratbay Myrzakulov
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In this letter, we explore exact solutions for the Horava-Lifshitz gravity. We use of an extension of this theory with first order dynamical lapse function. The equations of motion have been derived in a fully consistent scenario. We assume that there are some spherically symmetric families of exact solutions of this extended theory of gravity. We obtain exact solutions and investigate the singularity structures of these solutions. Specially, an exact solution with the regular horizon is found.Keywords: quantum gravity, Horava-Lifshitz gravity, black hole, spherically symmetric space times
Procedia PDF Downloads 5691150 Variable Frequency Converter Fed Induction Motors
Authors: Abdulatif Abdulsalam Mohamed Shaban
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A.C motors, in general, have superior performance characteristics to their d.c. counterparts. However, despite these advantage a.c. motors lack the controllability and simplicity and so d.c. motors retain a competitive edge where precise control is required. As part of an overall project to develop an improved cycloconverter control strategy for induction motors. Simulation and modelling techniques have been developed. This contribution describes a method used to simulate an induction motor drive using the SIMULINK toolbox within MATLAB software. The cycloconverter fed induction motor is principally modelled using the d-q axis equations. Results of the simulation for a given set of induction motor parameters are also presented.Keywords: simulation, converter, motor, cycloconverter
Procedia PDF Downloads 5971149 An Accurate Prediction of Surface Temperature History in a Supersonic Flight
Authors: A. M. Tahsini, S. A. Hosseini
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In the present study, the surface temperature history of the adaptor part in a two-stage supersonic launch vehicle is accurately predicted. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux. The one-dimensional heat conduction in solid phase is used to compute the temperature history. The instantaneous surface temperature is used to improve the applied heat flux, to improve the accuracy of the results.Keywords: aerodynamic heating, heat conduction, numerical simulation, supersonic flight, launch vehicle
Procedia PDF Downloads 4451148 A Study on Stochastic Integral Associated with Catastrophes
Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan
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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).Keywords: stochastic integrals, single–server queue model, catastrophes, busy period
Procedia PDF Downloads 6331147 Analytical Investigation of Modeling and Simulation of Different Combinations of Sinusoidal Supplied Autotransformer under Linear Loading Conditions
Authors: M. Salih Taci, N. Tayebi, I. Bozkır
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This paper investigates the operation of a sinusoidal supplied autotransformer on the different states of magnetic polarity of primary and secondary terminals for four different step-up and step-down analytical conditions. In this paper, a new analytical modeling and equations for dot-marked and polarity-based step-up and step-down autotransformer are presented. These models are validated by the simulation of current and voltage waveforms for each state. PSpice environment was used for simulation.Keywords: autotransformer modeling, autotransformer simulation, step-up autotransformer, step-down autotransformer, polarity
Procedia PDF Downloads 3041146 Complex Fuzzy Evolution Equation with Nonlocal Conditions
Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli
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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups
Procedia PDF Downloads 2691145 Prediction of Finned Projectile Aerodynamics Using a Lattice-Boltzmann Method CFD Solution
Authors: Zaki Abiza, Miguel Chavez, David M. Holman, Ruddy Brionnaud
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In this paper, the prediction of the aerodynamic behavior of the flow around a Finned Projectile will be validated using a Computational Fluid Dynamics (CFD) solution, XFlow, based on the Lattice-Boltzmann Method (LBM). XFlow is an innovative CFD software developed by Next Limit Dynamics. It is based on a state-of-the-art Lattice-Boltzmann Method which uses a proprietary particle-based kinetic solver and a LES turbulent model coupled with the generalized law of the wall (WMLES). The Lattice-Boltzmann method discretizes the continuous Boltzmann equation, a transport equation for the particle probability distribution function. From the Boltzmann transport equation, and by means of the Chapman-Enskog expansion, the compressible Navier-Stokes equations can be recovered. However to simulate compressible flows, this method has a Mach number limitation because of the lattice discretization. Thanks to this flexible particle-based approach the traditional meshing process is avoided, the discretization stage is strongly accelerated reducing engineering costs, and computations on complex geometries are affordable in a straightforward way. The projectile that will be used in this work is the Army-Navy Basic Finned Missile (ANF) with a caliber of 0.03 m. The analysis will consist in varying the Mach number from M=0.5 comparing the axial force coefficient, normal force slope coefficient and the pitch moment slope coefficient of the Finned Projectile obtained by XFlow with the experimental data. The slope coefficients will be obtained using finite difference techniques in the linear range of the polar curve. The aim of such an analysis is to find out the limiting Mach number value starting from which the effects of high fluid compressibility (related to transonic flow regime) lead the XFlow simulations to differ from the experimental results. This will allow identifying the critical Mach number which limits the validity of the isothermal formulation of XFlow and beyond which a fully compressible solver implementing a coupled momentum-energy equations would be required.Keywords: CFD, computational fluid dynamics, drag, finned projectile, lattice-boltzmann method, LBM, lift, mach, pitch
Procedia PDF Downloads 4081144 Numerical Study of Flow around Flat Tube between Parallel Walls
Authors: Hamidreza Bayat, Arash Mirabdolah Lavasani, Meysam Bolhasani, Sajad Moosavi
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Flow around a flat tube is studied numerically. Reynolds number is defined base on equivalent circular tube and it is varied in range of 100 to 300. Equations are solved by using finite volume method and results are presented in form of drag and lift coefficient. Results show that drag coefficient of flat tube is up to 66% lower than circular tube with equivalent diameter. In addition, by increasing l/D from 1 to 2, the drag coefficient of flat tube is decreased about 14-27%.Keywords: laminar flow, flat-tube, drag coefficient, cross-flow, heat exchanger
Procedia PDF Downloads 4951143 Pressure Gradient Prediction of Oil-Water Two Phase Flow through Horizontal Pipe
Authors: Ahmed I. Raheem
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In this thesis, stratified and stratified wavy flow regimes have been investigated numerically for the oil (1.57 mPa s viscosity and 780 kg/m3 density) and water twophase flow in small and large horizontal steel pipes with a diameter between 0.0254 to 0.508 m by ANSYS Fluent software. Volume of fluid (VOF) with two phases flows using two equations family models (Realizable k-Keywords: CFD, two-phase flow, pressure gradient, volume of fluid, large diameter, horizontal pipe, oil-water stratified and stratified wavy flow
Procedia PDF Downloads 4241142 Creative Mathematically Modelling Videos Developed by Engineering Students
Authors: Esther Cabezas-Rivas
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Ordinary differential equations (ODE) are a fundamental part of the curriculum for most engineering degrees, and students typically have difficulties in the subsequent abstract mathematical calculations. To enhance their motivation and profit that they are digital natives, we propose a teamwork project that includes the creation of a video. It should explain how to model mathematically a real-world problem transforming it into an ODE, which should then be solved using the tools learned in the lectures. This idea was indeed implemented with first-year students of a BSc in Engineering and Management during the period of online learning caused by the outbreak of COVID-19 in Spain. Each group of 4 students was assigned a different topic: model a hot water heater, search for the shortest path, design the quickest route for delivery, cooling a computer chip, the shape of the hanging cables of the Golden Gate, detecting land mines, rocket trajectories, etc. These topics should be worked out through two complementary channels: a written report describing the problem and a 10-15 min video on the subject. The report includes the following items: description of the problem to be modeled, detailed obtention of the ODE that models the problem, its complete solution, and interpretation in the context of the original problem. We report the outcomes of this teaching in context and active learning experience, including the feedback received by the students. They highlighted the encouragement of creativity and originality, which are skills that they do not typically relate to mathematics. Additionally, the video format (unlike a common presentation) has the advantage of allowing them to critically review and self-assess the recording, repeating some parts until the result is satisfactory. As a side effect, they felt more confident about their oral abilities. In short, students agreed that they had fun preparing the video. They recognized that it was tricky to combine deep mathematical contents with entertainment since, without the latter, it is impossible to engage people to view the video till the end. Despite this difficulty, after the activity, they claimed to understand better the material, and they enjoyed showing the videos to family and friends during and after the project.Keywords: active learning, contextual teaching, models in differential equations, student-produced videos
Procedia PDF Downloads 1391141 Differential Transform Method: Some Important Examples
Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen
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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions
Procedia PDF Downloads 5271140 Two-Dimensional Analysis and Numerical Simulation of the Navier-Stokes Equations for Principles of Turbulence around Isothermal Bodies Immersed in Incompressible Newtonian Fluids
Authors: Romulo D. C. Santos, Silvio M. A. Gama, Ramiro G. R. Camacho
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In this present paper, the thermos-fluid dynamics considering the mixed convection (natural and forced convections) and the principles of turbulence flow around complex geometries have been studied. In these applications, it was necessary to analyze the influence between the flow field and the heated immersed body with constant temperature on its surface. This paper presents a study about the Newtonian incompressible two-dimensional fluid around isothermal geometry using the immersed boundary method (IBM) with the virtual physical model (VPM). The numerical code proposed for all simulations satisfy the calculation of temperature considering Dirichlet boundary conditions. Important dimensionless numbers such as Strouhal number is calculated using the Fast Fourier Transform (FFT), Nusselt number, drag and lift coefficients, velocity and pressure. Streamlines and isothermal lines are presented for each simulation showing the flow dynamics and patterns. The Navier-Stokes and energy equations for mixed convection were discretized using the finite difference method for space and a second order Adams-Bashforth and Runge-Kuta 4th order methods for time considering the fractional step method to couple the calculation of pressure, velocity, and temperature. This work used for simulation of turbulence, the Smagorinsky, and Spalart-Allmaras models. The first model is based on the local equilibrium hypothesis for small scales and hypothesis of Boussinesq, such that the energy is injected into spectrum of the turbulence, being equal to the energy dissipated by the convective effects. The Spalart-Allmaras model, use only one transport equation for turbulent viscosity. The results were compared with numerical data, validating the effect of heat-transfer together with turbulence models. The IBM/VPM is a powerful tool to simulate flow around complex geometries. The results showed a good numerical convergence in relation the references adopted.Keywords: immersed boundary method, mixed convection, turbulence methods, virtual physical model
Procedia PDF Downloads 1081139 Fokas-Lenells Equation Conserved Quantities and Landau-Lifshitz System
Authors: Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy
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Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair
Procedia PDF Downloads 971138 Parallel Multisplitting Methods for DAE’s
Authors: Ahmed Machmoum, Malika El Kyal
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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems
Procedia PDF Downloads 5411137 A Problem in Microstretch Thermoelastic Diffusive Medium
Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar
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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem
Procedia PDF Downloads 609