Search results for: lagrangian analysis

Authors: Riaz Ahmad, Jiazhong Zhang, Asma Farooqi

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In this study, mass transport between separation bubbles and the flow around a two-dimensional airfoil are numerically investigated using Lagrangian Coherent Structures (LCSs). Finite Time Lyapunov Exponent (FTLE) technique is used for the computation to identify invariant manifolds and LCSs. Moreover, the Characteristic Base Split (CBS) scheme combined with dual time stepping technique is applied to simulate such transient flow at low Reynolds number. We then investigate the evolution of vortex structures during the transport process with the aid of LCSs. To explore the vortex formation at the surface of the airfoil, the dynamics of separatrix is also taken into account which is formed by the combination of stable-unstable manifolds. The Lagrangian analysis gives a detailed understanding of vortex dynamics and separation bubbles which plays a significant role to explore the performance of the unsteady flow generated by the airfoil. Transport process and flow separation phenomena are studied extensively to analyze the flow pattern by Lagrangian point of view.

Keywords: transport phenomena, CBS Method, vortex formation, Lagrangian Coherent Structures

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Authors: Mahmood Khalghollah, Mohammad Tavallaeinejad, Mohammad Eghtesad

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The method of Controlled Lagrangian is an energy shaping control technique for under actuated Lagrangian systems. Energy shaping control design methods are appealing as they retain the underlying nonlinear dynamics and can provide stability results that hold over larger domain than can be obtained using linear design and analysis. In the present study, controlled lagrangian is employed for designing a controller in an under actuated rotating flexible plate system. In the system of rotating flexible plate, due to its nonlinear characteristics and coupled dynamics of rigid and flexible components, controller design is a known challenge. In this paper, controller objectives are considered to be vibration reduction of flexible component and position control of the tip of the plate. To achieve the goals, a method based on both kinetic and potential energy shaping is introduced. The stability of the closed-loop system is investigated and proved around its equilibrium points. Moreover, the proposed controller is shown to be robust against disturbance and plant uncertainties.

Keywords: controlled lagrangian, underactuated system, flexible rotating plate, disturbance

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Authors: Xijun Yu, Zhenzhen Li, Zupeng Jia

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This paper presents a new cell-centered Lagrangian scheme for two-dimensional compressible flow. The new scheme uses a semi-Lagrangian form of the Euler equations. The system of equations is discretized by Discontinuous Galerkin (DG) method using the Taylor basis in Eulerian space. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently by a nodal solver. The mesh moves with the fluid flow. The time marching is implemented by a class of the Runge-Kutta (RK) methods. A WENO reconstruction is used as a limiter for the RKDG method. The scheme is conservative for the mass, momentum and total energy. The scheme maintains second-order accuracy and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.

Keywords: cell-centered Lagrangian scheme, compressible Euler equations, RKDG method

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Authors: Rajib Mia, Badam Singh Kushvah

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In this present paper, we use the photogravitational version of the restricted three body problem (RTBP) in binary systems. In the photogravitational RTBP, an infinitesimal particle (dust grain) is moving under the gravitational attraction and radiation pressure from the two bigger primaries. The third particle does not affect the motion of two bigger primaries. The zero-velocity curves, zero-velocity surfaces and their projections on the plane are studied. We have used existing analytical method to solve the equations of motion. We have obtained the Lagrangian points in some binary stellar systems. It is found that mass reduction factor affects the Lagrangian points. The linear stability of Lagrangian points is studied and found that these points are unstable. Moreover, trajectories of the infinitesimal particle at the triangular points are studied.

Keywords: binary systems, Lagrangian points, linear stability, photogravitational RTBP, trajectories

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Authors: Gao Youtao, Zhao Tanran, Jin Bingyu, Xu Bo

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Global navigation satellite system(GNSS) can deliver navigation information for spacecraft orbiting on low-Earth orbits and medium Earth orbits. However, the GNSS cannot navigate the spacecraft on high-Earth orbit or deep space probes effectively. With the deep space exploration becoming a hot spot of aerospace, the demand for a deep space satellite navigation system is becoming increasingly prominent. Many researchers discussed the feasibility and performance of a satellite navigation system on periodic orbits around the Earth-Moon libration points which can be called Lagrangian point satellite navigation system. Autonomous orbit determination (AOD) is an important performance for the Lagrangian point satellite navigation system. With this ability, the Lagrangian point satellite navigation system can reduce the dependency on ground stations. AOD also can greatly reduce total system cost and assure mission continuity. As the elliptical restricted three-body problem can describe the Earth-Moon system more accurately than the circular restricted three-body problem, we study the autonomous orbit determination of Lagrangian navigation constellation using only crosslink range based on elliptical restricted three body problem. Extended Kalman filter is used in the autonomous orbit determination. In order to compare the autonomous orbit determination results based on elliptical restricted three-body problem to the results of autonomous orbit determination based on circular restricted three-body problem, we give the autonomous orbit determination position errors of a navigation constellation include four satellites based on the circular restricted three-body problem. The simulation result shows that the Lagrangian navigation constellation can achieve long-term precise autonomous orbit determination using only crosslink range. In addition, the type of the libration point orbit will influence the autonomous orbit determination accuracy.

Keywords: extended Kalman filter, autonomous orbit determination, quasi-periodic orbit, navigation constellation

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Pooya Niksiar, Ali Ashrafizadeh, Mehrzad Shams, Amir Hossein Madani

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There are many computationally demanding applications in science and engineering which need efficient algorithms implemented on high performance computers. Recently, Graphics Processing Units (GPUs) have drawn much attention as compared to the traditional CPU-based hardware and have opened up new improvement venues in scientific computing. One particular application area is Computational Fluid Dynamics (CFD), in which mature CPU-based codes need to be converted to GPU-based algorithms to take advantage of this new technology. In this paper, numerical solutions of two classes of discrete fluid flow models via both CPU and GPU are discussed and compared. Test problems include an Eulerian model of a two-dimensional incompressible laminar flow case and a Lagrangian model of a two phase flow field. The CUDA programming standard is used to employ an NVIDIA GPU with 480 cores and a C++ serial code is run on a single core Intel quad-core CPU. Up to two orders of magnitude speed up is observed on GPU for a certain range of grid resolution or particle numbers. As expected, Lagrangian formulation is better suited for parallel computations on GPU although Eulerian formulation represents significant speed up too.

Keywords: CFD, Eulerian formulation, graphics processing units, Lagrangian formulation

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Authors: Ravi Soni, Irfan Pathan, Manish Pande

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The current product development process needs simultaneous consideration of different physics. The performance of the product needs to be considered under both structural and fluid loads. Examples include ducts and valves where structural behavior affects fluid motion and vice versa. Simulation of fluid-structure interaction involves modeling interaction between moving components and the fluid flow. In these scenarios, it is difficult to calculate the damping provided by fluid flow because of dynamic motions of components and the transient nature of the flow. Abaqus Explicit offers general capabilities for modeling fluid-structure interaction with the Coupled Eulerian-Lagrangian (CEL) method. The Coupled Eulerian-Lagrangian technique has been used to simulate fluid spillage through fuel valves during dynamic closure events. The technique to simulate pressure drops across Eulerian domains has been developed using stagnation pressure. Also, the fluid flow is calculated considering material flow through elements at the outlet section of the valves. The methodology has been verified on Eaton products and shows a good correlation with the test results.

Keywords: Coupled Eulerian-Lagrangian Technique, fluid structure interaction, spillage prediction, stagnation pressure

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Authors: Raquel Nieto, Marta Vázquez, Anita Drumond, Luis Gimeno

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One of the hot spots of climate change is the increment of ocean evaporation. The best estimation of evaporation, OAFlux data, shows strong increasing trends in evaporation from the oceans since 1978, with peaks during the hemispheric winter and strongest along the paths of the global western boundary currents and any inner Seas. The transport of moisture from oceanic sources to the continents is the connection between evaporation from the ocean and precipitation over the continents. A key question is to try to relate evaporative source regions over the oceans where trends have occurred in the last decades with their sinks over the continents to check if there have been also any trends in the precipitation amount or its characteristics. A Lagrangian approach based on FLEXPART and ERA-interim data is used to establish this connection. The analyzed period was 1980 to 2012. Results show that there is not a general pattern, but a significant agreement was found in important areas of climate interest.

Keywords: ocean evaporation, Lagrangian approaches, contiental precipitation, Europe

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Authors: Khaled I. Nawafleh

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In this paper, it provide the canonical approach for studying dissipated oscillators based on the doubling of degrees of freedom. Clearly, expressions for Lagrangians of the elementary modes of the system are given, which ends with the familiar classical equations of motion for the dissipative oscillator. The equation for one variable is the time reversed of the motion of the second variable. it discuss in detail the extended Bateman Lagrangian specifically for a dual extended damped oscillator time-dependent. A Hamilton-Jacobi analysis showing the equivalence with the Lagrangian approach is also obtained. For that purpose, the techniques of separation of variables were applied, and the quantization process was achieved.

Keywords: doubling of degrees of freedom, dissipated harmonic oscillator, Hamilton-Jacobi, time-dependent lagrangians, quantization

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Authors: Ce Liu, Wei Huo

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A nonlinear trajectory tracking controller for quadrotor helicopter based on controlled Lagrangian (CL) method is proposed in this paper. A Lagrangian system with virtual angles as generated coordinates rather than Euler angles is developed. Based on the model, the matching conditions presented by nonlinear partial differential equations are simplified and explicitly solved. Smooth tracking control laws and the range of control parameters are deduced based on the controlled energy of closed-loop system. Besides, a constraint condition for reference accelerations is deduced to identify the trackable reference trajectories by the proposed controller and to ensure the stability of the closed-loop system. The proposed method in this paper does not rely on the division of the quadrotor system, and the design of the control torques does not depend on the thrust as in backstepping or hierarchical control method. Simulations for a quadrotor model demonstrate the feasibility and efficiency of the theoretical results.

Keywords: quadrotor, trajectory tracking control, controlled lagrangians, underactuated system

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Suman Dutta, Manish Agrawal, C. S. Jog

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Accurate computation of hydrodynamic forces on floating structures and their deformation finds application in the ocean and naval engineering and wave energy harvesting. This manuscript presents a monolithic, finite element strategy for fluid-structure interaction involving hyper-elastic solids partly submerged in an incompressible fluid. A velocity-based Arbitrary Lagrangian-Eulerian (ALE) formulation has been used for the fluid and a displacement-based Lagrangian approach has been used for the solid. The flexibility of the ALE technique permits us to treat the free surface of the fluid as a Lagrangian entity. At the interface, the continuity of displacement, velocity and traction are enforced using the mortar method. In the mortar method, the constraints are enforced in a weak sense using the Lagrange multiplier method. In the literature, the mortar method has been shown to be robust in solving various contact mechanics problems. The time-stepping strategy used in this work reduces to the generalized trapezoidal rule in the Eulerian setting. In the Lagrangian limit, in the absence of external load, the algorithm conserves the linear and angular momentum and the total energy of the system. The use of monolithic coupling with an energy-conserving time-stepping strategy gives an unconditionally stable algorithm and allows the user to take large time steps. All the governing equations and boundary conditions have been mapped to the reference configuration. The use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. The robustness and good performance of the proposed method are demonstrated by solving benchmark problems from the literature.

Keywords: ALE, floating body, fluid-structure interaction, monolithic, mortar method

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Authors: Abdulrahman Aljabri, Essam R. I. Mahmoud, Hamad Almohamedi, Zhengyi Jiang

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Cold rolled thin strip has received intensive attention through technological and theoretical progress in the rolling process, as well as researchers have focused on its control during rolling as an essential parameter for producing thinner strip with good shape and profile. An advanced approach has been proposed to analysis the thin strip profile in cold rolling of pair roll crossing and shifting mill using Finite Element Analysis (FEA) with an ALE technique. The ALE (Arbitrary Lagrangian-Eulerian) techniques to enable more flexibility of the ALE technique in the adjustment of the finite element mesh, which provides a significant tool for simulating the thin strip under realistic rolling process constraint and provide accurate model results. The FEA can provide theoretical basis for the 3D model of controlling the strip shape and profile in thin strip rolling, and deliver an optimal rolling process parameter, and suggest corrective changes during cold rolling of thin strip.

Keywords: pair roll crossing, work roll shifting, strip shape and profile, finite element modeling

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Authors: H. Shokouhmand, H. Sobhani, B. Sajadi, M. Degheh

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In recent years, experimental and numerical investigation of water UV reactors has increased significantly. The main drawback of experimental methods is confined and expensive survey of UV reactors features. In this study, a CFD model utilizing the eulerian-lagrangian framework is applied to analysis the disinfection performance of a closed conduit reactor which contains four UV lamps perpendicular to the flow. A discrete ordinates (DO) model was employed to evaluate the UV irradiance field. To investigate the importance of each of lamps on the inactivation performance, in addition to the reference model (with 4 bright lamps), several models with one or two bright lamps in various arrangements were considered. All results were reported in three inactivation kinetics. The results showed that the log inactivation of the two central bright lamps model was between 88-99 percent, close to the reference model results. Also, whatever the lamps are closer to the main flow region, they have more effect on microbial inactivation. The effect of some operational parameters such as water flow rate, inlet water temperature, and lamps power were also studied.

Keywords: Eulerian-Lagrangian framework, inactivation kinetics, log inactivation, water UV reactor

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Authors: Rajib Mia, Badam Singh Kushvah

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The present research was motivated by the recent discovery of the binary star systems. In this paper, we use the restricted three-body problem in the binary stellar systems, considering photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the Lagrangian points. The stability and periodic orbits of collinear points and the stability and trajectories of the triangular points are studied in stellar binary systems Kepler-34, Kepler-35, Kepler-413 and Kepler-16 systems. A detailed comparison is made among periodic orbits and trajectories.

Keywords: exoplanetary systems, lagrangian points, periodic orbit, restricted three body problem, stability

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Authors: Wissem Tighidet, Faïçal Naït Bouda, Moussa Allouche

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The numerical study of the Fluid-Structure Interaction (FSI) in a partially filled flexible tank submitted to a horizontal harmonic excitation motion. It is investigated by using two-way Fluid-Structure Interaction (FSI) in a flexible tank by Coupling between the Transient Structural (Mechanical) and Fluid Flow (Fluent) in ANSYS-Workbench Student version. The Arbitrary Lagrangian-Eulerian (ALE) formulation is adopted to solve with the finite volume method, the Navier-Stokes equations in two phases in a moving domain. The Volume of Fluid (VOF) method is applied to track the free surface. However, the equations of the dynamics of the structure are solved with the finite element method assuming a linear elastic behavior. To conclude, the Fluid-Structure Interaction (IFS) has a vital role in the analysis of the dynamic behavior of the rectangular tank. The results indicate that the flexibility of the tank walls has a significant impact on the amplitude of tank sloshing and the deformation of the free surface as well as the effect of liquid sloshing on wall deformation.

Keywords: arbitrary lagrangian-eulerian, fluid-structure interaction, sloshing, volume of fluid

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Authors: Han Ding, Wang Xiaoliang, Duan Dengping

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During the process of airship design, the layout and the geometric shape of the hull and fins are crucial to the motion characteristics of the airship. In this paper, we obtained the quantification motion sensitivity of the airship to geometric parameters through turning circles and horizontal/vertical zigzag maneuvers by the parameterization of airship shape and building the dynamic model using Lagrangian approach and MATLAB Simulink program. In the dynamics simulation program, the affection of geometric parameters to the mass, center of gravity, moments of inertia, product of inertia, added mass and the aerodynamic forces and moments have been considered.

Keywords: airship, Lagrangian approach, turning circles, horizontal/vertical zigzag maneuvers

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Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

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The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure, interaction, one-way method, two-way method

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

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New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball

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Authors: Sarra Zaied, Arthur Bonpain, Pierre Yves Fravallo

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The permanent supply of marine litter implies their accumulation in the oceans, which causes the presence of more compact wastes layers. Their Spatio-temporal distribution is never homogeneous and depends mainly on the hydrodynamic characteristics of the environment and the size and location of the wastes. As part of optimizing collect of marine plastic wastes, it is important to measure and monitor their evolution over time. For this, many research studies have been dedicated to describing the wastes behavior in order to identify their accumulation in oceans areas. Several models are therefore developed to understand the mechanisms that allow the accumulation and the displacements of marine litter. These models are able to accurately simulate the drift of wastes to study their behavior and stranding. However, these works aim to study the wastes behavior over a long period of time and not at the time of waste collection. This work investigates the transport of floating marine litter (FML) to provide basic information that can help in optimizing wastes collection by proposing a model for predicting their behavior during collection. The proposed study is based on a Lagrangian modeling approach that uses the main factors influencing the dynamics of the waste. The performance of the proposed method was assessed on real data collected from the Copernicus Marine Environment Monitoring Service (CMEMS). Evaluation results in the Java Sea (Indonesia) prove that the proposed model can effectively predict the position and the velocity of marine wastes during collection.

Keywords: floating marine litter, lagrangian transport, particle-tracking model, wastes drift

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: Qi Wu, Dian-Yong Chen, Feng-Kun Guo, Gang Li

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In the past decade, a growing number of new hadron states have been observed, which are dubbed as XYZ states in the heavy quarkonium mass regions. In this work, we present our study on the production of some new hadron states. In particular, we investigate the processes Υ(5S,6S)→ Zb (10610)/Zb (10650)π, Bc→ Zc (3900)/Zc (4020)π and Λb→ Pc (4312)/Pc (4440)/Pc (4457)K. (1) For the production of Zb (10610)/Zb (10650) from Υ(5S,6S) decay, two types of bottom-meson loops were discussed within a nonrelativistic effective field theory. We found that the loop contributions with all intermediate states being the S-wave ground state bottom mesons are negligible, while the loops with one bottom meson being the broad B₀* or B₁' resonance could provide the dominant contributions to the Υ(5S)→ Zb⁽'⁾ π. (2) For the production of Zc (3900)/Zc (4020) from Bc decay, the branching ratios of Bc⁺→ Z (3900)⁺ π⁰ and Bc⁺→ Zc (4020)⁺ π⁰ are estimated to be of order of 10⁽⁻⁴⁾ and 10⁽⁻⁷⁾ in an effective Lagrangian approach. The large production rate of Zc (3900) could provide an important source of the production of Zc (3900) from the semi-exclusive decay of b-flavored hadrons reported by D0 Collaboration, which can be tested by the exclusive measurements in LHCb. (3) For the production of Pc (4312), Pc (4440) and Pc (4457) from Λb decay, the ratio of the branching fraction of Λb→ Pc K was predicted in a molecular scenario by using an effective Lagrangian approach, which is weakly dependent on our model parameter. We also find the ratios of the productions of the branching fractions of Λb→ Pc K and Pc→ J/ψ p can be well interpreted in the molecular scenario. Moreover, the estimated branching fractions of Λb→ Pc K are of order 10⁽⁻⁶⁾, which could be tested by further measurements in LHCb Collaboration.

Keywords: effective Lagrangian approach, hadron loops, molecular states, new hadron states

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Authors: Timur S. Zaripov, Artur K. Gilfanov, Sergei S. Sazhin, Steven M. Begg, Morgan R. Heikal

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The calculation of the concentration of inertial droplets in complex flows is encountered in the modelling of numerous engineering and environmental phenomena; for example, fuel droplets in internal combustion engines and airborne pollutant particles. The results of recent research, focused on the development of methods for calculating concentration and their implementation in the commercial CFD code, ANSYS Fluent, is presented here. The study is motivated by the investigation of the mixture preparation processes in internal combustion engines with direct injection of fuel sprays. Two methods are used in our analysis; the Fully Lagrangian method (also known as the Osiptsov method) and the Eulerian approach. The Osiptsov method predicts droplet concentrations along path lines by solving the equations for the components of the Jacobian of the Eulerian-Lagrangian transformation. This method significantly decreases the computational requirements as it does not require counting of large numbers of tracked droplets as in the case of the conventional Lagrangian approach. In the Eulerian approach the average droplet velocity is expressed as a function of the carrier phase velocity as an expansion over the droplet response time and transport equation can be solved in the Eulerian form. The advantage of the method is that droplet velocity can be found without solving additional partial differential equations for the droplet velocity field. The predictions from the two approaches were compared in the analysis of the problem of a dilute gas-droplet flow around an infinitely long, circular cylinder. The concentrations of inertial droplets, with Stokes numbers of 0.05, 0.1, 0.2, in steady-state and transient laminar flow conditions, were determined at various Reynolds numbers. In the steady-state case, flows with Reynolds numbers of 1, 10, and 100 were investigated. It has been shown that the results predicted using both methods are almost identical at small Reynolds and Stokes numbers. For larger values of these numbers (Stokes — 0.1, 0.2; Reynolds — 10, 100) the Eulerian approach predicted a wider spread in concentration in the perturbations caused by the cylinder that can be attributed to the averaged droplet velocity field. The transient droplet flow case was investigated for a Reynolds number of 200. Both methods predicted a high droplet concentration in the zones of high strain rate and low concentrations in zones of high vorticity. The maxima of droplet concentration predicted by the Osiptsov method was up to two orders of magnitude greater than that predicted by the Eulerian method; a significant variation for an approach widely used in engineering applications. Based on the results of these comparisons, the Osiptsov method has resulted in a more precise description of the local properties of the inertial droplet flow. The method has been applied to the analysis of the results of experimental observations of a liquid gasoline spray at representative fuel injection pressure conditions. The preliminary results show good qualitative agreement between the predictions of the model and experimental data.

Keywords: internal combustion engines, Eulerian approach, fully Lagrangian approach, gasoline fuel sprays, droplets and particle concentrations

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Authors: Kumaresh Selvakumar, Man Young Kim

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Selective catalytic reduction (SCR) converts the nitrogen oxides with the aid of a catalyst by adding aqueous urea into the exhaust stream. In this work, the urea water droplets are sprayed over the exhaust gases by treating with Lagrangian particle tracking. The evaporation of ammonia from a single droplet of urea water solution is investigated computationally by convection-diffusion controlled model. The conversion to ammonia due to thermolysis of urea water droplets is measured downstream at different sections using finite rate/eddy dissipation model. In this paper, the mixer installed at the upstream enhances the distribution of ammonia over the entire domain which is calculated for different time steps. Calculations are made within the respective duration such that the complete decomposition of urea is possible at a much shorter residence time.

Keywords: convection-diffusion controlled model, lagrangian particle tracking, selective catalytic reduction, thermolysis

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Authors: Govind Sharma, Bahni Ray

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Ubiquitous nature of particle settling is governed by the presence of the surrounding fluid medium. Thermally stratified fluid alters the settling phenomenon of particles as well as their interactions. Direct numerical simulation (DNS) is carried out with an open-source library Immersed Boundary Adaptive Mesh Refinement (IBAMR) to quantify the fundamental mechanism based on Distributed Lagrangian Multiplier (DLM). The presence of background density gradient due to thermal stratification replaces the drafting-kissing-tumbling in a homogeneous fluid to drafting-kissing-separation behavior. Simulations are performed with a varying range of particle-fluid density ratios, and it is shown that the stratification effect on particle interactions varies with density ratio. It is observed that the combined role of buoyancy and inertia govern the physical mechanism of particle-particle interaction.

Keywords: direct numerical simulation, distributed lagrangian multiplier, rigidity constraint, sedimentation, stratification

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Authors: Fadi Al-Badour, Nesar Merah, Abdelrahman Shuaib, Abdelaziz Bazoune

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In the current work, a Coupled Eulerian Lagrangian (CEL) model is developed to simulate the friction stir welding (FSW) process of dissimilar Aluminum alloys (Al 6061-T6 with Al 5083-O). The model predicts volumetric defects, material flow, developed temperatures, and stresses in addition to tool reaction loads. Simulation of welding phase is performed by employing a control volume approach, whereas the welding speed is defined as inflow and outflow over Eulerian domain boundaries. Only material softening due to inelastic heat generation is considered and material behavior is assumed to obey Johnson-Cook’s Model. The model was validated using published experimentally measured temperatures, at similar welding conditions, and by qualitative comparison of dissimilar weld microstructure. The FE results showed that most of developed temperatures were below melting and that the bulk of the deformed material in solid state. The temperature gradient on AL6061-T6 side was found to be less than that of Al 5083-O. Changing the position Al 6061-T6 from retreating (Ret.) side to advancing (Adv.) side led to a decrease in maximum process temperature and strain rate. This could be due to the higher resistance of Al 6061-T6 to flow as compared to Al 5083-O.

Keywords: friction stir welding, dissimilar metals, finite element modeling, coupled Eulerian Lagrangian Analysis

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Authors: Soroush Maddah, Houra Asgarian, Mahdi Navidbakhsh

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In the present paper, the problem of pulsatile micropolar blood flow through an elastic artery has been studied. An arbitrary Lagrangian-Eulerian (ALE) formulation for the governing equations has been produced to model the fully-coupled fluid-structure interaction (FSI) and has been solved numerically using finite difference scheme by exploiting a mesh generation technique which leads to a uniformly spaced grid in the computational plane. Effect of the variations of cardiac output and wall artery module of elasticity on blood pressure with blood-pressure regulating drugs like Atenolol has been determined. Also, a numerical model has been produced to define precisely the effects of various dosages of a drug on blood flow in arteries without the numerous experiments that have many mistakes and expenses.

Keywords: arbitrary Lagrangian-Eulerian, Atenolol, fluid structure interaction, micropolar fluid, pulsatile blood flow

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Authors: Ruo-Qian Wang

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Open-source CFD has become increasingly popular and promising. The recent progress in multiphase flow enables new CFD applications, which provides an economic and flexible research tool for complex flow problems. Our numerical study using four-way coupling Euler-Lagrangian Large-Eddy Simulations to resolve particle cloud dynamics with OpenFOAM and CFDEM will be introduced: The fractioned Navier-Stokes equations are numerically solved for fluid phase motion, solid phase motion is addressed by Lagrangian tracking for every single particle, and total momentum is conserved by fluid-solid inter-phase coupling. The grid convergence test was performed, which proves the current resolution of the mesh is appropriate. Then, we validated the code by comparing numerical results with experiments in terms of particle cloud settlement and growth. A good comparison was obtained showing reliability of the present numerical schemes. The time and height at phase separations were defined and analyzed for a variety of initial release conditions. Empirical formulas were drawn to fit the results.

Keywords: four-way coupling, dredging, land reclamation, multiphase flows, oil spill

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Authors: Thierno Diop, Michel Fortin, Jean Deteix

Abstract:

Since the precise formulation of the elastic part is irrelevant for the description of the algorithm, we shall consider a generic case. In practice, however, we will have to deal with a non linear material (for instance a Mooney-Rivlin model). We are interested in solving a finite element approximation of the problem, leading to large-scale non linear discrete problems and, after linearization, to large linear systems and ultimately to calculations needing iterative methods. This also implies that penalty method, and therefore augmented Lagrangian method, are to be banned because of their negative effect on the condition number of the underlying discrete systems and thus on the convergence of iterative methods. This is in rupture to the mainstream of methods for contact in which augmented Lagrangian is the principal tool. We shall first present the problem and its discretization; this will lead us to describe a general solution algorithm relying on a preconditioner for saddle-point problems which we shall describe in some detail as it is not entirely standard. We will propose an iterative approach for solving three-dimensional frictional contact problems between elastic bodies, including contact with a rigid body, contact between two or more bodies and also self-contact.

Keywords: frictional contact, three-dimensional, large-scale, iterative method

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