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Autore: Grafiati

Pubblicato: 8 giugno 2024

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1

Mast, Yannic, e Ralf Takors. "Transferring Bubble Breakage Models Tailored for Euler-Euler Approaches to Euler-Lagrange Simulations". Processes 11, n. 4 (27 marzo 2023): 1018. http://dx.doi.org/10.3390/pr11041018.

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Most bubble breakage models have been developed for multiphase simulations using Euler-Euler (EE) approaches. Commonly, they are linked with population balance models (PBM) and are validated by making use of Reynolds-averaged Navier-Stokes (RANS) turbulence models. The latter, however, may be replaced by alternate approaches such as Large Eddy simulations (LES) that play a pivotal role in current developments based on lattice Boltzmann (LBM) technologies. Consequently, this study investigates the possibility of transferring promising bubble breakage models from the EE framework into Euler-Lagrange (EL) settings aiming to perform LES. Using our own model, it was possible to reproduce similar bubble size distributions (BSDs) for EL and EE simulations. Therefore, the critical Weber (Wecrit) number served as a threshold value for the occurrence of bubble breakage events. Wecrit depended on the bubble daughter size distribution (DSD) and a set minimum time between two consecutive bubble breakage events. The commercial frameworks Ansys Fluent and M-Star were applied for EE and EL simulations, respectively. The latter enabled the implementation of LES, i.e., the use of a turbulence model with non-time averaged entities. By properly choosing Wecrit, it was possible to successfully transfer two commonly applied bubble breakage models from EE to EL. Based on the mechanism of bubble breakage, Wecrit values of 7 and 11 were determined, respectively. Optimum Wecrit were identified as fitting the shape of DSDs, as this turned out to be a key criterion for reaching optimum prediction quality. Optimum Wecrit values hold true for commonly applied operational conditions in aerated bioreactors, considering water as the matrix.

2

Askarishahi, Maryam, Mohammad-Sadegh Salehi e Stefan Radl. "Voidage correction algorithm for unresolved Euler–Lagrange simulations". Computational Particle Mechanics 5, n. 4 (30 aprile 2018): 607–25. http://dx.doi.org/10.1007/s40571-018-0193-8.

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3

Kasbaoui, M. Houssem, Donald L. Koch e Olivier Desjardins. "Clustering in Euler–Euler and Euler–Lagrange simulations of unbounded homogeneous particle-laden shear". Journal of Fluid Mechanics 859 (16 novembre 2018): 174–203. http://dx.doi.org/10.1017/jfm.2018.796.

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Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh–Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler–Lagrange formalism are compared to Euler–Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.

4

Liu, Xu, Mingbo Sun, Hongbo Wang, Peibo Li, Chao Wang, Guoyan Zhao, Yixin Yang e Dapeng Xiong. "A Heterogeneous Parallel Algorithm for Euler-Lagrange Simulations of Liquid in Supersonic Flow". Applied Sciences 13, n. 20 (12 ottobre 2023): 11202. http://dx.doi.org/10.3390/app132011202.

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In spite of its prevalent usage for simulating the full-field process of the two-phase flow, the Euler–Lagrange method suffers from a heavy computing burden. Graphics processing units (GPUs), with their massively parallel architecture and high floating-point performance, provide new possibilities for high-efficiency simulation of liquid-jet-related systems. In this paper, a central processing unit/graphics processing unit (CPU/GPU) parallel algorithm based on the Euler–Lagrange scheme is established, in which both the gas and liquid phase are executed on the GPUs. To realize parallel tracking of the Lagrange droplets, a droplet dynamic management method is proposed, and a droplet-locating method is developed to address the cell. Liquid-jet-related simulations are performed on one core of the CPU with a GPU. The numerical results are consistent with the experiment. Compared with a setup using 32 cores of CPUs, considerable speedup is obtained, which is as high as 32.7 though it decreases to 20.2 with increasing droplets.

5

Kozic, Mirko, Slavica Ristic, Mirjana Puharic e Boris Katavic. "Numerical simulation of multiphase flow in ventilation mill and channel with louvers and centrifugal separator". Thermal Science 15, n. 3 (2011): 677–89. http://dx.doi.org/10.2298/tsci101203018k.

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This paper presents the results of numerical flow simulation in ventilation mill of Kostolac B power plant, where louvers and centrifugal separator with adjustable blade angle are used. Numerical simulations of multiphase flow were performed using the Euler-Euler and Euler-Lagrange approach of ANSYS FLUENT software package. The results of numerical simulations are compared with measurements in the mill for both types of separators. Due to very complex geometry and large number of the grid cells, convergent solution with the Eulerian model could not be obtained. For this reason the mixture model was employed resulting in very good agreement with measurements, concerning the gas mixture distribution and velocity at the main and secondary burners. There was large difference between the numerical results and measurements for the pulverized coal distribution at the burners. Taking into consideration that we analyzed dilute mixture with very low volume fraction of the coal, the only choice was the Euler-Lagrange approach, i.e. discrete phase model limited to volume fraction of the discrete phase less than 10-12%. Obtained distributions of the coal at the burners agree well for both types of separators.

6

Weber, Andreas, e Hans-Jörg Bart. "Flow Simulation in a 2D Bubble Column with the Euler-lagrange and Euler-euler Method". Open Chemical Engineering Journal 12, n. 1 (25 gennaio 2018): 1–13. http://dx.doi.org/10.2174/1874123101812010001.

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Object: Bubbly flows, as present in bubble column reactors, can be simulated using a variety of simulation techniques. It is presented, how Computational Fluid Dynamics (CFD) methods are used to simulate a pseudo 2D bubble column using Euler-Lagrange (EL) and Euler-Euler (EE) techniques. Method: The presented EL method uses the open access software OpenFOAM to solve bubble dynamics with bubble interactions computed via Monte Carlo methods. The estimated bubble size distribution and the predicted hold-up are compared with experimental data and other simulative EE work with a reasonable consensus for both. Benchmarks with state of the art EE simulations shows that the EL approach shows good performance if the bubble number stays at a certain level, as the EL approach scales linearly with the number of bubbles simulated. Therefore, different computational meshes have been used to account for influence of the resolution quality. Conclusion: The EL approach indicated faster solution for all realistic cases, only deliberate decrease of coalescence rates could push CPU time to the limits. Critical bubble number - when EE becomes superior to the EL approach - was estimated to be 40.000 in this particular case.

7

Zhang, Shouxu, Weisheng Yan e Guangming Xie. "Consensus-based leader-following formation control for a group of semi-biomimetic robotic fishes". International Journal of Advanced Robotic Systems 14, n. 4 (1 luglio 2017): 172988141772078. http://dx.doi.org/10.1177/1729881417720784.

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In this article, we developed a consensus-based leader-following formation control algorithm for a group of robotic fishes modeled by Euler–Lagrange dynamics. The Euler–Lagrange dynamics has been simplified as a second-order dynamics using the input transformation technique. Two consensus-based formation control strategies are discussed under the scenario: (1) leader with constant velocity and (2) leader with time-varying velocity. Three formation-keeping examples are shown in the simulations to verify the obtained formation control algorithm.

8

Tausendschön, Josef, Jari Kolehmainen, Sankaran Sundaresan e Stefan Radl. "Coarse graining Euler-Lagrange simulations of cohesive particle fluidization". Powder Technology 364 (marzo 2020): 167–82. http://dx.doi.org/10.1016/j.powtec.2020.01.056.

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9

Dhotre, M. T., N. G. Deen, B. Niceno, Z. Khan e J. B. Joshi. "Large Eddy Simulation for Dispersed Bubbly Flows: A Review". International Journal of Chemical Engineering 2013 (2013): 1–22. http://dx.doi.org/10.1155/2013/343276.

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Large eddy simulations (LES) of dispersed gas-liquid flows for the prediction of flow patterns and its applications have been reviewed. The published literature in the last ten years has been analysed on a coherent basis, and the present status has been brought out for the LES Euler-Euler and Euler-Lagrange approaches. Finally, recommendations for the use of LES in dispersed gas liquid flows have been made.

10

Song, Juan, e Shu Cai Li. "Study on Numerical Simulation of Explosion in Soil Based on Fluid-Solid Coupling Arithmetic". Applied Mechanics and Materials 580-583 (luglio 2014): 2916–19. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2916.

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Numerical simulations play a significant role in explosion in a mass of soil due to an underground explosive. Common methods available in hydrocode for fluid-solid coupling process are contact algorithm, Lagrange algorithm, and Arbitrary Lagrange-Euler (ALE) algorithm. A numerical simulation of explosion process with concentrated charge in a mass of soil was carried out by using three methods in this paper. The dynamic response of soil medium, the formation and development law of explosion cavity and the explosion wave propagation law in soil were simulated. Merits and drawbacks of three different methods are analyzed in the aspect of modeling, simulation results and computing cost.

11

Ahmed, Saim, Ahmad Taher Azar, Mohamed Tounsi e Zeeshan Anjum. "Trajectory Tracking Control of Euler–Lagrange Systems Using a Fractional Fixed-Time Method". Fractal and Fractional 7, n. 5 (27 aprile 2023): 355. http://dx.doi.org/10.3390/fractalfract7050355.

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The results of this research provide fixed-time fractional-order control for Euler–Lagrange systems that are subject to external disturbances. The first step in the process of developing a new system involves the introduction of a method known as fractional-order fixed-time non-singular terminal sliding mode control (FoFtNTSM). The advantages of fractional-order calculus and NTSM are brought together in this system, which result in rapid convergence, fixed-time stability, and smooth control inputs. Lyapunov analysis reveals whether the closed-loop system is stable over the duration of the time period specified. The performance of the suggested method when applied to the dynamics of the Euler–Lagrange system is evaluated and demonstrated with the help of computer simulations.

12

Gullerud, Arne, e Jeromy Hollenshead. "Coupled Euler-Lagrange simulations of metal fragmentation in pipe bomb configurations". Procedia Engineering 204 (2017): 202–7. http://dx.doi.org/10.1016/j.proeng.2017.09.774.

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13

Kusaka, Takashi, e Takayuki Tanaka. "Partial Lagrangian for Efficient Extension and Reconstruction of Multi-DoF Systems and Efficient Analysis Using Automatic Differentiation". Robotics 11, n. 6 (9 dicembre 2022): 149. http://dx.doi.org/10.3390/robotics11060149.

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In the fields of control engineering and robotics, either the Lagrange or Newton–Euler method is generally used to analyze and design systems using equations of motion. Although the Lagrange method can obtain analytical solutions, it is difficult to handle in multi-degree-of-freedom systems because the computational complexity increases explosively as the number of degrees of freedom increases. Conversely, the Newton–Euler method requires less computation even for multi-degree-of-freedom systems, but it cannot obtain an analytical solution. Therefore, we propose a partial Lagrange method that can handle the Lagrange equation efficiently even for multi-degree-of-freedom systems by using a divide-and-conquer approach. The proposed method can easily handle system extensions and system reconstructions, such as changes to intermediate links, for multi-degree-of-freedom serial link manipulators. In addition, the proposed method facilitates the derivation of the equations of motion-by-hand calculations, and when combined with an analysis algorithm using automatic differentiation, it can easily realize motion analysis and control the simulation of multi-degree-of-freedom models. Using multiple pendulums as examples, we confirm the effectiveness of system expansion and system reconstruction with the partial Lagrangians. The derivation of their equations of motion and the results of motion analysis by simulation and motion control experiments are presented. The system extensions and reconstructions proposed herein can be used simultaneously with conventional analytical methods, allowing manual derivations of equations of motion and numerical computer simulations to be performed more efficiently.

14

Djizi, Hamza, Zoubir Zahzouh e Azzedine Bouzaouit. "Quadcopter Prototype Stability Assessment With Pid Controller And Euler-Lagrange Approach". Scientific Bulletin of Electrical Engineering Faculty 23, n. 1 (1 settembre 2023): 15–20. http://dx.doi.org/10.2478/sbeef-2023-0003.

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Abstract The increasing use of drones in various fields has led to their popularity in developed countries due to their ease of use and manufacture. This Miniature Pilotless Aircraft has numerous beneficial usages such as express shipping, gathering information, crop monitoring, cargo transport, storm tracking, geographic mapping of inaccessible terrain, search and rescue operations, among others. This study aims to investigate the stability of a quadcopter through simulations based on the mathematical model that describes the quadcopter’s dynamic and flight mechanics, using the Euler-Lagrange approach. It conducts simulations in MATLAB and present the principles that govern quadcopter stability, focusing on setting the PID coefficients to achieve optimal stability. This study provides insights into the principles of drone mechanics and stability, enabling us to better understand the quadcopter’s behavior and performance.

15

Ivančo, Vladimír, e Martin Orečný. "Modelling a Liquid Material in Drop Test Simulations of a Cask for Liquid Radioactive Waste". Applied Mechanics and Materials 611 (agosto 2014): 145–55. http://dx.doi.org/10.4028/www.scientific.net/amm.611.145.

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The aim of this paper is the comparison of different material models for the simulation of fluid impact on a cask for transport of radioactive liquid material. Simulated is a 9 m drop test performed according to International Atomic Energy Agency regulations. In order to reduce computational time, proposed is to model the transported fluid as a hypothetic linearly elastic material. This enables us to use less time demanding FE explicit dynamic analysis based on Lagrange formulation only instead of combination of Lagrange and Euler formulations. Compared are the results obtained for three elastic material and three fluid models based on different equations of state.

16

Kopper, Patrick, Stephen M. Copplestone, Marcel Pfeiffer, Christian Koch, Stefanos Fasoulas e Andrea Beck. "Hybrid parallelization of Euler–Lagrange simulations based on MPI-3 shared memory". Advances in Engineering Software 174 (dicembre 2022): 103291. http://dx.doi.org/10.1016/j.advengsoft.2022.103291.

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17

Sontheimer, M., A. Kronenburg e O. T. Stein. "Grid dependence of evaporation rates in Euler–Lagrange simulations of dilute sprays". Combustion and Flame 232 (ottobre 2021): 111515. http://dx.doi.org/10.1016/j.combustflame.2021.111515.

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18

Ireland, Peter J., e Olivier Desjardins. "Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling". Journal of Computational Physics 338 (giugno 2017): 405–30. http://dx.doi.org/10.1016/j.jcp.2017.02.070.

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19

Finn, Justin R., Ming Li e Sourabh Vasant Apte. "EULER-LAGRANGE SIMULATIONS OF SEDIMENT TRANSPORT IN OSCILLATORY BOUNDARY LAYERS WITH BEDFORMS". Coastal Engineering Proceedings 1, n. 34 (30 ottobre 2014): 80. http://dx.doi.org/10.9753/icce.v34.sediment.80.

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20

Leprevost, Antonin, Vincent Faucher e Maria Adela Puscas. "A Computationally Efficient Dynamic Grid Motion Approach for Arbitrary Lagrange–Euler Simulations". Fluids 8, n. 5 (16 maggio 2023): 156. http://dx.doi.org/10.3390/fluids8050156.

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The present article addresses the topic of grid motion computation in Arbitrary Lagrange–Euler (ALE) simulations, where a fluid mesh must be updated to follow the displacements of Lagrangian boundaries. A widespread practice is to deduce the motion for the internal mesh nodes from a parabolic equation, such as the harmonic equation, introducing an extra computational cost to the fluid solver. An alternative strategy is proposed to minimize that cost by changing from the parabolic equation to a hyperbolic equation, implementing an additional time derivative term allowing an explicit solution of the grid motion problem. A fictitious dynamic problem is thus obtained for the grid, with dedicated material parameters to be carefully chosen to enhance the computational efficiency and preserve the mesh quality and the accuracy of the physical problem solution. After reminding the basics of the ALE expression of the Navier–Stokes equations and describing the proposed hyperbolic equation for the grid motion problem, the paper provides the necessary characterization of the influence of the fictitious grid parameters and the analysis of the robustness of the new approach compared to the harmonic reference equation on a significant 2D test case. A 3D test case is finally extensively studied in terms of computational performance to highlight and discuss the benefits of the hyperbolic equation for ALE grid motion.

21

Sanjosé, M., J. M. Senoner, F. Jaegle, B. Cuenot, S. Moreau e T. Poinsot. "Fuel injection model for Euler–Euler and Euler–Lagrange large-eddy simulations of an evaporating spray inside an aeronautical combustor". International Journal of Multiphase Flow 37, n. 5 (giugno 2011): 514–29. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2011.01.008.

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22

Chaudhry, Ahmad Zamir, Guang Pan e Yao Shi. "Numerical evaluation of the hydrodynamic impact characteristics of the air launched AUV upon water entry". Modern Physics Letters B 34, n. 14 (4 marzo 2020): 2050149. http://dx.doi.org/10.1142/s0217984920501493.

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In this paper, water entry process of air launched AUV is investigated by employing fully coupled finite element method and arbitrary Lagrange–Euler formulation (FEM-ALE) and using penalty coupling technique. Numerical model is established to describe the hydrodynamic characteristics and flow patterns of a high-speed water entry AUV. The effectiveness and accuracy of the numerical simulation are verified quantitatively by the experiments of the earlier study. Selection of suitable advection method and mesh convergence study is carried out during experimental validation process. It is found that appropriate mesh size of impact domain is crucial for numerical simulations and second-order Van Leer advection method is more appropriate for high speed water entry problems. Subsequently, the arbitrary Lagrange–Euler (ALE) algorithm is used to describe the variation laws of the impact load characteristics with water entry velocities, water entry angles and different AUV masses. Dimensionless impact coefficient of AUV at different velocities calculated using ALE method is compared with SPH results. This reveals that ALE method can also simulate the water entry process accurately with less computational cost. This research work can provide beneficial reference information for structure design of AUV and for selection of the water entry parameters.

23

Li, Zhi Chuan, Qi Hu Sheng, Liang Zhang, Zhi Ming Cong e Jin Jiang. "Numerical Simulation of Blade-Wake Interaction of Vertical Axis Tidal Turbine". Advanced Materials Research 346 (settembre 2011): 318–23. http://dx.doi.org/10.4028/www.scientific.net/amr.346.318.

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To study the blade-wake interaction of vertical axis tidal turbine (VATT)，particles were placed in the flow field to trace blade wake during numerical simulation. Numerical simulations were conducted utilizing Euler-Lagrange model. In the simulations, the continuous phase was solved by Reynolds-averaged Navier-Stocks(RANS) equation combined with SST turbulence model and the particle trajectories of the dispersed phase were determined by momentum equation. Numerical results of predicting instantaneous blade forces and blade wakes showed good agreement with the test data. The model was also compared with previous classic free vortex model (V-DART), vortex method combined with finite element analysis (FEVDTM) and 2-D vortex panel model (VPM2D). It showed that the present model was much better than the former.

24

Liu, K., P. D. Huck, A. Aliseda e S. Balachandar. "Investigation of turbulent inflow specification in Euler–Lagrange simulations of mid-field spray". Physics of Fluids 33, n. 3 (1 marzo 2021): 033313. http://dx.doi.org/10.1063/5.0042900.

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Hoppe, F., e M. Breuer. "A deterministic breakup model for Euler–Lagrange simulations of turbulent microbubble-laden flows". International Journal of Multiphase Flow 123 (febbraio 2020): 103119. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2019.103119.

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26

Verhnjak, O., M. Hriberšek, P. Steinmann e J. Ravnik. "A novel two-way coupling model for Euler-Lagrange simulations of multiphase flow". Engineering Analysis with Boundary Elements 119 (ottobre 2020): 119–32. http://dx.doi.org/10.1016/j.enganabound.2020.07.012.

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27

Radl, Stefan, e Sankaran Sundaresan. "A drag model for filtered Euler–Lagrange simulations of clustered gas–particle suspensions". Chemical Engineering Science 117 (settembre 2014): 416–25. http://dx.doi.org/10.1016/j.ces.2014.07.011.

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28

Antunes, Gabriella Gonçalves Borges, Andreas Bück, Felipe Pamplona Mariano, Anderson Gomes Girardi e Dyrney Araújo dos Santos. "Particle dynamics in a pseudo-2D spouted bed: Experiments and Euler–Lagrange simulations". Chemical Engineering Journal 491 (luglio 2024): 152007. http://dx.doi.org/10.1016/j.cej.2024.152007.

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29

Shen, Shaobo, Liyue Fu, Aiguo Song e Tao Li. "Sequential Predictors for Uncertain Euler–Lagrange Systems with Large Transmission Delays". Fractal and Fractional 7, n. 3 (8 marzo 2023): 244. http://dx.doi.org/10.3390/fractalfract7030244.

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This paper investigates the state prediction problems for uncertain Euler–Lagrange systems with large time delays during data transmissions. A set of sequential predictors is proposed to estimate the actual real-time states of the systems by using the delayed information of measurements. The arbitrarily large delays are handled by applying adequate numbers of serial sub-predictors. Meanwhile, the novel prediction structure of each subsystem is designed to deal with nonlinearities and unknown dynamics in the systems. Then, the predictor design is extended to the case without using delayed velocity measurements by updating the structure of the first sub-predictor. Sufficient conditions for the design of predictor gains, ensuring the boundness of prediction errors, are obtained through Lyapunov–Krasovskii functionals. The effectiveness and robustness of the uncertainties of the proposed method are verified by comparative results in simulations.

30

van Wachem, Berend, Thomas Curran e Fabien Evrard. "Fully Correlated Stochastic Inter-Particle Collision Model for Euler–Lagrange Gas–Solid Flows". Flow, Turbulence and Combustion 105, n. 4 (6 febbraio 2020): 935–63. http://dx.doi.org/10.1007/s10494-020-00111-7.

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AbstractIn Lagrangian stochastic collision models, a fictitious particle is generated to act as a collision partner, with a velocity correlated to the velocity of the real colliding particle. However, most often, the fluid velocity seen by this fictitious particles is not accounted for in the generation of the fictitious particle velocity, leading to a de-correlation between the fictitious particle velocity and the local fluid velocity, which, after collision, leads to an unrealistic de-correlation of the real particle velocity and the fluid velocity as seen by the particle. This de-correlation, in turn, causes a spurious decrease of the particle kinetic energy, even though the collisions are assumed perfectly elastic. In this paper, we propose a new model in which the generated fictitious particle velocity is correctly correlated to both the real particle velocity and the local fluid velocity at the particle, hence preventing the spurious loss of the total particle kinetic energy. The model is suitable for small inertial particles. Two algorithms for integrating the collision frequency are also compared to each other. The models are validated using large eddy simulation (LES) of mono-dispersed particle-laden stationary homogeneous isotropic turbulence. Simulations are conducted with spherical particles with different turbulent Stokes number, $$St_t = [0.75 - 5.8]$$ S t t = [ 0.75 - 5.8 ] , and volume fractions, $$\alpha _p = [0.014 - 0.044]$$ α p = [ 0.014 - 0.044 ] , and are compared to the results of the LES using a deterministic discrete particle simulation model.

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Balachandar, S., Kai Liu e Mandar Lakhote. "Self-induced velocity correction for improved drag estimation in Euler–Lagrange point-particle simulations". Journal of Computational Physics 376 (gennaio 2019): 160–85. http://dx.doi.org/10.1016/j.jcp.2018.09.033.

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Gruber, Michael C, Stefan Radl e Johannes G Khinast. "Coalescence and Break-Up in Bubble Columns: Euler-Lagrange Simulations Using a Stochastic Approach". Chemie Ingenieur Technik 85, n. 7 (23 maggio 2013): 1118–30. http://dx.doi.org/10.1002/cite.201300024.

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Fakhri, Somayeh, e Sayed Hodjatollah Momeni-Masuleh. "AN EXPLICIT SPECTRAL COLLOCATION METHOD FOR THE DRUG RELEASE CORONARY STENTS". Mathematical Modelling and Analysis 27, n. 3 (12 agosto 2022): 452–70. http://dx.doi.org/10.3846/mma.2022.15066.

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This research aims to solve a comprehensive one-dimensional model of drug release from cardiovascular stents in which the drug binding is saturable and reversible. We used the Lagrange collocation method for space dimension and the modified Euler method for time discretization. The existence and uniqueness of the solution, are provided. The consistency, stability, and convergence analysis of the proposed scheme are provided, to show that numerical simulations are valid. Numerical results accurate enough and efficient just by using fewer mesh.

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Unger, Laura, Juan Sebastián Gómez Bonilla, Dyrney Araújo dos Santos e Andreas Bück. "Particle Residence Time Distribution in a Concurrent Multiphase Flow Reactor: Experiments and Euler-Lagrange Simulations". Processes 10, n. 5 (17 maggio 2022): 996. http://dx.doi.org/10.3390/pr10050996.

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The present work focuses on investigating the residence time behavior of microparticles in a concurrent downer reactor through experiments and numerical simulations. For the numerical simulations, a three-dimensional multiphase model was developed using the Euler-Lagrange approach. The experiments were performed in a 0.8 m-long steel reactor with gravitational particle injection. The effects of different operating conditions, e.g., the sheath gas velocity on the particle residence time distribution were assessed. An increase in the sheath gas flow rate led to a decrease in the peak residence time, although the maximum residence time increased. Regarding the lowest sheath gas flow rate, the particles’ peak residence time was twice as high compared to the peak residence time within the highest flow rate. The particles’ residence time curves presented a broad distribution coinciding with the size distribution of the powder. The numerical results agreed with the experimental data; thus, this study presents a numerical model for predicting the particle residence time behavior in a concurrent downer reactor. Furthermore, the numerical simulations contributed to a better understanding of the particle residence time behavior inside a concurrent downer reactor which is essential for optimizing thermal rounding processes. Dimensionless correlations for the observed effects are developed.

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Jajarmi, Amin, e Dumitru Baleanu. "Suboptimal control of fractional-order dynamic systems with delay argument". Journal of Vibration and Control 24, n. 12 (30 gennaio 2017): 2430–46. http://dx.doi.org/10.1177/1077546316687936.

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In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler–Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations. The new scheme is also effective for the delay fractional optimal control problems influenced by the external persistent disturbances. Numerical simulations and comparative results verify that the proposed approach is efficient and easy to implement.

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Fu, Tao, Yun-Ting Tsai e Qiang Zhou. "Numerical Simulation of Magnesium Dust Dispersion and Explosion in 20 L Apparatus via an Euler–Lagrange Method". Energies 15, n. 2 (6 gennaio 2022): 402. http://dx.doi.org/10.3390/en15020402.

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Computational fluid dynamics (CFD) was used to investigate the explosion characteristics of a Mg/air mixture in a 20 L apparatus via an Euler–Lagrange method. Various fluid properties, namely pressure field, velocity field, turbulence intensity, and the degree of particle dispersion, were obtained and analyzed. The simulation results suggested that the best delayed ignition time was 60 ms after dust dispersion, which was consistent with the optimum delayed ignition time adopted by experimental apparatus. These results indicate that the simulated Mg particles were evenly diffused in the 20 L apparatus under the effect of the turbulence. The simulations also reveal that the pressure development in the explosion system can be divided into the pressure rising stage, the maximum pressure stage, and pressure attenuation stage. The relative error of the maximum explosion pressure between the simulation and the experiments is approximately 1.04%. The explosion model provides reliable and useful information for investigating Mg explosions.

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SOWARD, A. M., e P. H. ROBERTS. "The hybrid Euler–Lagrange procedure using an extension of Moffatt's method". Journal of Fluid Mechanics 661 (2 agosto 2010): 45–72. http://dx.doi.org/10.1017/s0022112010002867.

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The hybrid Euler–Lagrange (HEL) description of fluid mechanics, pioneered largely by Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646), has had to face the fact, in common with all Lagrangian descriptions of fluid motion, that the variables used do not describe conditions at the coordinate x, upon which they depend, but conditions elsewhere at some displaced position xL(x, t) = x + ξ(x, t), generally dependent on time t. To address this issue, we employ ‘Lie dragging’ techniques of general tensor calculus to extend a method introduced by Moffatt (J. Fluid Mech., vol. 166, 1986, pp. 359–378) in the fluid dynamic context, whereby the point x is dragged to xL(x, t) by a ‘fictitious steady flow’ η*(x, t) in a unit of ‘fictitious time’. Whereas ξ(x, t) is a Lagrangian concept intimately linked to the location xL(x, t), the ‘dragging velocity’ η*(x, t) has an essentially Eulerian character, because it describes the fictitious velocity at x itself. For the case of constant-density fluids, we show, using solenoidal η*(x, t) instead of solenoidal ξ(x, t), how the HEL theory can be cast into Eulerian form. A useful aspect of this Eulerian development is that the mean flow itself remains solenoidal, a feature that traditional HEL theories lack. Our method realizes the objective sought by Holm (Physica D, vol. 170, 2002, pp. 253–286) in his derivation of the Navier–Stokes–α equation, which is the basis of one of the methods currently employed to represent the sub-grid scales in large-eddy simulations. His derivation, based on expansion to second order in ξ, contained an error which, when corrected, implied a violation of Kelvin's theorem on the constancy of circulation in inviscid incompressible fluid. We show that this is rectified when the expansion is in η* rather than ξ, Kelvin's theorem then being satisfied to all orders for which the expansion converges. We discuss the implications of our approach using η* for the Navier–Stokes–α theory.

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Hoppe, F., e M. Breuer. "A deterministic and viable coalescence model for Euler–Lagrange simulations of turbulent microbubble-laden flows". International Journal of Multiphase Flow 99 (febbraio 2018): 213–30. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2017.10.009.

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Hoppe, Felix, e Michael Breuer. "Euler-Lagrange Simulations of Turbulent Two-phase Flows with an Advanced Deterministic Bubble Coalescence Model". PAMM 17, n. 1 (dicembre 2017): 655–56. http://dx.doi.org/10.1002/pamm.201710296.

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Bösenhofer, Markus, Mario Pichler e Michael Harasek. "Heat Transfer Models for Dense Pulverized Particle Jets". Processes 10, n. 2 (26 gennaio 2022): 238. http://dx.doi.org/10.3390/pr10020238.

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Heat transfer is a crucial aspect of thermochemical conversion of pulverized fuels. Over-predicting the heat transfer during heat-up leads to under-estimation of the ignition time, while under-predicting the heat loss during the char conversion leads to an over-estimation of the burnout rates. This effect is relevant for dense particle jets injected from dense-phase pneumatic conveying. Heat fluxes characteristic of such dense jets can significantly differ from single particles, although a single, representative particle commonly models them in Euler–Lagrange models. Particle-resolved direct numerical simulations revealed that common representative particles approaches fail to reproduce the dense-jet characteristics. They also confirm that dense clusters behave similar to larger, porous particles, while the single particle characteristic prevails for sparse clusters. Hydrodynamics causes this effect for convective heat transfer since dense clusters deflect the inflowing fluid and shield the center. Reduced view factors cause reduced radiative heat fluxes for dense clusters. Furthermore, convection is less sensitive to cluster shape than radiative heat transfer. New heat transfer models were derived from particle resolved simulations of particle clusters. Heat transfer increases at higher void fractions and vice versa, which is contrary to most existing models. Although derived from regular particle clusters, the new convective heat transfer models reasonably handle random clusters. Contrary, the developed correction for the radiative heat flux over-predicts shading effects for random clusters because of the used cluster shape. In unresolved Euler–Lagrange models, the new heat transfer models can significantly improve dense particle jets’ heat-up or thermochemical conversion modeling.

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Tamimi, Jasem. "Modeling, simulation and control of a twin-inverted pendulum on a moving cart". International Journal of Modeling, Simulation, and Scientific Computing 12, n. 04 (22 febbraio 2021): 2150027. http://dx.doi.org/10.1142/s1793962321500276.

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In this paper, a mathematical model of a twin-inverted pendulum on a moving cart has been derived. This is done using the Lagrange–Euler method and, hence, a highly nonlinear mathematical model is resulted from this derivation. These nonlinear and unstable dynamics are written in a simple matrix form. For this challenging system, we use two types of efficient control approaches to treat the control problem of the twin inverted pendulum, namely, linear quadratic regulator (LQR) and nonlinear model predictive control (NMPC). Simulations with several scenarios are also presented to demonstrate the control performances and the model validity.

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Kreitmayer, Diana, Srikanth R. Gopireddy, Tomomi Matsuura, Yuichi Aki, Yuta Katayama, Taihei Sawada, Hirofumi Kakihara et al. "Numerical and Experimental Investigation of the Hydrodynamics in the Single-Use Bioreactor Mobius® CellReady 3 L". Bioengineering 9, n. 5 (11 maggio 2022): 206. http://dx.doi.org/10.3390/bioengineering9050206.

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Two-way Euler-Lagrange simulations are performed to characterize the hydrodynamics in the single-use bioreactor Mobius® CellReady 3 L. The hydrodynamics in stirred tank bioreactors are frequently modeled with the Euler–Euler approach, which cannot capture the trajectories of single bubbles. The present study employs the two-way coupled Euler–Lagrange approach, which accounts for the individual bubble trajectories through Langrangian equations and considers their impact on the Eulerian liquid phase equations. Hydrodynamic process characteristics that are relevant for cell cultivation including the oxygen mass transfer coefficient, the mixing time, and the hydrodynamic stress are evaluated for different working volumes, sparger types, impeller speeds, and sparging rates. A microporous sparger and an open pipe sparger are considered where bubbles of different sizes are generated, which has a pronounced impact on the bubble dispersion and the volumetric oxygen mass transfer coefficient. It is found that only the microporous sparger provides sufficiently high oxygen transfer to support typical suspended mammalian cell lines. The simulated mixing time and the volumetric oxygen mass transfer coefficient are successfully validated with experimental results. Due to the small reactor size, mixing times are below 25 s across all tested conditions. For the highest sparging rate of 100 mL min−1, the mixing time is found to be two seconds shorter than for a sparging rate of 50 mL min−1, which again, is 0.1 s longer than for a sparging rate of 10 mL min−1 at the same impeller speed of 100 rpm and the working volume of 1.7 L. The hydrodynamic stress in this bioreactor is found to be below critical levels for all investigated impeller speeds of up to 150 rpm, where the maximum levels are found in the region where the bubbles pass behind the impeller blades.

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Cheng, Lei, Guo Jie Huang, Jian Wei Wang, Wei Xiao e Shui Sheng Xie. "Numerical Simulation of Extrusion Process to Produce Complex Aluminum Profiles Using the ALE Approach". Advanced Materials Research 1004-1005 (agosto 2014): 1260–64. http://dx.doi.org/10.4028/www.scientific.net/amr.1004-1005.1260.

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Although still having certain limitations, the numerical simulation technology has been increasingly applied to aid in optimizing the aluminum extrusion process and die design. In the present research, numerical simulations of the profiles extrusion process were performed, using the Finite Volume Method (FVM) and Finite Element Method (FEM) to make use of the individual merits of the Euler approach and Lagrange approach, respectively. The application of the simulation technology to produce large, complex profiles has, however, been quite limited. In order to solve the limited, numerical simulation of aluminum profiles with large and complicated cross-section in extrusion process was achieved using Arbitrary Lagrangian-Eulerian (ALE) approach, and non-uniform velocities at the die exit, leading to extrudate distortions, were predicted. Extrusion experiments proved that the die with the optimized design could circumvent the distortion problem. The numerical simulation technology can indeed be effectively used to reduce the number of die trials and offer the potential to realize zero die trial.

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Ramírez Pérez, Natalia Andrea, Camilo Andrés Pérez Triana e Harold Vacca González. "Calculating geodesics:". Ingeniería Solidaria 18, n. 1 (11 gennaio 2022): 1–18. http://dx.doi.org/10.16925/2357-6014.2022.01.09.

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Introduction: The article is the product of the research “Connections on Semi-Riemannian Geometry and Christoffel Coefficients – Towards the study of the computational calculation of geodesics”, developed at the Pascual Bravo University Institution in the year 2021. Problem: Based on solutions of the Euler-Lagrange equations, the explicit calculation of geodesics on certain manifolds is possible. However, there are several cases in which it is impossible to continue calculating analytically and we have to resort to a numerical calculation. In this sense, several geometric and dynamic characteristics of geodesics, unexpectedly emerge. Objective: The objective of the research is to calculate geodesics of a Riemannian or semi-Riemannian manifold using SageMath as software to more easily go beyond what intuition provides. Methodology: First, some simple examples of characterizations of geodesics on certain manifolds, based on solutions of the Euler-Lagrange equations, are presented. Then, an ellipsoid is selected as a test subject with which to numerically calculate geodesics, observing how it changes depending on whether it is defined within a Spherical, Triaxial or Mercator coordinate system. Results: With the flexibility of software like SageMath, an explicit expression of the differential equations was made possible along with, from numeric solutions for these equations, their corresponding simulations depending on the selected parameters. Conclusion: These simulations confirm that great circles are not the only geodesics existing on the ellipsoid, but rather there are many other types of geodesic curves, some of which can be dense curves on the surface and others can be closed curves. At the same time, this shows a relationship between the existence of certain types of geodesic curves and the parameterization of the surface.

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Lück, Sebastian, Tim Wittmann, Jan Göing, Christoph Bode e Jens Friedrichs. "Impact of Condensation on the System Performance of a Fuel Cell Turbocharger". Machines 10, n. 1 (13 gennaio 2022): 59. http://dx.doi.org/10.3390/machines10010059.

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A mobile fuel cell systems power output can be increased by pressure amplification using an electric turbocharger. These devices are subject to frequent transient manoeuvres due to a multitude of load changes during the mission in automotive applications. In this paper, the authors describe a simulation approach for an electric turbocharger, considering the impact of moist air and condensation within the cathode gas supply system. Therefore, two simulation approaches are used: an iterative simulation method and one based on a set of ordinary differential equations. Additional information is included from turbine performance maps taking into account condensation using Euler–Lagrange CFD simulations, which are presented. The iterative calculation approach is well suited to show the impact of condensation and moist air on the steady state thermodynamic cycle and yields a significant shift of the steady state operating line towards the surge line. It is shown that a substantial risk of surge occurs during transient deceleration manoeuvres triggered by a load step.

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Taborda, Manuel A., Ragna Kipping, Uwe Hampel e Martin Sommerfeld. "Advanced analysis of bubble columns: Comparison of Euler/Lagrange simulations and experiments under CO2 chemisorption conditions". Chemical Engineering Research and Design 170 (giugno 2021): 389–405. http://dx.doi.org/10.1016/j.cherd.2021.04.020.

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Cheng, Zhen, Julien Chauchat, Tian-Jian Hsu e Joseph Calantoni. "Eddy interaction model for turbulent suspension in Reynolds-averaged Euler–Lagrange simulations of steady sheet flow". Advances in Water Resources 111 (gennaio 2018): 435–51. http://dx.doi.org/10.1016/j.advwatres.2017.11.019.

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LIU, TIANSHU, e LIXIN SHEN. "Fluid flow and optical flow". Journal of Fluid Mechanics 614 (16 ottobre 2008): 253–91. http://dx.doi.org/10.1017/s0022112008003273.

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The connection between fluid flow and optical flow is explored in typical flow visualizations to provide a rational foundation for application of the optical flow method to image-based fluid velocity measurements. The projected-motion equations are derived, and the physics-based optical flow equation is given. In general, the optical flow is proportional to the path-averaged velocity of fluid or particles weighted with a relevant field quantity. The variational formulation and the corresponding Euler–Lagrange equation are given for optical flow computation. An error analysis for optical flow computation is provided, which is quantitatively examined by simulations on synthetic grid images. Direct comparisons between the optical flow method and the correlation-based method are made in simulations on synthetic particle images and experiments in a strongly excited turbulent jet.

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Gu, Rongrong, e Xudong Sun. "Fault-Tolerant Cooperative Control of Multiple Uncertain Euler-Lagrange Systems with an Uncertain Leader". Electronics 13, n. 11 (27 maggio 2024): 2068. http://dx.doi.org/10.3390/electronics13112068.

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This paper explores the fault-tolerant cooperative control of multiagent systems, which are modeled via an uncertain leader system and multiple uncertain Euler–Lagrange systems with actuator faults. A self-adjusting observer is initially proposed to estimate the signal of the uncertain leader for different followers and compute the observer gain in real time. An adaptive fault-tolerant controller is designed based on the above observer and nonsingular fast terminal sliding mode surface. This controller estimates lumped uncertainty and ensures that tracking errors are ultimately bounded. The controller designed in this paper has the following three advantages. Firstly, the observer can estimate and transmit the leader’s state to each follower even without precise knowledge of the leader’s system matrix. Secondly, the controller is robust to actuator faults, uncertain parameters and external disturbances, the upper bounds of which can be arbitrarily large and unidentified. Thirdly, the controller has a simple structure and is also suitable for situations where the actuator is healthy. Lastly, simulations are provided to demonstrate the effectiveness of both the observer and the controller with or without actuator fault.

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Elliott, Charles M., e Björn Stinner. "Computation of Two-Phase Biomembranes with Phase DependentMaterial Parameters Using Surface Finite Elements". Communications in Computational Physics 13, n. 2 (febbraio 2013): 325–60. http://dx.doi.org/10.4208/cicp.170611.130112a.

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AbstractThe shapes of vesicles formed by lipid bilayers with phase separation are governed by a bending energy with phase dependent material parameters together with a line energy associated with the phase interfaces. We present a numerical method to approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces, isoparametric quadratic surface finite elements and the phase field approach for the phase separation. Furthermore, the method involves an iterative solution scheme that is based on a relaxation dynamics coupling a geometric evolution equation for the membrane surface with a surface Allen-Cahn equation. Remeshing and grid adaptivity are discussed, and in various simulations the influence of several physical parameters is investigated.