Zeitschriftenartikel: „Euler-Lagrange numerical simulation“

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Kozic, Mirko, Slavica Ristic, Mirjana Puharic und Boris Katavic. „Numerical simulation of multiphase flow in ventilation mill and channel with louvers and centrifugal separator“. Thermal Science 15, Nr. 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.

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Sokolichin, A., G. Eigenberger, A. Lapin und A. Lübert. „Dynamic numerical simulation of gas-liquid two-phase flows Euler/Euler versus Euler/Lagrange“. Chemical Engineering Science 52, Nr. 4 (Februar 1997): 611–26. http://dx.doi.org/10.1016/s0009-2509(96)00425-3.

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3

Song, Juan, und Shu Cai Li. „Study on Numerical Simulation of Explosion in Soil Based on Fluid-Solid Coupling Arithmetic“. Applied Mechanics and Materials 580-583 (Juli 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.

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Murray, J. J., und C. P. Neuman. „Linearization and Sensitivity Models of the Newton-Euler Dynamic Robot Model“. Journal of Dynamic Systems, Measurement, and Control 108, Nr. 3 (01.09.1986): 272–76. http://dx.doi.org/10.1115/1.3143779.

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Within the framework of the Newton-Euler formulation of robot dynamics, linearized and trajectory sensitivity models are constructed about a nominal trajectory. The approach illustrates the property that linearization of the O(N) recursive Newton-Euler formulation leads to O(N) recursive algorithms. These algorithms are conceived for simulation, parameter identification, and real-time control applications which require the numerical evaluation of the linearized or trajectory sensitivity models. The O(N) linearized recursive algorithms complement their O(N5) linearized Lagrange (Lagrange-Euler) counterparts which are conceived for physical insight, and manipulator and controller design.

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Liu, Xu, Mingbo Sun, Hongbo Wang, Peibo Li, Chao Wang, Guoyan Zhao, Yixin Yang und Dapeng Xiong. „A Heterogeneous Parallel Algorithm for Euler-Lagrange Simulations of Liquid in Supersonic Flow“. Applied Sciences 13, Nr. 20 (12.10.2023): 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.

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Longatte, E., Z. Bendjeddou und M. Souli. „Application of Arbitrary Lagrange Euler Formulations to Flow-Induced Vibration Problems“. Journal of Pressure Vessel Technology 125, Nr. 4 (01.11.2003): 411–17. http://dx.doi.org/10.1115/1.1613950.

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Most classical fluid force identification methods rely on mechanical structure response measurements associated with convenient data processes providing turbulent and fluid-elastic forces responsible for possible vibrations and damage. These techniques provide good results; however, they often involve high costs as they rely on specific modelings fitted with experimental data. Owing to recent improvements in computational fluid dynamics, numerical simulation of flow-induced structure vibration problems is now practicable for industrial purposes. As far as flow structure interactions are concerned, the main difficulty consists in estimating numerically fluid-elastic forces acting on mechanical components submitted to turbulent flows. The point is to take into account both fluid effects on structure motion and conversely dynamic motion effects on local flow patterns. This requires a code coupling to solve fluid and structure problems in the same time. This ability is out of limit of most classical fluid dynamics codes. That is the reason why recently an improved numerical approach has been developed and applied to the fully numerical prediction of a flexible tube dynamic response belonging to a fixed tube bundle submitted to cross flows. The methodology consists in simulating at the same time thermo-hydraulics and mechanics problems by using an Arbitrary Lagrange Euler (ALE) formulation for the fluid computation. Numerical results turn out to be consistent with available experimental data and calculations tend to show that it is now possible to simulate numerically tube bundle vibrations in presence of cross flows. Thus a new possible application for ALE methods is the prediction of flow-induced vibration problems. The full computational process is described in the first section. Classical and improved ALE formulations are presented in the second part. Main numerical results are compared to available experimental data in section 3. Code performances are pointed out in terms of mesh generation process and code coupling method.

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Tao, Yujia, Xiulan Huai, Ziyi Guo und Ran Yin. „Numerical simulation of spray performance based on the Euler-Lagrange approach“. Journal of Thermal Science 18, Nr. 1 (18.02.2009): 91–96. http://dx.doi.org/10.1007/s11630-009-0091-8.

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Deen, N. G., M. A. Van Der Hoef, M. Van Sint Annaland und J. A. M. Kuipers. „Numerical simulation of dense gas-particle flows using the Euler Lagrange approach“. Progress in Computational Fluid Dynamics, An International Journal 7, Nr. 2/3/4 (2007): 152. http://dx.doi.org/10.1504/pcfd.2007.013007.

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Tang, Guo Zhi, Yuan Ren und Zhou Wang. „Localization Study of a Cold Atom BEC in Two-Dimensional Bessel Optical Lattices“. Key Engineering Materials 787 (November 2018): 105–12. http://dx.doi.org/10.4028/www.scientific.net/kem.787.105.

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In order to investigate the stability and dynamics properties of a cold atom Bose-Einstein Condensate (BEC) in two-dimensional Bessel optical lattices, the stability condition of the system is analyzed and the corresponding Gross-pitaevskii equation (GPE) is solved in this paper by time-dependent variational method and numerical simulation. Firstly, the Euler-Lagrange equation containing the parameters describing the system stability and the effective potential energy needed by the variational analysis method to analyze the system stability is obtained by using the adjustable exponent Gaussian trial wave function. Secondly, according to the analytical solution of Euler-Lagrange equation and the local minimum value of potential energy, the stability condition of the system is further illuminated. Finally, the influence mechanism of these parameters on the local dynamics is revealed by solving the corresponding GPE with numerical method.

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Li, Zhi Chuan, Qi Hu Sheng, Liang Zhang, Zhi Ming Cong und Jin Jiang. „Numerical Simulation of Blade-Wake Interaction of Vertical Axis Tidal Turbine“. Advanced Materials Research 346 (September 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.

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Wang, Gong Xi, und Wei Jia Zhao. „A Numerical Approach for Simulating a Self-Contacted Elastic Rod“. Advanced Materials Research 941-944 (Juni 2014): 2336–40. http://dx.doi.org/10.4028/www.scientific.net/amr.941-944.2336.

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A challenging problem in the numerical simulation of a self-contacted elastic rod is the change of topological structure during the contacting process. In this article, a numerical approach is introduced to simulate a self-contacted Cosserat rod. By introducing the angular velocity and Euler parameters as the state variables, an improved Lagrange equation is introduced. A finite element method is built to deal with the simplified model, and numerical examples are given.

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Li, Bingcheng, Min Zeng und Qiuwang Wang. „Numerical Simulation of Erosion Wear for Continuous Elbows in Different Directions“. Energies 15, Nr. 5 (04.03.2022): 1901. http://dx.doi.org/10.3390/en15051901.

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The purpose of the present study is to simulate the continuous bend erosion process in different directions, using the dense discrete particle model (DDPM). The influence of the length of the straight pipe in the middle of the continuous bend is investigated. The Rosin–Rammler method is introduced to define the diameter distribution of erosion particles, which is theoretically closer to the actual engineering erosion situation. The numerical model is based on the Euler–Lagrange method, in which the continuous phase and the particle phase are established on a fixed Euler grid. The Lagrange model is used to track the particles, and the interaction between particles is simulated by particle flow mechanics theory. The velocity field distribution, pressure variation, and turbulent kinetic energy of gas–solid two-phase flow, composed of natural gas and gravel in the pipeline, are studied. The simulation results, using the one-way coupled DPM and the four-way coupled DDPM, are compared and analyzed. The results show that the DDPM has good accuracy in predicting the distribution of the continuous bend erosion processes in different directions. The erosion rates of particles with an average distribution size of 50 μm are significantly increased (8.32 times), compared with that of 10 μm, at the same gas transmission rate. It is also indicated that it is important to consider the impact between particles and the coupling between fluid and particles in the erosion simulation of the continuous elbow when using the CFD method.

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Masterov, M. V., M. W. Baltussen und J. A. M. Kuipers. „Numerical simulation of a square bubble column using Detached Eddy Simulation and Euler–Lagrange approach“. International Journal of Multiphase Flow 107 (Oktober 2018): 275–88. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2018.06.006.

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Zhang, Heng, und Yan Chao Yin. „Turbulence Numerical Simulation and Particle Track Analysis of Slurry Pump Impeller“. Advanced Materials Research 655-657 (Januar 2013): 336–39. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.336.

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In order to improve the pump wear performance and optimize pump design, the Euler-Lagrange approach is chosen to simulate the flow in the impeller. The fluid phase is treated as a continuum by solving the N-S equations, while the dispersed phase is solved by using Lagrange Method through the calculated flow field. The results show that the reflex appears in the blade inlet of pressure sides in high flow conditions, but appears in the blade inlet of suction sides in low flow conditions, which possibly induce the cavitation erosion. In low flow conditions, reflex and eddies appear in the blade outlet of both the pressure sides and the suction sides, and the reflex areas even extend to the middle of blades. In the range of simulated conditions, the suction sides don’t collide with particles. The pressure sides collide with particles in the form of continuous impact in low flow conditions but scratch in high flow conditions.

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Chaudhry, Ahmad Zamir, Guang Pan und Yao Shi. „Numerical evaluation of the hydrodynamic impact characteristics of the air launched AUV upon water entry“. Modern Physics Letters B 34, Nr. 14 (04.03.2020): 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.

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Fornalik-Wajs, Elzbieta, Aleksandra Roszko, Janusz Donizak und Anna Kraszewska. „Comparison of the experimental and numerical analyses of silver nanofluid under influence of strong magnetic field“. International Journal of Numerical Methods for Heat & Fluid Flow 30, Nr. 6 (06.07.2019): 3139–62. http://dx.doi.org/10.1108/hff-11-2018-0714.

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Purpose Nanofluids’ properties made them interesting for various areas like engineering, medicine or cosmetology. Discussed here, research pertains to specific problem of heat transfer enhancement with application of the magnetic field. The main idea was to transfer high heat rates with utilization of nanofluids including metallic non-ferrous particles. The expectation was based on changed nanofluid properties. However, the results of experimental analysis did not meet it. The heat transfer effect was smaller than in the case of base fluid. The only way to understand the process was to involve the computational fluid dynamics, which could help to clarify this issue. The purpose of this research is deep understanding of the external magnetic field effect on the nanofluids heat transfer. Design/methodology/approach In presented experimental and numerical studies, the water and silver nanofluids were considered. From the numerical point of view, three approaches to model the nanofluid in the strong magnetic field were used: single-phase Euler, Euler–Euler and Euler–Lagrange. In two-phase approach, the momentum transfer equations for individual phases were coupled through the interphase momentum transfer term expressing the volume force exerted by one phase on the second one. Findings Therefore, the results of numerical simulation predicted decrease of convection heat transfer for nanofluid with respect to pure water, which agreed with the experimental results. The experimental and numerical results are in good agreement with each other, which confirms the right choice of two-phase approach in analysis of nanofluid thermo-magnetic convection. Originality/value The Euler–Lagrange exhibit the best matching with the experimental results.

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Cheng, Lei, Guo Jie Huang, Jian Wei Wang, Wei Xiao und Shui Sheng Xie. „Numerical Simulation of Extrusion Process to Produce Complex Aluminum Profiles Using the ALE Approach“. Advanced Materials Research 1004-1005 (August 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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Hu, Wei, Yong Hu Wang und Cai Hua Chen. „Numerical Simulation of Aircraft Ditching Based on ALE Method“. Applied Mechanics and Materials 668-669 (Oktober 2014): 490–93. http://dx.doi.org/10.4028/www.scientific.net/amm.668-669.490.

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Aircraft Ditching is related primarily with the aviation safety. Firstly, the full-scaled shape of Boeing 777-200 is modeled according to the lost MH370 aircraft on 8th March. And then an Arbitrary Lagrange-Euler (ALE) fluid-field model is created for water and air domain. Next some simulation cases are implemented related to different vertical velocities using LS-DYNA nonlinear finite-element code, with the same horizontal velocity and attack angle. At the same time, the variations of the velocity of the head and tail are discussed. Consequently, Ditching overload peak occurs at the highest vertical velocity. The simulation results can deeply be applied to accident analysis of aircraft impacting on water.

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Shams, E., J. Finn und S. V. Apte. „A numerical scheme for Euler-Lagrange simulation of bubbly flows in complex systems“. International Journal for Numerical Methods in Fluids 67, Nr. 12 (29.10.2010): 1865–98. http://dx.doi.org/10.1002/fld.2452.

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Kusaka, Takashi, und Takayuki Tanaka. „Partial Lagrangian for Efficient Extension and Reconstruction of Multi-DoF Systems and Efficient Analysis Using Automatic Differentiation“. Robotics 11, Nr. 6 (09.12.2022): 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.

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HOLZHÜTER, THOMAS, und THOMAS KLINKER. „METHOD TO SOLVE THE NONLINEAR INFINITE HORIZON OPTIMAL CONTROL PROBLEM WITH APPLICATION TO THE TRACK CONTROL OF A MOBILE ROBOT“. International Journal of Bifurcation and Chaos 17, Nr. 10 (Oktober 2007): 3607–11. http://dx.doi.org/10.1142/s0218127407019445.

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We present a numerical method to solve the infinite time horizon optimal control problem for low dimensional nonlinear systems. Starting from the linear-quadratic approximation close to the origin, the extremal field is efficiently calculated by solving the Euler–Lagrange equations backward in time. The resulting controller is given numerically on an interpolation grid. We use the method to obtain the optimal track controller for a mobile robot. The result is a globally asymptotically stable nonlinear controller, obtained without any specific insight into the system dynamics.

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Fakhri, Somayeh, und Sayed Hodjatollah Momeni-Masuleh. „AN EXPLICIT SPECTRAL COLLOCATION METHOD FOR THE DRUG RELEASE CORONARY STENTS“. Mathematical Modelling and Analysis 27, Nr. 3 (12.08.2022): 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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Aregba–Driollet, D., J. Breil, S. Brull, B. Dubroca und E. Estibals. „Modelling and numerical approximation for the nonconservative bitemperature Euler model“. ESAIM: Mathematical Modelling and Numerical Analysis 52, Nr. 4 (Juli 2018): 1353–83. http://dx.doi.org/10.1051/m2an/2017007.

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This paper is devoted to the study of the nonconservative bitemperature Euler system. We firstly introduce an underlying two species kinetic model coupled with the Poisson equation. The bitemperature Euler system is then established from this kinetic model according to an hydrodynamic limit. A dissipative entropy is proved to exist and a solution is defined to be admissible if it satisfies the related dissipation property. Next, four different numerical methods are presented. Firstly, the kinetic model gives rise to kinetic schemes for the fluid system. The second approach belongs to the family of the discrete BGK schemes introduced by Aregba–Driollet and Natalini. Finally, a quasi-linear relaxation approach and a Lagrange-remap scheme are considered.

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Hu, Lili, Xinyong Wang und Hongmin Li. „Distributed consensus of a class of networked nonlinear systems by non-uniform sampling with probabilistic transmission delays and its application to two-link manipulators“. Transactions of the Institute of Measurement and Control 40, Nr. 11 (30.05.2017): 3314–22. http://dx.doi.org/10.1177/0142331217707368.

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This paper investigates the primary problem of distributed consensus for Euler–Lagrange systems networked by using non-uniform sampling information with probabilistic transmission delay. In a real-world application, the information is likely to be exchanged in a discrete-time interval manner. Employing sampled-data information can save the energy cost and reduce the communication network burden. For the reasons given above, sampling control is applied in this paper. Meanwhile, we focus on the study of non-uniform sampling information exchanges in the communication network which is described in this paper. In order to verify the distributed consensus of Euler–Lagrange systems, matrix theory, algebraic graph theory and Lyapunov stability theory are applied. A distinctive feature of this paper is that the transmission delay is defined as the probability of time-varying delay. A numerical simulation is given to demonstrate the benefits and effectiveness of the proposed schemes.

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Szabo, Peter, und Ole Hassager. „Simulation of free surfaces in 3-D with the arbitrary Lagrange-Euler method“. International Journal for Numerical Methods in Engineering 38, Nr. 5 (15.03.1995): 717–34. http://dx.doi.org/10.1002/nme.1620380502.

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Zine, Houssine, und Delfim F. M. Torres. „A Stochastic Fractional Calculus with Applications to Variational Principles“. Fractal and Fractional 4, Nr. 3 (01.08.2020): 38. http://dx.doi.org/10.3390/fractalfract4030038.

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We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler–Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.

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Dong, Gui Yang, Ye Fa Tan, Hong Wei Li, Chun Hua Zhou, Wei Gang Wang und Xiang Hong. „Numerical Simulation of Gas-Solid Two-Phase Flow in Air Pre-Cleaner Based on CFD“. Advanced Materials Research 834-836 (Oktober 2013): 1423–27. http://dx.doi.org/10.4028/www.scientific.net/amr.834-836.1423.

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Computational grids of the complex internal flow passage in air pre-filter were generated, using the partitioned mixed grids. Based on the method of user-defined functions controlling sliding mesh, a program of defining moving boundary was proposed, and numerical simulation of the rotor movement transient controlled by the flow field of air pre-filter was achieved. Based on the theory of Euler-Lagrange phase flows, stochastic particle trajectory model and cell source method were adopted to calculate the trajectories and concentration distributions of particle phase in air pre-filter.

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Fu, Tao, Yun-Ting Tsai und Qiang Zhou. „Numerical Simulation of Magnesium Dust Dispersion and Explosion in 20 L Apparatus via an Euler–Lagrange Method“. Energies 15, Nr. 2 (06.01.2022): 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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Xu, Hong, Hua Dong Yang und Guang Ru Hua. „The Effect of Inlet Conditions on Particle Deposition in Axial Flow Compressor“. Advanced Materials Research 915-916 (April 2014): 1066–69. http://dx.doi.org/10.4028/www.scientific.net/amr.915-916.1066.

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Axial flow compressor is an important component, so the compressor performance is of crucial. Fouling changes blade geometry and blade surface roughness is increased, thus aerodynamic performance is affected. The flow of gas phase and gas-solid coupling phase are implemented to reveal the effect of inlet condition on particle deposition. Based on Euler-Lagrange model, this paper made numerical simulation of gas-solid two phase flow in the axial flow compressor rotor cascade. Simulation result shows that the increase of inlet temperature can result in the reduction of particle volume fraction. And particle mass concentration is affected by particle mass flow rate.

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Cheng, Lei, Shui Sheng Xie, You Feng He, Guo Jie Huang und Yao Fu. „Finite Volume Simulation in Porthole Dies Extrusion of Aluminum Profiles“. Advanced Materials Research 291-294 (Juli 2011): 290–96. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.290.

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FEM simulation of aluminum profiles in porthole die extrusion process using Lagrange mesh description will inevitably bring mesh self-contact, severe grid distortion and frequent remeshing, which will result in the loss of computational accuracy and excessive calculation time. In order to solve the above mentioned problems, numerical simulation of aluminum profiles with large and complicated cross-section in extrusion process was achieved using finite volume method based on Euler mesh description. The metal flow behavior and welding course was investigated in detail, which can provide the theoretical guide for porthole die design and optimization. In addition, extrusion experiment was carried out by numerical simulation results. The experimental extrudate was in good agreement with the simulation results, which laid a good solid foundation for non-steady state extrusion process analysis of large scale and complicated cross-section profiles.

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Chen, Shiming, Yan Chen, Zhaojie Wu, Junze Jiang, Jiang Li und Weixing Hua. „A Hybrid Euler–Lagrange Model for the Paint Atomization Process of Air Spraying“. Processes 10, Nr. 12 (26.11.2022): 2513. http://dx.doi.org/10.3390/pr10122513.

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The modeling of the paint atomization process is a barrier in computational fluid dynamics numerical simulation for the whole process of air spraying, and seriously restricts robot intelligent spray gun trajectory planning and the improvement of coating quality. Consequently, a multi-scale paint atomization model based on the hybrid Euler–Lagrange method was established in this paper, which included a large liquid micelle motion model, a particle motion model, and a turbulence flow model. The Euler method was adopted to capture the gas–liquid interface in the atomization flow field to describe the deformation and motion of large liquid micelles. The identification and transformation mechanisms of large liquid micelles and small particles were constructed by the particle motion model, and the motion of small droplets generated by paint atomization was tracked by the Lagrange method. The turbulence motion of the fluid in the process of paint atomization was described by a two-equation turbulence model. The model calculation method consisting of a finite-volume model, an adaptive hexcore mesh technique and a pressure-based coupled algorithm was established. The multi-scale atomization model was solved and model validation was carried out, which included mesh independence verification and model reliability analysis. The numerical simulation results predicted the atomization flow field parameters, paint atomization shapes, and the changing process from paint to liquid droplets, which was consistent with the experimental data. As a result, the established multi-scale atomization model in this paper is reliable for studying the paint atomization process of air spraying.

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Aquelet, Nicolas, und Benjamin Tutt. „Euler-Lagrange coupling for porous parachute canopy analysis“. International Journal of Multiphysics 1, Nr. 1 (Januar 2007): 53–68. http://dx.doi.org/10.1260/175095407780130517.

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33

Kato, Masayuki. „Numerical Simulation on Electromagnetic Energy Harvester Oscillated by Speed Ripple of AC Motors“. Energies 16, Nr. 2 (13.01.2023): 940. http://dx.doi.org/10.3390/en16020940.

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The suppression of torque ripples in an interior permanent magnet synchronous motor (IPMSM) is essential to improve its efficiency and responsiveness. Here, we report on the development of an electromagnetic energy harvester incorporated into an IPMSM to suppress its torque ripples. The proposed harvester is driven to oscillations by the speed ripple of the AC motor. We derived the motion and circuit equations for the motor and the harvester according to Euler–Lagrange equations. We discussed the principle of electrical power generation and used MATLAB/Simulink numerical simulations to investigate the dynamic behavior of the proposed harvester. Our findings revealed that the active Coriolis force unnecessarily reduces the motor’s original torque, leading to unsuccessful power generation. Nevertheless, our results demonstrated that the reactive Coriolis force successfully suppresses the motor torque ripple.

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Xue, Hai Feng, Xiong Chen, Yong Ping Wang und Ya Zheng. „Numerical Simulation of Two-Phase Flow under High Acceleration in SRM with Submerged Nozzle“. Advanced Materials Research 712-715 (Juni 2013): 1253–58. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.1253.

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The two-dimension axisymmetric and two-phase flow in a full-size solid rocket motor with submerged nozzle under high acceleration condition has been simulated with Euler-Lagrange model. Without acceleration and under high axial acceleration on particle trajectories, the influences of different particle diameters were analyzed. The difference between gas flow field and two-phase flow field is significant. The particle accumulation zone above the inner wall of chamber and nozzle is mainly concentrated in two regions. The axial acceleration will intensify the impaction to the end of the chamber. The accretion of the particle phase diameter will increase the inertia of the particle phase, which may cause the following property worse, and the particles can easily form a highly-concentrated aggregation flow.

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Rosales, Claudio, Daniel Gandolfo, Gustavo Scaglia, Mario Jordan und Ricardo Carelli. „Trajectory tracking of a mini four-rotor helicopter in dynamic environments - a linear algebra approach“. Robotica 33, Nr. 08 (25.04.2014): 1628–52. http://dx.doi.org/10.1017/s0263574714000952.

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SUMMARYThis paper presents the design of a controller that allows a four-rotor helicopter to track a desired trajectory in 3D space. To this aim, a dynamic model obtained from Euler-Lagrange equations describes the robot. This model is represented by numerical methods, with which the control actions for the operation of the system are obtained. The proposed controller is simple and presents good performance in face of uncertainties in the model of the system to be controlled. Zero-convergence proof is included, and simulation results show a good performance of the control system.

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ARAKI, Koji, Katsuteru HASHIMOTO, Tomio OKAWA, Kenji YOSHIDA, Tadayoshi MATSUMOTO und Isao KATAOKA. „626 Development of Numerical Simulation Method of Dispersed Two-Phase Flow Using a Euler-Lagrange Model“. Proceedings of Conference of Kansai Branch 2000.75 (2000): _6–51_—_6–52_. http://dx.doi.org/10.1299/jsmekansai.2000.75._6-51_.

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37

Sun, Longquan, Duliang Wang, Yingyu Chen und Guoxun Wu. „Numerical and experimental investigation on the oblique water entry of cylinder“. Science Progress 103, Nr. 3 (Juli 2020): 003685042094088. http://dx.doi.org/10.1177/0036850420940889.

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The study of water entry cavity and the analysis of load characteristics are hot topics in water entry research. The coupled Euler–Lagrange method is used to carry out simulation research on the water entry process of a cylinder. Aiming at the water vapor mixing phenomenon caused by structure slamming on the water at the initial time of water entry, the slamming load is further studied by correcting the sound speed in the water. The differences between the calculated results obtained by adjusting the number of units in the numerical simulation prove the convergence of the numerical method. Water entry experiments of a cylinder were carried out, and the results are in good agreement with the simulation data. The motion state simulation and analysis are carried out for the process of water entry with different initial speeds and angles. The changes in the structure’s positions, air cavities, and slamming loads are obtained. The rule of slamming pressure with the water entry angle and the relationship between pressure and acceleration are determined.

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Xia, Tian Xiang, Tong Zhao, Liang Zou, Li Zhang und Feng Zhu. „Research on Two-Dimensional MHD Simulations of X-Pinch Implosion and its Physical Aspects“. Applied Mechanics and Materials 525 (Februar 2014): 316–19. http://dx.doi.org/10.4028/www.scientific.net/amm.525.316.

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Based on a large quantity of experimental work and study of the two-dimensional MHD (Magnetohydrodynamic) simulation describing the implosion dynamics of X-pinch, at the same time taking basic physical processes of implosion into account, this paper seeks to build a two-dimensional MHD simulation model on implosion dynamics throughout the whole constriction evolution (including formation of dense plasma, compression, generation of hot spot, X-ray pulsed radiation), determine the target area for numerical simulation, as well as the initial time for simulation and plasma initial state. As for two-dimensional MHD models which indicate the physical process during different stages, a clear boundary condition is explored along with Lagrange-Euler numerical method which strives to reproduce the dynamics of the X-pinch implosion and better study the physical properties during the X-pinch implosion dynamics. Results of this thesis will enrich the X-pinch research areas of basic theories and analytical methods, which is of great theoretical significance and application value.

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Knížat, Branislav, Matej Vach, Marek Mlkvik, Peter Mlynár, František Világi, Róbert Olšiak und František Urban. „Numerical and Experimental Study of a Large-Scale Natural Circulation Helium Loop“. Applied Sciences 13, Nr. 5 (22.02.2023): 2826. http://dx.doi.org/10.3390/app13052826.

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This paper deals with the one-dimensional unsteady fluid flow model of a natural circulation loop. The governing equations are solved according to both the Euler and Lagrange approaches on two parallel computational grids. The linearization of equations and a semi-implicit discretization scheme are used to enhance the algorithm’s effectiveness. The results of the simulations were verified by using experimental data obtained on an experimental rig that was a scale model of an emergency system for the removal of residual heat after reactor shutdown. The parameters compared were the helium temperature at two locations and the heater outlet pressure. The simulation results generally did not differ from the experimental data by more than 10%. The best agreement was obtained for scenarios in which the helium pressure was highest in combination with slow changes in the input parameters (less than 4%). Conversely, the results differed the most for the scenario with extremely fast device cooling (20%).

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Ouafik, Youssef. „Modelling and simulation of a dynamic contact problem in thermo-piezoelectricity“. Engineering and Applied Science Letters 4, Nr. 2 (29.06.2021): 43–52. http://dx.doi.org/10.30538/psrp-easl2021.0069.

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In this work, we numerically study a dynamic frictional contact problem between a thermo-piezoelectric body and a conductive foundation. The linear thermo-electro-elastic constitutive law is employed to model the thermo-piezoelectric material. The contact is modelled by the Signorini condition and the friction by the Coulomb law. A frictional heat generation and heat transfer across the contact surface are assumed. The heat exchange coefficient is assumed to depend on contact pressure. Hybrid formulation is introduced, it is a coupled system for the displacement field, the electric potential, the temperature and two Lagrange multipliers. The discrete scheme of the coupled system is introduced based on a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivate. The thermo-mechanical contact is treated by using an augmented Lagrangian approach. A solution algorithm is discussed and implemented. Numerical simulation results are reported, illustrating the mechanical behavior related to the contact condition.

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Zeng, Peigao, Yi Jiang, Lina Yang, Ying Yang und Song Yan. „Influence of Different Altitudes on the Solid Rocket Contrail Formation in the Near Field“. International Journal of Aerospace Engineering 2023 (19.06.2023): 1–13. http://dx.doi.org/10.1155/2023/6577249.

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Detecting the infrared characteristics of the contrails is a reasonable approach to tracing the rocket, and the particle properties of the contrails are the basis of the infrared analysis. The conventional numerical approach to obtaining the particle properties is a Euler/Lagrange method or a simple Euler/Euler method, difficultly obtaining more accurate results because it ignores the particle size distribution in parcels or cells. A modified Euler/Euler method is applied to simulate the contrail formation in the near field of a solid rocket motor at different altitudes, which considers the size distribution by adding the first- to second-order particle radius moments based on the simple Euler/Euler method. The simulation results show that the crystals are generated at altitudes from 10 km to 20 km and that the contrails are visible at altitudes from 10 km to 15 km, where the radii of the crystals are from 0.1 μm to 0.3 μm. The visible contrails indicate that aviation vehicles are cruising at altitudes from 10 km to 15 km, and the smaller crystals indicate that the contrails are generated by rockets, not aircraft. Our work can provide important insight for the follow-up infrared analysis of the contrails based on the obtained particle radii.

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Hao, Dong, und Jing Yu. „Structural response characteristics of TMA during water-entry procedure“. Journal of Physics: Conference Series 2585, Nr. 1 (01.08.2023): 012003. http://dx.doi.org/10.1088/1742-6596/2585/1/012003.

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Abstract This work presents a comprehensive numerical investigation of the structural responses of the Trans-Medium Aircrafts (TMA) during a water-entry event and the max mises-stress, the acceleration, and the water-entry deepness are analyzed and discussed. The simulating finite element model of the elastic field and the fluid field are imitated and solved by the coupled euler lagrange (CEL) method. The water-entry velocity is set from 0 m/s to 8 m/s. From the results, the max mises-stress is about 24 MPa and the max acceleration of all simulation conditions is 110000 m/s2. Considering the elastic effect of the TMA structure, the current research is of great importance to the TMA’s structural design scheme.

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Chen, Xiong, Hai Feng Xue und Yong Luo. „Numerical Research about Two-Phase Flow under Different Acceleration in SRM with Embedded Nozzle“. Applied Mechanics and Materials 365-366 (August 2013): 233–36. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.233.

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The complex gas-solid two-phase flow in a full-sized solid rocket motor with embedded nozzle under different acceleration condition was simulated with Euler-Lagrange model. Influences of different particle diameters and acceleration conditions on particle trajectories were analyzed. Simulation results show that the difference between gas flow field and two-phase flow field is significant. The particle accumulation zone above inner wall of chamber and nozzle is mainly concentrated in two regions. The accretion of the particle diameter will cause the following property worse, and the particles can easily form a highly-concentrated aggregation flow. With the increasing of axial-acceleration, the impact point in line2 will move backward in rear head.

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Surianinov, M. G., S. Jgalli und Al Echcheikh El Alaoui Douaa. „NUMERICAL MODELING OF THE DISTRIBUTION OF SNOW LOAD ON A HYPERBOLIC PARABOLOID. THEORETICAL BASIS“. Bulletin of Odessa State Academy of Civil Engineering and Architecture, Nr. 85 (28.12.2021): 43–51. http://dx.doi.org/10.31650/2415-377x-2021-85-43-51.

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Abstract. The paper discusses the choice of a method for studying the distribution of snow loads on a biconcave roof of a hyperbolic paraboloid and its theoretical justification. It is noted that the numerical modeling of the aerodynamic characteristics of buildings and structures is a difficult and resource-intensive task due to the design features of building objects, which, as a rule, have a complex geometric shape, as well as due to a complex unsteady flow resulting from their flow around them. In addition, the task becomes more complicated due to the interference of vortex structures between different objects. Overcoming these objective difficulties became possible with the advent of modern specialized software systems, primarily ANSYS Fluent. Opportunities have appeared for accurate modeling with verification of the results obtained, which implies the use of an effective, well-tested mathematical apparatus. To implement the theory of two-phase flow, two methods based on numerical modeling are mainly used: the Euler-Lagrange method and the Euler-Euler method. The second method is used in the work. Comparative analysis, which investigates two-phase flow around different structures using different turbulence models (including RSM model, SST k-ω model, k-ε model and k-kl-ω model), shows that the k-kl-ω model is the best fit with experiment. ANSYS Fluent supports four multiphase models, i.e. VOF model, Mixture model, Wet Steam and Euler model. Compared to the other three models, the Mixture model provides better stability and lower computational costs, while the Euler model provides better accuracy, but at a higher computational cost . With a rather complex geometry and flow conditions, the use of the RANS approach does not lead to reliable simulation results. Moreover, unsteady turbulent flows cannot be reproduced. In real situations, landslides, saltations, and the suspended state of snow particles are closely related to the real effects of microbursts and bursts present at the surface of the boundary layer. Therefore, in further research, it is advisable to apply alternative approaches to RANS, which include Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and the hybrid RANS-LES approach to turbulence modeling, which combine efficiency LES techniques in tear-off free zones and the cost-effectiveness of RANS in near-wall areas.

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Yaguchi, Takaharu. „Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations“. ESAIM: Mathematical Modelling and Numerical Analysis 47, Nr. 5 (01.08.2013): 1493–513. http://dx.doi.org/10.1051/m2an/2013080.

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46

Liang, Zhen-gang, Bai-xu Chen, Yu-xiang Nan, Jian-wei Jiang und Li Ding. „Research on the computing method for the forming velocity of circumferential multiple explosive formed projectiles“. Journal of Defense Modeling and Simulation: Applications, Methodology, Technology 17, Nr. 2 (26.02.2019): 125–36. http://dx.doi.org/10.1177/1548512919833187.

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To evaluate the damage capability of circumferential multiple explosive formed projectiles (MEFPs), it is required to predict the EFP forming velocity accurately and quickly. According to the circumferential MEFP liner characteristics of uniform circumferential distribution and layered axial structure, a simplified physical model of circumferential MEFPs is put forward innovatively. The Lagrange and Euler coupling algorithm is selected to simulate the simulation model, which is verified as equivalent to the circumferential MEFPs. Based on the energy conservation principle and the simplified equivalent physical model, the calculating model of the circumferential MEFP forming velocity is derived. The correctness and accuracy of the calculation model are verified by using the numerical simulation software and the test device of the round-shaped charge model.

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Ding, Zhi Ying, Zhi Ying Zhang und Jun Fu. „Numerical Simulation and Experimental Research of Blade Erosion in Particulate Gas Turbine“. Advanced Materials Research 1006-1007 (August 2014): 188–92. http://dx.doi.org/10.4028/www.scientific.net/amr.1006-1007.188.

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Euler-Lagrange method is adopted to simulate 3-D viscous turbulent flow field of a one-stage gas turbine. Gas-solid two-way coupling is realized to analyze the trajectories and slip of 1000 beam particles, with diameter 5~50μm, then calculate the mass erosion rate based on the impact velocity and attack angles. Simulation exhibits: erosion wear is mainly caused by impact of larger particles (>10μm), erosion areas are mainly concentrated on the roots of pressure surface entrance of static blade and on the rear pressure surface of rotor blade. Comparing experiments are conducted between the substrate of X20Cr13 and the specimen with steel-bead injection. Experiment indicates: the attack angle corresponding to the maximal mass loss for substrate is about 40°, while the steal-bead injection is about 50°. Within the scope of the attack angle 20°~80°, the mass loss of the reinforced specimen is obviously less than that of the substrate, and under other angles of attack, the two kinds of material’s erosion tolerance are close to each other.

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MUNNIER, ALEXANDRE, und BRUNO PINÇON. „LOCOMOTION OF ARTICULATED BODIES IN AN IDEAL FLUID: 2D MODEL WITH BUOYANCY, CIRCULATION AND COLLISIONS“. Mathematical Models and Methods in Applied Sciences 20, Nr. 10 (Oktober 2010): 1899–940. http://dx.doi.org/10.1142/s0218202510004829.

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Articulated solid bodies (ASB) is a basic model for the study of shape-changing underwater vehicles made of rigid parts linked together by pivoting joints. In this paper we study the locomotion of such swimming mechanisms in an ideal fluid. Our study ranges over a wide class of problems: several ASBs can be involved (without being hydrodynamically decoupled), the fluid-bodies system can be partially or totally confined and fluid circulation, buoyancy force and possible collisions between bodies are taken into account. We derive the Euler–Lagrange equation governing the dynamics of the system, study its well-posedness and describe a numerical scheme implemented in a Matlab toolbox (Biohydrodynamics Toolbox).

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Zhang, Tingting, Junlian Yin und Dezhong Wang. „Numerical simulation of bubble separation length in a gas–liquid separator based on the Euler–Lagrange method“. Journal of Mechanical Science and Technology 31, Nr. 11 (November 2017): 5123–29. http://dx.doi.org/10.1007/s12206-017-1006-3.

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50

Jiang, Xiaolong, Xiaoyong Bai, Zanfu Yang und Shuo Ma. „Synchronization Tracking Of Uncertain Nonidentical Multi-USV system“. Journal of Physics: Conference Series 2283, Nr. 1 (01.06.2022): 012003. http://dx.doi.org/10.1088/1742-6596/2283/1/012003.

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Abstract We propose a distributed adaptive synchronous tracking control algorithm for the heterogeneous multi-unmanned surface vehicles described by the Euler-Lagrange system. In multi-unmanned surface vehicles system, the inter-communication state can be represented by a directed topology graph, and only part of unmanned surface vehicles can directly acquire the accurate information of time-varying reference trajectory. The proposed algorithm can implement synchronous tracking for multiple unmanned surface vehicles without knowing global communication information by elaborately selecting Lyapunov functions. We conduct theoretical analysis of the stability of closed-loop systems according to the Lyapunov stability theory. And we also verify the effectiveness of proposed scheme through numerical simulation.

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