Numerical Simulation of Magnesium Dust Dispersion and Explosion in 20 L Apparatus via an Euler–Lagrange Method

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.

Design of a 3DOF XYZ Bi-Directional Motion Platform Based on Z-Shaped Flexure Hinges

This paper presents a design of a 3DOF XYZ bi-directional motion platform based on Z-shaped flexure hinges. In the presented platform, bridge-type mechanisms and Z-shaped flexure hinges are adopted to amplify its output displacement. Bi-direction motion along the X-axis and Y-axis follows the famous differential moving principle DMP, and the bi-directional motion along the Z-axis is realized by using the reverse arrangement of the Z-shaped flexure hinges along the X-axis and Y-axis. Statics analysis of the proposed platform is carried out by the energy method, compliance matrix method, and force balance principle. Meanwhile, the Lagrange method is used to analyze the dynamics of the platform. A series of simulations are conducted to demonstrate the effectiveness of the proposed design. The simulation results show that the average displacements of the platform in the XYZ-axis are ±125.58 μm, ±126.37 μm and ±568.45 μm, respectively.

Parallel transport and geodesics

The mathematics of parallel transport and of affine and metric geodesics is presented. The geodesic equation is obtained in several different ways, bringing out its role both as a geometric statement and as an equation of motion. The Euler-Lagrange method to find metric geodesics, and hence Christoffel symbols, is explained. The role of conserved quantities is discussed. Killing’s equation and Killing vectors are introduced. Fermi-Walker transport (the non-rotating freely falling cabin) is defined and discussed. Gravitational redshift is calculated, first in general and then in specific cases.

Numerical Simulation on Gas-Solid Two-Phase Flow in Horizontal Pneumatic Conveying Pipe Based on DPM Model

The determination of pipe deposition and optimum conveying velocity in pneumatic conveying has an important impact on conveying efficiency. The Euler-Lagrange method DPM model is used to analyse five different particle sizes and densities of small particles, and the flow pattern in the horizontal pipeline at different particle sizes and densities is derived from the graphs of the maximum discrete phase concentration, particle trajectory and discrete phase concentration distribution for each working condition. The simulation results show that the deposition increases with particle size and density, the optimum conveying speed increases with particle size and density, the larger the deposition, the larger the required conveying velocity. The velocity of 2 m/s can make the particles below 20μm suspended transport, the velocity of 4 m/s allows particles with a particle size of 30μm and a density of 1000 kg/m3 or less to be transported in suspension and 6 m/s allows particles with a density of 2000 kg/m3 or less to be transported in suspension. The aim is to provide a reference for the design of pneumatic conveying systems and the selection of the optimum conveying velocity.

Genetic Programming Based Identification of an Overhead Crane

Overhead cranes carry out an important function in the transportation of loads in industry. The ability to transport a payload quickly and accurately without excessive oscillations could reduce the chance of accidents as well as increase productivity. Accurate modelling of the crane system dynamics reduces the plant-model mismatch which could improve the performance of model-based controllers. In this work the simulation model to be identified is developed using the Euler-Lagrange method with friction. A 5-step ahead predictor, as well as a 10-step ahead predictor, are obtained using multi-gene genetic programming (MGGP) using input-output data. The weights of the genes are obtained by using least squares. The results of 15 different genetic programming runs are plotted on a complexity-mean square error graph with the Pareto optimal solutions shown.

Criteria ruling particle agglomeration

Most of the technically important properties of nanomaterials, such as superparamagnetism or luminescence, depend on the particle size. During synthesis and handling of nanoparticles, agglomeration may occur. Agglomeration of nanoparticles may be controlled by different mechanisms. During synthesis one observes agglomeration controlled by the geometry and electrical charges of the particles. Additionally, one may find agglomeration controlled by thermodynamic interaction of the particles in the direction of a minimum of the free enthalpy. In this context, one may observe mechanisms leading to a reduction of the surface energy or controlled by the van der Waals interaction. Additionally, the ensemble may arrange in the direction of a maximum of the entropy. Simulations based on Monte Carlo methods teach that, in case of any energetic interaction of the particles, the influence of the entropy is minor or even negligible. Complementary to the simulations, the extremum of the entropy was determined using the Lagrange method. Both approaches yielded identical result for the particle size distribution of an agglomerated ensemble, that is, an exponential function characterized by two parameters. In this context, it is important to realize that one has to take care of fluctuations of the entropy.

DEVELOPMENT OF THE COMPOSITION OF A COMPOSITE MATERIAL BASED ON THERMOREACTIVE BINDER ED-20

The aim of the study is to determine the effect of the type of structural modifier and filler on the structure formation and technological properties of potting composite polymeric materials (HCPM) and protective coatings for sheet and complex-configuration technological equipment, taking into account their rheological properties. Compositions of composite polymer materials based on a thermosetting binder of epoxy-diane resin ED-20 filled with a mineral filler - kaolin modified with gassipol resin (GS) - were developed using Newton's interpolation formula and the Lagrange method. The optimal amount of gossypol resin determined in the composition of the composite – in the amount of 6-10 mass., including in relation to sheet coverings and 8-12 wt. h. for parts of large-size complex-configuration technological equipment