Lagrangian Coordinate System Research Articles

Technological features of hail suppression activities in the Republic of Moldova

Modern components of the technology ofhail suppression activities in the Republic ofMoldova are considered. The following elements of this technology are implemented: ASU-MRL software- and-hardware complexes; the corporate information network for cloud data acquisition and transmission based on the ASU-MRL data; Alazan’-6 and Loza-2 anti-hail complexes equipped with highly ac-ive crys-al-iz-ng components based on silver iodide; the guidance papers by the special-sts of the Special Weather Modification Service of the Republic of Moldova including those on the presentation of the radar echo of the horizontal cross-sections of clouds in the Lagrangian coordinate system; the improved methodology ofhail suppression activities.

Effect of particle diameter and injection position on the separation performance of cyclone separators

Effects of the particle diameter and particle injection position on the gas–solid two-phase flow have important implications in the tangential inlet cyclone separator. The Navier–Stokes equation coupled with the Reynolds stress model in Euler coordinate system is adopted to describe the gas flow and the discrete phase model in Lagrange coordinate system is used to calculate the particle trajectories. Results show that the separation efficiency varies with the injection position at the inlet cross-section. It is found that the separation efficiency is increased with the increase of the particle diameter. However, when the particle diameter exceeds a critical size, the particles will deposit on the wall of the conical chamber, which leads to lower separation efficiency. The present simulation indicates that the critical size is 24 [Formula: see text].

Numerical sloshing simulations: Comparison between lagrangian and lumped mass models applied to two compartments with mass transfer

In the present paper, 2D numerical simulation of sloshing waves coupled to the flooding flow between two compartments is carried out employing lumped mass and Lagrangian methods. The first method used is a Lumped Mass method with a moving free surface (LM), which is based on the motion equations for the gravity centre of mass within a compartment. In this method, the free surface is modelled as a planar surface, with limited degrees of freedom. The second one is the so-called Moving Particle Semi-Implicit (MPS) method, a robust method based on particle interactions in a Lagrangian coordinate system. Sloshing simulations are performed within a closed domain, in which the free surface is modelled as a deformable surface for a single-phase flow. An improved boundary wall condition scheme is applied. By applying these two methods the hydrodynamic features of the sloshing flow under sway and roll motion and several water levels are investigated. The excitation frequencies are set near the natural wave frequencies. Furthermore, the complexity added to the sloshing wave by the flow exchange passing through an opening are reported, taking into account two opening configurations. The numerical results are validated by corresponding experimental data. Comparison of the numerical results against the experimental data shows, in general, good agreement. Two main stages of accuracy levels are observed for lower and higher frequencies. At the first stage, the Lumped Mass and the Moving Particle Semi-Implicit methods present similar results, whereas at the last stage the MPS model is seen to be more suitable for the sloshing simulations, in which wave breaking is the dominant phenomenon.

GEOMETRICALLY NONLINEAR FINITE ELEMENT ANALYSIS OF ARBITRARY THIN PLATES

Many plate structures used especially in naval and aerospace applications undergo deflections that are not small in comparison to the thickness of the plate, but they are still small compared to other dimensions of the plate, so analysis must include the effects of the large displacements on the structures. This report developed an elegant finite element formulation for analyzing the geometrically nonlinear static behavior of arbitrary-shaped thin plates. An arbitrary planform of a whole plate was mapped into a square domain where a cubic serendipity shape function represented the arbitrary geometry. An ACM plate-bending element along with the inplane deformations was considered for the displacement function. The nonlinear formulation was done in the total Lagrangian coordinate system using [N]-notation, and the nonlinear governing equations were solved by Newton Raphson iterative method. It was found that the element was capable of accommodating different geometries just like isoparametric element. The efficacy of the element was shown by comparing the deflections and stresses at critical points of the plates of square, skewed, and circular geometries with previously published results.

The Lagrangian coordinate system and what it means for two-dimensional crowd flow models

A continuum crowd flow model is solved using the Lagrangian coordinate system. The system has proven to give computational advantages over the traditional Eulerian coordinate system for (one-dimensional) road traffic flow. Our extension of the model and simulation method to (two-dimensional) crowd flow paves the way to explore the advantages for crowd flow simulation. Detailed analysis of the advantages is left for future research. However, this paper provides a first exploration and shows that a model and simulation method for two-dimensional crowd flow can be developed using Lagrangian numerical techniques and that it leads to accurate simulation results.

Research on the Close-In Flow Field Characteristics of Spherical TNT Charge Bursting in Real Air

In order to describe the close-in flow field characteristics and the propagation of shock wave of spherical TNT charge bursting in real air, the special features of air under high temperature and high pressure are taken into account and a complete set of dimensionless hydrodynamic equations in Lagrangian distance coordinate system is established by using the state equations of real air. After that, a set of transformed hydrodynamic equations in shock moving coordinates is employed to simplify the numerical calculation. Combining the artificial viscosity technique and shock fitting technique, a method for calculating the whole flow field of TNT bursting in real air is developed. As an example, the calculation results are in good agreement with the existing literature, and experiments data shows that the theory established in this paper is suitable for describing the close-in characteristics and calculating shock wave propagation in distance region of TNT charge bursting in real air.

Studying the separation of particles in a turbulent vortex flow

This work deals with modeling the aerodynamics of a two-phase vortex turbulent flow in the separation chamber of a pneumatic centrifugal classifier. The velocity field of a gas-phase vortex turbulent flow is determined based on Reynolds equations closed with the Wilcox two-parametric turbulence model. The motion of a finely dispersed solid phase is modeled by calculating the trajectories of individual particles in the Lagrangian coordinate system with allowance for inertial, centrifugal, gravitational, and aerodynamic forces. The effect of the turbulent diffusion of particles due to the pulsating motion of a gas phase is predicted based on a semi-empirical probabilistic model. As shown by numerical calculations, the allowance for this phenomenon has a considerable effect on the separation of particles. The reliability of obtained results is confirmed by test studies and the comparison of numerical calculations with known experimental data. The effect of regime parameters on the aerodynamics and separation of finely dispersed particles in a pneumatic centrifugal classifier is also analyzed.

Numerical simulation of surface acoustic wave actuated enantiomer separation by the finite element immersed boundary method

Enantiomers are chiral objects such as chemical molecules that can be distinguished by their handedness. They typically occur as racemic compounds of left- and right-handed species which may have completely different properties. Therefore, in applications such as drug design in pharmacology, enantiomer separation is an important issue. Here, we present a new technology for enantiomer separation by surface acoustic wave generated vorticity patterns consisting of pairwise counter-rotating vortices in a carrier fluid. The enantiomers are injected onto the surface of the fluid between two counter-rotating vortices such that right-handed (left-handed) enantiomers get attracted by left-rotating (right-rotating) vortices. In particular, we are concerned with the numerical simulation of this separation process by an application of the finite element immersed boundary method which relies on the solution of a coupled system consisting of the incompressible Navier–Stokes equations and the equations of motion of the immersed enantiomers described with respect to an Eulerian and a Lagrangian coordinate system. For a model system of deformable, initially L-shaped enantiomers the results of the numerical simulations reveal a perfect separation.

A CHARACTERIZATION ON BREAKDOWN OF SMOOTH SPHERICALLY SYMMETRIC SOLUTIONS OF THE ISENTROPIC SYSTEM OF COMPRESSIBLE NAVIER–STOKES EQUATIONS

We study an initial boundary value problem on a ball for the isentropic system of compressible Navier--Stokes equations, in particular, a criterion of breakdown of the classical solution. For smooth initial data away from vacuum, it is proved that the classical solution which is spherically symmetric loses its regularity in a finite time if and only if the concentration of mass forms around the center in Lagrangian coordinate system. In other words, in Euler coordinate system, either the density concentrates or vanishes around the center. For the latter case, one possible situation is that a vacuum ball appears around the center and the density may concentrate on the boundary of the vacuum ball simultaneously.

Vehicle Specific Behaviour in Macroscopic Traffic Modelling through Stochastic Advection Invariant

In this contribution a new model to include stochastic vehicle specific behaviour and interaction in traffic flow modelling is presented. The First Order Model with Stochastic Advection (FOMSA) is presented as a first order macroscopic kinematic wave model in a platoon-based Lagrangian coordinate system. The use of Lagrangian coordinates allows characteristics of specific vehicles or vehicle-groups to propagate along with the traffic flow using a vehicle specific invariant. The invariant reflects how vehicle or platoon specific characteristics propagate with the vehicles and influence the local behaviour of a vehicle or platoon on a macroscopic level and in interaction with other surrounding vehicles. It represents a local vehicle specific adjustment to the critical density and makes use of two parameters: a stochastic boundary parameter and a transition parameter. These parameters indicate the extent of differences between vehicles or platoons. A case study is also presented in which a demonstration of the model is given and the face validity and sensitivity of the parameters are shown. Previously, similar approaches have made use of second order model descriptions. The formulation of this model as a first order model makes use of the advantages of first order models and also applies the improved accuracy of Lagrangian coordinates over the Eulerian coordinate system in time-stepping.

Growth of a spherical micro-void in an infinite elastoplastic body under thermal load

The growth of preexisting spherical micro-void in an infinite elastoplastic body under thermal load is analyzed. Based on the geometrical nonlinearity with large deformation and the yield criterion of perfect plasticity, a mathematical model of the problem is presented. The Lagrangian and Euler coordinate systems are introduced to describe the thermal expansion deformation. By the elastoplastic analysis, the distributions of the stresses near the cavity are obtained. When the initial radius of a preexisting micro-void tends to be infinitely small, the critical temperature of cavitation can be calculated. The instability of the micro-void inside the infinite body is discussed. The results of numeric computation indicate that the radius of the cavity and the radius of the plastic zone would rapidly grow when the remote temperature increases and approaches the critical temperature.

Numerical computation of periodic responses of nonlinear large-scale systems by shooting method

Geometrically nonlinear vibrations of three-dimensional elastic structures, due to harmonic external excitations, are investigated in the frequency domain. The material of the structure is assumed to be linearly elastic. The equation of motion is derived by the conservation of linear momentum in Lagrangian coordinate system and it is discretized into a system of ordinary differential equations by the finite element method. The shooting method is used, to obtain the periodic solutions. A procedure which transforms the initial value problem into a two point boundary value problem, for the periodicity condition, and then it finds the initial conditions which lead to periodic response, is developed and presented, for systems of second order ordinary differential equations. The Elmer software is used for computing the local and global mass and stiffness matrices and the force vector, as well for computing the correction of the initial conditions by the shooting method. Stability of the solutions is studied by the Floquet theory. Sequential continuation method is used to define the prediction for the next point from the frequency response diagram. The main goal of the current work is to investigate and present the potential of the proposed numerical methods for the efficient computation of the frequency response functions of large-scale nonlinear systems, which often result from space discretization of real life engineering applications.

Unsteady flows with a constant total pressure, described by the equations of ideal magnetohydrodynamics

Exact solutions of the equations of ideal magnetohydrodynamics describing the class of unsteady flows of an electrically conducting fluid with a constant total pressure are constructed. The solutions are written in the Lagrange coordinate system; arbitrariness in its choice was used to parameterize magnetic field lines. The wide functional arbitrariness the solutions provide a significant variation in the picture of the described fluid motions. An example of unsteady flow of an ideal electrically conducting fluid in a cylindrical channel with fixed magnetic tubes is given.

Linking hydrophobicity and hydrodynamics by the hybrid fluctuating hydrodynamics and molecular dynamics methodologies

The development of a hybrid fluctuating hydrodynamics (FHD) and molecular dynamics (MD) simulation method that combines the molecular dynamics of moving particles with the fluctuating hydrodynamics of solvent fields on Eulerian grid cells is presented. This method allows resolution of solute-solvent interfaces and realization of excluded volumes of particles in the presence of hydrodynamic coupling. With these capabilities, we show that the ubiquitous forces mediated by the solvent, hydrophobicity and hydrodynamics, can be linked in a mesoscopic simulation. The strategies we devise to overcome the numerical issues of mixing variables in the Eulerian and Lagrangian coordinate systems, i.e., using a pair of auxiliary fluids to realize the excluded volumes of particles and assigning collocating gridding systems on solutes to interface with solvent fields, are also presented. Simulation results show that the hybrid FHD and MD method can reproduce the solvation free energies and scaling laws of particles dynamics for hydrophobes of different sizes. The collapse of two hydrophobic particles was also simulated to illustrate that the hybrid FHD and MD method has the potential to be generally applied to study nanoscale self-assembly and dynamics-structure-function relationships of biomolecules.

Forecast of convective storms evolution based on the analysis of their radar echo and wind hodograph in the troposphere in the moving coordinate system

Generalized are the results of the research carried out by the Special Service for Weather Modification of the Republic of Moldova and of the features of formation and evolution of cumulonimbus clouds Cb based on studying their radar echo in the Lagrange (moving) coordinate system. Besides the regularities proceeding from the ideas about the evolution of Cb on the sides of atmospheric mesoscale structures [16], the features of evolution of powerful Cb are revealed at the significant wind shear. The direction and evolution features of Cb can be predicted using the wind hodograph in the troposphere plotted in the moving coordinate system. Results of the research are used in the Special Service for Weather Modification of the Republic of Moldova during the operational activities on hail suppression for predicting the areas of formation of new convective cells and for optimizing the size of the areas for their seeding with the crystallizing reagent.

Design of resonant frequencies of the piezoelectric actuator with integrated components

The piezoelectric actuators have been applied to various electrical devices such as piezoelectric speakers, buzzers, haptics, and ultrasonic transducers. The improvement of the electromechanical conversion efficiency is the most important issue of piezoelectric actuator systems in mobile devices. The electrical power consumption of actuators must be suppressed as possible, due to mobile devices having small batteries. The frequency response around the mechanical resonance should be carefully designed for low power consumption driving. The resonant frequencies of the piezoelectric actuators consist of integrated components, for example, metal corns of ultrasonic speakers, are decided by the energy dispersion of the total system. Therefore, design factors such as sizes and physical properties of each component, are necessary to optimize the resonant frequencies for practical applications. The total energy of the piezoelectric system is described by Lagrange-Maxwell equation. Even though it is not easy to solve the differential equations written in the Lagrangian coordinate system by the exact calculation, useful information for design of the system can be derived by the approximate calculation. In this paper, we will indicate the design guideline to optimize resonant frequencies of the piezoelectric actuators with integrated components, based on the analysis in the Lagrangian coordinate system.

Moving particle method for modeling wave interaction with porous structures

This paper presents a numerical model for simulating wave interaction with porous structures. Incompressible smoothed particle hydrodynamics in porous media (ISPHP) method is introduced in this study as a mesh free particle approach that is capable of efficiently tracking the large deformation of free surfaces in a Lagrangian coordinate system. The developed model solves two porous and pure fluid flows simultaneously by means of one equation that is equivalent to the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the extended Forchheimer equation for the flows inside the porous media. Interface boundary between pure fluid and porous media is effectively modeled by the SPH integration technique. A two-step semi-implicit scheme is also used to solve the fluid pressure satisfying the fluid incompressibility criterion.The developed ISPHP model is then validated via different experimental and numerical data. Fluid flow pattern through porous dam with different porosities is studied and regular wave attenuation over porous seabed is investigated. As a practical case, wave running up and overtopping on a caisson breakwater protected by a porous armor layer are modeled. The results show good agreements between numerical and laboratory data in terms of free surface displacement, overtopping rate and pressure distribution. Based on this study, ISPHP model is an efficient method for simulating the coastal applications with porous structures.

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose--Einstein condensates (BECs) in a rotational frame with or without long-range dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross--Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the two-dimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI.

Numerical Simulations of Combustion and Decomposition Processes in Precalciner with Two Different Heights of Raw Meal Inlets

To reduce energy consumption, numerical simulations of combustion and decomposition processes in a precalciner were carried out with two different heights of raw meal inlets. In Euler coordinate system the gas phase is expressed with k-ε two-equation model, in Lagrange coordinate system the solid phase is expressed with discrete phase model (DPM), the chemical reaction is expressed with species transport model, and the radiation is expressed with P1 radiation model. The results show that when the raw meal inlets are near the jetting coal pipes, there is much better dispersing condition of CaCO3 but a much poorer coal combustion condition, resulting in a much higher CaCO3 decomposition rate but a lower coal burn-off rate than that when the raw meal inlets are far away from the jetting coal pipes. It is advised to install both the two heights of raw meal inlets in order to obtain not only high CaCO3 decomposition rate but also high coal burn-off rate.

Phase-plane analysis of conserved higher-order traffic flow model

The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.