Motion Of Continuum Research Articles

Specific Aspects of Modeling Gas Mixture Explosions in the Atmosphere

Aspects of mathematical and physical modeling of deflagration explosions emerging during atmospheric (outdoor) accidental explosions are addressed. It has been demonstrated that when physically modeling accidental deflagration explosions, a stoichiometric mixture in the shape of a sphere or hemisphere supported by the ground should be used. This allows us to research the parameters of blast loads for the worst-case accidental scenarios or address the accident using the most conservative approach. A technique has been provided allowing one to create a mixture of a given blend composition in the shape of a sphere or hemisphere supported by the ground in outdoor conditions. It has been demonstrated that there is an ability to conduct modeling studies of accidental atmospheric explosions. We have provided examples of modeling studies of accidental atmospheric explosions; a methodology for analyzing experimental results has also been reviewed. The article discusses the mathematical modeling of outdoor (unobstructed) accidental deflagration explosions. It has been demonstrated that it is most reasonable to base computational experiments on linearized (acoustic) equations of continuum motion, as the visible flame propagation rate emerging during explosive combustion is small (compared to the speed of sound). There has been a satisfactory agreement between the numerical analysis and the experimental data.

Characterizing Ion Transport in Electrolytes via Concentration and Velocity Profiles

AbstractCurrent flowing through an electrolyte is accompanied by continuum motion of ions and solvent, species concentration profiles, and the electric field. While, historically, the understanding of electrolyte transport has predominantly relied on interpreting macroscopic voltage (or current) measurements, recent advances in imaging and spectroscopic techniques allow velocity and concentration profiles to be probed directly. Such detailed information creates exciting opportunities—ranging from verifying theories describing transport in previously studied Li‐ion electrolytes, to new approaches for measuring properties as well as accurately and precisely quantifying transport in more complex electrolytes. Such emerging directions are herein discussed.

Microbubble PhoXonic resonators: Chaos transition and transfer

We report the activation of optomechanical chaotic oscillations in microbubble resonators (MBRs) through a blue-side excitation of its optical resonances. We confirm the sequence of quasi-periodical oscillation, spectral continuum and aperiodic motion; as well as the transition to chaos without external feedback or modulation of the laser source. In particular, quasi periodic transitions and a spectral continuum are reported for MBRs with diameters up to 600 µm, whereas only an abrupt transition into a spectral continuum is observed for larger microbubbles.

Random continuum and Brownian motion

We describe a probabilistic model involving iterated Brownian motion for constructing a random chainable continuum. We show that this random continuum is indecomposable.

Mathematical simulation of gas-dust flow in a nozzle-type separator

The study is about developing a gasdynamic model of motion of multispeed continua for the case of nozzles with complex geometry. These nozzles imitate the shape of a two-stage confiisor-shaped dust cleaner. The paper studied the influence of force interaction between the gas phase and solid phase in the flow duct of the nozzle; this effect was studied for a wide range of input flow parameters. A special focus was on the regimes of gas-solid flows through curved channels for the case of high loads of solids at the nozzle inlet. A mathematical model was developed that takes into account the impact from the wall-bounced particles upon the distributions of gas phase and solid phase for the entire region. It was shown that account for particle bouncing produces an extremum in solids concentration distribution in the flow duct of the separator.

Geometrodynamic Models of Continuum Mesomechanics: Dynamic Degrees of Freedom with Non-Eulerian Space-Time Evolution

The paper proposes a Lagrangian formalism for describing the space-time dynamics of complex continuum motion with addition variables—non-Eulerian dynamic degrees of freedom. The new variables are interpreted in terms of mechanics and geometry, and principles are suggested for their tracking in experiments. The formalism offers invariant tensor representations of Lagrangians in a system with an extended set of independent variables, explains the mechanical meaning of their respective coefficients, and gives Euler—Lagrange equations for this type of multidimensional variational problems. It is hypothesized that the bundle geometry of dynamic degrees of freedom is a generalized structure for fluctuation and other models of complex continuum evolution. The proposed method is analyzed as applied to dynamic equations of developed turbulence, and an interpretation on its basis is given to turbulence degeneration into unsteady Euler fields.

Simulation of continuous flows with discrete models

The vast majority of heat and power processes include the motion of significant amounts of gases and liq-uids. This makes it important and quite urgent to develop approaches for computer simulation and visualiza-tion of continuum flows in technological devices and pipelines. A whole set of new approaches to mathematical modelling of continuum flows has been recently developed. The most common one is using discrete mathematical models for these purposes. Discrete approaches can simplify modeling procedures in cases where traditional methods require complex time-consuming calculations. At the same time, correct-ness of description of various flow regimes by the discrete methods is often questioned. The second problem of the mentioned models is a large-scale transition from model discrete parameters to generally accepted macroscopic characteristics of flows. The purpose of this work is to determine continuous flow regimes that can be correctly described by certain models. The paper considers discrete dynamic models in the form of lattice gases. A continuum in this case is represented by a set of particles moving only in allowed directions. Despite certain limitations, there is solid evidence that lattice gases quite successfully describe a whole range of hydrodynamic phenomena, and the obtained results do not contradict the generally accepted views on the physical nature of continuum motion processes. The paper describes approaches that allow estimating flow parameters using generally accepted macroscopic indicators. It also studies possible application areas of lattice gas models using the motion of virtual particles on a spatial lattice (HPP and FHP models) and the model based on the discrete analogue of the Boltzmann equation (LBM model) to simulate and visualize continuum flows. The obtained data are in good agreement with the generally accepted results and do not contradict the provisions of classical hydrodynamics. The paper shows that the models considering particle collisions (HPP and FHP) are applicable to describing gas flows in laminar regimes. The LBM model should be considered to be more correct for simulation and visualization of real fluid flows.

Cooperative aerial lift and manipulation (CALM)

This paper proposes a novel paradigm for aerial payload transport and object manipulation by an unmanned aerial vehicle (UAV) team. This new paradigm, called cooperative payload lift and manipulation (CALM), applies the continuum deformation agent coordination approach to transport and manipulate objects autonomously with collision avoidance guarantees. CALM treats UAVs as moving supports during transport and as stationary supports during object manipulation. Constraints are formulated to assure sufficient thrust forces are available to maintain stability and follow prescribed motion and force/torque profiles. CALM uses tensegrity muscles to carry a suspended payload or a manipulation object rather than cables. A tensegrity structure is lightweight and can carry both the tension and compression forces required during cooperative manipulation. During payload transport, UAVs are categorized as leaders and followers. Leaders define continuum deformation shape and motion profile while followers coordinate through local communication. Each UAV applies input–output (IO) feedback linearization control to track the trajectory defined by continuum deformation. For object manipulation, the paper proposes a new hybrid force controller to stabilize quadcopters when smooth or sudden (impulsive) forces and moments are exerted on the system.

On three facts of reticences in the classical mathematical modeling of elastic materials

Three facts of reticences (passing over in silence, an absence of comments) in the procedures of mathematical modeling of elastic materials are described and commented. The first fact consists in a reticence of one of the first steps in the mentioned above procedure – an assumption that the kinematics of deformation is described by the linear approximation of motion of material continuum, namely by gradients of deformation. In the paper, a novel nonlinear approach to this procedure is offered. The second and third facts are associated with constitutive relations. The second fact consists in the absence of necessary comments relative to determination of smallness of strains and gradients of displacements (absence of comments relative to a criterion of applicability of the linear model) because the criterion $ |u_{i,k}|\ll 1$ is sufficiently abstract. It is shown that there exists a based on the nonlinear Cauchy relations approximate procedure of determination of threshold values of strains and gradients of deformations starting with which a nonlinearity of process appears. The third fact consists in the absence of comments relative to essential differences between the nonlinear constitutive equations, which are written for the ordered pairs "Lagrange stress tensor – Cauchy-Green strain tensor" and "Kirchhoff stress tensor – gradients of displacements". It is shown on an example of the shear stress and the Murnaghan model of nonlinear elastic deformation that deviation from the corresponding straight lines of linear deformation for different pairs differs in many times in the range of small strains and small gradients of displacements. The general estimate of facts of reticences looks positive, because for one part of scientists-mechanicians the reticences form the comfort feeling of monolithic character of the classical theory of elasticity, whereas for another part the reticences form a space for development of the theory of elasticity.

Equations and closure models for material pulverization and debris flow

A transition from interacting continua to a disperse debris flow is numerically simulated using a multi-velocity formulation based on the ensemble phase average. The numerical calculation takes advantage of the recently developed dual domain material point method, which overcomes numerical instabilities, numerical diffusion and mesh distortion issues encountered in other numerical methods in cases of large material deformations. Comparisons with experiments show that the difference between the average of the velocity gradient and the gradient of the average velocity is important. To consider the transition from a continuum motion to a disperse flow, a model for this difference is expressed in terms of the effective plastic strain and the critical strain of the material. Although the model results in excellent comparisons to the experimental results, more work to study the difference and the model is needed for broader applications.

The equations of motion of a collisionless continuum

The equations of motion of a collisionless continuum are derived within an Eulerian approach. They differ from the classical equations of motion of an ideal gas, which take into account heat conduction phenomena. Several problems related to the weak convergence of the solutions of the equations of motion of a continuum when there is an unbounded increase in time are discussed. The problem of the correctness of the operation of truncating the exact infinite chain of equations of a collisionless gas is examined.

Symmetry Reduced Dynamics of Charged Molecular Strands

The equations of motion are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that these equations are nonlocal when the screened Coulomb interactions, or Lennard–Jones potentials between pairs of charges, are included. The nonlocal dynamics is derived in the convective representation of continuum motion by using modified Euler–Poincaré and Hamilton–Pontryagin variational formulations that illuminate the various approaches within the framework of symmetry reduction of Hamilton’s principle for exact geometric rods. In the absence of nonlocal interactions, the equations recover the classical Kirchhoff theory of elastic rods. The motion equations in the convective representation are shown to arise by a classical Lagrangian reduction associated to the symmetry group of the system. This approach uses the process of affine Euler–Poincaré reduction initially developed for complex fluids. On the Hamiltonian side, the Poisson bracket of the molecular strand is obtained by reduction of the canonical symplectic structure on phase space. A change of variables allows a direct passage from this classical point of view to the covariant formulation in terms of Lagrange–Poincaré equations of field theory. In another revealing perspective, the convective representation of the nonlocal equations of molecular strand motion is transformed into quaternionic form.

Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

Cometary gas relations 1P/Halley

AbstractPhotographic and photoelectric observations of comet 1P/Halley's ionised gas coma from CO+ at 4,250 Å and neutral gas coma from CN at 3,880 Å were part of the Bochum Halley Monitoring Program, conducted at the European Southern Observatory, La Silla, Chile, from February 17 to April 17, 1986.In this spectral range it is possible to see the continuum formation, motion and expansion of plasma and neutral gas structures. To observe the morphology of these structures, 32 CO+ photos (glass plates) from comet 1P/Halley obtained by means of an interference filter have been analysed. They have a field of view of 28.6 × 28.6 degrees and were obtained from March 29 to April 17, 1986 with exposure times between 20 and 120 minutes.All photos were digitised with a PDS 2020 GM microdensitometer. After digitisation, the data were reduced to relative intensities, and those with proper calibrations were also converted to absolute intensities, expressed in terms of column densities. The CO+ absolute intensity values still contain the continuum intensity. To calculate the CO+ column density it is necessary to subtract this continuum intensity.The relations between CO+ and CN in average column density values (NCO+/NCN) are 11.6 for a circular diaphragm with average diameter (Φ) of 6.1 arcminutes which corresponds to a distance from the nucleus (ρ) equal to 6.3 × 104 km; 20.0 for Φ = 7.1 arcminutes and ρ = 7.3 × 104 km; 8.1 for Φ = 8.5 arcminutes and ρ = 8.7 × 104 km; 35.6 for Φ = 11.9 arcminutes and ρ = 1.2 × 105 km; and 31.3 for Φ = 16.7 arcminutes and ρ = 1.7 × 105 km. These values are in perfect agreement with the data for short distances (ρ from 3.9 × 103 to 1.2 × 104 km) and small slit diameters (Φ from 0.4 to 1.2 arcminutes).With the use of diaphragms with large diameters it is possible to get some information about the outer coma of the comet (in this paper, from 60,000 until 170,000 km away from the nucleus). At these distances, the CO+ column density changes only due to the geometrical dilution, because the CO+ parent molecules are already photoionised or photodissociated.

Turbulent migration of finely disperse suspensions in vortex chambers

Hydrodynamics and dust deposition in vortex chambers are investigated, and corresponding mathematical models developed. Data on the separation efficiency of solid particles due to inertial deposition and turbulent migration are obtained on the basis of mathematical experimentation. Basic equations of motion of continua, and generally accepted semi-empirical approaches to description of the motion of a disperse phase are the basis of the model developed. Results of numerical experiments are in agreement with published experimental data. The results obtained can be used to calculate optimal production parameters in vessels designed for cleaning of gaseous effluents.

A Hamiltonian particle method for non‐linear elastodynamics

AbstractParticle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles. They have a great degree of flexibility, for instance, in dealing with complex large deformations or the fragmentation of solids. In this paper, a particle method for non‐linear elastodynamics of compressible and incompressible materials is developed based on a discretization of the Lagrangian from which the governing equations of elastodynamics are derived using the principle of least action. The discretized Lagrangian leads to a finite‐dimensional Hamiltonian system via the Legendre transformation. If the material is incompressible, the Hamiltonian system is accompanied by holonomic constraints. Depending on whether the material is compressible or incompressible, the symplectic scheme adopted for numerical time integration is either the Störmer/Verlet scheme or the RATTLE method, respectively. The resulting particle method inherits the symplectic structure possessed by the governing equations of elastodynamics. In the case of incompressible materials, incompressibility is strictly enforced at each time step. Some numerical tests indicate the excellence of the method for conservation of mechanical energy besides that of linear and angular momenta. Copyright © 2007 John Wiley & Sons, Ltd.

Numerical modeling of the thermomechanical behavior of steels with allowance for the propagation of Luders bands

A thermomechanical model based on physical representations of the motion of dislocation continuum and a model for the initiation and propagation of plastic shear are proposed to describe slow flows of the type of Luders bands. Two-dimensional calculations of Luders band propagation are performed for HSLA-65 steel samples under compression at various strain rates and temperatures. The calculation results are in good agreement with experimental data.

Hamiltonian moving-particle semi-implicit (HMPS) method for incompressible fluid flows

Particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles, and thus have a great degree of flexibility, for instance, in dealing with the complex motion of surfaces or boundaries. In this paper, a particle method is developed from a direct discretization of the Lagrangian for inviscid incompressible fluid flows. The discretized Lagrangian is transformed into a Hamiltonian with holonomic constraints that stem from the incompressibility condition. The RATTLE algorithm that is a symplectic scheme for holonomically constrained Hamiltonian systems is adopted so that the resulting particle method inherits structures possessed by the partial differential equations that govern inviscid incompressible flows. The algorithm of the particle method is semi-implicit, so we call it the Hamiltonian moving-particle semi-implicit (HMPS) method. Some numerical tests indicate the excellence of the HMPS method in conservation of mechanical energy (as well as linear and angular momenta).

An isotropic dynamically consistent gradient elasticity model derived from a 2D lattice

This paper presents a derivation of a second-order isotropic continuum from a 2D lattice. The derived continuum is isotropic and dynamically consistent in the sense that it is unconditionally stable and prohibits the infinite speed of energy propagation. The Lagrangian density of the continuum is obtained from the Lagrange function of the underlying lattice. This density is used to obtain the expressions for standard and higher-order stresses in direct correspondence with the equations of the continuum motion. The derived continuum is characterized by two additional parameters relative to the classical elastic continuum. These are the characteristic lengthscale and a dimensionless continualization parameter, which characterizes indirectly the timescale of the derived continuum. The margins for the latter parameter are found from the stability analysis. It is envisaged that the continualization parameter could be measured employing a high-frequency pulse propagating along the surface of the continuum. Excitation and propagation of such pulse is studied theoretically in this paper.

Validation of 3-D CFD Model of Tritium Transport in the Atmosphere

When solving 3-D problems for the atmospheric impurity transport in the bounded area, it is essential for the atmospheric dynamics to be correctly computed taking into account the actual terrain topography and environments specified by the boundary conditions. Such conditions as turbulence, convection, condensation and moisture evaporation processes, etc. are to be also taken into account as well as the interaction processes among impurities (gases, aerosols), atmosphere and the Earth’s surface.3-D computational fluid dynamics model(CFD) developed on the basis of SRP hydrodynamic code was used to simulate tritium plume evolution and tritium transport in atmosphere under the area with relatively complex topography. SRP code is based on the continuum motion equations (Navier-Stockes equations) and thermodynamic relations taking into account specific features of atmospheric flows and complex topography and is designed to use on PC-type computers.The model has been validated using experimental release of tritium with specified source term and meteorology. Due to low release height above the underlying surface a fine grid was used in the vertical direction near the underlying surface. HT and HTO/H2O vertical fluxes were taken into account. Evolution of HT and HTO activities at 2 sampling locations along the plume axe were available for model-experiment inter-comparison. The modeling results of HT and HTO activities in the air during plume travel are in satisfactory agreement with observed values.