Macroscopic Velocity Field Research Articles

Simultaneous measurement of velocity field of liquid–solid particle flow in pipelines and analysis of flow characteristics

The liquid–solid particle flow within a horizontal pipeline is a typical particle-laden flow. The interplay between loaded particles and carrier phase engenders significant complexities in the dynamic behavior of such flows. We investigated the dynamics of a liquid–solid particle flow featuring dilute, slightly buoyant, hundred-micron-sized spherical particles fully suspended in the turbulent flow in a pipe, where Re is 7038. Cases with solid volume fractions of 0, 2.67 × 10-4, 5.33 × 10-4, 8.00 × 10-4, 1.07 × 10-3 and 1.33 × 10-3 were considered in this study. Experimental measurement techniques were utilized to acquire images of particles in the two-phase flow across the entire flow field via optical field feedback. Particle image velocimetry (PIV) and particle tracking velocimetry (PTV) were employed to simultaneously obtain liquid-phase velocity fields and particle trajectories. This approach allowed for a comprehensive depiction of the velocity field of each phase. Subsequently, a detailed explanation and analysis of the flow characteristics of the liquid–solid particle flow were provided based on the distribution of macroscopic velocity fields, the microscopic vorticity field, particle velocity vectors, and velocity slip. As a result, it was found that with the addition of solid particles and an increase in volume concentration, the drag effect of the solid phase and the trend of accumulation near the lower wall caused a decrease in the liquid phase velocity profile and deformation of the parabolic shape. In the liquid–solid particle flow with a volume concentration of 1.33 × 10-3, compared to the single-liquid phase flow, the standard deviation of velocity in the central region increased from 0.0097 m/s to 0.0159 m/s, and in the near-wall region, it increased from 0.0257 m/s to 0.0347 m/s, representing increases of 1.54 times and 1.26 times respectively. The proportion of medium vortices increased from 17 % to 30 %, nearly doubling. This study actively explores the concurrent measurement and flow characteristics of liquid–solid particle flow.

Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks

We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disordered phase (liquid-like) and an ordered phase, e.g., stripes or crystal lattices. For stripes, the interface dynamics are shown to be strongly anisotropic. We also show that the model is able to evolve the classical PFC at mechanical equilibrium. However, in contrast to previous approaches, it is not restricted to a single-crystal configuration or small distortions from a fixed reference lattice. To showcase the capabilities of this approach, we consider a few examples, from the annihilation of dislocation loops in a single crystal at mechanical equilibrium to the relaxation of a microstructure including crystalline domains with different orientations and grain boundaries. During the self-annihilation of a mixed type dislocation loop (i.e., not shear or prismatic), long-range elastic effects cause the loop to move out of plane before the annihilation event.

Discharge of elongated grains in silos under rotational shear.

The discharge of elongated particles from a silo with rotating bottom is investigated numerically. The introduction of a slight transverse shear reduces the flow rate Q by up to 70% compared with stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Focusing on the dependency of flow rate Q on orifice diameter D, the spheres and rods show two distinct trends. For rods, in the small-aperture limit Q seems to follow an exponential trend, deviating from the classical power-law dependence. These macroscopic observations are in good agreement with our earlier experimental findings [Phys. Rev. E 103, 062905 (2021)2470-004510.1103/PhysRevE.103.062905]. With the help of the coarse-graining methodology we obtain the spatial distribution of the macroscopic density, velocity, kinetic pressure, and orientation fields. This allows us detecting a transition from funnel to mass flow pattern caused by the external shear. Additionally, averaging these fields in the region of the orifice reveals that the strong initial decrease in Q is mostly attributed to changes in the flow velocity, while the weakly increasing trend at higher rotation rates is related to increasing packing fraction. Similar analysis of the grain orientation at the orifice suggests a correlation of the flow rate magnitude with the vertical orientation and the packing fraction at the orifice with the order of the grains. Lastly, the vertical profile of mean acceleration at the center of the silo denotes that the region where the acceleration is not negligible shrinks significantly due to the strong perturbation induced by the moving wall.

Thermodynamically consistent incorporation of entanglement spatial fluctuations in the slip-link model

We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.

From point particles to body points

<abstract> Given a spacetime background against which to observe it, a material system in motion can be modeled discretely, as a collection of particles called 'point masses', or continuously, as a dense and deformable object (a <italic>body</italic>, in the language of continuum mechanics) occupying a region consisting of 'material points'. In that the discrete and continuous descriptions have a common conceptual framework, the scale gap can be got over, provided a coarsening procedure is devised. Here we restrict attention to kinematics, and consider four such bottom-up procedures, two statistical and two deterministic, to derive a macroscopic velocity field from a microscopic one. We show that, to do this, introducing space and time <italic>mesoscopic</italic> scales is of the essence. We also show under what assumptions a macroscopic motion of the given material system can be associated with a microscopically-informed velocity field. Interestingly, no matter what coarsening procedure one chooses, the points of the resulting continuous description of the system's motion carry intrinsic physical information and may be persistently labelled: we propose to call them <italic>body points</italic>. </abstract>

Particle flow rate in silos under rotational shear.

Very recently, To etal. have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall [Phys. Rev. E 100, 012906 (2019)10.1103/PhysRevE.100.012906]. Here we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate Q as a function of the frequency of rotation f. Namely, we find that for small outlet diameters D the flow rate increased with f, while for larger D a nonmonotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors, macroscopic velocity and density fields, we obtain that the nonmonotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure 〈p^{k}〉 and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that 〈p^{k}〉 changes nonmonotonically, which might explain the nonmonotonic behavior of Q when varying the rotational shear.

Numerical study on enhancement of heat transfer in hybrid nano-micropolar fluid

Hybrid nanoparticles correlations together with governing models for the flow of micropolar fluid are used to develop novel complex coupled nonlinear set of differential equations. The solutions are computed by using the finite element method (FEM) and results are validated after convergence and grid-free analysis. The macroscopic velocity and micro-rotation field are investigated versus parametric variation. The temperature field is examined for various emerging dimensionless parameters. A significant improvement in the thermal performance of micropolar fluid due to simultaneous dispersion of Cu and Al2O3 (hybrid nanoparticles) is noted. Therefore, simultaneous dispersion of Cu and Al2O3 for significant improvement in thermal performance of micropolar fluid is recommended rather the dispersion of copper nanoparticles. Surprisingly micro rotation field for nano micropolar mixture near the vicinity of the wall is less than the micro-rotation field for hybrid nano-micropolar fluid. However, away from the wall opposite dynamics for the micro-rotation field are observed.

Gauge-field model of superfluid turbulence in the zero-temperature limit

We present a gauge-field extension of the Bose condensate model that describes superfluid turbulence generated by the macroscopic motion of the superfluid. We first establish that the condensate model is dual to the short-range interacting loop gas model, wherein the loops represent quantum vortex lines. Vortex lines form, interact and proliferate as a result of the superfluid motion. Our extension is based on incorporating the Biot–Savart interaction between vortex lines, which is lacking in the loop gas model. We show that the extended loop gas is dual to a Ginzburg–Landau model, wherein the gauge coupling is between the macroscopic velocity field of the superfluid and the condensate. Applying the model to cylindrical and pipe flows, we describe how turbulence transitions with and without intermediate vortex flow, respectively.

Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow

We study correlations of hydrodynamic fluctuations in shear flow analytically and also by dissipative particle dynamics~(DPD) simulations. The hydrodynamic equations are linearized around the macroscopic velocity field and then solved by a perturbation method in Fourier-transformed space. The autocorrelation functions~(ACFs) from the analytical method are compared with results obtained from DPD simulations under the same shear-flow conditions. Upto a moderate shear rate, various ACFs from the two approaches agree with each other well. At large shear rates, discrepancies between the two methods are observed, hence revealing strong additional coupling between different fluctuating variables, which is not considered in the analytical approach. In addition, the results at low and moderate shear rates can serve as benchmarks for developing multiscale algorithms for coupling of heterogeneous solvers, such as a hybrid simulation of molecular dynamics and fluctuating hydrodynamics solver, where thermal fluctuations are indispensable.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure.

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

A new macroscopic description of capillary transport of liquid and gas in porous materials is presented within the framework of multiphase continuum mechanics. It is assumed that unsaturated porous material form a macroscopic continuum composed of three constituents: gas, mobile liquid and capillary liquid, while the skeleton is rigid with an isotropic pore space structure. The capillary liquid forms a thin layer on the internal contact surface with the skeleton, is immoveable and contains the whole capillary energy. The remaining part of the liquid, surrounded by the layer of the capillary liquid and menisci, forms the constituent called mobile liquid. Both liquids exchange mass, momentum and energy in the vicinity of menisci surfaces during their motion, which is described by an additional macroscopic velocity field. A macroscopic scalar quantity is introduced, parametrizing changes of saturations, which for quasi static and stationary processes is equal to the capillary pressure. This quantity extends the dimensionality of the description of mechanical processes taking place in unsaturated porous materials. For the three fluid constituents of the medium, balance equations of mass and linear momentum and evolution equations for saturations are formulated. The constitutive relations for quantities describing mechanical processes in such a medium are proposed based on the dissipation inequality of mechanical energy for the whole system. A new approach is proposed, similar to that used in rational thermodynamics, based on entropy inequality analysis and the Lagrange multipliers method.

POLARIZED LINE FORMATION IN MOVING ATMOSPHERES WITH PARTIAL FREQUENCY REDISTRIBUTION AND A WEAK MAGNETIC FIELD

The dynamical state of the solar and stellar atmospheres depends on the macroscopic velocity fields prevailing within them. The presence of such velocity fields in the line formation regions strongly affects the polarized radiation field emerging from these atmospheres. Thus it becomes necessary to solve the radiative transfer equation for polarized lines in moving atmospheres. Solutions based on the "observer's frame method" are computationally expensive to obtain, especially when partial frequency redistribution (PRD) in line scattering and large-amplitude velocity fields are taken into account. In this paper we present an efficient alternative method of solution, namely, the comoving frame technique, to solve the polarized PRD line formation problems in the presence of velocity fields. We consider one-dimensional planar isothermal atmospheres with vertical velocity fields. We present a study of the effect of velocity fields on the emergent linear polarization profiles formed in optically thick moving atmospheres. We show that the comoving frame method is far superior when compared to the observer's frame method in terms of the computational speed and memory requirements.

Simulating flows in multi-layered and spatially-variable permeability media via a new Gray Lattice Boltzmann model

The simulation of flow in porous and fibrous permeable media is of high importance in many scientific and industrial applications. Although the finite element models at the representative elementary volume scales are used to solve a huge amount of scientific and engineering problems, they are hardly used to efficiently simulate pore-fluid flow problems at the particle scales. This encourages the development of numerical models to match the needs of such studies. In this paper, we propose a new Gray Lattice Boltzmann numerical model for simulating fluid flow in permeable media. Unlike most previous models, our proposed model has the ability to simulate multi-layers and space-variable permeability while preserving the continuity of the macroscopic velocity field. The model is verified with the available analytical solutions and a derived analytical expression for the case of variable porosity. In addition, we examine the importance of introducing a transition layer with a defined porosity function near the boundaries and interfaces. If this layer exists in practice, then the numerical results reveal that it cannot be neglected, and its impact is significant on the obtained velocity distribution. Finally, in the light of the obtained results, we can state that the proposed model has great potential to simulate complex and heterogeneous media with smoothness and accuracy, so that it may enrich the research content of the emerging computational geosciences.

Fluctuating hydrodynamics and mesoscopic effects of spatial correlations in dissipative systems with conserved momentum

We introduce a model described in terms of a scalar velocity field on a 1D lattice, evolving through collisions that conserve momentum but do not conserve energy. Such a system possesses some of the main ingredients of fluidized granular media and naturally models them. We deduce non-linear fluctuating hydrodynamics equations for the macroscopic velocity and temperature fields, which replicate the hydrodynamics of shear modes in a granular fluid. Moreover, this Landau-like fluctuating hydrodynamics predicts an essential part of the peculiar behaviour of granular fluids, like the instability of homogeneous cooling state at large size or inelasticity. We also compute the exact shape of long range spatial correlations which, even far from the instability, have the physical consequence of noticeably modifying the cooling rate. This effect, which stems from momentum conservation, has not been previously reported in the realm of granular fluids.

A simple lattice Boltzmann model for turbulence Rayleigh–Bénard thermal convection

A simple lattice Boltzmann thermal model is proposed for simulating the turbulence Rayleigh–Bénard convection. This new model introduces a mesoscopic external force term in the lattice Boltzmann equation to consider the effect of the buoyant body force and introduces a temperature density distribution function to simulate the temperature field. The macroscopic density and velocity fields are simulated using the density distribution function. The results show that this simple model is able to simulate turbulence Rayleigh–Bénard convection in the current simulation range of 106⩽Ra⩽1012. It is shown that the energy spectra of the velocity and temperature are in good agreement with the Bolgiano–Obukhov-like (BO59) scaling.

The Nature of Space and of the Gravitational Physics in the Light of Recent New Experimental Observations and Within the Scenario of the Higgs Mechanism

Recent new highly precise experimental observations, achieved with the help of the tightly synchronized clocks of the GPS, reveal very clearly that real space, ruling the inertial motion of matter and the propagation of light, is moving round earth and round the sun according to a Keplerian velocity field, consistent with the local main astronomical motions. Such real space is well at hand in the Quantum Field Theory (QFT), underlying the Standard Elementary Particle Model (SEPM). The QFT entails the idea that space is filled up with the Higgs condensate (HC), a Bose-Einstein condensate of the zero spin Higgs bosons and a very powerfull quantum space (QS), stable up to 1015 degrees Kelvin. According to QFT, likewise the superconducting condensate confines magnetic fields by the Meissner effect, making them short-range and giving inertial mass to the photons, the HC confines the matter fields by the Higgs Mechanism, giving mass to the elementary particles, that is, providing them with mechanical properties. This lets clear that the HC rules the inertial motion of matter and the propagation of light and hence is the locally ultimate reference for rest and for motion of matter and light. Moreover, likewise superconductors, develop a macroscopic velocity field of the superconducting condensate (screening currents), expelling magnetic fields, the HC too may develop a macroscopic velocity field of the condensate (screening currents) in the form of a Keplerian velocity field of the QS, consistent with the local main astronomical motions, round each matter body throughout the universe. The present work demonstrates that this Keplerian velocity field of the QS appropriately induces the observed gravitational dynamics on earth, in the solar system as well as the galactic gravitational dynamics without the need of dark matter. This Keplerian velocity field is the quintessence of the gravitational fields. It thrusts and compresses the matter fields into compact bodies. It also provides a dominant antigravitation mechanism accelerating the expansion of the universe. It finally is shown that this QS-dynamics correctly and appropriately gives rise, in terms of simple and genuine physical effects, to all the other observed effects, caused by the gravitational fields on the propagation of light and on the rate of the clocks. Keywords: Dark Energy, dark matter, gravitational effects, gravitational fields, gravitational physics, gravity.

The precision of line position measurements of unresolved quasar absorption lines and its influence on the search for variations of fundamental constants

Optical quasar spectra can be used to trace variations of the fine-structure constant alpha. Controversial results that have been published in last years suggest that in addition to to wavelength calibration problems systematic errors might arise because of insufficient spectral resolution. The aim of this work is to estimate the impact of incorrect line decompositions in fitting procedures due to asymmetric line profiles. Methods are developed to distinguish between different sources of line position shifts and thus to minimize error sources in future work. To simulate asymmetric line profiles, two different methods were used. At first the profile was created as an unresolved blend of narrow lines and then, the profile was created using a macroscopic velocity field of the absorbing medium. The simulated spectra were analysed with standard methods to search for apparent shifts of line positions that would mimic a variation of fundamental constants. Differences between position shifts due to an incorrect line decomposition and a real variation of constants were probed using methods that have been newly developed or adapted for this kind of analysis. The results were then applied to real data. Apparent relative velocity shifts of several hundred meters per second are found in the analysis of simulated spectra with asymmetric line profiles. It was found that each system has to be analysed in detail to distinguish between different sources of line position shifts. A set of 16 FeII systems in seven quasar spectra was analysed. With the methods developed, the mean alpha variation that appeared in these systems was reduced from the original Dalpha/alpha=(2.1+/-2.0)x10^-5 to Dalpha/alpha=(0.1+/-0.8)x10^-5. We thus conclude that incorrect line decompositions can be partly responsible for the conflicting results published so far.

SCATTERING POLARIZATION IN THE Ca II INFRARED TRIPLET WITH VELOCITY GRADIENTS

Magnetic field topology, thermal structure and plasma motions are the three main factors affecting the polarization signals used to understand our star. In this theoretical investigation, we focus on the effect that gradients in the macroscopic vertical velocity field have on the non-magnetic scattering polarization signals, establishing the basis for general cases. We demonstrate that the solar plasma velocity gradients have a significant effect on the linear polarization produced by scattering in chromospheric spectral lines. In particular, we show the impact of velocity gradients on the anisotropy of the radiation field and on the ensuing fractional alignment of the CaII levels, and how they can lead to an enhancement of the zero-field linear polarization signals. This investigation remarks the importance of knowing the dynamical state of the solar atmosphere in order to correctly interpret spectropolarimetric measurements, which is important, among other things, for establishing a suitable zero field reference case to infer magnetic fields via the Hanle effect.

Mean-field theory of collective motion due to velocity alignment

Establishing a direct link between individual based models and the corresponding population description is a common challenge in theoretical ecology. Swarming is a prominent example, where collective effects arising from interactions of individuals are essential for the understanding of large-scale spatial population dynamics, and where both levels of modeling have been often employed without establishing this connection.Here, we consider a system of self-propelled agents with velocity alignment in 2D and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker–Planck equation and a moment expansion of the probability density. We analyze the stationary solutions corresponding to macroscopic collective motion (ordered state) and the disordered solution with no collective motion in the spatially homogeneous system. In particular, we discuss the impact of different propulsion functions governing individual dynamics. Our results predict a strong impact of individual dynamics on the mean field onset of collective motion (continuous vs discontinuous). In addition to the macroscopic density and velocity fields, we consider the effective “temperature” field, measuring velocity fluctuations around the mean velocity. We show that the temperature decreases strongly with increasing level of collective motion despite constant fluctuations on individual level, which suggests that extreme caution should be taken in deducing individual behavior, such as, state-dependent individual fluctuations from mean-field measurements (Yates et al., 2009).

Transport in disordered media with spatially nonuniform fields

The theoretical treatment of transport in a disordered system in the presence of a system-wide force field F(x) or spatially varying macroscopic velocity field v(x) is developed in the framework of continuous time random walk (CTRW). The physical basis of CTRW and related fractional derivative equations relies on a mapping of the aggregate of transition rates w(s,s'), between sites s and s', in the Master equation describing the system kinetics, onto a joint probability distribution function psi(s,t). This distribution is calculated from the ensemble average of a position-dependent functional of w(s,s'); the procedure is effective when the scale of heterogeneities is much smaller than the system size. However, statistical homogeneity does not hold in the presence of large heterogeneities, which control the macroscopic v(x), or in the case of an interaction of F(x) with the transition rates. The transport equation, incorporating large-scale heterogeneity, involves the use of a local ensemble average to obtain a position-dependent psi(s,t;x); this determines a memory function, M(t;x), which is convoluted with the advection-dispersion operator. A prototype transport equation for a system with statistical inhomogeneity is developed as an integrodifferential equation. It is solved numerically for particles migrating with a steady-state Darcy velocity v(x , determined for different permeability fields and boundary conditions. The nature of the solutions as a function of key transport parameters (e.g., a characteristic time tc) is explored, and solutions are also compared to those of the advection-dispersion equation for v(x) and to a laboratory experiment. This transport equation is in contrast to the fractional Fokker-Planck equation, which is based on a decoupling of F(x) or v(x) with the transition rates w(s,s'). Further, an analytic expression for the effect of a variance of the ensemble average on the solution of the CTRW transport equation is derived.