Motion Of Fluid Particles Research Articles

Lagrangian motion of fluid particles in gravity–capillary standing waves

A third-order analytical solution for the gravity–capillary standing wave is derived in Lagrangian coordinates through the Lindstedt–Poincare perturbation method. By numerical computation, the dynamical properties of nonlinear standing waves with surface tension in finite water depth, including particle trajectory and surface profile are investigated. We find that the presence of surface tension leads to a change of the crest form. Moreover, we also find that the particle trajectories near the surface oscillate back and forth along the arcs which will change from concave to convex as the inverse Bond number increases. There is no mass transport of the particles in a wave period.

Differences between the motion of a helical vortex and the movement of fluid particles along its axis

The motion of a helical vortex and the movement of the fluid particles along its axis are analyzed. The same form of the helical axis of the vortex and the trajectory of the particles sometimes leads to a false assumption of equality of these two different motions. The correct identification of both motions, however, is essential when considering the helical vortices in the wakes of rotors, or the displacement of the core of helicoidal tornado, etc. Only the same helical shape is the vortex axis and the streamline of the fluid particles can mistakenly merge these two different motions as the identical travel. We describe an experiment that clearly separates these two motions for the case of a stationary helical vortex, along the axis of which the fluid particles intensively move. The result shows that the absolute velocity of fluid particles does not coincide with the motion of the helical vortex as a whole.

Numerical and Experimental Study of Multiphase Transient Core-Annular Flow Patterns in a Spouted Bed

Abstract Dense solid–gas bubbling systems with combined fluid-particle motion are among one of the most extensively used fluidization forms used in the chemical industry. Therefore, it is important to have a good understanding of the hydrodynamic behavior of bubbles. In this paper, both the experiment and numerical simulations are used to investigate the flow patterns in a spouted bed. For numerical simulations, the bidirectional coupling simulations using computational fluid dynamics (CFD) with discrete element method (DEM) are conducted. The results show that the simulations can accurately predict the bubbles morphology compared with the experimental results. When the number of particles is 30,000, only a single core-annular flow pattern appears. When the number of particles is increased to 36,500, the single bubble in the spouted bed transitions into two and a double core-annular flow pattern emerges. As the number of particles is increased to 43,000, a complex multicore-annular flow pattern appears. These flow patterns are also observed in the experiments using high-speed imaging camera. This paper analyzes and explains the causes of these flow phenomena from the dynamic characteristics of particle phase and fluid phase. These results have great significance in providing guidance for optimization of dense phase bubbling spouted beds.

Single-particle Lagrangian statistics from direct numerical simulations of rotating-stratified turbulence

Geophysical fluid flows are predominantly turbulent and often strongly affected by the Earth's rotation, as well as by stable density stratification. Using direct numerical simulations of forced Boussinesq equations, we study the influence of these effects on the motion of fluid particles, focusing on cases where the frequencies associated with rotation and stratification (RaS), $N$ and $f$ respectively, are held at a fixed ratio $N/f=5$. As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which can also be seemingly described by simply comparing the time scale $1/N$ and $\tau_\eta$ (the Kolmogorov time scale). We perform a detailed study of Lagrangian statistics of acceleration, velocity and related quantities in the two regimes. The flow anisotropy induces a clear difference between particle motion in the horizontal and vertical directions. In the regime $N\tau_\eta <1$, acceleration statistics in both horizontal and vertical directions, exhibit well known characteristics of isotropic turbulence. In contrast for $N\tau_\eta >1$, they are directly influenced by imposed RaS. The Lagrangian velocity statistics exhibit visible anisotropy for all runs; nevertheless the degree of anisotropy becomes very strong in the regime $N\tau_\eta >1$. We find that in the regime $N\tau_\eta <1$, rotation enhances the mean displacement of particles in horizontal planes at short times, but inhibits them at longer times. This inhibition of horizontal displacement becomes stronger for $N\tau_\eta >1$, with no clear diffusive behavior. Displacements in the vertical direction are always inhibited. The inhibition becomes extremely strong when $N\tau_\eta >1$, with the particles almost being trapped horizontally.

Transient sensitivity analysis and topology optimization for particle motion in steady state laminar fluid

A new topology optimization scheme considering the transient particle motion in steady state laminar fluid is developed in the present study. To efficiently control the transient motion of particles in steady state laminar fluid, it is possible to apply the fluid topology optimization method considering the particle and fluid interaction condition. Inside steady state laminar fluid, particles move due to the fluid drag forces which are the functions of the fluid velocity and the velocities of particles. Indeed, the motions of particles can be controlled and optimized by changing the movement of fluid for several engineering applications. From a topology optimization point of view, the design variables determining the Darcy’s forces in fluid are optimized in order to control the velocities of particles. The transient sensitivity analysis is newly derived considering the steady laminar fluid and Newton’s 2nd equation. Through several optimization examples, the validity and the application of the present topology optimization method are illustrated.

Meshless Fluid Structural Interaction (FSI) Simulation of Deformation of Flexible Structure due to Water Dam Break

A new meshless-based solver has been used to study the deformation of flexible structure due to water dam break. This meshless Fluid Structural Interaction (FSI) solver couples the Smoothed Particle Hydrodynamics (SPH) and Lattice-Spring Model (LSM). SPH and LSM are used to model the motions of fluid and solid particles, respectively. As both are essentially particle-based methods, the force coupling at the interface is straightforward. The numerical results have been compared with the benchmark numerical solutions of dam break problem and good agreement has been found.

On the Role of Size Differences in Synchronized Motion of Magnetic Particles in Fluid: A Study on Trimers

Synchronized motion and pattern formation of magnetic particle aggregates in variable magnetic field is of growing interest from the point of view of both fundamental science and its applications. In this article, the role of size differences in synchronized motion of magnetic particles under external rotating magnetic field at low Reynolds number flow regimes is considered. Several different motion regimes are observed in simulations as a function of particle size differences and field rotation rate. Simulation indicates phase-like transitions between different motion regimes when particle size differences become significant. It is also shown that particle size differences permit the possibility of locomotion for particle aggregates which cannot be observed for uniform particle sizes.

Mean flows induced by inertia–gravity waves in a vertically confined domain

The Lagrangian-mean motion of fluid particles induced by horizontally localized small-amplitude wavepackets of vertically trapped inertia–gravity waves is computed analytically, at second order in wave amplitude, and the results are supported by direct nonlinear numerical simulations. The leading-order motion is assumed to be inertia–gravity waves, which is applicable to oceanic mesoscale flows in regions where wave activity is as strong as or stronger than the balanced flow. The analytical computation is based on time-dependent asymptotic wave–mean interaction theory, and the numerical simulation uses a Galerkin-truncated -plane nonlinear hydrostatic Boussinesq model that retains the barotropic mode and two baroclinic modes (vertical wavenumbers 0, and ), this being the minimal set on which consistent wave–mean interactions can take place. Two novel dynamical effects are revealed: First, we find that the barotropic component robustly dominates the Lagrangian-mean flow response, which is contrary to earlier findings for the same problem. Second, we discovered a new wavepacket regime in which the baroclinic mean-flow response consists of the persistent radiation of resonantly forced secondary internal waves. The latter effect occurs in an oceanically accessible parameter regime.

Effect of impeller blade curvature on the hydrodynamics and power consumption in a stirred tank

The performance of curved bladed turbines (CBTs) for the agitation of Newtonian fluids in cylindrical tanks is investigated. The efficiency of CBT is compared with that of the standard Rushton turbine. Also, effects of the blade height of the new designed impeller are highlighted. The computational fluid dynamics (CFD) study is performed to observe the axial, radial and tangential components of velocities, flow patterns and power consumption. The obtained results revealed that the increase of blade curvature reduces the power consumption. Also, a slight decrease of power number is observed in the turbulent flow regime within unbaffled tanks. In a comparison between the cases studied, the best axial circulation of fluid is given by the impeller with flat blades. The increase of the height of curved blades has generated a stronger tangential flow and enhanced the axial movement of fluid particles, but with further penalty in power input.

Surface Gravity Waves: Shallow Water Fluid Particle Physics

One of Newton’s mathematical solutions to a hypothetical orbital problem, recently verified by an independent physics model, is applied to the fluid particle motion in shallow water surface gravity waves. What is the functional form of the central force, with origin at the ellipse’s center, which will keep a body in the orbit? Newton found out it is the spring force, which is linear. All fluid particles in shallow water waves move in ellipses. By a superposition of solutions in a linear problem, the application of Newton’s result to shallow water waves is combined with a feature not noticed by Newton: the orbital period is independent of the semi-major and semi-minor axes. Two conclusions reached are that the wave period of shoaling waves should be constant and that there is no friction in these waves.

Frictionless Surface Gravity Waves

A physical explanation is given for the observations that ocean surface gravity waves can travel up to half way around the world from generation in a wind storm to dissipation on shore. Inherent in these waves is an orbital fluid particle motion, known from laboratory experiments, that has no friction according to the Navier-Stokes equations. The prediction is based on application of Bernoulli’s law to all the closed orbital paths of the fluid particles and the cross-stream force balance on the particles between a pressure gradient and the centrifugal force in each orbital loop.

CFD APPROACH TO ANALYSIS OF THE FLOW CHARACTERISTICS OF A HIGH-PRESSURE FRANCIS TURBINE

With the growth of computational mechanics, the virtual hydraulic machines are becoming more and more realistic to get minor details of the flow, which are not possible in model testing. In present work, 3D turbulent real flow analyses in hydraulic Francis turbine have been carried out at three guide vane opening and different rotation speed using Ansys CFX computational fluid dynamics (CFD) software. The average values of flow parameters like velocities and flow angles at the inlet and outlet of runner, guide vane and stay vane of turbine are computed to derive flow characteristics. To improve the energy performance at the preliminary design stage of the turbine, numerical flow simulations should be carried out. This CFD approach reduces costs and time in comparison with the experimental approach and makes it possible to improve and analyze turbine performance and its design before the model is manufactured. The computational complex of programs provides an opportunity to see the picture of pressure distribution, the field of velocity vectors and the movement of fluid particles for substantiation and analysis of results. The results of the computational study confirm that the hydraulic efficiency of a hydraulic turbine largely depends on the losses in the guide vane and the runner, which means it is these elements that should be given the most attention, their design and coordination of the flow in them. Analysis of the energy loss in the flow part of the Francis turbine was carried out using programs for calculating fluid flow in two-dimensional and three-dimensional formulation. The obtained calculated data correspond to the previously known experimental recommendations for high-pressure Francis turbine. The issues of increasing the energy performance of a projected high-pressure Francis turbine were considered.

Tagged particle correlations in a dense fluid: Role of microscopic dynamics

We study the self diffusion process in a dense fluid in two cases for which the individual fluid particles follow respectively deterministic Newtonian dynamics (ND) and stochastic Brownian dynamics (BD). The role of correlated motion of fluid particles on the single particle diffusion is taken in to account here using mode coupling models. We demonstrate the subtle difference present in the corresponding mode coupling corrections to diffusion constants for fluids with BD and ND by carefully analysing the equations of fluctuating nonlinear hydrodynamics (FNH) in the respective cases. Finally, we use recently developed model for dynamics of binary mixtures to model a BD fluid in terms of a ND mixture whose species have a very large mass ratio. Here the high inertia larger particles are identified as Brownian and a mechanical interpretation of the noise in a Brownian fluid is made in terms of the smaller particles randomly colliding with them.

Turbulence of generalised flows in two dimensions

This paper discusses the generalised least-action principle and the associated concept of generalised flow introduced by Brenier (J. Am. Math. Soc., vol. 2, 1989, pp. 225–255), from the perspective of turbulence modelling. In essence, Brenier’s generalised least-action principle is a probabilistic generalisation of Arnold’s geometric interpretation of ideal fluid mechanics, whereby strong solutions to the Euler equations are deduced from minimising an action over Lagrangian maps. While Arnold’s framework relies on the deterministic concept of Lagrangian flow, Brenier’s least-action principle describes solutions to the Euler equations in terms of non-deterministic generalised flows, namely probability measures over sets of Lagrangian trajectories. In concept, generalised flows seem naturally fit to describe turbulent Lagrangian trajectories in terms of stochastic processes, an approach that originates from Richardson’s seminal work on turbulent dispersion. Still, Brenier’s generalised least-action principle has so far hardly found any practical application in the realm of fluid mechanics, let alone for turbulence modelling. The purpose of the present paper is to provide a hydrodynamical perspective on Brenier’s principle, and to assess its skills at coarse graining the Lagrangian motion of fluid particles, in order to reconstruct the space–time dynamics of the underlying Eulerian velocity fields. In practice, we rely on a statistical-mechanics interpretation of the concept of generalised flows, whereby the latter become akin to statistical ensembles of suitably defined ‘permutation flows’. We then employ Monte Carlo techniques to numerically solve the generalised least-action principle, and analyse the Eulerian and Lagrangian statistical features of the associated generalised flows. For simplicity, we restrict ourselves to two dimensions of space and consider situations of increasing complexity, ranging from solid rotation and cellular flows to freely decaying two-dimensional turbulence. Our analysis highlights a major caveat of the generalised variational principle. When used over long time lags, e.g. longer than a well-defined hydrodynamic turnover time, it generates artificial generalised flows, with non-physical statistical features. We argue that this limitation is not specifically inherent to Brenier’s formulation, but rather to the variational framework being formulated as a two-end boundary-value problem. When appropriately used over sufficiently short times, the generalised least-action principle is however relevant, and generalised flows can be explicitly constructed, that represent a space–time coarse graining of the underlying dynamics. We show numerical evidence that Brenier’s principle may then even accommodate irreversible Eulerian behaviours. This suggests that, if carefully used, generalised variational formulations could provide new tools to coarse grain genuine multi-scale hydrodynamics.

Optimization of waterflooding performance by using finite volume-based flow diagnostics simulation

From a visual point of view, volumetric information about reservoir portioning and communication such as sweep, flow patterns, and drainage zones are longer better interpreted and pictured when presented by an average volumetric flux calculation. To this hand, finite volume discretization can be used to substitute streamline simulation-based finite difference to assess flow diagnostic information. Herein, we use finite volume-based flow diagnostics to optimize waterflooding. In particular, we discretize in finite volume the flow equation from Darcy’s law single-phase incompressible flow steady state combining with two auxiliary flow equations, time of flight and stationary tracers using the two-point flux approximation to describe fluid particles motion and flow lines. In addition, with the estimation of dynamic heterogeneity, we compute the Lorenz coefficient to highlight the reservoir flow and storage capacity characterization. To optimize waterflooding rates, we first, use an objective function the equalized Lorenz coefficient got through the evaluation of average travel time in cells to increase sweep efficiency and decrease the dynamic heterogeneity coefficient. Second, following the same target, we use the flow diagnostic interactive tools to study the volumetric sweep displacement front and harmonize the flooding breakthrough. In this work, our conceptual approach is to see the reservoir initially filled with oil; then, optimizing the Lorenz coefficient leads us to an oil recovery improvement. To be pragmatic, we apply our waterflooding performance optimization model on two case studies, the ninth SPE comparative solution project, a reexamination of black-oil (synthetic case) and ZHNBA Chinese oilfield (real field dataset).

The self-induced motion of a helical vortex

Helical vortices have been studied for more than a century to understand basic aspects of fluid motion. Helical vortices appear both in nature, e.g. as tornadoes, and in many industrial applications associated with mixing and in wakes behind rotors. Owing to the complexity of the equations governing the self-induced motion of helical vortices, it has up to now not been possible to obtain closed-form solutions describing all aspects of the motion. An important issue concerns the difference between the self-induced motion of the helical structure and the movement of fluid particles located on the helix. Here, we revisit the equations governing both the motion of the helical vortex structure and the motion of material fluid elements on the axis of the helix, and for both cases derive closed-form solutions for the resulting velocities. As a part of the paper, we also devise potential applications of the achieved knowledge.

RESEARCH OF FLUID FLOW IN TWO-DIMENSIONAL AND THREE-DIMENSIONAL FORMULATION IN THE FLOW PART OF A HIGH-PRESSURE FRANCIS TURBINE

The paper presents some results of a computational study of the spatial flow of a viscous fluid in a high-pressure Francis turbine Fr500 (in the optimal mode). To improve the energy performance at the preliminary design stage of the turbine, numerical flow simulations should be carried out. The difficulty of solving the problem posed is due both to the complex spatial geometry of the blade system of the runner and the varying degree of influence of the working bodies on the formation of energy characteristics. This CFD approach reduces costs and time in comparison with the experimental approach and makes it possible to improve and analyze turbine performance and its design before the model is manufactured. The computational complex of programs provides an opportunity to see the picture of pressure distribution, the field of velocity vectors and the movement of fluid particles for substantiation and analysis of results. Numerical modeling of the spatial flow in the flow part of the turbine was carried out to determine changes in the energy characteristics, therefore, the k - ε turbulence model was chosen, this model is the most successful model of first-level turbulence of the circuit. The results of the computational study confirm that the hydraulic efficiency of a hydraulic turbine largely depends on the losses in the guide vane and the runner, which means it is these elements that should be given the most attention, their design and coordination of the flow in them. Analysis of the energy loss in the flow part of the Francis turbine was carried out using programs for calculating fluid flow in two-dimensional and three-dimensional formulation. The obtained calculated data correspond to the previously known experimental recommendations for high-pressure Francis turbine. The issues of increasing the energy performance of a projected high-pressure Francis turbine were considered.

Analysis of energy losses in smooth pipes

Pipe is a closed conduit, usually of circular section, which is used for carrying fluids under pressure. The pipe running partially full, in such a case atmospheric pressure exists inside the pipe, also behaves like an open channel. In general, energy or head losses on pipe consisted of major energy losses due to friction and minor energy losses due to sudden enlargement of pipe, sudden contraction of pipe, bend in pipe, an obstruction in pipe, pipe fittings etc. The main purpose from this research is to analyse energy losses in smooth pipes. There are several steps in analysing such as calculating Reynolds Number (Re) in order to determine flow type, calculating friction factor by using several formulas, and calculating roughness value (k) on smooth pipe with different various scenarios. The experimental study was performed at Hydraulics and Fluid Mechanics Laboratory to process the analysis. The results indicated that the flow type is turbulent when Reynolds Number (Re) is more than 4000. The turbulent flow is characterized by random and irregular movement of fluid particles. The other result also shown that roughness value (k) in smooth pipe is inverse proportion to Reynolds Number.

A Lagrangian approach for computational acoustics with particle-based method

Although Eulerian approaches are standard in computational acoustics, they are less effective for problems with moving boundaries and multiphase systems like bubble acoustics. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically with particle-based methods. Fluid dynamic equations is divided into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, the smoothed particle hydrodynamics (SPH) method and the corrective smoothed particle (CSP) method are introduced to solve the perturbation equations in Lagrangian form. A hybrid meshfree and finite-difference time-domain boundary treatment technique is utilized to represent acoustic boundaries. Finally, applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP method exhibits accuracy convergence in cases with different background flow. Different acoustic boundary conditions are validated as being effective for benchmark problems in computational acoustics.

Anisotropic dynamics of nanoparticles in clusters at a solid-liquid interface by laser trapping

It is well-recognized that the Brownian motion of particles in fluids is random. Nevertheless, there can be characteristics depending on the specific physical conditions. We analyze the system of nanoparticle clusters formed by the laser trapping force field at the solid-liquid interface, based on the microscopy movie data. Since the laser trapping force field is basically a function of radial distance from the focal point in the two dimension at the liquid-solid interface, we examine the difference of displacement distributions in the radial and circumferential directions. The results show that the basic characteristics in this system depends on the laser power, and there is an anisotropy in the stochastic motion of the nanoparticles.