Lagrangian Particle Dynamics Research Articles

A drag coefficient model for Lagrangian particle dynamics relevant to high-speed flows

A blended drag coefficient model is constructed using a series of empirical relations based on Reynolds number, Mach number, and Knudsen number. When validated against experiments, the drag coefficient model produces matching values with a standard deviation error of 2.84% and a maximum error of 11.87%. The model is used in a Lagrangian code which is coupled to a hypersonic aerothermodynamic CFD code, and the particle velocity and trajectory are validated against experimental results. The comparative results agree well and show that the new blended drag coefficient model is capable of predicting the particle motion accurately over a range of Reynolds number, Mach number, and Knudsen number.

Effects of hydrophobicity, tethering and size on flow-induced activation of von Willebrand factor multimers

Von Willebrand factor (VWF) is a multimeric protein of blood plasma that mediates platelet adhesion to injury under strong hemodynamic flows in arterias and microvasvulature. We present a 3D coarse-grained computer model of VWF multimers in flowing viscous fluid that explicitely grasps the dynamics, the conformational changes and the hydrodynamics-induced activation of adhesivity of these protein concatamers to GPIb receptor of blood platelets. The model is based on the fluctuating Lattice Boltzmann method for modelling the hydrodynamics in the simulation box and the Lagrangian particle dynamics coupled to the fluid by a viscous drag force. The model has been validated by the comparison with the experimental data found in literature. We studied the effect of hydrophobic interactions on the conformational dynamics of VWF multimers. The simulations suggest that the contour length is an important parameter that controls the functionality of VWF multimers in blood. We also demonstrate that tethering to the surface of a vessel wall promoted the flow-induced activation of VWF, while those multimers that remain untethered and move freely in the blood plasma require a stronger shearing to get activated.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Hydrodynamic repulsion of spheroidal microparticles from micro-rough surfaces.

Isolation of microparticles and biological cells from mixtures and suspensions is a central problem in a variety of biomedical applications. This problem, for instance, is of an immense importance for microfluidic devices manipulating with whole blood samples. It is instructive to know how the mobility and dynamics of rigid microparticles is altered by the presence of micrometer-size roughness on walls. The presented theoretical study addresses this issue via computer simulations. The approach is based on a combination of the Lattice Boltzmann method for calculating hydrodynamics and the Lagrangian Particle dynamics method to describe the dynamics of cell membranes. The effect of the roughness on the mobility of spheroidal microparticles in a shear fluid flow was quantified. We conclude that mechanical and hydrodynamic interactions lift the particles from the surface and change their mobility. The effect is sensitive to the shape of particles.

Continuous time random walks for the evolution of Lagrangian velocities

We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of the mean particle velocity, velocity covariance and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions which are tailed toward low velocities as well as marked differences depending on the initial conditions. The developed CTRW approach predicts the Lagrangian particle dynamics from an arbitrary initial condition based on the Eulerian velocity distribution and a characteristic correlation scale.

Experimental and numerical parametric analysis of a reoriented duct flow

This study concerns a coupled experimental–numerical analysis of scalar transport in reoriented duct flows found in industrial mixing processes. To this end the study adopts the Rotated Arc Mixer (RAM) as the representative configuration. The focus is on the effects of geometrical (i.e. reorientation angle Θ) and temporal (i.e. reorientation frequency τ) parameters of generic inline mixing devices on the Lagrangian particle dynamics and scalar field evolution. Lagrangian dynamics are investigated by constructing Poincaré sections from analytic flow solutions and stroboscopic measurements of particle positions in 2D RAM laboratory setup. In order to obtain the optimal mixing and homogenization of scalar fields, dye visualizations are performed for an extensive set of parameters. The mixing quality in parameter space is quantitatively evaluated by means of the intensity of segregation. These results are used to determine the optimum forcing protocol. The outcome of this study validates the qualitative agreement in mixing characteristics of 2D time-periodic and 3D spatially-periodic flows and confirms the good mixing performance found before for certain RAM configurations. Moreover, we demonstrate that even more efficient protocols can be devised by suitably tuning the sequence of the reorientation angle. This knowledge might eventually lead to optimized 3D reoriented duct flow mixers.

Linear Eсkman friction in the mechanism of the cyclone-anticyclone vortex asymmetry and in a new theory of rotating superfluid

The observed experimental and natural phenomenon of cyclone-anticyclone vortex asymmetry implies that a relatively more stable and showing a longer life, as well as a relatively more intense mode of rotation with an anticyclonic circulation direction (opposite to the direction of rotation of the medium as a whole) is realized as compared with an oppositely directed rotation of the cyclonic vortex mode. Until now, however, it was not a success to identify a universal triggering mechanism responsible for the formation of the corresponding breaking of chiral vortex symmetry. In this paper we reveal the said linear universal instability mechanism of breaking of chiral symmetry in the sign of vortex circulation in the rotating medium in the presence of linear Eckman friction. Results Obtained is a condition for the linear dissipative - centrifugal instability (DCI), which leads (only when considering the external linear Eckman friction for an abovethreshold value of rotation frequency of the underlying boundary surface of fluid) to the breaking of chiral symmetry in the Lagrangian fluid particle dynamics and the corresponding realization of the cyclone-anticyclone vortex asymmetry. Conclusion A new non-stationary solution to the problem for the disc which carries out weak axial-torsional oscillations in fluid with the frequency which are superimposed on its rotation with the previously considered frequency 0 ω in connection with the experimental data on the rotating superfluid helium II (see [ 16, 17 ]) has been found. It gives the possibility to conclude that the effects of external, linear on velocity, friction forces must be important to include into consideration for the solve of any fundamental problems of hydrodynamics in bounded systems (as for the blood dynamics in cardiovascular system, for example).

Relating Lagrangian and Eulerian horizontal eddy statistics in the surfzone

AbstractConcurrent Lagrangian and Eulerian observations of rotational, low‐frequency (10−4 to 10−2 Hz) surfzone eddies are compared. Surface drifters were tracked for a few hours on each of 11 days at two alongshore uniform beaches. A cross‐shore array of near‐bottom current meters extended from near the shoreline to seaward of the surfzone (typically 100 m wide in these moderate wave conditions). Lagrangian and Eulerian mean alongshore velocities V are similar, with a midsurfzone maximum. Cross‐shore dependent Lagrangian (σL) and Eulerian (σE) rotational eddy velocities, estimated from low‐pass filtered drifter and current meter velocities, respectively, also generally agree. Cross‐shore rotational velocities have a midsurfzone maximum whereas alongshore rotational velocities are distributed more broadly. Daily estimates of the Lagrangian time scale, the time for drifter velocities to decorrelate, vary between 40 and 300 s, with alongshore time scales greater than cross‐shore time scales. The ratio of Lagrangian to apparent Eulerian current meter decorrelation times TL/TA varies considerably, between about 0.5 and 3. Consistent with theory, some of the TL/TA variation is ascribable to alongshore advection and TL/TA is proportional to V/σ, which ranges between about 0.6 and 2.5. Estimates of TL/TA vary between days with similar V/σ suggesting that surfzone Lagrangian particle dynamics vary between days, spanning the range from “fixed‐float” to “frozen‐field” [Lumpkin et al., 2002], although conclusions are limited by the statistical sampling errors in both TL/TA and V/σ.

Lagrangian Detection of Wind Shear for Landing Aircraft

AbstractRecent studies have shown that aerial disturbances affecting landing aircraft have a coherent signature in the Lagrangian aerial particle dynamics inferred from ground-based lidar scans. Specifically, attracting Lagrangian coherent structures (LCSs) mark the intersection of localized material upwelling within the cone of the lidar scan. This study tests the detection power of LCSs on historical landing data and corresponding pilot reports of disturbances from Hong Kong International Airport. The results show that a specific LCS indicator, the gradient of the finite-time Lyapunov exponent (FTLE) field along the landing path, is a highly efficient marker of turbulent upwellings. In particular, in the spring season, projected FTLE gradients closely approach the efficiency of the wind shear alert system currently in operation at the airport, even though the latter system relies on multiple sources of data beyond those used in this study. This shows significant potential for the operational use of FTLE gradients in the real-time detection of aerial disturbances over airports.

Modeling of Bombardment Ejections in the Rotorcraft Brownout Problem

The modeling of bombardment ejections, as they affect the uplift of dust particles and the formation of a brownout dust cloud generated by a rotorcraft in ground effect operations, is discussed. Bombardment ejections take place when a previously suspended particle in the flow collides with a sediment bed and ejects many more particles, leaving a crater behind. A model, based in part from research in aeolian sediment transport, was developed to better represent the mechanisms of bombardment-induced particle ejections during rotorcraft brownout conditions. This method was then coupled to a Lagrangian solver for the rotor flow and a Lagrangian particle dynamics simulation. It is shown how bombardment can play a critical role in the uplift and entrainment of smaller-sized particles from the underlying bed below a rotor. In particular, it is shown how the rotor blade tip vortices and/or regions of flow recirculation near the rotor can eject many particles by bombardment, resulting in the rapid development of intense dust clouds. The formation of vortex wake bundling ahead of the rotor disk was shown to provide the conditions particularly ripe for the ejection and uplift of large quantities of dust particles by means of bombardment mechanisms.

An improved known vicinity algorithm based on geometry test for particle localization in arbitrary grid

The known vicinity algorithm based on the geometry test for the particle localization problem in the hybrid Eulerian–Lagrangian model was extended and enhanced aiming at the connected grids with convex polygon/polyhedral cells. Such extensions were achieved by proposing novel improvements. Specifically, a new “side function”, to determine the relative position of the particle and the cell, was introduced to build a more formal test process. In addition, a binary search method was developed to accelerate the particle in cell test and trajectory/face intersection test for grids consisting of arbitrary polygon/polyhedral cells. Further, the particle location problem without the known vicinity position was established and solved by special boundary treatment through considering the internal/external boundary and larger particle displacement in one single Lagrangian step. The improved algorithm was applied to the particle location problem with both two dimensional and three dimensional Eulerian grids. Additionally, the proposed algorithm was compared with the previous ones to exhibit its higher efficiency and broader application. Sample cases focusing the water impingement computation for aircraft icing were solved by adopting this algorithm assisted by the Lagrangian particle dynamics model, and the computational results were verified by the experiments.

Three-dimensional instabilities in non-parallel shear stratified flows

The instabilities of non-parallel flows ($\overline{U}(x_3)$, $\overline{V}(x_3), 0)$ ($\overline{V} \ne 0$) such as those induced by polarized inertia-gravity waves embedded ina stably stratified environment are analyzed in the contextof the 3D Euler-Boussinesq equations. We derive a sufficient conditionfor shear stability and a necessary condition for instability in the case ofnon-parallel velocity fields. Three dimensional numerical simulations of the full nonlinear equations are conducted to characterize the respective modes of instability, their topology and dynamics, and subsequent breakdown into turbulence.We describe fully three-dimensional instability mechanisms, and study spectral properties of the most unstable modes.Our stability/instability criteria generalizes that inthe case of parallel shear flows ($\bar{V}=0$), where stability properties are governedby the Taylor-Goldstein equations previously studiedin the literature.Unlike the case of parallel flows, the polarized horizontal velocity vector rotating with respect to the vertical coordinate ($x_3$) excites unstable modes that have different spectral properties depending on the orientation of the velocity vector. At each vertical level, the horizontal wave vector of the fastest growing mode is parallel to the local vector ($ d\overline{U}(x_3)/dx_3$, $d \overline{V}(x_3)/dx_3)$. We investigate three-dimensional characteristics ofthe unstable modes and present computational results on Lagrangian particle dynamics.

Spatial Markov processes for modeling Lagrangian particle dynamics in heterogeneous porous media

We investigate the representation of Lagrangian velocities in heterogeneous porous media as Markov processes. We use numerical simulations to show that classical descriptions of particle velocities using Markov processes in time fail because low velocities are much more strongly correlated in time than high velocities. We demonstrate that Lagrangian velocities describe a Markov process at fixed distances along the particle trajectories (i.e., a spatial Markov process). This remarkable property has significant implications for modeling effective transport in heterogeneous velocity fields: (i) the spatial Lagrangian velocity transition densities are sufficient to fully characterize these complex velocity field organizations, (ii) classical effective transport descriptions that rely on Markov processes in time for the particle velocities are not suited for describing transport in heterogeneous porous media, and (iii) an alternative effective transport description derives from the Markovian nature of the spatial velocity transitions. It expresses particle movements as a random walk in space time characterized by a correlated random temporal increment and thus generalizes the continuous time random walk model to transport in correlated velocity fields.

Cluster integration method in Lagrangian particle dynamics

An efficient and robust approach is proposed in order to conduct numerical simulations of collisional particle dynamics in the Lagrangian framework. Clusters of particles are made of particles that interact or may interact during the next global time-step. Potential collision partners are found by performing a test move, that follows the patterns of a hard-sphere model. The clusters are integrated separately and the collisional forces between particles are given by a soft-sphere collision model. However, the present approach also allows longer range inter-particle forces. The integration of the clusters can be done by any one-step ordinary differential equation solver, but for dilute particle systems, the variable step-size Runge–Kutta solvers as the Dormand and Prince scheme [J. Comput. Appl. Math. 6 (1980) 19] are superior. The cluster integration method is applied on sedimentation of 5000 particles in a two-dimensional box. A significant speed-up is achieved. Compared to a traditional discrete element method with the forward Euler scheme, a speed-up factor of three orders of magnitude in the dilute regime and two orders of magnitude in the dense regime were observed. As long as the particles are dilute, the Dormand and Prince scheme is ten times faster than the classical fourth-order Runge–Kutta solver with fixed step size.

LES of bubble dynamics in wake flows

The results of large eddy simulations (LES) of turbulent bubbly wake flows are presented. The LES technique was applied together with the Lagrangian particle dynamics method and a random flow generation (RFG) technique to the cases of a two-phase bubbly mixing layer and the high-Reynolds number bubbly ship-wake flows. The validation was performed on the experimental data for the bubbly mixing layer. Instantaneous distributions and probability density functions of bubbles in the wake were obtained using a joint LES/RFG approach. Separate estimates of bubble decay due to dissolution and buoyancy effects were obtained. The analysis of bubble agglomeration effects was done on the basis of experimental data for a turbulent vortex to satisfy one-way coupling that is used in this study.

Multiphysics Modelling Environment for Continuum And Discrete Dynamics

A model-development environment for simulation of discrete and continuum dynamics in complex 3D geometries is described. This environment is based on 3D libraries for manipulation of geometrical primitives, object-oriented multidomain modelling paradigm, continuum solvers on unstructured meshes, discrete particle solvers, and a tool-assisted grid generation technique. The numerical approach is based on combined control-volume and finite-element methods of continuum mechanics and Lagrangian particle dynamics method. Several prototype example cases of complex continuum mechanical systems are considered, such as flow in bifurcating channels, including particle transport and deposition, flow interactions with flexible membranes and rigid structures, and a simplified model of molecular dynamics represented by a system of particles and bonds.

Multiphysics Modelling Environment for Continuum and Discrete Dynamics

AbstractA model-development environment for simulation of discrete and continuum dynamics in complex 3D geometries is described. This environment is based on 3D libraries for manipulation of geometrical primitives, object-oriented multidomain modelling paradigm, continuum solvers on unstructured meshes, discrete particle solvers, and a tool-assisted grid generation technique. The numerical approach is based on combined control-volume and finite-element methods of continuum mechanics and Lagrangian particle dynamics method. Several prototype example cases of complex continuum mechanical systems are considered, such as flow in bifurcating channels, including particle transport and deposition, flow interactions with flexible membranes and rigid structures, and a simplified model of molecular dynamics represented by a system of particles and bonds.

Design relations for predicting surface-ice clearing capacity of open channels

Numerical simulations are performed to evaluate the impact of various hydraulic and environmental parameters on the ice clearing capacity of a Lac St-Pierre navigation channel. The Lagrangian particle-dynamics (Pdyn) model is used to simulate a wide range of "operating" conditions that are representative of conditions observed on Lac St-Pierre. Simple relationships are developed that express both ice velocity and flux as functions of the geometry of the channel (width and plan-form shape) and ambient conditions (ice concentration, thickness, water current, wind magnitude and direction). These relationships reflect the importance of wind characteristics and areal ice concentration in regard to predicting both surface ice velocities and flux.Key words: ice clearing, channel geometry, ambient conditions.

3-Dimensional Large Signal Modelling of High Power CCTWTs

An improved 3-dimensional large-signal model has been developed for design and interactive simulation of high power Coupled Cavity Travelling-Wave Tubes (CCTWTs) based on Lagrangian particle dynamics. It has been shown that both the accuracy and computational speed can be improved by suitably modelling the rf beam incorporating a few modifications in the existing theory. In order to validate the efficiency of the model, two tubes have been analysed, one a low power low space-charge NASA CTS 200W tube and the other a high power high space-charge 10KW tube for which experimental results are available in the literature. The analytical results show good agreement with the experimental results with an increase in the computational speed by 20-22%.