Force-coupling Method Research Articles

Accelerating the force-coupling method for hydrodynamic interactions in periodic domains

The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for periodic domains involves utilising a compact or exponentially decaying kernel function to spread the force on the structure to a regular grid where the resulting flow and interactions can be computed efficiently using an FFT-based solver. A limitation to this approach is that the grid spacing must be chosen to resolve the kernel and thus, these methods can become inefficient when the separation between the structures is large compared to the kernel width. In this paper, we address this issue for the force-coupling method (FCM) by introducing a modified kernel that can be resolved on a much coarser grid, and subsequently correcting the resulting interactions in a pairwise fashion. The modified kernel is constructed to ensure rapid convergence to the exact hydrodynamic interactions and a positive-splitting of the associated mobility matrix. We provide a detailed computational study of the methodology and establish the optimal choice of the modified kernel width, which we show plays a similar role to the splitting parameter in Ewald summation. Finally, we perform example simulations of rod sedimentation and active filament coordination to demonstrate the performance of fast FCM in application.

Electro-Magnetic and Stress Analysis of a −400 T2/m High-Field Gradient Magnet with a Room-Temperature Bore Size of 200 mm

High-field-strength gradient superconducting magnets have been widely used in many fields. With advancements in technology, the demand for large-aperture magnets is gradually increasing, but there is relatively little research on the design and stress–strain of large-aperture gradient magnets. This article presents the design and analysis of a superconducting magnet characterized by a high field strength of 10 T, a strong gradient of −400 T2/m, and a large room-temperature bore of 200 mm. The aim of this project is to establish an experimental setup for the growth of Ga1−xInxSb crystals. The study starts with an overview of the development process and applied research related to strong-gradient magnets. The study employs a magneto–electric force coupling method based on generalized stretching to theoretically optimize the gradient coil pre-stress parameters through orthogonalization parameter scanning. In addition, an analysis of the stress distribution in both the magnet coil and the mandrel is carried out. The results indicate that the stress and strain values for both the gradient coils and the frame are within the allowable range of their respective materials. The magnets can be designed to operate stably in theory. This article may provide a reference for designers in related fields in optimizing the design and stress–strain analysis of large, strong-gradient magnets.

Hydrodynamic irreversibility of non-Brownian suspensions in highly confined duct flow

The irreversible behaviour of a highly confined non-Brownian suspension of spherical particles at low Reynolds number in a Newtonian fluid is studied experimentally and numerically. In the experiment, the suspension is confined in a thin rectangular channel that prevents complete particle overlap in the narrow dimension and is subjected to an oscillatory pressure-driven flow. In the small cross-sectional dimension, particles rapidly separate to the walls, whereas in the large dimension, features reminiscent of shear-induced migration in bulk suspensions are recovered. Furthermore, as a consequence of the channel geometry and the development and application of a single-camera particle tracking method, three-dimensional particle trajectories are obtained that allow us to directly associate relative particle proximity with the observed migration. Companion simulations of a steadily flowing suspension highly confined between parallel plates are conducted using the force coupling method, which also show rapid migration to the walls as well as other salient features observed in the experiment. While we consider relatively low volume fractions compared to most prior work in the area, we nevertheless observe significant and rapid migration, which we attribute to the high degree of confinement.

Comprehensive study on the nonlinear parameter vibrations of the rotor system due to the varying compliance of ball bearing

In this paper, based on the restoring force coupling method, a novel mathematical model is established to study the VC parameter vibration responses of the ball bearing-rotor system, and both the rotor radial and tilting motions have been considered. Firstly, the steady state analysis on the stiffness fluctuation is conducted to determine the equivalent linear resonant frequencies of the nonlinear ball bearing-rotor system. Secondly, both the two-way sweep-frequency and fixed frequency-analysis are adopted to study the different transient response mechanisms of the rotor VC parameter vibrations, Finally, the results show that not only the multiple resonant responses including the super-harmonic, sub-harmonic, Hopf bifurcation and chaos are generated for the rotor parametric vibration, but also the complex internal resonance phenomenon occurs when the rotor natural frequency ratio in different radial directions is close to 1:2.

Computing hydrodynamic interactions in confined doubly periodic geometries in linear time.

We develop a linearly scaling variant of the force coupling method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.

A PD-FEM approach for fast solving static failure problems and its engineering application

A method of coupling of peridynamics (PD) and finite element method (FEM) for fast solving static failure problems is proposed. It is based on the force coupling method and adopts interface elements to couple the PD and FE subregions. By assembling the global matrix of the coupling model and using the adaptive dynamic relaxation (ADR) method to solve it, the static solution of elasticity and crack growth problems can be obtained quickly. By introducing short-range repulsive force and re-defining the coupling force, it is not only suitable for simulating tensile failure problems, but also suitable for compression failure problems. Through comparative analysis, the accuracy and effectiveness of this approach are verified. And then the method is successfully applied to simulate the excavation process of an underground cavern group, and the simulation of damage and failure process of engineering rock mass under complex tension–compression conditions has been realized. The stability characteristics of the surrounding rock are revealed by analyzing the damage and deformation evolution laws. It provides an effective numerical simulation method for predicting the excavation damage zone (EDZ) distribution characteristics and deformation law of the surrounding rock during the excavation of an underground cavern group. At the same time, compared with pure PD, the calculation efficiency is greatly improved, which is of great significance for the realization of engineering-scale simulation.

Hydrochemical interactions of phoretic particles: a regularized multipole framework

Abstract

Parallel accelerated Stokesian dynamics with Brownian motion

We present scalable algorithms to simulate large-scale stochastic particle systems amenable for modeling dense colloidal suspensions, glasses and gels. To handle the large number of particles and consequent many-body interactions present in such systems, we leverage an Accelerated Stokesian Dynamics (ASD) approach, for which we developed parallel algorithms in a distributed memory architecture. We present parallelization of the sparse near-field (including singular lubrication) interactions, and of the matrix-free many-body far-field interactions, along with a strategy for communicating and mapping the distributed data structures between the near- and far field. Scaling to up to tens of thousands of processors for a million particles is demonstrated. In addition, we propose a novel algorithm to efficiently simulate correlated Brownian motion with hydrodynamic interactions. The original Accelerated Stokesian Dynamics approach requires the separate computation of far-field and near-field Brownian forces. Recent advancements propose computation of a far-field velocity using positive spectral Ewald decomposition. We present an alternative approach for calculating the far-field Brownian velocity by implementing the fluctuating force coupling method and embedding it using a nested scheme into ASD. This straightforward and flexible approach reduces the computational time of the Brownian far-field force construction from O(NlogN)1+|α| to O(NlogN).

Numerical Study of the Lift Force, Velocities and Pressure Distribution of a Single Air Bubble and Two Interacting Air Bubbles Rising in Quiescent Liquid

The study of multiphase flow consisting of liquid and air bubbles has been attracting the interest of many researchers. Numerical methods for such a system are, however, facing difficulty in numerical accuracy and a heavy computational load. In this paper, we made corrections to the modified force-coupling method in our previous papers and applied it to the numerical studies of a single air bubble rising near a vertical wall and two interacting air bubbles rising in line in quiescent liquid. Corrections were made to the effective ranges of the force-coupling method. The calculation results showed that the lift force acting on an air bubble obtained by the experimental data was more accurately reproduced than those by our previous method. We accurately calculated the time evolution of the velocities of interacting two air bubbles rising in line obtained in the previous experiments and resolved the physical mechanism of the relative movement of two bubbles. We also found the present method is much quicker and needs much smaller memory capacity than other methods, such as the volume of fluid method.

Shear thinning in non-Brownian suspensions explained by variable friction between particles

We propose to explain shear-thinning behaviour observed in most concentrated non-Brownian suspensions by variable friction between particles. Considering the low magnitude of the forces experienced by the particles of suspensions under shear flow, it is first argued that rough particles come into solid contact through one or a few asperities. In such a few-asperity elastic–plastic contact, the friction coefficient is expected not to be constant but to decrease with increasing normal load. Simulations based on the force coupling method and including such a load-dependent friction coefficient are performed for various particle volume fractions. The results of the numerical simulations are compared to viscosity measurements carried out on suspensions of polystyrene particles ($40~\unicode[STIX]{x03BC}\text{m}$in diameter) dispersed in a Newtonian silicon oil. The agreement is shown to be satisfactory. Furthermore, the comparison between the simulations conducted either with a constant or a load-dependent friction coefficient provides a model for the shear-thinning viscosity. In this model the effective friction coefficient$\unicode[STIX]{x1D707}^{eff}$is specified by the effective normal contact force which is simply proportional to the bulk shear stress. As the shear stress increases,$\unicode[STIX]{x1D707}^{eff}$decreases and the jamming volume fraction increases, leading to the reduction of the viscosity. Finally, using this model, we show that it is possible to evaluate the microscopic friction coefficient for each applied shear stress from the rheometric measurements.

Conditional stability of particle alignment in finite-Reynolds-number channel flow

Finite-size neutrally buoyant particles in a channel flow are known to accumulate at specific equilibrium positions or spots in the channel cross-section, if the flow inertia is finite at the particle scale. Experiments in different conduit geometries have shown that while reaching equilibrium locations, particles tend also to align regularly in the streamwise direction. In this paper, the force coupling method was used to numerically investigate the inertia-induced particle alignment, using square-channel geometry. The method was first shown to be suitable to capture the quasisteady lift force that leads to particle cross-streamline migration in channel flow. Then the particle alignment in the flow direction was investigated by calculating the particle relative trajectories as a function of flow inertia and of the ratio between the particle size and channel hydraulic diameter. The flow streamlines were examined around the freely rotating particles at equilibrium, revealing stable small-scale vortices between aligned particles. The streamwise interparticle spacing between aligned particles at equilibrium was calculated and compared to available experimental data in square-channel flow [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. The new result highlighted by our numerical simulations is that the interparticle spacing is unconditionally stable only for a limited number of aligned particles in a single train, the threshold number being dependent on the confinement (particle-to-channel size ratio) and on the Reynolds number. For instance, when the particle Reynolds number is ≈1 and the particle-to-channel height size ratio is ≈0.1, the maximum number of stable aligned particles per train is equal to 3. This agrees with statistics realized on the experiments of [Gao et al., Microfluid. Nanofluid. 21, 154 (2017)]. It is argued that when several particles are hydrodynamically connected moving as a unique structure (the train) with a steady streamwise velocity, large-scale hydrodynamic perturbations induced at the train scale prohibit small-scale vortex connection between the leading and second particles, forcing the leading particle to leave the train.

Simulation study of particle clouds in oscillating shear flow

Simulations of cylindrical clouds of concentrated, neutrally buoyant, suspended particles are used to investigate the dispersion of the particles in an oscillating Couette flow. In experiments by Metzger & Butler (Phys. Fluids, vol. 24 (2), 2012, 021703) with spherical clouds of non-Brownian particles, the clouds are shown to elongate at volume fraction $\unicode[STIX]{x1D719}=0.4$ but form ‘galaxies’ where the cloud rotates as a single body with extended arms when $\unicode[STIX]{x1D719}>0.4$ and the ratio of the cloud radius to particle radius, $R/a$, is sufficiently large. The simulations, which use the force coupling method, are completed for $\unicode[STIX]{x1D719}=0.4$ and $\unicode[STIX]{x1D719}=0.55$, with $R/a$ between $5$ and $20$. The cloud shape for $\unicode[STIX]{x1D719}=0.4$ is shown to be reversible at low strain amplitude, and extend in the streamwise direction along the centre of the cloud at moderate strain amplitude. For higher strain amplitude the clouds extend near the channel walls to form a parallelogram. The results demonstrate that the particle contact force determines the transition between these states and plays a large role in the irreversibility of the parallelograms. Rotating galaxies form at $\unicode[STIX]{x1D719}=0.55$ with $R/a\geqslant 15$, and are characterized by a particle-induced flow in the wall-normal direction.

Modulation of the regeneration cycle by neutrally buoyant finite-size particles

Direct numerical simulations of turbulent suspension flows are carried out with the force-coupling method in plane Couette and pressure-driven channel configurations. Dilute to moderately concentrated suspensions of neutrally buoyant finite-size spherical particles are considered when the Reynolds number is slightly above the laminar–turbulent transition. Tests performed with synthetic streaks, in both turbulent channel and Couette flows, show clearly that particles trigger the instability in channel flow whereas the plane Couette flow becomes laminar. Moreover, we have shown that particles have a pronounced impact on pressure-driven flow through a detailed temporal and spatial analysis whereas they have no significant impact on the plane Couette flow configuration. The substantial difference between the two flow configurations is related to the spatial preferential distribution of particles in the large-scale rolls (inactive motion) in Couette flow, whereas they are accumulated in the ejection (active motion) regions in pressure-driven flow. Through investigation of particle modification in two distinct flow configurations, we were able to show the specific response of turbulent structures and the modulation of the fundamental mechanisms composing the regeneration cycle in the buffer layer of the near-wall turbulence. Especially for pressure-driven flow, the particles enhance the lift-up and let it act continuously whereas the particles do not significantly alter the streak breakdown process. The reinforcement of the streamwise vortices is attributed to the vorticity stretching term by the wavy streaks. The smaller and more numerous wavy streaks enhance the vorticity stretching and consequently strengthen the circulation of large-scale streamwise vortices in suspension flow.

Simulations of Brownian tracer transport in squirmer suspensions

In addition to enabling movement towards environments with favourable living conditions, swimming by microorganisms has also been linked to enhanced mixing and improved nutrient uptake by their populations. Experimental studies have shown that Brownian tracer particles exhibit enhanced diffusion due to the swimmers, while theoretical models have linked this increase in diffusion to the flows generated by the swimming microorganisms, as well as collisions with the swimmers. In this study, we perform detailed simulations based on the force-coupling method and its recent extensions to the swimming and Brownian particles to examine tracer displacements and effective tracer diffusivity in squirmer suspensions. By isolating effects such as hydrodynamic or steric interactions, we provide physical insight into experimental measurements of the tracer displacement distribution. In addition, we extend results to the semi-dilute regime where the swimmer–swimmer interactions affect tracer transport and the effective tracer diffusivity no longer scales linearly with the swimmer volume fraction.

Transport of finite-size particles in a turbulent Couette flow: The effect of particle shape and inertia

The transport of finite-size particles in a turbulent plane Couette flow has been studied by particle-resolved numerical simulations based on the Force Coupling Method. The influence of the deviation of particle shape from sphericity was addressed, using neutrally buoyant spheroids with aspect ratio ranging from 0.5 to 2. The particle transport was compared to the case where the inertia of spherical particles was varied by considering different particle densities (while keeping comparable Stokes number). This work has shown that close to the wall, the symmetry axis of oblate particles is almost parallel to the wall-normal direction and the major axis of prolate particles tends to align in the flow direction. Both types of particles have a kayaking type of rotation in the core region which yields homogeneous collisions. The spatial particle distribution is strongly correlated to coherent structures. However, strong deviations occur for the most inertial particles which accumulate in the near wall region. Successive stages of accumulation and release in the streaks are observed while the regeneration cycle of turbulence proceeds. The case of massless bubbles is characterized by a very strong correlation with the large scale vortices that span over the depth of the Couette gap. Even though the particles do not modify drastically the flow, they have some effect on the fluctuating energy, as suggested from the pdf. This effect is more clear for non-spherical particles compared to the spherical ones with various density ratios.

Numerical study of the interaction between two air bubbles by the modified force-coupling method

Numerical study of the interaction between two air bubbles by the modified force-coupling method

A General Shear-Dependent Model for Thrombus Formation.

Modeling the transport, activation, and adhesion of platelets is crucial in predicting thrombus formation and growth following a thrombotic event in normal or pathological conditions. We propose a shear-dependent platelet adhesive model based on the Morse potential that is calibrated by existing in vivo and in vitro experimental data and can be used over a wide range of flow shear rates (). We introduce an Eulerian-Lagrangian model where hemodynamics is solved on a fixed Eulerian grid, while platelets are tracked using a Lagrangian framework. A force coupling method is introduced for bidirectional coupling of platelet motion with blood flow. Further, we couple the calibrated platelet aggregation model with a tissue-factor/contact pathway coagulation cascade, representing the relevant biology of thrombin generation and the subsequent fibrin deposition. The range of shear rates covered by the proposed model encompass venous and arterial thrombosis, ranging from low-shear-rate conditions in abdominal aortic aneurysms and thoracic aortic dissections to thrombosis in stenotic arteries following plaque rupture, where local shear rates are extremely high.

Application of the Modified Force-Coupling Method of Tracing the Trajectories of Spherical Bubbles with Solid-Like and Slip Surfaces

The force-coupling method (FCM) developed by Maxey and Patel (2001) was modified and applied to trace the trajectories of spherical bubbles with solid-like and slip surfaces. Careful comparison was made to the experimental results of Takemura et al. (2000, 2002a, 2002b). First, the result obtained by use of the original version of the FCM was compared to the experimental results. It was found that the original FCM was not feasible for tracing spherical bubble trajectories. Then, a correction was made to the FCM calculation of the bubble velocity by renormalization in terms of the bubble Reynolds number, which could very well trace the trajectory of the bubble with a solid-like, no-slip surface, but not that of a bubble with a slip surface. Finally, a substantial correction was made to the monopole term of the FCM, which could trace the trajectory of a bubble with a solid-like or slip surface very well even for the Reynolds number up to 20.

Rheology of non-Brownian suspensions of rough frictional particles under shear reversal: A numerical study

We perform particle scale simulations of suspensions submitted to shear reversal. The simulations are based on the Force Coupling method, adapted to account for short range lubrication interactions together with direct contact forces between particles, including surface roughness, contact elasticity, and solid friction. After shear reversal, three consecutive steps are identified in the viscosity transient: An instantaneous variation, followed by a rapid contact force relaxation, and finally a long time evolution. The separated contributions of hydrodynamics and contact forces to the viscosity are investigated during the transient, allowing a qualitative understanding of each step. In addition, the influence of the contact law parameters (surface roughness height and friction coefficient) on the transient is evaluated. Concerning the long time transient, the difference between the steady viscosity and minimum viscosity is shown to be proportional to the contact contribution to the steady viscosity, allowing in principle easy determination of the latter in experiments. The short time evolution is studied as well. After the shear reversal, the contact forces vanish over a strain that is very short compared to the typical strain of the long time transient, allowing to define an apparent step between the viscosity before shear reversal and after contact force relaxation. This step is shown to be an increasing function of the friction coefficient between particles. Two regimes are identified as a function of the volume fraction. At low volume fraction, the step is small compared to the steady contact viscosity, in agreement with a particle pair model. As the volume fraction increases, the value of the viscosity step increases faster than the steady contact viscosity, and, depending on the friction coefficient, may approach it.

1407 Force-coupling methodによる気泡と壁面の相互作用に関する研究(流体工学VIII)

1407 Force-coupling methodによる気泡と壁面の相互作用に関する研究(流体工学VIII)