Boundary Element Simulation Research Articles

Boundary element simulations of dynamic wetting with a mesoscale contact line model

It is known that numerical simulations of moving contact lines are challenging owing to the fact that multiple scales are inherently involved. In this paper, we propose an efficient boundary element method for numerical simulations of dynamic wetting/dewetting. The flow domain is truncated in a mesoscopic scale, where boundary conditions resulted from a wedge flow and the asymptotic theory of the intermediate region are imposed. This procedure avoids the high resolution near the contact line in full-scale simulations and hence significantly reduces the computational cost. Numerical tests for dip coating problem show that the meniscus profiles and slopes produced by the proposed method agree well with high-resolution full-scale simulations as well as the local asymptotic theory.

Optimal hydraulic PTO and linear permanent magnet generator for a floating two-buoy wave energy converter

A fully coupled fluid-structure-power take-off model is used to investigate the optimal energy capture of a floating two-buoy wave energy converter excited by regular waves and irregular waves. The system incorporates hydraulic power take-off and a linear permanent magnet generator. By considering the coupling relationship between the power take-off parameters for regular waves, a power take-off parameter interval is determined for the optimization model. Parametric optimization of the hydraulic power take-off and linear permanent magnet generator systems is proposed, based on response surface methodology in conjunction with central combination design for sensitivity analysis and optimal configuration of different parameters. The methodology efficiently predicts optimal electric efficiency while reducing the requirement for multiple boundary element simulations. It is found that a model with predicted optimal configuration of the hydraulic power take-off system can achieve 10 % more electrical efficiency than that with linear permanent magnet generator. Comparison between the energy capacities of the different systems indicates that a device with linear permanent magnet generator attains higher energy conversion efficiency within a wider power take-off bandwidth. This study provides guidance for the design and selection of efficient power take-off systems for floating two-buoy wave energy converters.

Reflective vortex focusing for acoustic contact-free object rotation

The use of acoustic vortex waves with angular momentum is a promising means of transferring mechanical torque to an object without making any physical contact. However, the existing passive-conversion vortex lenses are unable to produce strong acoustic radiation torque. To address this issue, we propose a flat reflector sculpted by spiral grooves. It reflects and converts incident waves into vortex-focusing waves that generate radiation torque. Compared with a transmission-type lens, a reflection-type vortex focusing plate exhibits superior functionality in converging sound waves and creating a stronger circular intensity flow. In this work, we analyze the vortex-focusing sound by Rayleigh-Sommerfeld integral theory and boundary element simulation, confirmed by experiments. The number, depth and direction of spiral grooves determine the topological charge, focusing intensity and torque direction, respectively. We evaluate the local and total acoustic radiation forces and torques, acting on small and large fixed spherical targets in the vortex-focusing beam. As a result, spinning a centimeter-size origami pinwheel several times larger than the wavelength at 40 kHz is realized without direct contact, by utilizing the enhanced acoustic radiation torque converged by the reflector. This technology enables efficient convergence of acoustic waves and simultaneous contactless transfer of mechanical torque to an object, thereby presenting potential applications in sound energy harvesting and wireless power supplies.

Slow motion of a sphere near a sinusoidal surface

Particle motion near non-plane surfaces can exhibit intricate hydrodynamics, making it an attractive tool for manipulating particles in microfluidic devices. To understand the underlying physics, this work investigates the Stokesian dynamics of a sphere near a sinusoidal surface, using a combination of perturbation analysis and boundary element simulation. The Lorentz reciprocal theorem is employed to solve the particle mobility near a small-amplitude surface. Compared with a plane wall, the curved topography induces additional translation and rotation velocity components, with the direction depending on the location of the sphere and the wavelength of the surface. At a fixed distance from the surface, the longitudinal and vertical mobilities of the sphere are strongly affected by the wavelength and amplitude of the surface, whereas its transverse mobility is only mildly influenced. When a sphere settles perpendicular to a sinusoidal surface, the far-field hydrodynamic effect drives the particle towards the local hill, while the near-field effect attracts the particle to the valley. These results provide valuable insights into the particle motion near surfaces with complex geometry.

Asymmetric bistability of chiral particle orientation in viscous shear flows.

The migration of helical particles in viscous shear flows plays a crucial role in chiral particle sorting. Attaching a nonchiral head to a helical particle leads to a rheotactic torque inducing particle reorientation. This phenomenon is responsible for bacterial rheotaxis observed for flagellated bacteria as Escherichia coli in shear flows. Here, we use a high-resolution microprinting technique to fabricate microparticles with controlled and tunable chiral shape consisting of a spherical head and helical tails of various pitch and handedness. By observing the fully time-resolved dynamics of these microparticles in microfluidic channel flow, we gain valuable insights into chirality-induced orientation dynamics. Our experimental model system allows us to examine the effects of particle elongation, chirality, and head heaviness for different flow rates on the orientation dynamics, while minimizing the influence of Brownian noise. Through our model experiments, we demonstrate the existence of asymmetric bistability of the particle orientation perpendicular to the flow direction. We quantitatively explain the particle equilibrium orientations as a function of particle properties, initial conditions and flow rates, as well as the time-dependence of the reorientation dynamics through a theoretical model. The model parameters are determined using boundary element simulations, and excellent agreement with experiments is obtained without any adjustable parameters. Our findings lead to a better understanding of chiral particle transport and bacterial rheotaxis and might allow the development of targeted delivery applications.

Bioeffects of microbubbles in tissue engineering: Modeling collapsing jets and microstreaming

Ultrasound contrast agents are micron-sized bubbles coated with lipids/proteins to stabilize them in the bloodstream. Apart from enhancing the contrast of the image, they have been implicated in numerous harmful and beneficial bioeffects. I will present an overview of our research emphasizing recent efforts on microbubbles-based non-invasive pressure estimation and ultrasound-assisted bone and cartilage tissue engineering in 3D printed scaffolds. Low-intensity pulsed ultrasound (LIPUS) in conjunction with microbubbles has been shown in our lab to facilitate bone and cartilage formation from mesenchymal stem cells. We will discuss nonlinear shape oscillations of microbubbles and acoustic microstreaming that are responsible for such bioeffects. We studied them using boundary element (BEM) simulation and perturbative analysis of an encapsulated microbubble near a vessel wall. For the BEM solution, the coating of the microbubble is modeled as a viscoelastic interface using an in-house developed strain-softening model (exponential elasticity model). The influence of the shell model on the stability of the numerical simulation during the microbubble jet formation has been investigated. The effects of ultrasound excitation parameters and mechanical properties of the coating, i.e., shell viscosity and elasticity, on the bubble behaviors and the velocity and pressure in the surrounding fluid, have been studied.

Multi‐fidelity Gaussian processes for an efficient approximation of frequency sweeps in acoustic problems

AbstractThis paper presents a multi‐fidelity model for the acceleration of frequency sweep analyses in acoustics. In traditional analyses, the frequency‐dependent Helmholtz equation is repetitively solved at each frequency. Using the boundary element method requires then a plethora of evaluations resulting in high computational costs. In the proposed method, the fidelity levels are realized as Gaussian processes, which are conditioned on observations obtained by boundary element simulations. A coarse boundary element mesh is considered as the low‐fidelity model, whereas a fine mesh is adopted as the high‐fidelity model. To validate the proposed framework, the vehicle interior noise problem is investigated. The results demonstrate that multi‐fidelity Gaussian processes efficiently accelerate the frequency sweep analysis, as they provide accurate and fast predictions across the entire frequency range of interest. As a beneficial side effect, the present method takes uncertainties into account. This allows to consider limited information on the model, which is particularly important in early design phases.

Performance prediction and design parameters sensitivity analysis of two-body point absorber wave energy harvesters

This paper introduces a novel model for predicting the performance and conducting sensitivity analysis of design parameters in two-body point absorber wave energy converters. The key novelty lies in the examination of design parameter sensitivity and their interaction effects on performance. The model utilizes the response surface method (RSM) in conjunction with central composite design to establish analytical equations for efficiently predicting the resonance frequency and peak generated power of the two-body wave energy converters based on geometric parameters and wave height. This eliminates the need for complex analytical solutions and boundary element simulations. The accuracy and reliability of the RSM prediction models are validated through state-of-the-art numerical simulations and analysis of variance (ANOVA). Using these RSM prediction models, the study proceeds to design and optimize two-body point absorbers for locations along the coastlines of the six Australian states, focusing on two objectives: maximizing peak output power and maximizing the power-to-weight ratio at each location. By incorporating the second optimization target, it is observed that impressive power output with smaller device dimensions or a higher power-to-weight ratio can be achieved across all six Australian states. The developed response surface method prediction model is a versatile mathematical framework applicable to all two-body point absorber wave energy converters and can be adapted for optimizing other types of wave energy converters with expansive search spaces. Australia was selected as a case study due to its abundant wave energy density along its southern shorelines. Notably, no similar studies addressing these specific aspects have been reported in the literature, making this work the first of its kind.

Inverse scheme for sound source identification in a vehicle trailer

Tire/road noise is a highly relevant topic for improving the comfort and experience of drivers and residents living in high-traffic areas. With the growing numbers of electric cars, the relevance of tire noise even increases since it is the dominant sound source in the middle-speed range. We investigate acoustic sources relevant to tire/road interactions. In doing so, we apply different sound source localization algorithms to measurement data acquired inside a large measurement trailer equipped with microphone arrays. The methods for sound source identification used are well-known beamforming-based algorithms and inverse schemes based on finite element or boundary element simulations. The latter schemes require the identification of the acoustic properties of the trailer in the stationary case. In this contribution, we present the characterization process and the results of the sound source localization in this stationary case.

Boundary Element Analysis for Mode III Crack Problems of Thin-Walled Structures from Micro- to Nano-Scales

This paper develops a new numerical framework for mode III crack problems of thin-walled structures by integrating multiple advanced techniques in the boundary element literature. The details of special crack-tip elements for displacement and stress are derived. An exponential transformation technique is introduced to accurately calculate the nearly singular integral, which is the key task of the boundary element simulation of thin-walled structures. Three numerical experiments with different types of cracks are provided to verify the performance of the present numerical framework. Numerical results demonstrate that the present scheme is valid for mode III crack problems of thin-walled structures with the thickness-to-length ratio in the microscale, even nanoscale, regime.

Numerical investigation of the effect of surface viscosity on droplet breakup and relaxation under axisymmetric extensional flow

In this study, we perform boundary-integral simulations to investigate the role of interfacial viscosity in the deformation and breakup of a single droplet suspended in an axisymmetric extensional flow under the Stokes flow regime. We model the insoluble surfactant monolayer using the Boussinesq–Scriven constitutive relationship for a Newtonian interface. We compare the deformation and breakup results from our boundary-element simulations with results from small deformation perturbation theories. We observe that the surface shear/dilational viscosity increases/decreases the critical capillary number beyond which the droplet becomes unstable and breaks apart by reducing/increasing the droplet deformation at a given capillary number compared with a clean droplet. We present the relative importance of surface shear and dilational viscosity on droplet stability based on their measured values reported in experimental studies on surfactants, lipid bilayers and proteins. In the second half of the paper, we incorporate the effect of surfactant transport by solving the time-dependent convection–diffusion equation and consider a nonlinear equation of state (Langmuir adsorption isotherm) to correlate the interfacial tension with the changes in surfactant concentration. We explore the coupled influence of pressure-dependent surface viscosity and Marangoni stresses on droplet deformation and breakup. In the case of a droplet with pressure-dependent surface shear viscosity, we find that a droplet with pressure-thinning/thickening surfactant is less/more deformed than a droplet with pressure-independent surfactant. We conclude by discussing the combined impact of surface viscosity and surfactant transport on the relaxation of an initially extended droplet in a quiescent external fluid.

Small deformation theory for a magnetic droplet in a rotating field

A three-dimensional small deformation theory is developed to examine the motion of a magnetic droplet in a uniform rotating magnetic field. The equations describing the droplet's shape evolution are derived using two different approaches—a phenomenological equation for the tensor describing the anisotropy of the droplet and the hydrodynamic solution using the perturbation theory. We get a system of ordinary differential equations for the parameters describing the droplet's shape, which we further analyze for the particular case when the droplet's elongation is in the plane of the rotating field. The qualitative behavior of this system is governed by a single dimensionless quantity τω—the product of the characteristic relaxation time of small perturbations and the angular frequency of the rotating magnetic field. Values of τω determine whether the droplet's equilibrium will be closer to an oblate or a prolate shape, as well as whether its shape will undergo oscillations as it settles to this equilibrium. We show that for small deformations, the droplet pseudo-rotates in the rotating magnetic field—its long axis follows the field, which is reminiscent of a rotation; nevertheless, the torque exerted on the surrounding fluid is zero. We compare the analytic results with boundary element simulation to determine their accuracy and the limits of the small deformation theory.

Boundary element simulation of a collapsing coated microbubble near a plane

Ultrasound contrast agents are gas core micron size bubbles coated with a layer of lipids/proteins to stabilize them against premature dissolution in the bloodstream. In addition to enhancing the contrast of the image, contrast agents have been implicated in numerous harmful and beneficial bioeffects. In the present study, ultrasound excited collapse of a coated microbubble near a plane has been studied using an axisymmetric Boundary Element method. The coating of the microbubble is modeled as a viscoelastic interface using an in-house developed strain-softening model (exponential elasticity model). The influence of the shell model on the stability of the numerical simulation during the microbubble jet formation has been investigated. The numerical approach was compared and validated with earlier studies. The effects of ultrasound excitation parameters and mechanical properties of the coating, i.e., shell viscosity and elasticity, on the bubble behaviors and the velocity and pressure in the surrounding fluid have been studied.

Crack-front model for adhesion of soft elastic spheres with chemical heterogeneity

Adhesion hysteresis can be caused by elastic instabilities that are triggered by surface roughness or chemical heterogeneity. However, the role of these instabilities in adhesion hysteresis remains poorly understood because we lack theoretical and numerical models accounting for realistic roughness. Our work focuses on the adhesion of soft elastic spheres with low roughness or weak heterogeneity, where the indentation process can be described as a Griffith-like propagation of a nearly circular external crack. We discuss how to describe the contact of spheres with chemical heterogeneity that leads to fluctuations in the local work of adhesion. We introduce a variational first-order crack-perturbation model and validate our approach using boundary-element simulations. The crack-perturbation model faithfully predicts contact shapes and hysteretic force-penetration curves, provided that the contact perimeter remains close to a circle and the contact area is simply connected. Computationally, the crack-perturbation model is orders of magnitude more efficient than the corresponding boundary element formulation, allowing for realistic heterogeneity fields.

Rheotaxis and migration of an unsteady microswimmer

Rheotaxis and migration of cells in a flow field have been investigated intensively owing to their importance in biology, physiology and engineering. In this study, first, we report our experiments showing that the microalgae Chlamydomonas can orient against the channel flow and migrate to the channel centre. Second, by performing boundary element simulations, we demonstrate that the mechanism of the observed rheotaxis and migration has a physical origin. Last, using a simple analytical model, we reveal the novel physical mechanisms of rheotaxis and migration, specifically the interplay between cyclic body deformation and cyclic swimming velocity in the channel flow. The discovered mechanism can be as important as phototaxis and gravitaxis, and likely plays a role in the movement of other natural microswimmers and artificial microrobots with non-reciprocal body deformation.

Three-dimensional parabolic equation for infrasound propagation above topography

The parabolic equation (PE) is one of the most popular methods for the modeling of low-frequency sound in the atmosphere. Over the past decades, considerable efforts have been dedicated to the inclusion of medium inhomogeneities, such as wind and turbulence, extending the PE to more realistic atmospheric conditions. On the other hand, few models take topography into account, while its effects on infrasound propagation are important in some cases. A new development has enabled the inclusion of irregular terrain in the narrow-angle 3DPE for a moving inhomogeneous medium [Khodr et al., JASA (2020)]. A coordinate transform similar to the Beilis-Tappert mapping used in 2D [Parakkal et al., JASA (2012)] is introduced to account for the variation in topography. The numerical solution relies on a Crank–Nicolson implicit scheme along the propagating direction. The pressure field at every step is computed with an iterative fixed-point algorithm which consists of a succession of tridiagonal systems that can be efficiently solved. A validation is performed against 3D Boundary Element simulations for propagation above a Gaussian hill in a homogeneous atmosphere. The existence of transversal scattering in the shadow zone, not represented by 2D models, is highlighted. Further developments include the extension of the method to a split-step wide-angle formulation. [This work was conducted at the University of Bristol in partnership with AWE Blacknest.]

Efficient and realistic 3-D boundary element simulations of underground construction using isogeometric analysis

The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The innovations refer to the introduction of isogeometric concepts, elasto-plastic analysis and the simulation of ground support. The introduction of isogeometric concepts for the description of the excavation boundaries results in less user and analysis effort, since complex geometries can be modelled with few parameters and degrees of freedom. No mesh generation is necessary. Heterogeneous and inelastic ground conditions are considered via general inclusions and rock bolts via linear inclusions. A comparison of results of test examples with other numerical methods and analytical solutions confirms the efficiency and accuracy of the proposed implementation. A practical example with a complex geometry is presented.

Analysis and Research on the Influence of Sonar Dome on Ship’s Underwater Electrostatic Field

This paper firstly analyzes the influence of the sonar dome on the ship’s underwater electrostatic field in theory, and then uses boundary element software to simulate and analyze this kind of influence. It is found that the sonar dome can be used as a cathode to participate in the electrochemical corrosion of ships, forming a “propeller-hull-sonar dome” corrosion system. In this case, the “dubble compensation anode” method is proposed in order to control the electric field signature, and the effectiveness of this method is verified by the boundary element simulation software.

Exploiting Combinatorics to Investigate Plasmonic Properties in Heterogeneous AgAu Nanosphere Chain Assemblies

AbstractChains of coupled metallic nanoparticles are of special interest for plasmonic applications because they can sustain highly dispersive plasmon bands, allowing strong ballistic plasmon wave transport. Whereas early studies focused on homogeneous particle chains exhibiting only one dominant band, heterogeneous assemblies consisting of different nanoparticle species came into the spotlight recently. Their increased configuration space principally allows engineering multiple bands, bandgaps, or topological states. Simultaneously, the challenge of the precise arrangement of nanoparticles, including their distances and geometric patterns, as well as the precise characterization of the plasmonics in these systems, persists. Here, the surface plasmon resonances in heterogeneous AgAu nanoparticle chains are reported. Wrinkled templates are used for directed self‐assembly of monodisperse gold and silver nanospheres as chains, which allows assembling statistical combinations of more than 109 particles. To reveal the spatial and spectral distribution of the plasmonic response, state‐of‐the‐art scanning transmission electron microscopy coupled with electron energy loss spectroscopy accompanied by boundary element simulations is used. A variety of modes in the heterogeneous chains are found, ranging from localized surface plasmon modes occurring in single gold or silver spheres, respectively, to modes that result from the hybridization of the single particles. This approach opens a novel avenue toward combinatorial studies of plasmonic properties in heterosystems.

A Fourier transform formulation for radiation from an unbaffled cylinder.

A formulation based on the Fourier transform and generalized functions, and implemented with a fast Fourier transform, is developed to solve a classic acoustics problem: radiation from an unbaffled cylinder with flat endcaps. The endcaps as well as the cylindrical surface have a specified modal vibration pattern, and the problem is solved using the sum of two independent formulations based on the Fourier transform: (1) a vibrating cylinder with rigid endcaps and (2) a rigid cylindrical tube with vibrating diaphragms at its ends. The resulting nearfield solution correctly models the diffraction effects generated at the sharp ends of the cylinder. Calculation of the farfield radiated pressure follows directly from the nearfield solutions with a slight modification to the standard formulas. Results from the formulations are validated with a boundary element simulation and show excellent agreement with errors of less than 1%.