Immersed Boundary Research Articles

Numerical investigation of dust sedimentation effects on wall adsorption of indoor SVOC by the immersed boundary-lattice Boltzmann method

In this work the lattice Boltzmann method (LBM) is used to investigate semi-volatile organic compounds (SVOCs) mass transfer under the influence of particle sedimentation in the boundary-layer scale region. For the fluid-particle interaction, the direct-forcing immersed boundary (IB) method is applied to calculate the hydro-dynamic force. A mass-transfer IB method is employed to calculate the fluid-particle SVOC flux. Particles with zero and saturated initial-concentrations are studied to investigate the effects of clean and polluted particles. Effects of fluid/particle equilibrium coefficients, as well as particle diameters, are discussed. Wall adsorptions under the influence of multiple particles are also investigated. Numerical simulations reveal that a particle always intensifies wall adsorption independent of its initial SVOC concentration. The influences of particles on wall adsorption are associated with disturbance effect (disturbing air due to particle moving) and medium effect (SVOC mass transfer between particles and their surrounding air). Disturbance effect of clean particles overwhelms their medium effect while medium effect is dominant for saturated particles. Disturbance effect and medium effect both increase with particle diameter, and medium effect is more sensitive to particle diameter. Competitive adsorption occurs in presence of a number of particles and has an indirect impact on wall adsorption.

Dependence of the wake recovery downstream of a Vertical Axis Wind Turbine on its dynamic solidity

The momentum recovery downstream of a Vertical Axis Wind Turbine (VAWT) is analyzed as a function of its dynamic solidity, modified changing both the number of blades and the rotational speed of the turbine. Computations were carried out using Large-Eddy Simulations (LES), coupled with an Immersed-Boundary (IB) methodology. The streamwise increase of the momentum deficit in the near wake was found dominated by negative cross-stream advection, due to wake expansion, and especially negative pressure transport. Both of them were found larger at higher values of dynamic solidity. Downstream of the near wake region, the instability of the shear layers at both edges of the wake produced a substantial change of the wake topology and balance across momentum transport terms. The collapse of the shear layers into the wake core promoted wake recovery, via both positive cross-stream advection and turbulent transport. The destabilization of the wake system occurred earlier at larger values of dynamic solidity, producing this way a faster wake recovery, in spite of larger values of momentum deficit within the near wake. The switch to the wake of a bluff body was characterized by an increase of the energy at frequencies lower than that of the blades passage.

Study of drafting, kissing and tumbling process of two particles with different sizes using immersed boundary method in a confined medium

This paper numerically demonstrates the drafting, kissing, tumbling (DKT) phenomenon between two interacting circular, impermeable particles of different sizes in a confined medium for different scenarios using Immersed Boundary (IB) method in 2D. Two cases were considered for this particular problem. In the first case, referred to as Case 1, the trailing particle was larger in size than the leading particle and in Case 2, it was the other way round. The main emphasis of this paper was to investigate the effect of diameter ratio, γ, of the two particles, on the dynamics of the two sedimenting particles. In Case 1, it was observed that upon increasing γ from unity onwards, the particles underwent from repeated to one cycle of DKT. In Case 2, the impact of γ was more prominent. For γ<2, the particles underwent two cycles of DKT process. For γ≥2 the particles first parted away from each other, but then quickly started drafting towards each other. Subsequently, after one cycle of DKT, they permanently parted away from each other. This paper also investigated the effect of initial vertical distance between the two sedimenting particles. The results presented in here are in good agreement with other published articles on similar problems.

An immersed boundary formulation incorporating a two-layer wall model approach for RANS simulations with complex geometry

We propose an immersed boundary (IB) formulation incorporating a two-layer wall model approach for Reynolds-averaged Navier-Stokes (RANS) simulations with complex geometry. The main objective of the present study is to broaden the capability of the IB method to high-Reynolds number turbulent flows with non-equilibrium effects. A two-layer wall model is applied to the IB method by considering a thin boundary layer approximation near the wall in order to reduce the computational cost of resolving the turbulent boundary layer. Tangential pressure gradient and convective terms are included in the thin boundary layer equation to make the wall model suitable for non-equilibrium flows, in which cross-derivative terms are modeled along the wall-normal direction to maintain the ordinary differential form of the equation. Turbulent viscosity in the inner layer is determined using a simplified k−ϵ−fμ model, that performs better than the typical mixing-length model in the separation and reattachment regions, where the friction velocity uτ becomes zero. To impose the mass conservation constraint near the IB surface with marginal computational cost, the IB approximated domain method is applied. The proposed IB formulation is validated using numerical simulations of two-dimensional turbulent channel flow, backward-facing step flow, turbulent flow around a circular cylinder, and three-dimensional turbulent flow over a wall-mounted circular sphere with a relatively coarse grid near the IB surface. The results demonstrate that the proposed IB formulation captures the flow patterns well and accurately predicts wall shear stress for both equilibrium and non-equilibrium flows, even with a relatively coarse grid near the wall.

Evaluating Implementations of the Immersed Boundary Method in the Weather Research and Forecasting Model

AbstractThe terrain-following coordinate system used by many atmospheric models can cause numerical instabilities due to discretization errors as resolved terrain slopes increase and the grid becomes highly skewed. The immersed boundary (IB) method, which does not require the grid to conform to the terrain, has been shown to alleviate these errors, and has been used successfully for high-resolution atmospheric simulations over steep terrain, including vertical building surfaces. Since many previous applications of IB methods to atmospheric models have used very fine grid resolution (5 m or less), the present study seeks to evaluate IB method performance over a range of grid resolutions and aspect ratios. Two classes of IB algorithms, velocity reconstruction and shear stress reconstruction, are tested within the common framework of the Weather Research and Forecasting (WRF) Model. Performance is evaluated in two test cases, one with flat terrain and the other with the topography of Askervein Hill, both under neutrally stratified conditions. WRF-IB results are compared to similarity theory, observations, and native WRF results. Despite sensitivity to the location at which the IB intersects the model grid, the velocity reconstruction IB method shows consistent performance when used with a hybrid RANS/LES surface scheme. The shear stress reconstruction IB method is not sensitive to the grid intersection, but is less consistent and near-surface velocity errors can occur at coarse resolutions. This study represents an initial investigation of IB method variability across grid resolutions in WRF. Future work will focus on improving IB method performance at intermediate to coarse resolutions.

An immersed boundary method for fluid–structure–acoustics interactions involving large deformations and complex geometries

This paper presents an immersed boundary (IB) method for fluid–structure–acoustics interactions involving large deformations and complex geometries. In this method, the fluid dynamics is solved by a finite difference method where the temporal, viscous and convective terms are respectively discretized by the third-order Runge–Kutta scheme, the fourth-order central difference scheme and a fifth-order W/TENO (Weighted/Targeted Essentially Non-oscillation) scheme. Without loss of generality, a nonlinear flexible plate is considered here, and is solved by a finite element method based on the absolute nodal coordinate formulation. The no-slip boundary condition at the fluid–structure interface is achieved by using a diffusion-interface penalty IB method. With the above proposed method, the aeroacoustics field generated by the moving boundaries and the associated flows are inherently solved. In order to validate and verify the current method, several benchmark cases are conducted: acoustic waves scattered from a stationary cylinder in an inviscid quiescent flow, sound generation by a stationary and a rotating cylinder in a uniform flow, sound generation by an insect in hovering flight, deformation of a red blood cell induced by acoustic waves and acoustic waves scattered by a stationary sphere. The comparison of the sound scattered by a cylinder shows that the present IB–WENO scheme, a simple approach, has an excellent performance which is even better than the implicit IB–lattice Boltzmann method. For the sound scattered by a sphere, the IB–TENO scheme has a lower dissipation compared with the IB–WENO scheme. Applications of this technique to model fluid–structure-acoustics interactions of flapping foils mimicking an insect wing section during forward flight and flapping foil energy harvester are also conducted, considering the effects of foil shape and flexibility. The difference of the force and sound generations of the foils are compared. For wing during forward flight, the results show that flexible wing generates larger thrust with higher acoustic pressure. In terms of the energy harvester, the current results show that the geometrical shape has no significant effects on the force and sound generation, and the flexibility of the plate tends to deteriorate the power extraction efficiency. The flexible plate also induces larger fluctuating pressure at the frequency of 2f (f is the flapping frequency) and weaker sound at the frequencies of f and 3f. The successful validations and applications show that the IB method handled by delta function, whose accuracy is generally lower than that of the internal flow solver, is accurate for predicting the dilatation and acoustics, and thus is an attractive alternative for modeling fluid–structure–acoustics interactions involving large deformations and complex geometries.

Simulation of Fluid–Structure Interaction Problems with Thin Elastic Plate via the Coupling of Finite Element and Lattice Boltzmann Methods

A numerical framework is proposed to couple the finite element (FE) and lattice Boltzmann methods (LBM) for simulating fluid–structure interaction (FSI) problems. The LBM is used as an efficient method for solving the weakly-compressible fluid flows. The corotational FE method for beam elements is used to solve the thin plate deformation. The two methods are coupled via a direct-forcing immersed boundary (IB) method with a sub-iteration scheme. A virtual structure method has been developed to improve the computational accuracy. Validations of the proposed coupling method have been carried out by testing a vortex-induced vibration problem. The numerical results are in good agreement with [Li and Favier (2017), “A non-staggered coupling of finite element and lattice Boltzmann methods via an immersed boundary scheme for fluid-structure interaction,” Comput. Fluids 143, 90–102]. The proposed method does not require heavy linear algebra calculation, which is suitable for parallel computation.

Open-loop optimal control of a flapping wing using an adjoint Lattice Boltzmann method

We present the usage of an adjoint Lattice Boltzmann Method (LBM) for open-loop control of two-dimensional flapping wing motion. Movement of the wing is parametrised with periodic B-Splines, while the wing interacts with the surrounding flow via an Immersed Boundary (IB) method. Multi-objective optimisation is performed using a gradient optimisation algorithm, for which sensitivities are calculated with an adjoint method. The objectives selected were the mean lift force and mechanical power. To achieve performance suitable for optimisation, we also present an efficient GPU implementation of the LBM and adjoint LBM. The Immersed Boundary approach employed for the LBM is verified against results from the literature, while for the flapping case it is compared with two different Finite Volume Method (FVM) approaches. The obtained Pareto front of optimal designs shows a clear discrepancy between the power consumption and the mean lift force. A significant improvement of the basic wing design is demonstrated, and highlights the applicability of adjoint LBM simulations in complex open-loop control problems.

Numerical investigation on the incipient motion of non-spherical sediment particles in bedload regime of open channel flows

Theoretical analysis and nowadays advanced numerical simulations for bedload particle transport widely share a popular assumption: All sediments are spherical and can be simplified as spheres, which apparently differs from reality. In order to explore the shape effects of sediment particles on their transport and to find out the possible consequence originated from the spherical assumption, a particle resolved computational model is established by combining the large eddy simulation for fluid and the discrete element method for the solid particles using an immersed boundary (IB) technique. Using this model, simulations are conducted for spherical and non-spherical bedload particles in both laminar and turbulent open channel flows. Simulation results show that shape of sediment particles has direct influence on the incipient motion in both laminar and turbulent flows. In laminar flows, the widely adopted spherical particles tend to exhibit over 5 times higher traveling speed compared with the non-spherical particles, and over 4 times longer time lag during incipient motion. In turbulent flows, the disk-shaped non-spherical particle yields up to 60% higher travel speed, 50% larger saltation height and 126% longer saltation length compared with spherical particles. The travel modes of non-spherical sediment particles during incipient motion are also analyzed.

Numerical investigation of tsunami wave impacts on different coastal bridge decks using immersed boundary method

Due to the strong interaction between the bridges and the extreme waves generated by hurricanes and tsunamis, many coastal bridges were damaged in the past few decades. In this study, in order to investigate the effect of the extreme wave on a bridge, tsunami-like wave generated based on record in the Iwate station during 2011 Japan tsunami event instead of solitary wave is employed to impinge on the bridge with or without air vent. According to the Computational Fluid Dynamics (CFD) theory with a Volume of Fluid (VOF) interface tracking approach, a Numerical Wave Tank (NWT) is developed, in which the Immersed Boundary (IB) method is referred to simulate fluid and structure interaction. The model is calibrated with the experiment. In this numerical tank, the effects of tsunami-like waves with different prominent conditions including wave height and submersion depth on the bridges are studied. Besides, the efficiency of air vent in reducing the hydrodynamic load is also discussed. The results indicate that when the tsunami-like wave overtops the bridges, a noticeable overtopping, where the flow injects into the water fiercely and the whole flow field is very chaotic, is observed. The vertical forces on the bridges are larger than the horizontal forces, leading to many decks to collapse between two piers with small lateral displacement after the hurricanes and tsunamis. After the tsunami-like wave passes over the bridge, the oscillation of the residual wave causes the load oscillation of the bridge. The position of the bridge relative to the initial sea level has a serious impact on the forces on the bridge when the tsunami-like wave passes through it. With the increase of the wave height, the interaction intensity between the tsunami-like wave and the bridge is enhanced and the forces on the bridge also increase, but the effect duration reduces. After the air vent is installed, air vent can reduce the forces on the bridge and improve the efficiency of the bridge protection.

Two-Dimensional Free-Surface Flow Modeling for Wave-Structure Interactions and Induced Motions of Floating Bodies

In this study, the level set (LS) and immersed boundary (IB) methods were integrated into a Navier–Stokes equation two-phase flow solver, to investigate wave-structure interactions and induced motions of floating bodies in two dimensions. The movement of an interfacial boundary of two fluids, even with severe free-surface deformation, is tracked by using the level set method, while an immersed object inside a fluid domain is treated by the IB method. Both approaches can be implemented by solving the Navier–Stokes equations for viscous laminar flows with embedded objects in fluids. For accurate treatment of the solid–liquid phase, appropriate source terms as forcing functions to take into account the hydrodynamic effects on the body boundaries are added into the governing equations. The integrated compact interfacial tracking techniques between the interfaces of gas–liquid phase and the solid–liquid phase allow the use of a combined Eulerian Cartesian and Lagrangian grid system. Problems related to the fluid-structure interactions and induced motions of a floating body, such as (a) a dam-break wave over a dry bed; (b) a dam-break wave over either a submerged semicircular or rectangular cylinder; (c) wave decomposition process over a trapezoid breakwater; (d) a free-falling wedge into a water body; and (e) wave packet interacting with a floating body are selected to test the model performance. For all cases, the computed results are found to agree reasonably well with published experimental data and numerical solutions. For the case of modeling wave decomposition process, improved solutions are obtained. The detailed features of flow phenomena described by the physical variables of velocity, pressure and vorticity are presented and discussed. The present two-phase flow model is proved to have the advantage of simulating the cases with induced severe interfacial oscillations and coupled gas (or air) motions where the single-phase model may miss the contributions of the air motions on the interfaces. Additionally, the proposed method with uses of the LS and IB methods is demonstrated to be able to achieve the reliable predictions of complex flow fields.

Locomotion of a self-propulsive pitching plate in a quiescent viscous fluid

The locomotion of a flexible plate pitching in a quiescent viscous fluid is numerically studied by using the lattice Boltzmann method (LBM) for the fluid and a finite element method (FEM) for the plate, with an immersed boundary (IB) method for the fluid–structure interaction (FSI). In the simulation, the leading edge of the plate undergoes a prescribed pitching motion, and the entire plate moves freely due to the fluid–plate interaction. The effects of the pitching amplitude, bending rigidity, plate-to-fluid mass ratio and Reynolds number on the propulsive performance of the flexible plate are examined in a range of parameters. The numerical results show that a certain flexibility can remarkably improve the propulsive speed and efficiency. The optimal parameters for the pitching plate are obtained, i.e. [Formula: see text] ([Formula: see text] is a non-dimensional frequency, with [Formula: see text] means rigid plate and larger [Formula: see text] means more flexible) and 20° ≤ α0 ≤ 25° ( α0 is the pitching amplitude). The comparisons of three plate-to-fluid mass ratios (1.0, 2.5 and 5.0) show that the mass of the plate decreases the propulsive speed, but contrarily increases the efficiency. The results obtained in the present study provide an insight into the understanding of the performance of self-propulsive plate in pitching motion and can further guide the engineering design of micro aerial vehicles.

Simulation of the dynamic flow field in the left ventricle of the heart during diastolic filling

Fluid–structure interaction (FSI) problems in modeling flexible structures and moving boundaries can be simulated by combining the immersed boundary (IB) method and the Lattice–Boltzmann (LB) method. In this paper, we propose an FSI model of mitral valve leaflets and the left ventricle to simulate the flow field in the left ventricle during diastolic filling based on an IB–LB coupling scheme. Changes in the flow field and mitral valve leaflets in the FSI model are simulated with the IB–LB method, in which two arc-shaped flexible fibers simulate mitral valve leaflets immersed in the flow field. At the same time, a semi-elliptical model is used to simulate the left ventricle, which is simplified as a rigid boundary. The LB method is used to solve the Newtonian flow field, and the IB method is used to simulate the deformation of the flexible fiber interacting with the flow. In this paper, we introduce the basic principles underlying the combination of the LB and the IB methods and elucidate the coupling frame and the left ventricular flow model in detail. Finally, we verify the effectiveness of the coupled models by simulating the effects of diastolic jet flow on the motion of the mitral leaflets in the simplified left ventricular flow model.

A comparative study of bounce-back and immersed boundary method in LBM for turbulent flow simulation

In this study, we compared the modified bounce-back (BB) method and immersed boundary (IB) method for the treatments of no-slip boundary condition based on the Lattice Boltzmann Method (LBM) for turbulent flow. The benchmark case of flow past a square cylinder confined in a rectangular duct has been simulated with two schemes at Re d = 3000. The turbulent flow was modeled using Large Eddy Simulation (LES). The conventional Smagorinsky subgrid scheme was used to resolve the small-scale motions. The proposed algorithm is parallelized to run on NVIDIA Tesla P100 Graphics Processing Unit (GPU) using Compute Unified Device Architecture (CUDA) programming language. The results obtained from the bounce-back and immersed boundary method has been validated with the experimental and LES data reported in the literature for different turbulent statistics including time-averaged velocities, root-mean-square velocity fluctuations, and Reynolds shear stress. Later, the comparison between the two approaches discussed in terms of accurate predictions for the drag coefficient. The computational efficiency on GPU for both methods has also been reported. [copyright information to be updated in production process]

Role of Dipole Jet in Inclined Stroke Plane Kinematics of Insect Flight

The two-dimensional (2D) inclined stroke plane kinematics of insect wing is studied for various stroke plane angles using the Immersed Boundary (IB) solver. The numerical results revealed the dominant lift enhancement mechanisms for this class of flows. The generated dipole was analyzed to find the maximum velocity, inclination and spread. The analysis of these dipole characteristics for the different stroke plane angles exposed the alternate method to study the vertical force variation with the stroke plane angles. Lift enhancement mechanisms and dipole characteristics complement the high vertical force coefficient for the stroke plane angle of 60˚ commonly used by dragonflies during hover. The location of the dipole identified a region of influence around the wing and demonstrated the role of the dipole jet in multi-body dynamics and wall effects.

An immersed boundary-lattice Boltzmann method for gaseous slip flow

An immersed boundary (IB)-lattice Boltzmann (LB) method is proposed for microchannel slip flow encountered in microfluidics applications such as microelectromechanical Systems, filtration applications with nanofibers, polymer processing, and unconventional shale gas and coal seam gas applications. The LB method is theoretically analyzed to have an intrinsic ability to model velocity discontinuities at finite Knudsen numbers (Kn) when a sufficiently fine grid spacing and an external continuous perturbation, e.g., the body force of an IB method, are applied. Based on this analysis, an IB method coupled with a LB framework without ghost grids in nonfluid areas is proposed to study gaseous slip flow at finite Kn. In addition, an improved treatment to the suspending grids in nonfluid areas is proposed to assist the IB-LB method. In the simulations of two-dimensional Poiseuille and Couette flows for 0.01 ≤ Kn ≤ 1, the slip flow predicted by the proposed nonghost-grid IB-LB method achieves good agreement with that predicted by the linearized Boltzmann and/or Direct Simulation Monte Carlo methods up to Kn = 0.2. Since the proposed IB-LB method is free of adjustable parameters and slip velocity models, it provides a simple and promising pathway for modeling microscale flow applications for the validated regime, i.e., Kn &amp;lt; = 0.2.

An Immersed Boundary Method With Subgrid Resolution and Improved Numerical Stability Applied to Slender Bodies in Stokes Flow

The immersed boundary (IB) method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto immersed structures. To resolve slender fibers, the grid spacing must be on the order of the fiber radius, and thus the number of required grid points along the filament must be of the same order as the aspect ratio. Simulations of slender bodies using the IB method can therefore be intractable. A technique is presented to address this problem in the context of Stokes flow. The velocity of the structure is split into a component coming from the underlying fluid grid, which is coarser than normally required, and a component proportional to the force (a drag term). The drag coefficient is set so that a single sphere is represented exactly on a grid of arbitrary meshwidth. Implicit treatment of the drag term removes some of the stability restrictions normally associated with the IB method. This comes at a loss of accuracy, although tests are conducted that show 1--2 digits of relative accuracy can be obtained on coarser grids. After its accuracy and stability are tested, the method is applied to two real world examples: fibers in shear flow and a suspension of fibers. These examples show that the method can reproduce existing results and make reasonable predictions about the viscosity of an aligned fiber suspension.

Computational Model Construction and Analysis of the Hydrodynamics of a Rhinoptera Javanica

In this study, numerical simulations are employed to investigate the hydrodynamic performance and wake topology of a swimming Rhinoptera javanica. The study is motivated by the quest to understand the hydrodynamics of median and paired fin(MPF) mode with both spanwise and chordwise flexibility. The simulations employ an immersed boundary(IB)-simplified sphere function-based gas kinetic scheme(SGKS) method that allows us to simulate flows with complex moving boundaries on fixed Cartesian grids. A computational model is constructed based on biological data. The evolution of the hydrodynamic force and 3D vortex structures are presented. Besides, the effect of frequency and amplitude are also discussed to explain some behaviors of the actual Rhinoptera javanica. This work can provide a baseline for the design of a bio-inspired underwater vehicle.

An efficient Navier-Stokes based numerical wave tank using fast Poisson solvers and the immersed boundary method

An efficient numerical model for wave induced flows and their interaction with impermeable coastal structures, is presented. Using recent developments in the field of two-fluid (water/air) Navier-Stokes (NS) simulations, an efficient numerical wave tank (NWT) was developed which combines the Immersed Boundary (IB) method and Fast Direct Solvers (FDS). Conventional NS-based NWTs require significant computational resources which prevents their use in discretisation demanding cases or extensive parametric studies. The computational efficiency of the new NWT was achieved by replacing the conventional variable-coefficient Poisson equation with a constant-coefficient one which is solved with a FDS. Results of the accuracy, limitations, and computational performance of the NWT are presented and discussed based on several validation tests: (1) propagation of a 2nd-order Stokes wave, (2) formation of a standing wave, (3) spilling breaking over a mild slope bed, (4) three-dimensional (3D) interaction of a solitary wave with a vertical abutment, and (5) diffraction of a solitary wave by a single-row pile breakwater. The computational performance of the new NWT was demonstrated for problems with 1–280 million grid nodes. The overall speed-up of the new NWT increases with the problem size, and it is estimated to be about 30 for large 3D problems.

Numerical analysis on the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves

The collision of solitary waves is closely related to many physical problems. In this paper, the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves are analyzed using a self-developed two-dimensional two-phase flow model. Advanced Adaptive Mesh Refinement (AMR) grid is adopted to reduce the computational cost. The free surface is captured with the Volume of Fraction (VOF) method combined with Piecewise Linear Interface Calculation (PLIC). The Immersed Boundary (IB) method is used to account for the existence of the barrier. Several benchmark problems including solitary wave propagation, head-on collision of two solitary waves, and solitary wave past a submerged barrier are considered to validate the accuracy of the model. Then the model is utilized to simulate the head-on collision of two solitary waves with the existence of a submerged bottom-mounted barrier. Both the symmetric (two waves with equal amplitudes) and asymmetric (two waves with unequal amplitudes) head-on collisions are investigated. The results with and without the barrier are compared and analyzed in detail. Special attention is paid to the variations of the wave amplitudes and the vortex sheddings.