Immersed Boundary Model Research Articles

CFD-DEM Evaluation of the Clustering Behavior in a Riser-the Effect of the Drag Force Model.

Riser reactors are frequently applied in catalytic processes involving rapid catalyst deactivation. Typically heterogeneous flow structures prevail because of the clustering of particles, which impacts the quality of the gas-solid contact. This phenomenon results as a competition between fluid-particle interaction (i.e., drag) and particle-particle interaction (i.e., collisions). In this study, five drag force correlations were used in a combined computational fluid dynamics-discrete element method Immersed Boundary Model to predict the clustering. The simulation results were compared with experimental data obtained from a pseudo-2D riser in the fast fluidization regime. The clusters were detected on the basis of a core-wake approach using constant thresholds. Although good predictions for the global (solids volume fraction and mass flux) variables and cluster (spatial distribution, size, and number of clusters) variables were obtained with two of the approaches in most of the simulations, all the correlations show significant deviations in the onset of a pneumatic transport regime. However, the correlations of Felice (Int. J. Multiphase Flow1994, 20, 153-159) and Tang et al. [AIChE J.2015, 61 ( (2), ), 688-698] show the closest correspondence for the time-averaged quantities and the clustering behavior in the fast fluidization regime.

A sharp interface immersed boundary-discrete unified gas kinetic scheme for fluid-solid flows with heat transfer

Particulate flow with thermal convection involves lots of moving and complex fluid-solid interfaces, and hence generally sheets a great challenge to numerical methods. For interface-resolved simulation of that flow, we present a ghost-cell (GC) method in the framework of discrete unified gas kinetic scheme (DUGKS) in this study. As a sharp interface immersed boundary model, the particle surface is considered to be of zero thickness in GC. A computation cell with its center located inside the particle and intersected by the interface is transformed into the fictitious cell, and its information is reconstructed from neighboring fields. The fluid motion with heat transfer is solved by the recently proposed DUGKS. For updating the position of particles, we evaluate the hydrodynamic forces of fluid-solid interaction through the mesoscopic momentum flux. The particle-particle interaction is described by the repulsive force model. The accuracy of the method is corroborated by five benchmark cases of flow past a heated cylinder, sedimentation of a cold particle in a channel, a catalyst particle migrating in a box, drafting-kissing-tumbling process of two hot particles, and a group of particles settling in an enclosure. It is observed that GC-DUGKS well captures the character of the thermal particulate flows.

An immersed boundary model of magnetically driven flexible filaments with lattice Boltzmann hydrodynamics

An immersed boundary model of magnetically driven flexible filaments with lattice Boltzmann hydrodynamics

Immersed boundary method applied to flow past a tree skeleton

We present numerical predictions and experimental observations of the drag force on the major branches of a model tree as well as the wind field in its wake. The tree model was mounted on a force sensor in a wind tunnel. The numerical simulations solved both the Reynolds Averaged Navier Stokes and detached eddy simulations, in combination with an immersed boundary model representation of the tree, while the measurements were obtained in the WindEEE Dome. Contrary to previous studies on trees or fractal structures, we find that the simulated forces on the tree skeleton were strongly dependent on the roughness of its surface. Upon setting a proper surface roughness, the simulations were capable of predicting both forces and wake fields, which were in good agreement with the observations both in terms of mean wind speed, mean turbulence and spectra. Furthermore, both simulations and observations showed that turbulence and mean wind speed were reduced for up to a distance of two tree heights downwind of the tree skeleton, underlining the efficiency of trees to remove momentum from a flow.

A one-sided direct forcing immersed boundary method using moving least squares

This paper presents a one-sided immersed boundary (IB) method using kernel functions constructed via a moving least squares (MLS) method. The resulting kernels effectively couple structural degrees of freedom to fluid variables on only one side of the fluid-structure interface. This reduces spurious feedback forcing and internal flows that are typically observed in IB models that use isotropic kernel functions to couple the structure to fluid degrees of freedom on both sides of the interface. The method developed here extends the original MLS methodology introduced by Vanella and Balaras (2009) [27]. Prior IB/MLS methods have used isotropic kernel functions that coupled fluid variables on both sides of the boundary to the interfacial degrees of freedom. The original IB/MLS approach converts the cubic spline weights typically employed in MLS reconstruction into an IB kernel function that satisfies particular discrete moment conditions. This paper shows that the same approach can be used to construct one-sided kernel functions (kernel functions are referred to as generating functions in the MLS literature). We also examine the performance of the new approach for a family of kernel functions introduced by Peskin. It is demonstrated that the one-sided MLS construction tends to generate non-monotone interpolation kernels with large over- and undershoots. We present two simple weight shifting strategies to construct generating functions that are positive and monotone, which enhances the stability of the resulting IB methodology. Benchmark cases are used to test the order of accuracy and verify the one-sided IB/MLS simulations in both two and three spatial dimensions. This new IB/MLS method is also used to simulate flow over the Ahmed car model, which highlights the applicability of this methodology for modeling complex engineering flows.

Decoding the Relationships between Body Shape, Tail Beat Frequency, and Stability for Swimming Fish

As fish swim through a fluid environment, they must actively use their fins in concert to stabilize their motion and have a robust form of locomotion. However, there is little knowledge of how these forces act on the fish body. In this study, we employ a 3D immersed boundary model to decode the relationship between roll, pitch, and yaw of the fish body and the driving forces acting on flexible fish bodies. Using bluegill sunfish as our representative geometry, we first examine the role of an actuating torque on the stability of the fish model, with a torque applied at the head of the unconstrained fish body. The resulting kinematics is a product of the passive elasticity, fluid forces, and driving torque. We then examine a constrained model to understand the role that fin geometry, body elasticity, and frequency play on the range of corrective forces acting on the fish. We find non-monotonic behavior with respect to frequency, suggesting that the effective flexibility of the fins play an important role in the swimming performance.

Numerical simulation of three-phase flow in an external gear pump using immersed boundary approach

• Modelling the compressibility of gas is critical for predicting its effects on cavitation . • Effect of increased gas (NCG) content in the fluid is to decrease the cavitation. • More flow fluctuations are observed at the outlet with higher NCG content. • Modelling contact between the gears is critical for accurate cavitation prediction. • Higher gear RPM results in higher rate of cavitation. This paper presents a three-phase fully compressible model applied along with an immersed boundary model for predicting cavitation occurring in a two dimensional gear pump in the presence of non-condensable gas (NCG). Combination of these models is capable of overcoming numerical challenges such as modelling the contact between the gears and simulating the effect of NCG in cavitation. The model accounting for the effect of NCG also has broader applicability, since gas dissolved in liquids can come out of the solution when exposed to low pressures; this plays a significant role in the pump performance and cavitation erosion . Here the simulation results are presented for the gear pump at different operating conditions including the contact between gear, gear RPM and % of NCG; their effects on performance and cavitation is demonstrated. The results suggest that modelling the contact between the gears play a role in the cavitation prediction inside the gear pump. An increase in cavitation is observed when the contact is modelled even for the small pressure difference considered between the inlet and outlet. An increase in the RPM of the gears also results in increased cavitation within the pump, whereas an increase in the percentage of NCG content by a small amount can reduce the cavitation to a greater extent. This reduction is due to the expansion of the gas at a lower pressure which recovers the pressure and prevents or delays the phase-change process of the working fluid. The fluctuations in the outflow rate is also found to increase when the gears are in contact and also with increasing gas content.

A Thin Film Fluid Structure Interaction Model for the Study of Flexible Structure Dynamics in Centrifugal Pumps

This paper describes a fluid-structure interaction (FSI) model for the study of flexible cloth-like structures or the so-called rags in flows through centrifugal pumps. The structural model and its coupling to the flow solver are based on a Lagrangian formulation combining structural deformation and motion modeling coupled to a sharp interface immersed boundary model (IBM). The solution has been implemented in the open-source library OpenFOAM relying in particular on its PIMPLE segregated Navier–Stokes pressure–velocity coupling and its detached eddy simulation (DES) turbulence model. The FSI solver is assessed in terms of its capability to generate consistent deformations and transport of the immersed flexible structures. Two benchmark cases are covered and both involve experimental validation with three-dimensional (3D) structural deformations of the rag captured using a digital image correlation (DIC) technique. Simulations of a rag transported in a centrifugal pump confirm the suitability of the model to inform on the dynamic behavior of immersed structures under practical engineering conditions.

Image-based immersed boundary model of the aortic root

Each year, approximately 300,000 heart valve repair or replacement procedures are performed worldwide, including approximately 70,000 aortic valve replacement surgeries in the United States alone. Computational platforms for simulating cardiovascular devices such as prosthetic heart valves promise to improve device design and assist in treatment planning, including patient-specific device selection. This paper describes progress in constructing anatomically and physiologically realistic immersed boundary (IB) models of the dynamics of the aortic root and ascending aorta. This work builds on earlier IB models of fluid–structure interaction (FSI) in the aortic root, which previously achieved realistic hemodynamics over multiple cardiac cycles, but which also were limited to simplified aortic geometries and idealized descriptions of the biomechanics of the aortic valve cusps. By contrast, the model described herein uses an anatomical geometry reconstructed from patient-specific computed tomography angiography (CTA) data, and employs a description of the elasticity of the aortic valve leaflets based on a fiber-reinforced constitutive model fit to experimental tensile test data. The resulting model generates physiological pressures in both systole and diastole, and yields realistic cardiac output and stroke volume at physiological Reynolds numbers. Contact between the valve leaflets during diastole is handled automatically by the IB method, yielding a fully competent valve model that supports a physiological diastolic pressure load without regurgitation. Numerical tests show that the model is able to resolve the leaflet biomechanics in diastole and early systole at practical grid spacings. The model is also used to examine differences in the mechanics and fluid dynamics yielded by fresh valve leaflets and glutaraldehyde-fixed leaflets similar to those used in bioprosthetic heart valves. Although there are large differences in the leaflet deformations during diastole, the differences in the open configurations of the valve models are relatively small, and nearly identical hemodynamics are obtained in all cases considered.

A simple and efficient implicit direct forcing immersed boundary model for simulations of complex flow

This paper presents an implementation of an implicit immersed boundary (IB) method in a flow solver based on the fractional step method and the finite volume method for complex flows involving moving boundaries and complex geometries. In this implementation, a body force caused by the immersed body is first introduced into the N-S equation to model the effect of immersed boundary. However, the body force is not pre-calculated, but implicitly determined in such a way that the velocity at the immersed boundary interpolated from the corrected velocity field accurately satisfies the no-slip and no-penetration conditions. Then, the large-eddy simulation is applied in the solver, where the subgrid-scale stress is determined by the Smagorinsky–Lilly model. Near the immersed boundaries, the subgrid-scale stress is determined by a wall model where the wall shear stress is directly calculated from the Lagrangian force(which represents the action of fluid on solid) on the immersed boundary. Such treatment makes the simulations of high Reynolds number turbulent flows feasible with the IB method. The accuracy and capability of the present method are demonstrated by simulations of a variety of both two- and three-dimensional simulations, including laminar flow past static and oscillating cylinders, rotating hydrofoil and turbulent flow around a three-dimensional circular cylinder and a sphere. It shows that the present implementation provides an easy-to-use, inexpensive and accurate technique for computational fluid dynamics in industrially relevant problems.

Immersed Boundary Models for Quantifying Flow-Induced Mechanical Stimuli on Stem Cells Seeded on 3D Scaffolds in Perfusion Bioreactors.

Perfusion bioreactors regulate flow conditions in order to provide cells with oxygen, nutrients and flow-associated mechanical stimuli. Locally, these flow conditions can vary depending on the scaffold geometry, cellular confluency and amount of extra cellular matrix deposition. In this study, a novel application of the immersed boundary method was introduced in order to represent a detailed deformable cell attached to a 3D scaffold inside a perfusion bioreactor and exposed to microscopic flow. The immersed boundary model permits the prediction of mechanical effects of the local flow conditions on the cell. Incorporating stiffness values measured with atomic force microscopy and micro-flow boundary conditions obtained from computational fluid dynamics simulations on the entire scaffold, we compared cell deformation, cortical tension, normal and shear pressure between different cell shapes and locations. We observed a large effect of the precise cell location on the local shear stress and we predicted flow-induced cortical tensions in the order of 5 pN/μm, at the lower end of the range reported in literature. The proposed method provides an interesting tool to study perfusion bioreactors processes down to the level of the individual cell’s micro-environment, which can further aid in the achievement of robust bioprocess control for regenerative medicine applications.

A suspension balance direct-forcing immersed boundary model for wet granular flows over obstacles

This paper addresses a new suspension balance direct-forcing immersed boundary model (SB-DF-IBM), for wet granular flows over obstacles. We mean by “wet granular” term all non-Newtonian flows that are made of non-Brownian particles (rigid spheres) immersed in a Newtonian fluid. This new SB-DF-IBM couples the Suspension Balance Model (SBM) to a Direct-Forcing Immersed Boundary Method (DF-IBM). The mathematical formulation in this contribution is based on a mixed Eulerian–Lagrangian approach.A novel feature of this new formulation is that many Lagrangian particles of the same size of the suspended particles, can be introduced into the continuum medium. This extrapolates the physics from a macroscopic to a microscopic scale, making the SB-DF-IBM behaves as a Dynamic-Scale Model (DSM).This SB-DF-IBM is implemented, as a new solver, in the OpenFOAM® open-source Computational Fluid Dynamics (CFD) software. Then, a numerical study is conducted on isodense mono-dispersed suspension flows over a stationary cylinder, in both wide and micro-channels, to test the functionality and performances of this SB-DF-IBM. The pressure difference, drag and lift forces are addressed for different initial bulk concentrations between 0% and 50%.Moreover, the effect of a cylindrical obstacle on the suspension flow separation in a microchannel is analyzed. The numerical results are presented and compared to recent experimental measurements from the literature addressing the non-Newtonian response of a suspension flow.As a conclusion, this SB-DF-IBM is a promising tool that can be introduced into different CFD packages for simulating wet granular non-Newtonian flows over obstacles.

Immersed boundary-finite element model of fluid-structure interaction in the aortic root.

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to e-volve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid-structure interaction model of the aortic root, including the aortic valve leaflets, the sinsuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin's immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configurations of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high-Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left ventricular fluid dynamics.

A mass‐conservative staggered immersed boundary model for solving the shallow water equations on complex geometries

SummaryIn this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut‐cell/ghost‐cell method is used together with a direction‐splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second‐order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method. Copyright © 2015 John Wiley & Sons, Ltd.

A hybrid adaptive-gridding immersed-boundary lattice Boltzmann method for viscous flow simulations

Robust use of adaptive mesh refinement (AMR) techniques in the immersed-boundary (IB) lattice Boltzmann method (LBM) framework is seldom reported, but indeed expected owing to its foreseeable broad applicability and computational efficiency. This study is aimed at developing a highly hybrid computational framework that seamlessly incorporates the AMR algorithm in the IB–LBM approach, so that challenging problems, including the case of an obstacle that moves through a flowing fluid, can be numerically investigated. Owing to the feedback forcing based IB model, the advantages, such as simple mechanics principle, explicit interpolations, and inherent satisfaction of no-slip boundary condition for solid surfaces, are fully exhibited. Additionally, the “bubble” function is employed in the local mesh refinement process so that, for newly generated nodes belonging to a region with overlapping coarse and fine cells, the solution of second-order accuracy can be obtained only through the spatial interpolation but no temporal interpolation. With simulation interests in both steady and unsteady flows around a single cylinder and bi-cylinders, a number of test cases performed in this study have demonstrated the usefulness and effectiveness of the present hybrid AMR–IB–LBM approach.

An Immersed Boundary Model of the Cochlea with Parametric Forcing

The cochlea or inner ear has a remarkable ability to amplify sound signals. This is understood to derive at least in part from some active process that magnifies vibrations of the basilar membrane (BM) and the cochlear partition in which it is embedded, to the extent that it overcomes the effect of viscous damping from the surrounding cochlear fluid. Many authors have associated this amplification ability to some type of mechanical resonance within the cochlea, however there is still no consensus regarding the precise cause of amplification. Our work is inspired by experiments showing that the outer hair cells within the cochlear partition change their lengths when stimulated, which can in turn cause periodic distortions of the BM and other structures in the cochlea. This paper investigates a novel fluid-mechanical resonance mechanism that derives from hydrodynamic interactions between an oscillating BM and the surrounding cochlear fluid. We present a model of the cochlea based on the immersed boundary method, in which a small-amplitude periodic internal forcing due to outer hair cells can induce parametric resonance. A Floquet stability analysis of the linearized equations demonstrates the existence of resonant (unstable) solutions within the range of physical parameters corresponding to the human auditory system. Numerical simulations of the immersed boundary equations support the analytical results and clearly demonstrate the existence of resonant solution modes. These results are then used to illustrate the influence of parametric resonance on wave propagation along the BM and explicit comparisons are drawn with results from another two-dimensional cochlea model.

Quasi-static image-based immersed boundary-finite element model of left ventricle under diastolic loading.

Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart. © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd.

A minimally-resolved immersed boundary model for reaction-diffusion problems

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

Direct Numerical Simulations of gas–liquid–solid three phase flows

Gas–liquid–solid three phase flows are encountered in for example the Fischer–Tropsch process for the production of synthetic fuels in bubble slurry columns. To predict the hydrodynamics in large slurry bubble columns a multi-scale modeling approach can be used, which accounts for the large variation in time and length scales. In this paper, the smallest scale model has been developed using the Front Tracking model of Dijkhuizen et al. (2010b) and the Immersed Boundary model of Kriebitzsch (2011). In the Front Tracking model, each bubble is tracked separately. Furthermore, the Immersed Boundary method introduces the particle–fluid and the particle–particle (via a hard sphere model) interactions in the model. The resulting hybrid Front Tracking Immersed Boundary model is able to simulate dense three-phase flows and accounts for swarm effects in a fundamental manner. From our simulations we found that the relative drag coefficient of bubbles in three-phase flows seems to increase with increasing solids volume fraction. However, longer averaging periods are needed to derive a fully predictive correlation for the relative drag coefficient with respect to the solid volume fraction.

Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions

Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions