An Immersed Boundary Method Based on Volume Fraction

A computationally efficient Immersed Boundary Method (IBM) based on penalized direct forcing was employed to determine the permeability of a real porous medium. The porous medium was composed of about 9000 glass beads with an average particle diameter of 1.93 mm and a porosity of 0.367. The forcing of the IBM depends on the local solid volume fraction within a computational grid cell. The latter could be obtained from a high-resolution X-ray Computed Tomography (CT) scan of the packing. An experimental facility was built to determine the permeability of the packing experimentally. Numerical simulations were performed for the same packing based on the data from the CT scan. For a scan resolution of 0.1 mm the numerical value for the permeability was nearly 70% larger than the experimental value. An error analysis indicated that the scan resolution of 0.1 mm was too coarse for this packing.

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Direct Simulation of Dense Suspensions of Non-Spherical Particles

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-19002 ◽

2011 ◽

Cited By ~ 2

Author(s):

Orest Shardt ◽

Jos Derksen

Keyword(s):

Reynolds Number ◽

Red Blood Cells ◽

Sedimentation Rate ◽

Immersed Boundary Method ◽

Blood Cells ◽

Volume Fraction ◽

Immersed Boundary ◽

Direct Simulation ◽

Rigid Particles ◽

Boundary Method

We describe the direct simulation of high-solids-fraction suspensions of non-spherical rigid particles that are slightly denser than the fluid. The lattice-Boltzmann method is used to solve the flow of the interstitial Newtonian fluid, and the immersed boundary method is used to enforce a no-slip boundary condition at the surface of each particle. The surface points for the immersed boundary method are also employed for collision handling by applying repulsive forces between nearby surface points. Due to the finite number of these points, the method simulates rough surface collisions. We also discuss methods for integrating the equations of particle motion at low density ratios and propose a method with improved accuracy. Rigid particles shaped like red blood cells were simulated. Simulations of a single particle showed that the particle settles in its original orientation when the Reynolds number is low (1.2) but flips to a higher drag orientation when the Reynolds number is higher (7.3). A simulation with a 45% solids volume fraction and a low solid over fluid density ratio showed the possibility of simulating blood as it is found in the body. A simulation at a lower solids volume fraction (35%) was used to compare the results with the erythrocyte sedimentation rate (ESR), a common blood test. The sedimentation rate was estimated as 0.2 mm/hr, which is an order of magnitude lower than a typical ESR of about 6 mm/hr for a healthy adult. The most likely reasons for the discrepancy are the omission of agglomeration-inducing inter-cellular forces from the simulations and the treatment of the red blood cells as rigid particles.

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Effective Geometric Algorithms for Immersed Boundary Method Using Signed Distance Field

Journal of Fluids Engineering ◽

10.1115/1.4041758 ◽

2018 ◽

Vol 141 (6) ◽

Cited By ~ 2

Author(s):

Chenguang Zhang ◽

Chunliang Wu ◽

Krishnaswamy Nandakumar

Keyword(s):

Immersed Boundary Method ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Closed Surface ◽

Immersed Boundary ◽

Field Calculation ◽

Distance Field ◽

Signed Distance ◽

Boundary Method ◽

Signed Distance Field

We present three algorithms for robust and efficient geometric calculations in the context of immersed boundary method (IBM), including classification of mesh cells as inside/outside of a closed surface, projection of points onto a surface, and accurate calculation of the solid volume fraction field created by a closed surface overlapping with a background Cartesian mesh. The algorithms use the signed distance field (SDF) to represent the surface and remove the intersection tests, which are usually required by other algorithms developed before, no matter the surface is described in analytic or discrete form. The errors of the algorithms are analyzed. We also develop an approximate method on efficient SDF field calculation for complex geometries. We demonstrate how the algorithms can be implemented within the framework of IBM with a volume-average discrete-forcing scheme and applied to simulate fluid–structure interaction problems.

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A POROUS VISCOELASTIC MODEL FOR THE CELL CYTOSKELETON

The ANZIAM Journal ◽

10.1017/s1446181118000081 ◽

2018 ◽

Vol 59 (4) ◽

pp. 472-498 ◽

Cited By ~ 1

Author(s):

CALINA A. COPOS ◽

ROBERT D. GUY

Keyword(s):

Immersed Boundary Method ◽

Cell Biology ◽

Numerical Solutions ◽

Volume Fraction ◽

Viscoelastic Model ◽

Extracellular Fluid ◽

Microfluidic Channel ◽

Maxwell Model ◽

Immersed Boundary ◽

Boundary Method

The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid.

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An New Immersed Boundary Method With Level Set Based Geometry Representation and Volume Fraction Based Body Force Calculation

Volume 1: Flow Manipulation and Active Control; Bio-Inspired Fluid Mechanics; Boundary Layer and High-Speed Flows; Fluids Engineering Education; Transport Phenomena in Energy Conversion and Mixing; Turbulent Flows; Vortex Dynamics; DNS/LES and Hybrid RANS/LES Methods; Fluid Structure Interaction; Fluid Dynamics of Wind Energy; Bubble, Droplet, and Aerosol Dynamics ◽

10.1115/fedsm2018-83011 ◽

2018 ◽

Author(s):

Guangfa Yao

Keyword(s):

Level Set ◽

Immersed Boundary Method ◽

Body Force ◽

Volume Fraction ◽

The Body ◽

Immersed Boundary ◽

Immersed Boundary Methods ◽

Boundary Method ◽

Boundary Methods ◽

Fluid Solid Interaction

Immersed boundary method has got increasing attention in modeling fluid-solid interaction using computational fluid dynamics due to its robustness and simplicity. It simulates fluid-solid interaction by adding a body force in the momentum equation without a body conforming mesh generation involved. Different immersed boundary methods have been presented and applied to solve fluid flow with immersed solid bodies. The main difference between these immersed boundary methods is how the body force is calculated. In this paper, a new immersed boundary method is proposed. The body force is calculated based on the volume fraction of the solid body immersed in fluid. Compared to the existing and similar methods, the new method develops a mechanism to calculate the body force and thereby more accurately resolve the physics on the solid-fluid interface. The solid body is represented using a level set that facilitates the calculation of the solid volume fraction. The body force derivation is presented and the method is validated against the test cases with existing analytical solutions or well established numerical solutions. A good match was reached.

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Immersed boundary method for MHD unsteady natural convection around a hot elliptical cylinder in a cold rhombus enclosure filled with a nanofluid

SN Applied Sciences ◽

10.1007/s42452-021-04221-3 ◽

2021 ◽

Vol 3 (2) ◽

Author(s):

Ali Akbar Hosseinjani ◽

Amir H. Roohi

Keyword(s):

Magnetic Field ◽

Nusselt Number ◽

Natural Convection ◽

Immersed Boundary Method ◽

Average Nusselt Number ◽

Volume Fraction ◽

Magnetic Field Effect ◽

Elliptical Cylinder ◽

Immersed Boundary ◽

Boundary Method

AbstractIn this study, the numerical investigation of the natural convection heat transfer around a hot elliptical cylinder inside a cold rhombus enclosure filled with a nanofluid in the presence of a uniform magnetic field is conducted. An immersed boundary method as a computational tool has been extended and applied to solve the problem. The influence of various parameters such as cylinder diameters (a, b), Hartmann number (Ha = 0, 50 and 100), nanofluid volume fraction ($$\varphi = 0 , 2.5\% and 5\%$$ φ = 0 , 2.5 % a n d 5 % ), and Rayleigh number (Ra = 103, 104, 105, 106, and 107) has been studied. Streamlines and isotherms contours as well as average Nusselt number have been specified for different modes. An equation for the average Nusselt number as a function of mentioned parameters is presented in this paper. The results show that at lower Ra numbers of Ra = 103 and 104, the magnetic field effect is negligible. However, at higher Rayleigh numbers, the average Nusselt number (Nuave) decreases with the increasing Ha number. The maximum decrease in Nuave at Ra = 105, 106 and 107are calculated −8.15%, −23.4% and −27.3%, respectively. An asymmetry-unsteady flow is observed at $${\text{Ra}} = 10^{7}$$ Ra = 10 7 for Ha = 0. However, at higher Ha numbers a steady-symmetrical flow is formed.

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