An Efficient Immersed Boundary Method Based on Penalized Direct Forcing for Simulating Flows Through Real Porous Media

2012 ◽  
Author(s):  
Wim-Paul Breugem ◽  
Vincent van Dijk ◽  
René Delfos
Keyword(s):  
Porous Medium ◽  
Ct Scan ◽  
Immersed Boundary Method ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Particle Diameter ◽  
Immersed Boundary ◽  
Average Particle ◽  
Boundary Method ◽  
Direct Forcing

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.

Flows Through Real Porous Media: X-Ray Computed Tomography, Experiments, and Numerical Simulations

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Wim-Paul Breugem ◽  
Vincent van Dijk ◽  
René Delfos
Keyword(s):  
Computed Tomography ◽  
Porous Medium ◽  
Ct Scan ◽  
Numerical Simulations ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Immersed Boundary ◽  
Immersed Boundary Methods ◽  
X Ray ◽  
X Ray Computed

Two different direct-forcing immersed boundary methods (IBMs) were applied for the purpose of simulating slow flow through a real porous medium: the volume penalization IBM and the stress IBM. The porous medium was a random close packing of about 9000 glass beads in a round tube. The packing geometry was determined from an X-ray computed tomography (CT) scan in terms of the distribution of the truncated solid volume fraction (either 0 or 1) on a three-dimensional Cartesian grid. The scan resolution corresponded to 19.3 grid cells over the mean bead diameter. A facility was built to experimentally determine the permeability of the packing. Numerical simulations were performed for the same packing based on the CT scan data. For both IBMs the numerically determined permeability based on the Richardson extrapolation was just 10% lower than the experimentally found value. As expected, at finite grid resolution the stress IBM appeared to be the most accurate IBM.

Effective Geometric Algorithms for Immersed Boundary Method Using Signed Distance Field

2018 ◽  
Vol 141 (6) ◽  
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.

On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries

2012 ◽  
Vol 56 ◽  
pp. 61-76 ◽  
Author(s):  
Haoxiang Luo ◽  
Hu Dai ◽  
Paulo J.S.A. Ferreira de Sousa ◽  
Bo Yin
Keyword(s):  
Immersed Boundary Method ◽  
Moving Boundaries ◽  
Immersed Boundary ◽  
Boundary Method ◽  
Direct Forcing

Direct Simulation of Dense Suspensions of Non-Spherical Particles

2011 ◽  
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.

scholarly journals An Immersed Boundary Method Based on Volume Fraction

2015 ◽  
Vol 99 ◽  
pp. 677-685 ◽  
Author(s):  
Yuelong He ◽  
Dun Li ◽  
Shuai Liu ◽  
Handong Ma
Keyword(s):  
Immersed Boundary Method ◽  
Volume Fraction ◽  
Immersed Boundary ◽  
Boundary Method

A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Jianming Yang ◽  
Frederick Stern
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Sharp Interface ◽  
Immersed Boundary ◽  
Particulate Flows ◽  
Order Accuracy ◽  
Wide Range ◽  
Direct Forcing ◽  
Coarse Grids

In recent years, the immersed boundary method has been well received as an effective approach for the fully resolved simulations of particulate flows. Most immersed boundary approaches for numerical studies of particulate flows in the literature were based on various discrete delta functions for information transfer between the Lagrangian elements of an immersed object and the underlying Eulerian grid. These approaches have some inherent limitations that restrict their wider applications. In this paper, a sharp interface direct forcing immersed boundary approach based on the method proposed by Yang and Stern (Yang and Stern, 2012, “A Simple and Efficient Direct Forcing Immersed Boundary Framework for Fluid-Structure Interactions,” J. Comput. Phys., 231(15), pp. 5029–5061) is given for the fully resolved simulations of particulate flows. This method uses a discrete forcing approach and maintains a sharp profile of the fluid-solid interface. It is not limited to low Reynolds number flows and the immersed boundary discretization can be arbitrary or totally eliminated for particles with analytical shapes. In addition, it is not required to calculate the solid volume fraction in low density ratio problems. A strong coupling scheme is employed for the fluid-solid interaction without including the fluid solver in the predictor-corrector iterative loop. The overall algorithm is highly efficient and very attractive for simulating particulate flows with a wide range of density ratios on relatively coarse grids. Several cases are examined and the results are compared with reference data to demonstrate the simplicity and robustness of our method in particulate flow simulations. These cases include settling and buoyant particles and the interaction of two settling particles showing the kissing-drafting-tumbling phenomenon. Systematic verification studies show that our method is of second-order accuracy on very coarse grids and approaches fourth-order accuracy on finer grids.

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