Modeling Flows in Porous Media Using Immersed Boundary Based Lattice Boltzman Method

2012 ◽  
Author(s):  
Zhi-Gang Feng ◽  
Maria Andersson
Keyword(s):  
Porous Media ◽  
Drag Coefficient ◽  
Solid Fraction ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Immersed Boundary ◽  
Face Centered Cubic ◽  
Flows In Porous Media ◽  
Random Arrays ◽  
Arrays Of Spheres

Flows in porous media of fixed arrays of spheres have been studied numerically in the present work. The flow velocity and pressure fields are solved by the lattice Boltzmann method; the no-slip boundary condition at the solid-fluid interface is enforced by the immersed boundary method with the direct forcing scheme. This numerical method, which we call Proteus and initially was developed for simulations of particles in motion, has been extended to study flow over fixed arrays of spheres. The method is validated by comparing the simulated drag coefficient on a single sphere to the one obtained using an empirical drag law. The present method is then applied to obtain the dimensionless drag force on a sphere in both ordered face-centered cubic arrays of spheres and random arrays of spheres. Our results at low solid volume fraction for ordered arrays of spheres show good agreement with the theoretical solution of Hasimoto (1959). A correlation on the drag coefficient at solid fraction ranging from 0 to 0.66 has been derived based on our simulation results. This will help improve the modeling of particulate flows. The case of flow over random arrays of spheres at the solid fraction of 0.345 and flow Reynolds numbers up to 57 has also been studied. Our results agree well with the Ergun’s empirical correlation.

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.

Genetic Programming based Drag Model with Improved Prediction Accuracy for Fluidization Systems

2017 ◽  
Vol 15 (2) ◽  
Author(s):  
R. R. Sonolikar ◽  
M. P. Patil ◽  
R. B. Mankar ◽  
S. S. Tambe ◽  
B. D. Kulkarni
Keyword(s):  
Pressure Drop ◽  
Genetic Programming ◽  
Drag Coefficient ◽  
Prediction Accuracy ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Superior Performance ◽  
Momentum Exchange ◽  
Drag Model ◽  
Parameter Ranges

Abstract The drag coefficient plays a vital role in the modeling of gas-solid flows. Its knowledge is essential for understanding the momentum exchange between the gas and solid phases of a fluidization system, and correctly predicting the related hydrodynamics. There exists a number of models for predicting the magnitude of the drag coefficient. However, their major limitation is that they predict widely differing drag coefficient values over same parameter ranges. The parameter ranges over which models possess a good drag prediction accuracy are also not specified explicitly. Accordingly, the present investigation employs Geldart’s group B particles fluidization data from various studies covering wide ranges of Re and εs to propose a new unified drag coefficient model. A novel artificial intelligence based formalism namely genetic programming (GP) has been used to obtain this model. It is developed using the pressure drop approach, and its performance has been assessed rigorously for predicting the bed height, pressure drop, and solid volume fraction at different magnitudes of Reynolds number, by simulating a 3D bubbling fluidized bed. The new drag model has been found to possess better prediction accuracy and applicability over a much wider range of Re and εs than a number of existing models. Owing to the superior performance of the new drag model, it has a potential to gainfully replace the existing drag models in predicting the hydrodynamic behavior of fluidized beds.

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.

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.

scholarly journals Magneto-Hybrid Nanofluids Flow via Mixed Convection past a Radiative Circular Cylinder

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
E. R. EL-Zahar ◽  
A. M. Rashad ◽  
W. Saad ◽  
L. F. Seddek
Keyword(s):  
Circular Cylinder ◽  
Drag Coefficient ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convective Boundary Condition ◽  
Hybrid Nanofluid ◽  
Current Analysis ◽  
Convective Boundary ◽  
Fundamental Parameters ◽  
Grid Points

Abstract The goal of the current analysis is to scrutinize the magneto-mixed convective flow of aqueous-based hybrid-nanofluid comprising Alumina and Copper nanoparticles across a horizontal circular cylinder with convective boundary condition. The energy equation is modelled by interpolating the non-linear radiation phenomenon with the assisting and opposing flows. The original equations describing the magneto-hybrid nanofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-Chebyshev spectral method (HLCSM). HLCSM is a high order spectral semi-analytical numerical method that results in an analytical solution in η-direction and thereby the solution is valid in overall the η-domain, not only at the grid points. The impacts of diverse parameters on the allied apportionment are inspected, and the fallouts are described graphically in the investigation. The physical quantities of interest containing the drag coefficient and the heat transfer rate are predestined versus fundamental parameters, and their outcomes are elucidated. It is witnessed that both drag coefficient and Nusselt number have greater magnitude for Cu-water followed by hybrid nanofluid and Al2O3-water. Moreover, the value of the drag coefficient declines versus the enlarged solid volume fraction. To emphasize the originality of the current analysis, the outcomes are compared with quoted works, and excellent accord is achieved in this consideration.

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.

Quantifying and Modeling the Force Variation Within Random Arrays of Spheres

2016 ◽  
Author(s):  
G. Akiki ◽  
T. L. Jackson ◽  
S. Balachandar
Keyword(s):  
Lateral Force ◽  
Point Particle ◽  
Immersed Boundary ◽  
Immersed Boundary Methods ◽  
Lateral Forces ◽  
Random Arrays ◽  
Force Variation ◽  
Drag Models ◽  
Boundary Methods ◽  
Arrays Of Spheres

In this study, we perform fully-resolved direct numerical simulations (DNS) of a flow past random arrays of spheres using immersed boundary methods (IBM). These simulations are used to quantify the error arising from point-particle (PP) force models which assumes equal drag and zero lateral forces on all particles. The results show that the rms drag and lateral force fluctuation can be as high as 26% and 15% of the mean drag value, respectively. For each sphere, the hydrodynamic forces are shown to be dependent on the exact location of few neighboring spheres. A pairwise interaction extended point-particle (PIEP) model is then presented. The model can approximate the drag and lateral forces on each sphere by systematically accounting for the location of few of its neighbors. The perturbation from each neighbor is considered separately then linearly superposed to obtain the total variation of the drag and lateral force. Significant error reduction is observed when using PIEP model instead of mean drag models upon comparing to exact forces acquired from the DNS IBM simulations.

scholarly journals Double-Diffusive of a Nanofluid in a Rectangle-Shape Mounted on a Cavity Saturated by Heterogeneous Porous Media

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Abdelraheem M. Aly ◽  
Ehab Mohamed Mahmoud ◽  
Hijaz Ahmad ◽  
Shao-Wen Yao
Keyword(s):  
Porous Media ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Flow Speed ◽  
Heterogeneous Porous Media ◽  
Convection Flow ◽  
High Concentration ◽  
Buoyancy Ratio ◽  
Double Diffusive ◽  
Darcy Parameter

This study presents numerical simulations on double-diffusive flow of a nanofluid in two cavities connected with four vertical gates. Novel shape of an outer square shape mounted on a square cavity by four gates was used. Heterogeneous porous media and Al 2 O 3 -water nanofluid are filled in an inner cavity. Outer rectangle shape is filled with a nanofluid only, and its left walls carry high temperature T h and high concentration C h . The right walls of a rectangle shape carry low temperature T c and low concentration C c and the other walls are adiabatic. An incompressible smoothed particle hydrodynamics (ISPH) method is applied for solving the governing equations of velocities, temperature, and concentration. Results are introduced for the effects of a buoyancy ratio − 2 ≤ N ≤ 2 , Darcy parameter 10 − 3 ≤ Da ≤ 10 − 5 , solid volume fraction 0 ≤ ϕ ≤ 0.05 , and porous levels. Main results are indicated in which the buoyancy ratio parameter adjusts the directions of double-diffusive convection flow in an outer shape and inner cavity. Adding more concentration of nanoparticles reduces the flow speed and maximum of the velocity field. Due to the presence of a porous medium layer in an inner cavity, the Darcy parameter has slight changes inside the rectangle shape.

The first effects of fluid inertia on flows in ordered and random arrays of spheres

2001 ◽  
Vol 448 ◽  
pp. 213-241 ◽  
Author(s):  
REGHAN J. HILL ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Drag Force ◽  
Stokes Flow ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Fluid Inertia ◽  
Volume Fractions ◽  
Random Arrays ◽  
Long Time

Theory and lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at small Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is determined at small but finite Reynolds numbers, at solid volume fractions up to the close-packed limits of the arrays. For small solid volume fraction, the simulations are compared to theory, showing that the first inertial contribution to the drag force, when scaled with the Stokes drag force on a single sphere in an unbounded fluid, is proportional to the square of the Reynolds number. The simulations show that this scaling persists at solid volume fractions up to the close-packed limits of the arrays, and that the first inertial contribution to the drag force relative to the Stokes-flow drag force decreases with increasing solid volume fraction. The temporal evolution of the spatially averaged velocity and the drag force is examined when the fluid is accelerated from rest by a constant average pressure gradient toward a steady Stokes flow. Theory for the short- and long-time behaviour is in good agreement with simulations, showing that the unsteady force is dominated by quasi-steady drag and added-mass forces. The short- and long-time added-mass coefficients are obtained from potential-flow and quasi-steady viscous-flow approximations, respectively.

Sign in / Sign up

Export Citation Format

Share Document