Three‐dimensional immersed boundary conditions for moving solids in the lattice‐Boltzmann method

Abstract

SUMMARYThis paper establishes the range of validity for a previously published three-dimensional moving solid boundary condition for the lattice-Boltzmann method. This method was reasonably formulated from a mass and momentum balance perspective, but was only verified for a small range of (primarily twodimensional) problems. One of the advantages of this boundary condition is that it offers resolution at the sub-grid scale, allowing for accurate and stable calculation of the force and torque for solids which are moving through a lattice, even for small solid sizes relative to the computational grid size. We verify the boundary condition for creeping flows by comparison to analytical solutions that include both the force and the torque on fixed and moving spheres, and then follow this with comparisons to experimental and empirical results for both fixed as well moving spheres in inertial flows. Finally, we compare simulation results to numerical results of other investigators for the settling of an offset sphere and the drafting-kissing-tumbling of two sedimenting spheres. We found that an accurate calculation of the collision-operator weighting used to obtain sub-grid-scale resolution was necessary in order to prevent spikes in the velocities, forces, and moments when solid objects cross-computational cells. The wide range of comparisons collected and presented in this paper can be used to establish the validity of other numerical models, in addition to the one examined here.

Kinematics and dynamics of suspended gasifying particle

“…is the equilibrium distribution function in the D3Q19 method calculated by [33], f eq i = 3 Simulation of suspended particle…”

“…The results from both methods, UIBB and I /E V , show almost the same accuracy except for particle Reynolds number 10. Furthermore, the maximum deviation from the value of C d is 12% that is obtained by relation (33) and is 8% from IB solver [40] at Re = 10. However, this error drops about 3% by increasing the resolution of the particle from 5 to 10 lattices per radius.…”

“…7, the error drops from 12 to 4%. 6 The sedimentation velocity of settling single sphere at Re = 1.5 and Re = 31.9, a validation and resolution study against the experimental data E1 and E4 from [7], b comparison between two different methods for particle boundary Error(%) Fig. 7 Resolution study of a settling sphere for particle Reynolds number 31.9…”

“…For instance, the rate of gas-solid reactions depends on both available surface area and particle size [3]. Therefore, the study of each individual gasifying particle with different size and shape helps to understand certain properties of the particle flow in large scale.The motion of spherical and non-spherical particles has already been studied in different flow cases such as the settling of single spheres under gravity [4][5][6][7][8] and the rotation of an ellipsoid in simple shear flow [9][10][11][12][13][14]. The influence of mass injection from the surface of the solid particle has also been studied by previous authors [15][16][17] by implementing outflow on the boundary of a fixed sphere.…”

Resolution sensitivity of momentum‐exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method

“…The collision operator of LBM is modified in such a way that the response of a lattice node can transit smoothly from pure fluid to pure solid along with the increase of its volumetric fraction occupied by the solids. The IBS has been validated in both 2D and 3D and applied to simulate quite complicated problems such as drafting-kissing-tumbling of two settling particles and sand production in oil wells [27][28][29].…”