In this paper, an accurate and stable sharp interface immersed boundary method(IBM) is presented for the direct numerical simulation of particle laden flows. The current IBM method is based on the direct-forcing method by incorporating the ghost-cell approach implicitly. An important feature of this IBM is the sharp representation of the solid surface, contrary to other variants of IBM for freely moving particles in which the solid surface is diffuse. Moreover, a correction of the diameter is not necessary for obtaining accurate results. The current ghost-cell IBM is stable because spurious oscillations incurred due to discontinuity in the pressure and velocity field in moving particle simulations is avoided. An algorithm for accurate torque computation is developed. The proposed algorithm is verified by comparison to an analytical expression and is shown to give a substantial improvement over the existing method. Finally, the present IBM is validated for various test cases of single and multi-particle systems and is shown to be accurate and robust for a wide range of flow conditions.@en

An efficient and accurate model for the direct numerical simulations (DNS) of liquid-solid flows is presented in this work. In this numerical model, fluid-solid coupling is achieved by implementing the no-slip boundary condition at the particles’ surfaces by using a second order ghost-cell immersed boundary method, allowing for a fixed Cartesian grid to be used for solving the fluid equations. The particle-particle and particle-wall interactions are implemented using the soft sphere collision model. Lubrication forces are included through a sub-grid scale model because of its range of influence on a scale smaller than the grid size.
After the validation of the model, the transport of solid particles in a narrow channel is simulated to mimic the proppant transport in rock fractures in fracking process. The simulations are performed for solids volume fractions ranging from 1.7 to 20 % with the range of Reynolds and Archimedes number: 100-400 and 0-7848, respectively.@en

We report on simulations of an unsteady three dimensional viscoelastic fluid flow through a model porous medium, employing a finite volume methodology (FVM) with a staggered grid. Boundary conditions at the walls of the porous structures are imposed using a second order immersed boundary method (IBM), allowing for accurate simulations using a relatively coarse grid. We compare the viscoelastic stresses obtained using this new IBM technique with those published in literature and find good correspondence. Next, we applied this methodology to model viscoelastic fluids with a FENE-P constitutive model flowing through closely spaced cylinders. Using periodic boundary conditions, we modeled the flow behavior for Newtonian and viscoelastic fluids for successive contractions and expansions. We observe the presence of counter-rotating vortices in between the closely spaced cylinders. The viscoelastic flow structure is symmetric for lower Deborah (De) number, but onset of an asymmetry occurs after a critical De for an infinite array of cylinders. In the presence of side walls, we observe that the onset of flow asymmetry happens at a much lower De, which can be related to higher viscoelastic stresses normal to the flow direction and larger extensional viscosities which affect the curved streamlines. The three-dimensional flow characteristics for viscoelastic flow at higher De number are quite different in comparison with Newtonian flow behavior.

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