Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow. (English) Zbl 1178.76235
Summary: We discuss the generalization of a Lagrange multiplier-based fictitious domain method to the simulation of the motion of neutrally buoyant particles in a Newtonian fluid. Then we apply it to study the migration of neutrally buoyant circular cylinders in plane Poiseuille flow of a Newtonian fluid by direct numerical simulation. The Segré-Silberberg effect is found for the cases with one and several circular cylinders. In general, it is believed that the migration away from the center of the channel is due to an effect of the curvature of velocity profile. Via direct numerical simulation, we find that this effect is not weakened by the presence of many particles, but by the collisions among the particles. Experiments and simulations for hundreds of circular cylinder cases show that particles concentrate in the central region where the shear rate is low. A power law associated with the horizontal velocity of the mixture of fluid/particles is also presented.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D99 | Incompressible viscous fluids |
Software:
FISHPAKReferences:
| [1] | J. Adams, P. Swarztrauber, and, R. Sweet, FISHPAK: A Package of Fortran Subprograms for the Solution of Separable Elliptic Partial Differential Equations; J. Adams, P. Swarztrauber, and, R. Sweet, FISHPAK: A Package of Fortran Subprograms for the Solution of Separable Elliptic Partial Differential Equations |
| [2] | Asmolov, E. S., The inertial lift on a spherical particle in a plane Poiseuille flow at large channel number, J. Fluid Mech., 381, 63 (1999) · Zbl 0935.76025 |
| [3] | Bertrand, T.; Tanguy, P. A.; Thibault, F., A three-dimensional fictitious domain method for incompressible fluid flow problem, Int. J. Numer. Meth. Fluids, 25, 719 (1997) · Zbl 0896.76033 |
| [4] | Brenner, H., Hydrodynamic resistance of particles at small Reynolds numbers, Adv. Chem. Eng., 6, 287 (1966) |
| [5] | Bristeau, M. O.; Glowinski, R.; Periaux, J., Numerical methods for the Navier-Stokes equations: Applications to the simulation of compressible and incompressible viscous flow, Comput. Phys. Rep., 6, 73 (1987) |
| [6] | Cox, R. G.; Mason, S. G., Suspended particles in fluid flow through tubes, Annu. Rev. Fluid Mech., 3 (1971) · Zbl 0255.76106 |
| [7] | Dean, E. J.; Glowinski, R., A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow, C.R. Acad. Sci. Paris, Sér. 1, 325, 789 (1997) · Zbl 0901.76054 |
| [8] | Feng, J.; Hu, H. H.; Joseph, D. D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2: Couette and Poiseuille flows, J. Fluid Mech., 277, 271 (1994) · Zbl 0876.76040 |
| [9] | F. Feuillebois, Some theoretical results for the motion of solid spherical particles in a viscous fluid, in, Multiphase Science and Technology, edited by, G. F. Hewitt, J. M. Delhaye, and N. Zuber, Hemisphere, New York, 1989, Vol, 4, p, 583.; F. Feuillebois, Some theoretical results for the motion of solid spherical particles in a viscous fluid, in, Multiphase Science and Technology, edited by, G. F. Hewitt, J. M. Delhaye, and N. Zuber, Hemisphere, New York, 1989, Vol, 4, p, 583. |
| [10] | Fortes, A. F.; Joseph, D. D.; Lundgren, T. S., Nonlinear mechanics of fluidization of beds of spherical particles, J. Fluid Mech., 177, 467 (1987) |
| [11] | Glowinski, R.; Pan, T.-W.; Periaux, J., Distributed Lagrange multiplier methods for incompressible flow around moving rigid bodies, Comput. Meth. Appl. Mech. Eng., 151, 181 (1998) · Zbl 0916.76052 |
| [12] | Glowinski, R.; Pan, T.-W.; Hesla, T.; Joseph, D. D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, 25, 755 (1999) · Zbl 1137.76592 |
| [13] | Glowinski, R.; Pan, T.-W.; Hesla, T.; Joseph, D. D.; Periaux, J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phys., 169, 363 (2001) · Zbl 1047.76097 |
| [14] | Huang, P. Y.; Joseph, D. D., Effects of shear thinning on migration of neutrally buoyant particles in pressure driven flow of Newtonian and viscoelastic fluids, J. Non-Newtonian Fluid Mech., 90, 159 (2000) · Zbl 0980.76095 |
| [15] | Inamuro, T.; Maeba, K.; Ogino, F., Flow between parallel walls containing the lines of neutrally buoyant circular cylinders, Int. J. Multiphase Flow, 26, 1981 (2000) · Zbl 1137.76620 |
| [16] | Karnis, A.; Goldsmith, H. L.; Mason, S. G., The flow of suspensions through tubes. Part V: Inertial effects, Can. J. Chem. Eng., 44 (1966) |
| [17] | Leal, L. G., Particle motions in viscous, Annu. Rev. Fluid Mech., 12, 435 (1980) · Zbl 0474.76104 |
| [18] | Leighton, D.; Acrivos, A., The shear-induced migration of particles in concentrated suspensions, J. Fluid Mech., 181, 415 (1987) |
| [19] | G. I. Marchuk, Splitting and alternating direction methods, in, Handbook of Numerical Analysis, edited by, P. G. Ciarlet and J. L. Lions, North-Holland, Amsterdam, 1990, Vol, I, p, 197.; G. I. Marchuk, Splitting and alternating direction methods, in, Handbook of Numerical Analysis, edited by, P. G. Ciarlet and J. L. Lions, North-Holland, Amsterdam, 1990, Vol, I, p, 197. · Zbl 0875.65049 |
| [20] | Morris, J. F.; Brady, J. F., Pressure-driven flow of a suspension: Buoyancy effects, Int. J. Multiphase Flow, 24, 105 (1998) · Zbl 1121.76462 |
| [21] | Oliver, D. R., Influence of particle rotation on radial migration in the Poiseuille flow of suspensions, Nature, 194, 1269 (1962) |
| [22] | Pan, T.-W.; Glowinski, R., A projection/wave-like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the Navier-Stokes equations, Comput. Fluid Dyn. J., 9, 28 (2000) |
| [23] | Segré, G.; Silberberg, A., Radial particle displacements in Poiseuille flow of suspensions, Nature, 189, 209 (1961) |
| [24] | Segré, G.; Silberberg, A., Behavior of macroscopic rigid spheres in Poiseuille flow: Part I, J. Fluid Mech., 14, 115 (1962) · Zbl 0118.43203 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
