Journal
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
Volume 156, Issue 1-2, Pages 95-111Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jnnfm.2008.07.006
Keywords
Oldroyd-B fluid; Positive definiteness; Fictitious domain; Particulate flow; Finite element; Operator splitting
Categories
Funding
- NSF [ECS-9527123, CTS-9873236, DMS-9973318, CCR9902035, DMS-0209066, DMS-0443826]
- DOE/LASCI [R71700K-292-000-99]
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In this article we present a numerical method for simulating the sedimentation of circular particles in a two-dimensional channel filled with an Oldroyd-B fluid. We have combined a fictitious domain/distributed Lagrange multiplier method with a factorization approach from Lozinski and Owens [J. Non-Newtonian Fluid Mech. 112 (2003) 161] via an operator splitting technique. The new scheme preserves the positive definiteness of the conformation tensor at the discrete level. The method is validated by performing a convergence Study which shows that the results are independent of the mesh and time step sizes. Our results show that when the elasticity number(E) is less than a critical value (which depends upon the blockage ratio), two particles will sediment in the channel-like particles in Newtonian fluids; when the elasticity number is greater than the critical value, chains are formed for the case of two particles sedimenting in an Oldroyd-B fluid and the center line is aligned with the falling direction. These results agree with those presented in [P.Y. Huang, H.H. Hu, and D.D. Joseph, J. Fluid Mech. 362 (1998) 297]. For the cases of three and six particles, when the elasticity number is greater than a critical value and the viscoelastic Mach number is less than one, chains are also formed and move to the center of the channel. (c) 2008 Elsevier B.V. All rights reserved.
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