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Hydrodynamic interactions among fibers in high efficiency filters

Technical Report ·
OSTI ID:6866579
; ;  [1]
  1. Michigan Univ., Ann Arbor, MI (United States). Dept. of Mechanical Engineering and Applied Mechanics

In this report we present a review of the various analytical solutions for the two-dimensional flow in a model fibrous filter made of periodic arrangements of cylinders. These two-dimensional analytical solutions include the various treatments, namely the creeping flow, the inviscid flow, the swarm theory, and the Oseen approximation. We examine in detail the commonly used solutions of Happel, Kuwabara, and the swarm theory of Neale and Nader. We also examine the three-dimensional solutions of Banks obtained by the superposition of the two-dimensional analytical solutions. A review of the different numerical solution for the flow over cylinders is also given. In addition, we also present an analytical solution which is an extension to the Kuwabara solution and uses the actual boundaries of the square unit cell. The first term of this extended analytical solution is the Kuwabara solution. A two-dimensional numerical solution is also presented for the rectangular and square unit cells. This numerical solution is used to determine the effect of the unit cell anisotropy on the pressure drop across the unit cell. The numerical solution is used for comparison with the analytical solutions of Kuwabara, Happel, and our extended solution. The analytical solution of Kuwabara and Happel show significant error, especially near the boundaries of the unit cell. The extended analytical solution shows good agreement with the numerical results. The ongoing three-dimensional numerical solution of flow over cylinders is also discussed.

Research Organization:
Lawrence Livermore National Lab., CA (United States); Michigan Univ., Ann Arbor, MI (United States). Dept. of Mechanical Engineering and Applied Mechanics
Sponsoring Organization:
DOE; USDOE, Washington, DC (United States)
DOE Contract Number:
W-7405-ENG-48
OSTI ID:
6866579
Report Number(s):
UCRL-CR-111783; ON: DE93007117
Country of Publication:
United States
Language:
English