Analytical Solution of Flow Field and Pressure Drop for Filters with Noncircular Fibers
Titel:
Analytical Solution of Flow Field and Pressure Drop for Filters with Noncircular Fibers
Auteur:
Ouyang, Ming Liu, Benjamin Y. H.
Verschenen in:
Aerosol science and technology
Paginering:
Jaargang 23 (1995) nr. 3 pagina's 311-320
Jaar:
1995
Inhoud:
The Happel-Kuwabara cell model, which has been used exclusively for cylindrical fibers of a circular cross-section, has been extended in this study to fibers of an arbitrary cross-sectional shape. The general solution of the two-dimensional biharmonic equation ▿2(▿2ψ)=0 for the stream function, ψ, has been obtained. By forcing the truncated general solution to satisfy appropriate boundary conditions on the cylinder surface and at the outer cell boundary, the flow field around a fiber of an arbitrary cross-sectional shape can be solved analytically. The resulting dimensionless fiber drag can then be calculated as a function of fiber packing density. In addition, by imposing the slip boundary condition at the fiber surface, the flow field in the slip flow regime can be obtained. In cases where analytical solution with variable coefficients is too complicated or time consuming to obtain, analytical solution with constant coefficients can be obtained at considerable saving in computer time. The solution method developed is computationally very efficient. Many problems that required a supercomputer to solve using a finite difference or finite element approach can now be solved on a workstation or a personal computer using the present method.
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