Dean vortices applied to membrane process Part II: Numerical approach

This work is devoted to the numerical study of the flow inside helical hollow fibers. For a wide range of Reynolds numbers and of helix shapes, corresponding to woven or non-woven, permeable or non-permeable fibers, the corresponding three-dimensional velocity field is calculated in order to study the velocity profiles and the local wall shear stress. The influence of permeation is not qualitatively marked within the ranges of conditions that reproduce the classical experimental ultrafiltration conditions. The permeate flux density depends on the permeability of the membrane and is constant on the perimeter of a cross-section of the tube. For all the permeability situations considered, the Dean flow depends on three parameters: the Reynolds number, the curvature and the helix torsion. The effect of each of these parameters depends largely on the relative values of the two others. The Dean number makes it possible to predict the mean shear stress, as well as its distribution along the perimeter of a cross-section. For woven fibers, as their diameter is small, the pitch has a significant influence on the curvature.

[1]  Christophe A. Serra,et al.  Mass transfer improvement by secondary flows: Dean vortices in coiled tubular membranes , 1996 .

[2]  Kyoji Yamamoto,et al.  Stability of the flow in a helical tube , 1998 .

[3]  C. J. Bolinder.  The Effect of Torsion on the Bifurcation Structure of Laminar Flow in a Helical Square Duct , 1995 .

[4]  C Kleinstreuer,et al.  Hemodynamics simulation and identification of susceptible sites of atherosclerotic lesion formation in a model abdominal aorta. , 2003, Journal of biomechanics.

[5]  Clement Kleinstreuer,et al.  Micro-particle transport and deposition in a human oral airway model , 2002 .

[6]  Anne M. Robertson,et al.  Flow of second order fluids in curved pipes , 2000 .

[7]  G. Louridas,et al.  Haemodynamic factors and the important role of local low static pressure in coronary wall thickening. , 2002, International journal of cardiology.

[8]  H. Søeberg,et al.  Viscous flow in curved tubes—I. Velocity profiles , 1988 .

[9]  J. D. Seader,et al.  Entry region for steady viscous flow in coiled circular pipes , 1974 .

[10]  L. C. Truesdell,et al.  Numerical treatment of fully developed laminar flow in helically coiled tubes , 1970 .

[11]  L. Talbot,et al.  Flow in Curved Pipes , 1983 .

[12]  Abraham M. Lenhoff,et al.  Flow in curved ducts: bifurcation structure for stationary ducts , 1989, Journal of Fluid Mechanics.

[13]  M. Germano,et al.  On the effect of torsion on a helical pipe flow , 1982, Journal of Fluid Mechanics.

[14]  Georges Belfort,et al.  Flux enhancement during Dean vortex microfiltration. 8. Further diagnostics1 , 1997 .

[15]  D. Xie,et al.  Torsion effect on secondary flow in a helical pipe , 1990 .

[16]  P. Mishra,et al.  Momentum Transfer in Curved Pipes. 2. Non-Newtonian Fluids , 1979 .

[17]  Shinichiro Yanase,et al.  Resonant Interactions of Dean Vortices in a Curved Channel Flow , 1998 .

[18]  H. Itō,et al.  Laminar Flow in Curved Pipes , 1969 .

[19]  Ramon Molina Valle,et al.  Numerical hydrodynamic and thermal analysis of laminar flow in curved elliptic and rectangular ducts , 1999 .

[20]  Hassan Peerhossaini,et al.  Residence time distribution in twisted pipe flows: helically coiled system and chaotic system , 1997 .

[21]  Cécile Gaucher,et al.  Etude locale de l'hydrodynamique dans un module équipé d'une membrane plane d'ultrafiltration en céramique : influence de la contrainte pariétale sur le colmatage , 2001 .

[22]  W. R. Dean,et al.  Note on the motion of fluid in a curved pipe , 1959 .

[23]  Jacob H. Masliyah,et al.  Axially invariant laminar flow in helical pipes with a finite pitch , 1993, Journal of Fluid Mechanics.

[24]  W. R. Dean.  XVI. Note on the motion of fluid in a curved pipe , 1927 .

[25]  Thomas Hüttl,et al.  Reynolds‐stress balance equations in orthogonal helical coordinates and application , 2004 .

[26]  Rainer Friedrich,et al.  Influence of curvature and torsion on turbulent flow in helically coiled pipes , 2000 .

[27]  K. C. Cheng,et al.  Boundary vorticity method for laminar forced convection heat transfer in curved pipes , 1971 .

[28]  G. Belfort,et al.  Dean vortices with wall flux in a curved channel membrane system: 4. Effect of vortices on permeation fluxes of suspensions in microporous membrane , 1993 .

[29]  Hsiao C. Kao,et al.  Torsion effect on fully developed flow in a helical pipe , 1987, Journal of Fluid Mechanics.

[30]  Lei Xue,et al.  Study on laminar flow in helical circular pipes with Galerkin method , 2002 .

[31]  Massimo Germano,et al.  The Dean equations extended to a helical pipe flow , 1989, Journal of Fluid Mechanics.

[32]  Takehiko Inaba,et al.  Laminar Flow in a Helically Coiled Pipe , 1980 .

[33]  J. J. Ulbrecht,et al.  VELOCITY PROFILES OF NEWTONIAN AND NON-NEWTONIAN TOROIDAL FLOWS MEASURED BY A LDA TECHNIQUE , 1983 .