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Research Papers

# Comparison of Axisymmetric and Three-Dimensional Models for Gas Uptake in a Single Bifurcation During Steady Expiration

[+] Author and Article Information

Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802srinath.madasu@mayahtt.com

James S. Ultman, Ali Borhan

Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802

1

Corresponding author. Current address: Maya Heat Transfer Tech Ltd., 4999 St. Catherine Street West, Suite 400, Montreal, QC, H4B1N6, Canada.

J Biomech Eng 130(1), 011013 (Feb 11, 2008) (8 pages) doi:10.1115/1.2838041 History: Received December 29, 2006; Revised July 05, 2007; Published February 11, 2008

## Abstract

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP . The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, $30deg$, $70deg$, and $90deg$, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4–8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.

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## Figures

Figure 1

(a) Physical domain of ASPM for gas transport in lungs and (b) computational domain where R0 is the radius of the parent branch.

Figure 2

Comparison of average gas-phase mass transfer coefficient from the ASPM and experimental values (22) from literature as a function of Reynolds number during expiration

Figure 8

Comparison of Sherwood number from the ASPM and CFDM for symmetric and asymmetric bifurcations along major airway path during steady expiration

Figure 9

Axial distribution of radially averaged Concentration C¯ from ASPM and CFDM with a 70deg bifurcation angle for zero wall concentration condition at Re=243 and Pe=224.

Figure 3

Contour plot of nondimensional (a) x component of velocity (Ux) field, (b) y component of velocity (Uy) field, and (c) concentration (C) field using CFDM for three-dimensional single bifurcation with a 70deg bifurcation angle for zero wall concentration condition at Re=243 and Pe=224 for z=0 isosurface

Figure 4

Contour plot of nondimensional (a) axial velocity field (Uz), (b) radial velocity field (Ur), and (c) concentration field (C) using ASPM for axisymmetric single bifurcation for zero wall concentration condition at Re=243 and Pe=224

Figure 5

Comparison of Sherwood number from the ASPM and CFDM for different wall mass transfer coefficients during steady expiration for (a) 70deg bifurcation angle and (b) 30deg bifurcation angle

Figure 6

Comparison of Sherwood number from the ASPM for parabolic and flat inlet velocity profiles for different wall mass transfer coefficients during steady expiration

Figure 7

Contour plot of nondimensional concentration field for (a) symmetric, (b) asymmetric, and (c) ASPM single bifurcation model geometries for zero wall concentration condition at Re=365 and Pe=336 during steady expiration

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