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TECHNICAL PAPERS: Fluids/Heat/Transport

An Axisymmetric Single-Path Model for Gas Transport in the Conducting Airways

[+] Author and Article Information
Srinath Madasu1

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

Ali Borhan, James S. Ultman

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

1

E-mail: sum13@psu.edu

J Biomech Eng 128(1), 69-75 (Aug 03, 2005) (7 pages) doi:10.1115/1.2133762 History: Received April 21, 2005; Revised August 03, 2005

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel’s symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%–30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a model for the lung anatomy

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Figure 2

Physical domain (a) and computational domain (b) of the ASPM. Ri is the radius of a cylindrical branch i, and Ti indicates a conical transition region i located between branch i−1 and branch i.

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Figure 3

Distribution of nodes on a rectangular element used in the computation of the physical variables; solid circles represent the velocity, concentration nodes and open circles represent the pressure nodes

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Figure 4

Mesh of quadrilateral elements used in the mesh refinement study. This ASPM geometry corresponds to the trachea and first generation of the three-generation physical model used by Simone (14)

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Figure 5

Contour plots of axial velocity (a), radial velocity (b), pressure (c), and stream function (d) near the first leak of the five-generation ASPM for Re=365

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Figure 6

Axial distribution of pressure at the symmetry line of the five-generation ASPM for Re=365. Vertical lines indicate the location of the transition regions. Axial distance and pressure are plotted as dimensionless quantities.

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Figure 7

Radially averaged concentration profiles corresponding to the experiments of Scherer (4) at Re=182 and Pe=306. The inlet concentration curve at port 2 (a) and output concentration profile at port 3 (in the middle of the fifth generation branch) (b) are shown when a rectangular pulse of 0.3‐second width is introduced at port 2.

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Figure 8

Comparison of ASPM predictions to experimental data for benzene-inert gas dispersion (4), using two different leak concentrations at the transition region wall in the simulations, the bulk average concentration and the wall concentration

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Figure 9

Comparison of ASPM predictions to experimental data for helium-inert gas dispersion (14) in terms of the difference in residence times (a) and variances (b) between the trachea and third-generation branches

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