Optimum Bifurcating-Tube Tree for Gas Transport

[+] Author and Article Information
Tianshu Liu

Department of Mechanical and Aeronautical Engineering, Western Michigan University, Kalamazoo, MI 49008 tianshu.liu@wmich.edu

J. Fluids Eng 127(3), 550-553 (Mar 02, 2005) (4 pages) doi:10.1115/1.1899168 History: Received December 31, 2003; Revised January 24, 2005; Accepted March 02, 2005

This paper describes optimality principles for the design of an engineering bifurcating-tube tree consisting of the convection and diffusion zones to attain the most effective gas transport. An optimality principle is formulated for the diffusion zone to maximize the total diffusion mass-transfer rate of gas across tube walls under a constant total-volume constraint. This optimality principle produces a new diameter distribution for the diffusion zone in contrast to the classical distribution for the convection zone. In addition. this paper gives a length distribution for an engineering tree based on an optimality principle for minimizing the total weight of the tree under constraints of a finite surface and elastic criteria for structural stability. Furthermore, the optimum branching angles are evaluated based on local optimality principles for a single bifurcating-tube branch.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Geometry of tube bifurcation

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Figure 2

The theoretical diameter distributions for an engineering bifurcating-tube tree along with measured data for bronchial trees

Grahic Jump Location
Figure 3

The theoretical length distribution for an engineering bifurcating-tube tree along with measured data for bronchial trees



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