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Research Papers

Implementation and Validation of a 1D Fluid Model for Collapsible Channels

[+] Author and Article Information
Peter Anderson

Department of Mechanical Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: peter.anderson@alumni.ubc.ca

Sidney Fels

Department of Electrical and
Computer Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: ssfels@ece.ubc.ca

Sheldon Green

Department of Mechanical Engineering,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
e-mail: green@mech.ubc.ca

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received January 25, 2013; final manuscript received August 1, 2013; accepted manuscript posted September 6, 2013; published online October 1, 2013. Assoc. Editor: Ender A. Finol.

J Biomech Eng 135(11), 111006 (Oct 01, 2013) (7 pages) Paper No: BIO-13-1044; doi: 10.1115/1.4025326 History: Received January 25, 2013; Revised August 01, 2013; Accepted September 06, 2013

A 1D fluid model is implemented for the purpose of fluid-structure interaction (FSI) simulations in complex and completely collapsible geometries, particularly targeting the case of obstructive sleep apnea (OSA). The fluid mechanics are solved separately from any solid mechanics, making possible the use of a highly complex and/or black-box solver for the solid mechanics. The fluid model is temporally discretized with a second-order scheme and spatially discretized with an asymmetrical fourth-order scheme that is robust in highly uneven geometries. A completely collapsing and reopening geometry is handled smoothly using a modified area function. The numerical implementation is tested with two driven-geometry cases: (1) an inviscid analytical solution and (2) a completely closing geometry with viscous flow. Three-dimensional fluid simulations in static geometries are performed to examine the assumptions of the 1D model, and with a well-defined pressure-recovery constant the 1D model agrees well with 3D models. The model is very fast computationally, is robust, and is recommended for OSA simulations where the bulk flow pressure is primarily of interest.

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Figures

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Fig. 1

A midsagittal view of the upper airway from a computed tomography (CT) scan with important structures labeled

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Fig. 2

Mesh refinement study, showing numerical error p* as a function of αmin, for three levels of mesh quality: coarse (dashed-dotted red curve), medium (dashed blue curve), and fine (solid green curve)

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Fig. 3

Area and pressure curves at selected times for a closing and reopening geometry. Dashed blue line at t = 0.110 s, dashed-dotted green line at t = 0.125 s, dotted black line at t = 0.135 s, and solid red line at t = 0.136 s. (a) Area function at selected times. (b) Pressure function at selected times.

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Fig. 4

Case 1 simulations. (a) A 3D view of the geometry, colored by pressure. The flow is driven by a velocity inlet (upper right corner) and develops through a uniform pipe before entering the oral cavity of the idealized airway. The outlet (bottom left corner) is in the trachea. (b) A midsagittal view of velocities from an LES, illustrating the complexities of the flow. The 1D centerline with distance labels is included.

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Fig. 5

A comparison of the case 1 simulations: a 3D RANS (solid blue curve), a 3D LES (solid green curve), and the 1D model with χmin = 0.25 (dashed black curve). The bounds of the model are shown with χmin = 0.0 (solid red curve) and χmin = 1.0 (dashed red curve), and the effects of a small variation are shown with χmin = 0.20 (thin solid black curve) and χmin = 0.30 (thin dashed-dotted black curve).

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Fig. 6

LES results for case 1 (solid black curve), with ±1 standard deviation of pressure (dashed green curves)

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Fig. 7

Case 2 simulations. (a) A 3D view of the geometry, colored by pressure. The flow, which comes from the nasal cavity, enters the geometry at the pressure inlet (upper left corner) and exits in the upper trachea (bottom). The oral cavity (upper right) has no flow. (b) Velocities from an LES showing flow through a narrow constriction. The 1D centerline with distance labels is included.

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Fig. 8

A comparison of the case two simulations: a 3D RANS (solid blue curve), a 3D LES (solid green curve), and the 1D model with χmin = 0.20 (dashed black curve). The no-recovery case is shown with χmin = 0.0 (solid red curve), and the effects of a small variation are shown with χmin = 0.15 (thin solid black curve) and χmin = 0.25 (thin dashed-dotted black curve).

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