Abstract
We measured the pressure/flow relationships in a cast of human upper and central airways at high frequencies (3, 5, 8, 10, 12 and 15 Hz) and low stroke volumes (70, 110, 150 and 230 cm3). A particular effort was made to analyse the effect of the larynx on the pressure/flow relationships by comparing the experimental measurements obtained both with and without larynx. The larynx was found to have an effect on airflow patterns, increasing both turbulence and airway resistance. The phase lead of pressure relative to flow was smaller in the presence of the larynx than in its absence, indicating an increase in the resistive part of impedance by the larynx. In a dimensionless Moody plot of peak pressure and peak flow, data obtained at the various frequencies and stroke volumes formed a single curve as the steady-flow theory predicts, indicating an appearance of quasi-steady-state behaviour. In this case, the tracheal Reynolds number alone governs the dimensionless pressure drop. Plotted against Re/a (ratio of Reynolds and Womersley numbers) the normalised instantaneous pressure drop was generally smooth throughout the range of Re/α except for the appearance of a transition at the lowest frequency suggesting the onset of turbulent flow.
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Abbreviations
- a :
-
constant ranging between 1 and 2
- Cd :
-
discharge coefficient
- d :
-
diameter of the trachea
- f :
-
oscillation frequency
- Fn :
-
function
- K :
-
constant depending on airway geometry
- ΔP :
-
pressure difference
- ΔP m :
-
maximum pressure drop
- Re :
-
Reynolds number
- Re m :
-
maximum Reynolds number in the trachea
- S :
-
cross-sectional area
- u :
-
average velocity
- U m :
-
maximum mean velocity in the trachea
- V s :
-
stroke volume
- \(\dot V\) :
-
flow rate
- ω:
-
angular frequency
- α:
-
Womersely parameter
- α* :
-
turbulent unsteadiness parameter
- μ:
-
dynamic viscosity
- ν:
-
kinematic viscosity
- v * :
-
eddy viscosity
- σ:
-
density
- ϕ:
-
phase shift
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Jebria, A.B., Choukroun, M.L., Tabka, Z. et al. High-frequency oscillatory pressure/flow relationship in the airways of laryngo-tracheo-bronchial tree casts. Med. Biol. Eng. Comput. 26, 476–482 (1988). https://doi.org/10.1007/BF02441914
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DOI: https://doi.org/10.1007/BF02441914