Experiments on hydrodynamically developing flow in rectangular ducts of arbitrary aspect ratio

Pressure distributions in a static physical model of the uniform glottis: Entrance and exit coefficients

“…Ishizaka and Matsudaira 2 and Ishizaka and Flanagan 3 adopted the value of 1.375 for the entrance loss coefficient (in what they termed the "turbulent" flow approach) and used Newton's second law to derive an exit coefficient that depends on the ratio of the area of the glottal exit to the area of the vocal tract and whose value is substantially smaller than that given by van den Berg et al In addition, Ishizaka and Matsudaira 2 introduced a "laminar" approach that allowed the pressure drop to be defined by the growth of a boundary layer within the glottis. Using laryngeal geometry as an example, Beavers et al 4 have shown that the ratio of the pressure drop between the trachea and a specific crosssection on the inferior vocal fold surface to the kinetic pressure at that location will be 1.0. Downstream of that location the pressure continues to decrease such that the pressure drop at the actual entrance to the (uniform) glottis creates a ratio value greater than 1.0.…”

“…Since Beavers et al 4 found the location at which the ratio of 1.0 was achieved to have a significant dependence on glottal diameter and driving pressures, one would expect a constant entrance loss coefficient of 1.375 to be too great a simplification for accurate phonatory modeling.…”

A Nonlinear Multigrid Method for the Three-Dimensional Incompressible Navier–Stokes Equations

“…The grid points were slightly clustered in the x-direction near the channel entrance, while the grid was uniform in the other directions. The computed pressure coefficient along the channel centre-line was compared with the experimental data of Beavers et al [28] (Fig. 8).…”

Benchmarks for time-domain simulation of sound propagation in soft-walled airways: Steady configurations

“…White (1979) suggests a kinetic pressure loss coefficient ranging linearly from 1.0 to 1.42 with decreasing area ratio. Beavers et al (1970) and Li et al (2012) cast doubt on the formation of a vena contracta, however, regardless of how sharp the entry corner is. In either case, additional viscous or vorticity losses do occur at a sudden contraction.…”