Correlation of nonlinear orifice impedance

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Abstract
Dimensional analysis of the orifice impedance problem produces several sets of nondimensional variables which may be used to correlate nonlinear orifice behavior. Published experimental data on thin orifices were examined and it was found that tests with oil, water, and air can be correlated. Graphs of orifice resistance are given in nondimensional forms that are useful over a wide range of conditions. The form for resistance is R/ρ (νω)1/2 as a function of an aspect ratio parameter l/d, an orifice velocity parameter V/(νω)1/2, and a diameter-viscous parameter d/(ν/ω)1/2. For thin orifices the resistance is independent of d/(ν/ω)1/2 when this parameter is greater than 10. Nonlinear effects begin when V/(ν/ω)1/2=3. This parameter compares the displacement amplitude to the viscous diffusion length. The reactance end correction δ was normalized by the Rayliegh value of 8d/3π and correlated using the variables l/d, V/ωd, and d/(ν/ω)1/2. Again thin orifices show no dependence on d/(ν/ω)1/2 for values greater than 20 and the nonlinear reactance region begins at V/ωd=0.1. Thus, different parameters govern the onset of nonlinear resistance and reactance. Subject Classification: [43]85.20, [43]85.50; [43]28.60.

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