Abstract:
The characteristics of the free surface in an orifice driven by a periodic
forcing function have been studied both theoretically and experimentally. In the
theoretical study, two wall boundary condition cases were examined: 1) the radial
velocity at the wall of the orifice is zero; and 2) the axial velocity at the wall of the
orifice is zero. The result for both boundary conditions is a modal solution where
the predicted surface shape as a function of orifice radius and frequency are Bessel
functions. The modal frequencies and annular peak locations are also predicted, as
a function of orifice radius, for both boundary condition cases. The modal
frequencies and annular peak locations differ between the boundary condition
cases. The experimental results show: i) the axial velocity boundary condition
matches the general behavior of the surface at the wall better than the radial
velocity boundary condition case; ii) that the surface shapes generated have the
same characteristics as the Bessel function; and iii) near the centerline, the surface
shape is well modeled by the Bessel function. The experimental results also show
there is a significant shift downward of the observed modal frequencies from the
predicted frequencies. A correlation was developed to predict the measured modal
frequencies for the axial velocity boundary condition case based on the theoretical
predicted frequencies.
