Analysis of break frequencies downstream of a constriction in a cylindrical tube

Experiments were performed to correlate steady-flow power spectra downstream of a stenosis in a cylindrical tube with the flow geometry and velocity. The experiments were motivated by the need to improve quantitative phonoangiography. An objective break frequency (fb) was computed from spectra of velocity fluctuations, as measured with a hot film anemometer. Least squares fits with two independent variables were used to find an empirical relationship between a Strouhal number (S2), the contraction ratio (ds/D) and the Reynolds number (Re). The variables D and ds, are, respectively, the unobstructed tubing diameter and the inner diameter of the stenosis. The relationship found was S2 = Re 0.72(ds/D)0.26 The contraction ratio ds/D, can be found from the empirical relation in terms of known parameters. For the hot wire data the average error between the computed value of ds/D and the known value was 2.3%.