The Calculation of the Cut-in Length of the End Hole of Channel Without Clamping Shoulder by the Acoustic Design Development

Abstract

The analysis of known calculated dependences for determining the relative cut-in length of the end hole of the channel without clamping shoulder (end correction) needed to perform applicative acoustic calculation, in particular by the design of jet noise mufflers. The accuracy of the results obtained by calculating with the known dependencies is estimated. The method of calculating of the end correction with machine method is offered, the basis of which was used by the development of analytical dependence for calculating the values of the cut-in length of the holes without clamping shoulder with high accuracy adopted in this article as a reference. These values are calculated in Matlab system with relative and absolute accuracy 10–7 and 10–12, in particular, it was found that when ka=0l/a=0,6127, but not 0.6133 as it was previously thought in the world acoustics. A computer approach of calculation of the modified Bessel functions for large values of the argument was developed. A correction of design equations which are widely used in acoustic engineering development, which increases the accuracy of calculating the cut-in length of the end channels holes without clamping shoulder. The results are intended for use in both basic acoustic investigations and in their numerous practical applications.