nance frequencies predicted from the 1-D analysis are somewhat shifted (in frequency) from those predicted from the 3-D analysis. This shift is due to the non-inclusion of end-correction in the 1-D analysis to take into account the effect of the radiation reactance when an open-ended tube ends inside another tube of larger cross-section. Fig. 12 shows the effect of end-corrections on the transmission loss prediction from the present VS algorithm. The hypothetical additional lengths can be calculated based on two types of assumptions. When the open-ended tubes are assumed to be opening without a flange at the end, the end-correction is given by [5] DLOpenEnd ¼ 0:6r; ð15Þ
Fig. 11. Comparison of TLa spectrum from 3-D FEM analysis with that from the present Volume Synthesis algorithm at a higher fluid temperature.
Fig. 12. Comparison of TLa spectrum from showing the effect of end-correction in the VS algorithm.