Comparison of various methods for analyzing lined circular ducts

Over the years, lined ducts with bulk reacting linings have been investigated for their sound attenuation performance. The methods employed for these studies can be broadly categorized into three major types. In one approach, the duct is assumed to be of infinite length of which a slice of finite length is taken out to get a transfer matrix between the two end points of this slice. In another approach, the one dimensional, coupled wave equations are solved, with the pressure difference between the flow passage and the absorptive lining being supported by a perforated plate. In the third major approach, the three-dimensional wave equation is solved, taking into consideration the finite length boundary effects. In this paper, these three approaches are compared with respect to their limitations, simplicity and accuracy. Here, the lowest mode or the (0,0) mode only has been investigated. In the third approach, improvements are incorporated to make this method work accurately in the high frequency regions too. Relatively larger sized ducts are also examined for different values of d / h ratios.