Evaluation of sets of mode solutions in lined ducts. Part II: Round ducts, with flow

The sound field description in silencer ducts usually applies the field formulation as sums of silencer modes for which sets of such modes are needed. The numerical problems with known methods for the evaluation of mode sets mainly come from the requirement of ,,mode-safe" sets, and, in this context, with the definition and computation of either suited mode range limits and/or precise starters for numerical equation solvers. After a short description of that problem in the case of a flat duct, a method for the evaluation of mode sets, based on a continued-fraction formulation of the characteristic equation, will be described which delivers unambiguous mode solutions. The method will be described for both rectangular and circular ducts, with either locally or bulk reacting absorber linings, without and with a steady flow in the duct, for several kinds of sound field symmetries. The presented continued-fraction method is simple, fast, and safely computing. Whereas part I of the paper has developed and applied the method of continued fractions with rectangulat ducts, this part 11 will apply that method to round ducts and will discuss special problems which arise when steady flow is considered.