Order and realisability of impulse response filters for accurate identification of acoustical multi-ports from transient CFD

So-called network models are popular tools for the analysis of acoustic phenomena, e.g. in mufflers, in ventilation or pipeline systems, and in combustors (thermo-acoustic instabilities). The building blocks of such models are multi-ports, represented mathematically by their respective transfer matrices. Within the limitations of linear acoustics, transfer matrices provide a complete description of the dynamic characteristics of the individual multi-ports. They may be determined experimentally or in an approximate manner by analytical means. Alternatively, transfer matrices may be reconstructed from transient CFD simulation data with the help of system identification tools. Specifically, it is possible to determine the unit impulse responses of a multi-port with correlation analysis and then obtain transfer matrix coefficients via the z-transform. The present study is concerned with the optimal choice of parameters for accurate transfer matrix identification. Recommendations for the optimal choice of acoustic variables, sample increment, and sample length, as well as filter order, are formulated. Remarkably, it is found that in many cases the use of formally non-causal filters is advantageous. It is argued that this is a consequence of the fact that causal interrelationships imposed by the underlying laws of fluid mechanics are not always represented properly with the standard acoustic variables.