A Transmission Line Approach to the Acoustic Analysis of Piping Systems

Abstract

We present a wave transmission line model developed to understand the transmission of energy through fluid-filled piping systems. The piping systems are represented as a sequence of components, e.g. valves, bends, and other components, connected with straight pipe sections. The transmission line model makes use of experimentally- or analytically-determined scattering coefficients to represent component behavior. The coefficients capture important coupling between fluid and structure, and among different structural wave types. The measurement of these coefficients is the subject of a separate paper [1]. The straight pipe segments are modeled analytically using fluid-filled, thick shell theory. Their motion is described in terms of amplitudes of freely traveling, left-and-right propagating waves. Results are presented which compare transfer functions measured on a piping system to predictions from the transmission line model, where each component is modeled with experimentally determined scattering coefficients. Initial results highlight important issues regarding the use of reciprocity, passivity, and causality to improve the quality of coefficients which are difficult to measure (for example, where certain frequency bands had high signal to noise). Algorithms for determining whether measured coefficients meet constraints on passivity, reciprocity, and causality are introduced. Predictions comparing analytical and measured coefficients are shown for a single-component (elbow) piping system.