Time-harmonic analysis of acoustic pulsation in gas pipeline systems using the Finite Element Transfer Matrix Method: Theoretical aspects. (1st March 2023) - Tuozzo, Diego M.; Silva, Olavo M.; Kulakauskas, Lucas V.Q.; Vargas, Jacson G.; Lenzi, Arcanjo
Abstract: Structural vibration of gas pipeline systems can be strongly affected by the response of the acoustic domain represented by the gas being transported through pressurized pipes, cylinders and other related components. The resultant Acoustically Induced Vibration (AIV) can be a cause of failure, for example, in reciprocating compressor systems, where the discharge and suction pulsations are the main source of excitation. The objective of this work is to explore and enhance the use of the Finite Element Transfer Matrix Method (FETM) for solving time-harmonic acoustic problems related to AIV, whose results can be used to analyze pulsation in piping systems. Four different damping models are explored and implemented (apart from the classical undamped model) resulting in five different acoustic elements for the quiescent fluid case. In addition, two different damping models are analyzed for the case of a fluid with mean flow, and implemented through two flow-acoustic elements. The physical behavior of certain typical junctions is also investigated, represented by acoustic and flow-acoustic length corrections, and an FETM formulation is proposed to account for local non-linear effects in transfer impedance elements. Also, a discussion related to the minimum and maximum FETM element sizes is presented. A critical analysis of the effectiveness of the whole FETM strategy is performed using a variety of representative gas pipeline geometries as application examples with a particular set of boundary conditions for quiescent and moving fluid medium. Nodal pressure frequency plots of cases considering all the presented acoustic and flow-acoustic elements, and related damping models, are presented. Coherent results were achieved using the procedure when frequency plots are compared with experimental data and 3D FEM equivalent models. Highlights: The use of FETM for duct acoustics is enhanced to solve AIV problems. A detailed derivation of the FETM method for undamped and damped cases is presented. Flow effects in typical geometries junctions and perforated plates are considered. An FETM formulation is proposed to consider local effects in perforated plates. A discussion related to the minimum and maximum FETM element sizes is presented.