Investigating Frequency Dependence of Wave-Tank Interaction for a Water-Filled Cylindrical Pipe Using Transfer Matrix Method

High resolution imaging of water pipes requires high frequency (short wavelength) transient waves. While the boundary interaction of classical water hammer (low frequency transients (LFW)) with boundary elements (e.g., tanks) are well studied, the behaviour of high frequency waves (HFW) at pipe boundaries has not been addressed. This paper focuses on understanding the transmission and reflection of HFW at a pipe-tank boundary. The system comprises of a 2” 12m long steel pipe connected to PVC tanks at both ends and filled with water. A monopole source is used to internally excite the pipe system over a large frequency band (up to 50kHz). Characteristics of the multimodal radiation such as the acoustic impedance, reflectivity and directivity patterns at the boundary would be examined. The frequency dependent acoustic end correction would be obtained, and the response of the system would be compared with a numerical framework based on the transfer matrix method. Initial development considers a theoretical framework based on classical theory to characterize radiation near the pipe end where the increase in excitation frequency is expected to favor transmission of radiation at the pipe open end. Maximum acoustic power directivity is anticipated in the forward direction with high amplitudes for large frequencies. Whereas the application of the transfer matrix model to a simple pipe system suggested a shift in natural modes of the system in response to the frequency dependent end correction at the boundaries. It is expected that this investigation will guide the formulation of appropriate boundary conditions for HFW in a pipe that terminates at a tank. Such boundary conditions are instrumental for developing high resolution transient-based defect detection methods using high frequency probing waves.