Sound velocity measurement of pipeline fluids based on wavenumber-frequency spectrum

Accurate measurement of components in multiphase flows holds significant scientific and societal importance, particularly in the energy extraction sector, which is crucial for optimizing production efficiency. The components of multiphase flow can be determined by measuring the speed of sound in the pipeline fluid. However, traditional sound velocity measurement methods often suffer low repeatability and are unsuitable for multiphase flows. This paper introduces a new measurement technique based on the wavenumber-frequency (k−ω) spectrum to achieve accurate measurement of sound velocity in medium. Firstly, we derive the one-dimensional acoustic formula for the pipeline and establish the acoustic signal model at various positions along its axial direction. Next, we explore the frequency domain superposition characteristics of the downstream and upstream "acoustic ridges". Secondly, the theoretical formulas for calculating sound velocity in the single-phase and two-phase flow of air and water and the influence of different pipe materials, diameters and wall thickness on sound velocity are analyzed. Additionally, the sampling window length of the line array sensors is adjusted based on the speed of sound, the critical frequency corresponding to different pipe diameters is filtered and pre-processed. 2D Fast Fourier Transform (2D FFT) algorithm and frequency beam forming (FDBM) algorithm are applied to convert the data into the wavenumber-frequency domain for simulation and analysis. Finally, A DN50 stainless steel pipe equipped with piezoelectric array sensors was used to experiment. Compared to theoretical data, the relative error of the measured sound velocity in the single-phase flow of water is 2.13 %, with a repeatability of 0.78 %. For the two-phase flow of water and air, the relative error is 2.94 %, and the repeatability is 1.62 %. This demonstrates the feasibility of measuring sound velocity using the wavenumber-frequency spectrum. •One-dimensional acoustic model is used to measure the speed of sound in fluids within pipelines.•FDBM algorithm creates "acoustic ridge" in the wavenumber-frequency spectrum that reflect the speed of sound.•For single-phase flow of water, the relative error is 2.13 %, with a repeatability of 0.78 %. For two-phase flow of water and air, the relative error is 2.94 % and the repeatability is 1.62 %.