A method for determining natural frequencies of the dead-end branches of gas pipelines

The frequency spectra for the dead-end branches of gas pipelines, representing the acoustic resonators in a typical collector of a compressor station, are obtained using the methods of the classical theory of vibrations and waves. The half- and quarter-wave resonances of flat and cylindrical semi-open resonators are studied solving the wave equation by the method of separation of variables in an analytical form. Primarily, the qualitative theory of sound wave propagation is considered on the basis of a one-dimensional wave equation. The conclusions made are used for determining the natural frequencies in the two-dimensional problems with various types of symmetry. Minimum frequencies of flat and cylindrical resonators are found to be the same. By means of the numerical simulation methods applying the ANSYS FLUENT software package, the frequencies of vortex shedding at the edges of gas pipeline connections are determined. The obtained frequencies appear to be converging. Minimum self-oscillating frequencies of pressure pulsation during the vortex shedding or the Karman vortex street formation are potentially dangerous for technological systems of gas pipelines as they may resonate with natural frequencies of pipeline dead legs. The fundamental tone of such systems is characterized by minimum excitation energy and, consequently, by maximum amplitude. These resonance phenomena may cause a mechanical destruction of the pipeline manifolds.