Application of fourier method to study propagation of compression shock wave in pipelines with damper

The transition problems from one mode of steady flow to another in a pipeline with a constant gradient are considered. The pressure value is set at the inlet to the section, and an air chamber of a certain volume is installed at the outlet. Modeling of the process of compression shock wave propagation in an elementary section of the pipeline was conducted according to the linearized quasi-one-dimensional N.E. Zhukovskymodel, and the damper was considered according to the I.A. Charny model. The problem is solved by the method of separation of variables. It is shown that at an increase in the volume of the damper, the amplitude and frequency of perturbations decrease due to the transient process.

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