Oscillating Flow of a Compressible Fluid through Deformable Pipes and Pipe Networks: Wave Propagation Phenomena

摘要

Similarly to blood pulse propagation in the artery system, oscillating flow can propagate as a wave in fluid-saturated pipes, networks of pipes or, by extension, in porous media, if the fluid is compressible and/or the pipes are elastically deformable. First, propagation of flow waves generated in a semi-infinite pipe by harmonic pressure oscillations at the pipe entrance is analyzed. The dispersion equation is derived, allowing determination of the phase velocity and quality factor as functions of frequency. Wave reflections at the end of a finite-length pipe and ensuing interferences between forward and backward traveling waves are then examined. Because of fluid storage in the pipe, the amplitude of the AC volumetric fluxes entering and exiting the pipe at its upstream and downstream ends are not equal. Thus, two different, upstream and downstream, frequencydependent, AC hydraulic conductivities are introduced. Superposed on the classic viscous-inertial flow transition (controlled by the value of the pipe radius), these complex-valued parameters show another transition between an interference-free regime at low frequencies and a strong interference regime above a critical frequency that roughly scales as the pipe length. Because of attenuation, the flow wave interferences tend to gradually weaken with increasing frequencies. Finally, the single pipe model is used to investigate fluid flow waves through pipe networks with results very similar to those described above. The flow waves analyzed here are akin to the Biot’s slow P waves and their propagation properties could affect seismic soundings in some geological settings.