Periodically forced extensional pipe flow
Document typeBachelor thesis
Rights accessOpen Access
This project studies the flow of a fluid inside an infinite pipe with periodically forced extensional walls in the axial direction. The Navier-Stokes equations for an incompressible fluid inside the pipe are solved to find self-similar solutions of the problem. The system of PDEs is preconditioned using a spectral expansion in modulated Legendre polynomials, and is solved using an IMEX method. Anumerical exploration of time-periodic solutions in a wide parameter region has been conducted, and interesting non-linear phenomena is found for specific parameter regions. The system tends to converge to solutions with limit cycles of the same period as the oscillation. The frequency response of the system is studied. For small frequencies, the problem explores different solutions found in the ’non-forced’ problem , approaching stable limit cycles of high frequencies when the pipe is shrinking very slowly, and forming very fast axial jets. This behaviour is lost when the pipe oscillates at higher frequencies. Moreover, no stable solutions with azimuthal velocity are found, but a branch of unstable solutions with azimuthal velocity is born at a pitchfork bifurcation of cycles. In addition, cascade of period doubling bifurcations is found, leading the system to possible chaos.
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