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Bifurcations in a swirling flow

Abstract : This thesis presents a numerical and analytical study of the stability of incompressible swirling jets. The entrainment of fluid by the jet is modeled numerically by assuming open lateral and outlet boundaries, while the inlet flow is modeled as a Grabowski profile. The effect of a small viscosity near the critical swirl number is studied by means of axisymmetric numerical simulations and asymptotic analysis. A numerical arc-length continuation algorithm based on the recursive projection method (RPM) was implemented in order to identify steady state solutions, study their stability and follow them in parameter space. Continuation versus the swirl parameter reveals the existence of a saddle node bifurcation at high Reynolds number. Asymptotic analysis confirms these numerical results. The bifurcation diagram for a swirling jet with a recirculation bubble is studied in the axisymmetric case. It is shown that the steady solution undergoes a supercritical Hopf bifurcation. The global three-dimensional stability of the flow with a recirculation region is investigated numerically using an Arnoldi method. The axisymmetric vortex breakdown state is shown to be unstable to three-dimensional helical perturbations. Finally, the effect of an external pressure gradient on the bifurcation diagram is also investigated numerically. For a Reynolds number Re=1000, the predicted columnar state exists in the case of a favorable pressure gradient at high swirl parameter, but disappears when the pressure gradient reduced back to zero. This suggests a control strategy in order to delay the appearance of vortex breakdown.
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Submitted on : Thursday, November 25, 2010 - 2:45:13 PM
Last modification on : Wednesday, March 27, 2019 - 4:39:25 PM
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  • HAL Id : tel-00538944, version 1



Elena Vyazmina. Bifurcations in a swirling flow. Mathematics [math]. Ecole Polytechnique X, 2010. English. ⟨tel-00538944⟩



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