Analisi di stabilità globale di flussi reagenti a basso numero di Mach

This work is the result of a period of traineeship abroad within École Nationale Supérieure des Arts et Métiers and that’s concerned with the study of large-scale un- steady structures that increase self-sustained hydrodynamic oscillations, also known as global hydrodynamic instability: that controls flow’s dynamic in all practical cases, such as combustion chambers. The purpose of this work is an investigation of the instabilities you can find in reactive flows, treating a 1D benchmark problem, an axisymmetric lifted jet diffusion flame and a three-dimensional cellular jet diffu- sion flame. For each case, Direct Numerical Simulation (DNS) of the Navier–Stokes equations in the low Mach number limit is performed to know the time evolution of the flow. If the flow evolves into a steady-state we obtain the baseflow , which is peculiar solution of the N-S equations, that’s either stationnary or periodic in time. Even if the flow shows unstable configuration it’s possible to reach a steady-state by damping the most dangerous frequencies and thus quenching the corresponding instability with SFD (Selecive Frequency Damping, see [6]) computation: the result is so the baseflow. Such solution has been computed, one can then investigate the dynamics of infinitesimal perturbations evolving onto this given baseflow by linearising the non- linear Navier-Stokes equation around this peculiar solution. The linear stability of the base flow is then fully determined by the spectrum of eigenvalues whereas the associated leading eigenvectors provide the spatial distribution of the unstable perturbations. To obtain the spectrum we use Arnoldi eigenvalue solver subroutine (Loiseau, see [14]). All that has been performed using Nek5000, an incompressible flows code with the approximation of the Low Mach Number equations (LMN). All computations were executed on ENSAM’s multiprocessor servers, Occigen and Ada, supercom- puters of IDRIS (Institut du développement et des ressources en informatique sci- entifique).