Stability and control of unsteady phenomena in rotor/stator cavities using Large Eddy Simulation

Unsteady phenomena in rotor/stator cavity are well known to be the source of dangerous vibrations in space turbopump. Even though many palliative measures have been taken during their design, experimental campaigns often reveal high flow oscillations that can jeopardize turbomachinery components and even the rocket engine. Today, the origin of such flow instabilities usually called ’pressure band phenomenon’(PBP) is not well understood and difficult to predict numerically. The main goal of this thesis is to investigate such phenomenon mechanism to find technical solutions so as to control it. This problematic is addressed here trough two types of configuration: an academic rotor/stator cavity and a space turbopump cavity. When it comes to cavity flows, their rotating boundary layers are known to be three dimensional and receptive to several instabilities taking the form of spirals or annuli. Reynolds Averaged Navier-Stokes Simulations (RANS)failed to predict such unsteady systems. However, Large Eddy Simulation (LES) proved to be a relevant alternative in many similar applications and is therefore chosen for the present work. Using Power Spectral Analysis (PSD) and Dynamic Mode Decomposition (DMD) on LES predictions, one shows that the PBP is retrieved in an annular smooth rotor/stator cavity and it is composed of three modes driving all the system dynamics. To investigate these mode organization and their possible interactions, a new tool called Dynamic Mode Tracking /Control (DMT/DMTC) is introduced. DMT is constructed so as to extract "on-thefly" flow coherent structures with a given frequency on the basis of LES. Furthermore, augmenting the Navier-Stokes equations with a relaxation term coupled to DMT, DMTC allows to control and follow the evolution of a controlled mode as well as non controlled ones and thereby observe interactions. This strategy after validation is applied to the annular rotating cavity and shows that the low frequency mode is generated by the dominant mode of the system. To go further, Global Linear Stability Analysis (GLSA) augmented with adjoint methods is used to shed some light on all mode origins and points out that the low frequency and dominant modes are coming from the stationary boundary layer. In order to set up control strategies, the GLSA framework is further developed introducing the concept of the sensitivity to base flow modifications which gives the location where the flow should be modified if one wants to stabilize or at least shift a frequency mode. Applied to the academic cavity, one shows that contrary to most studies in the literature, controlling the stator boundary layer is the more efficient way to damp the PBP through suction/injection devices. Finally, gathering all the previous understanding of this flow, the LES framework enables to validate the control strategies proposed and to stabilize the PBP for very low suction amplitudes. To finish, the PBP is analyzed in real space turbompump cavities. In particular, the sensitivity of this specific phenomenon to geometry changes is investigated through two configurations: one without and one with the blades of the stator of the turbopump. Even though the introduction of the blades in the LES creates a more complex flow with the presence of shocks, similar pressure fluctuation spectra are retrieved in both configurations but with azimuthal wavenumber modes that are shifted. Following the studies on the academic cavity, an adapted GLSA to the non-linear dynamics of the turbopump enables to point out that even though the PBP modes are particularly marked in the mainstream of the system, the source of these modes is located in the subcavity in the rotor-stator wheel space. In particular, GLSA results indicate that two possible ways to control the phenomenon are possible: modifying the flow around the seal rim and or modifying the leak around the hub