Computational Fluid Dynamics (CFD) usually requires advanced and accurate diagnostics to help improve our understanding especially in the context of fully unsteady 3D simulations. To do so, two kinds of tools exist today: operator-based and data-based analyses. The most well known data-based analysis used in fluid mechanics is probably the dynamic mode decomposition. This method has indeed shown to be powerful to study CFD results without assumption. It is, however, memory consuming and very sensitive to noise while being used a posteriori. The objective of the following contribution is to relax such issues thanks to an operator-based analysis called Dynamic Mode Tracking (DMT). Based on the well-known selective frequency damping method, DMT relies on a specific implementation allowing the identification of flow activity of specific interest as the data are generated. The method shows to be well adapted for flows exhibiting a clear limit cycle with multiple specific frequencies. Focusing on one of these frequencies, DMT parameters can be adapted to study its temporal evolution giving insight into the mode spatial and temporal features. Thanks to DMT, a variant called Dynamic Mode Tracking and Control (DMTC) allows then to control the identified feature in the CFD simulation. To do so, DMT is coupled with the flow equations thanks to a feedback relaxation method resulting in an artificial control of the flow physics for a specific feature. The development and application of DMT as well as DMTC are illustrated on three problems. First, a simple flow problem based on the propagation of three acoustics waves to evidence the tracking capability of DMT is presented. The second example deals with the vortex shedding of a cylinder wake. For these two cases, DMTC is then applied to demonstrate the capacity of the approach. Finally, the method is applied to a complex configuration: a 3D swirled burner exhibiting a thermo-acoustic instability.

Self-sustained oscillations of rotor/stator cavity flows are well known to industry. This unsteady phenomenon can be very dangerous and jeopardize the structural integrity of aeronautical engines by damaging turbomachinery components or turbopumps in the context of space applications. Today, the origin of such flow instability and resulting limit-cycle is not well understood and still difficult to predict numerically. In order to have more insight of this phenomenon dynamic, an academic rotor/stator cavity is investigated in the present paper. The main motivation of this study is to highlight the benefit of conjunct numerical strategies relying on Large Eddy Simulations (LES) and flow stability analyses to understand driving instability mechanisms. More specifically, results of a local and global methods are devised and compared to a Dynamic Mode Decomposition (DMD) of LES predictions. Good agreements between the stability methods studied and the present features in the LES limitcycle are found. On this basis, a sensitivity and receptivity analysis of the flow is realized to point the origin of the two most unstable modes: i.e the position within the flow where the problem issues.

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Although rotating cavity flows are essential components of industrial applications, their dynamics is still largely misunderstood. From computer hard-drives to turbopumps of space launchers, designed devices often produce flow oscillations that can destroy the component prematurely, or produce disturbing noise or undesired operating modes of the system. The fundamentals of encountered static and rotating flow boundary layers have evidenced, a long time ago now, the presence of specific boundary layer instabilities and structures for low Reynolds numbers. For higher Reynolds numbers and fully enclosed systems, features are, however, more complex with the apparition of multifrequency oscillations populating the entire cavity limit cycle. For these flows, Large Eddy Simulation (LES) has illustrated the capacity of reproducing features and limit cycles. However, identifying the origin and region within these flows that are responsible for mode selections remains difficult if not impossible using such computational fluid dynamics tools. The present contribution evaluates a LES and a global stability analysis framework to identify the mechanisms responsible for the observed limit-cycles of two types of rotor-stator cavities. In particular, the presence of a central body or shaft and its impact on the instability selection is of interest here, i.e., the identification of the regions of mode activation for a cylindrical as well as an annular cavity is detailed. Results issued by the conjunct use of dynamical mode decomposition and Global Linear Stability Analysis (GLSA) confirm the observed LES dynamics. Most importantly, GLSA gives access to the triggering mechanisms at the root of the limit-cycles expression as well as hints on the mode selection. In that respect, a cylindrical cavity is shown to sustain more complex features than an annular cavity because of an enhanced flow curvature near the central shaft.