Local and Global Stability Analysis of an Academic Rotor/Stator Cavity

Abstract

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.

Modes identification and interactions in a rotor/stator academic cavity

“…This numerical study also confirmed the capability of Computational Fluid Dynamic (CFD) to capture the annular and spirals structures as observed by Schouveiler (2001). Recently, studies [Bridel-Bertomeu (2016), Queguineur et al (2018)] relying on LES [Sagaut (2002)] and Dynamical Mode Decomposition (DMD) [Schmid (2010)] as well as linear stability analyses allowed a deeper investigation of the trigger of global modes in such systems. In this case, Bridel-Bertomeu (2016) used a local stability approach to locate the wavemaker of each reported mode.…”

“…1. First, the mean flow issued by a Large Eddy Simulation (LES) of the cavity [Bridel-Bertomeu (2016), Queguineur et al (2018)] is used to conduct the global stability analysis. To do so, the code GIFIE developed by Bridel-Bertomeu ( 2016) is used to solve the eigenvalues problem of Eq.…”

“…In this case, Bridel-Bertomeu (2016) used a local stability approach to locate the wavemaker of each reported mode. Queguineur et al (2018) expanded this first study by analyzing the flow using a global stability analysis. This last method, contrary to a local approach, enables to compute more easily adjoint modes allowing to conduct optimisation studies.…”