Dynamic mode tracking and control with a relaxation method

Abstract

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.

Accelerating deep reinforcement learning strategies of flow control through a multi-environment approach

“…The importance of AFC is apparent from the large body of literature that discusses both theoretical, computational, and experimental aspects of the problem. In particular, active flow control has been discussed in simulations using both Reduced Order Models and harmonic forcing (Bergmann et al, 2005), direct simulations coupled with the adjoint method (Flinois & Colonius, 2015) or linearized models (Lee et al, 2001), and mode tracking methods (Queguineur et al, 2019). Realistic actuation mechanisms, such as plasma actuators (Sato et al, 2015), suction mechanisms (Wang et al, 2016), transverse motion (Li & Aubry, 2003), periodic oscillations (Lu et al, 2011), oscillating foils (Bao & Tao, 2013), air jets (Zhu et al, 2019), or Lorentz forces in conductive media (Breuer et al, 2004), are also discussed in details, as well as limitations imposed by real-wold systems (Belson et al, 2013).…”

On the effects of a separation bubble on fan noise

“…However, the HFPs can still be seen in the noise spectrum, and they appear at the same frequencies with or without the stator vanes. The tones observed in Figure 14 can be further investigated using a mode decomposition technique, which is known as Dynamic Mode Tracking (DMT) [41].…”

Krylov methods for large-scale dynamical systems: Application in fluid dynamics

“…To the best of our knowledge, nekStab is the first general-purpose computational framework capable of stabilizing fully 3D unstable periodic orbits (forced or unforced) and fixed points, as well as computing direct, adjoint modes and transient growth analyses for both steady and periodic flows. The menu of options includes a matrix-free Newton GMRES solver as well as other classical techniques such as selective frequency damping (SFD) [1], BoostConv [70], Time-Delayed Feedback (TDF) [210,237], and Dynamic Mode Tracking (DMT) [211], as well as post-processing routines such as the kinetic energy budget of the leading modes based on the Reynolds-Orr decomposition [38,154], steady-state base flow, and sensitivity analyzes [174].…”