Deconvolution of reacting-flow dynamics using proper orthogonal and dynamic mode decompositions

Area of Science:

• Fluid Dynamics
• Combustion Science
• Nonlinear Systems Analysis

Background:

• Reacting flows present significant analytical challenges due to nonlinearities and long-range couplings.
• Low-order models can infer dynamical features if flow constituents, symmetries, and interactions are understood.
• Modal decomposition of high-resolution imaging data is crucial for analyzing flow dynamics.

Purpose of the Study:

• To introduce a methodology for deducing flow constituents and their dynamics post-modal decomposition.
• To compare the strengths of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD).
• To analyze reacting flows behind symmetric bluff bodies and a cellular flame front.

Main Methods:

• Modal decomposition techniques, specifically Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD).
• Analysis of high-frequency, high-resolution imaging data (species-concentration and velocity fields).
• Application to two classes of problems: a cellular flame front and reacting flows behind bluff bodies.

Main Results:

• Both POD and DMD can deconvolve complex flow states, such as rotating rings in a flame front.
• DMD provides more detailed dynamical resolution, associating each mode with a unique complex growth rate.
• DMD effectively distinguishes between symmetric and von Karman vortices in bluff-body flows, and its phase dynamics reveal reproducible flow characteristics.

Conclusions:

• Dynamic Mode Decomposition (DMD) offers distinct advantages over Proper Orthogonal Decomposition (POD) for analyzing complex reacting flows.
• DMD's unique complex growth rates allow for the identification of reproducible flow modes, which energy-based POD may not differentiate.
• The phase dynamics of reproducible DMD modes provide a robust method for characterizing the dynamical behavior of complex flows, even with noisy data.