Finite-time Lyapunov exponent-based analysis for compressible flows

Area of Science:

• Fluid Dynamics
• Acoustics
• Computational Science

Background:

• Finite-time Lyapunov exponent (FTLE) effectively analyzes incompressible flows and coherent structures.
• Applications of FTLE include environmental flows, biological systems, and propulsion.
• Extending FTLE to compressible regimes is crucial for understanding complex phenomena like jet acoustics.

Purpose of the Study:

• To extend the finite-time Lyapunov exponent (FTLE) technique to compressible flow regimes.
• To associate coherent structures with acoustic waves in compressible flows, particularly for jet acoustics.
• To identify the sources of intermittent events in jet noise and their relationship with flow dynamics.

Main Methods:

• Developed an extension of FTLE for compressible flows, enabling association of coherent structures with acoustic waves.
• Utilized integration time as a pseudo-filter to separate wave dynamics from coherent structures in velocity fields.
• Applied FTLE to Large-Eddy Simulation data of a Mach 0.9 jet and analyzed jet noise pressure probe data.

Main Results:

• Demonstrated FTLE's capability to extract wave dynamics from velocity fields in compressible flows.
• Confirmed FTLE's effectiveness using forward and backward coefficients on known acoustic fields.
• Identified intermittent jet noise events linked to entrainment in the roll-up region and downstream emissive events post-potential core collapse.
• Observed acoustic disturbances originating near potential core collapse and propagating at a 30° angle.

Conclusions:

• FTLE is a viable tool for analyzing wave dynamics and coherent structures in compressible flows.
• The study elucidates the causal relationship between flow structures and acoustic wave generation in turbulent jets.
• FTLE provides insights into the sources of intermittent jet noise, linking them to specific flow instabilities and events.