Spectral energy cascade in thermoacoustic shock waves

Abstract

We have performed a theoretical and numerical investigation of thermoacoustically amplified quasi-planar nonlinear waves driven to the limit of shock-wave formation in a variable-area 2.58 m long looped resonator designed via eigenvalue analysis to maximize the growth rate of the second harmonic (265 Hz). High-order unstructured fully compressible Navier-Stokes simulations reveal the presence of three regimes: (i) Monochromatic harmonic growth, governed by linear thermoacoustics; (ii) Hierarchical spectral broadening, characterized by nonlinear energy cascade; (iii) Shock-wave dominated limit cycle, where energy production is balanced by dissipation occurring at the captured shock-thickness scale. We have modeled these regimes of thermoacoustic wave amplification based on first-principle governing equations and elucidated the physics of energy density production and saturation to a limit cycle.

References in corpus (1)

• High-fidelity simulation of a standing-wave thermoacoustic-piezoelectric engine

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• On the instabilities of intrinsic thermoacoustic modes in a thermoacoustic waveguide with anechoic terminations