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arXiv · 1701.08133

Spectral energy cascade in thermoacoustic shock waves

Prateek Gupta·Guido Lodato·Carlo Scalo
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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.

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Prateek Gupta, Guido Lodato, Carlo Scalo. 2017-01-27. Spectral energy cascade in thermoacoustic shock waves. https://doi.org/10.1017/jfm.2017.635

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