Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines

Journal Article · Tue Sep 01 04:00:00 EDT 1998 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.58.2818· OSTI ID:641615

Smith, E ^[1]

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1. Los Alamos National Laboratory, Earth and Environmental Sciences Division, Los Alamos, New Mexico 87545 (United States)

Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot{close_quote}s theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot{close_quote}s theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible {ital and irreversible} engines is shown to arise from the Ginzburg-Landau description of the broken phase. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 641615
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 3 Vol. 58; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ENTROPY
HEAT ENGINES
RESONATORS
SCALING LAWS
SYMMETRY BREAKING
THERMAL EFFICIENCY
THERMODYNAMIC CYCLES