Spectral energy cascade in thermoacoustic shock waves

  title={Spectral energy cascade in thermoacoustic shock waves},
  author={Prateek Gupta and Guido Lodato and Carlo Scalo},
  journal={Journal of Fluid Mechanics},
  pages={358 - 393}
We have investigated thermoacoustically amplified quasi-planar nonlinear waves driven to the limit of shock-wave formation in a variable-area looped resonator geometrically optimized to maximize the growth rate of the quasi-travelling-wave second harmonic. Optimal conditions result in velocity leading pressure by approximately $40^{\circ }$ in the thermoacoustic core and not in pure travelling-wave phasing. High-order unstructured fully compressible Navier–Stokes simulations reveal three… 

Spectral energy cascade and decay in nonlinear acoustic waves

We present a numerical and theoretical investigation of nonlinear spectral energy cascade of decaying finite-amplitude planar acoustic waves in a single-component ideal gas at standard temperature

Traveling and standing thermoacoustic waves in solid media

Real-fluid effects on standing-wave thermoacoustic instability

We have performed high-order compressible Navier–Stokes simulations of a thermoacoustically unstable resonator employing $\text{CO}_{2}$ in transcritical conditions. The parameter space spans the

Knudsen number effects on the nonlinear acoustic spectral energy cascade.

It is shown that an inertial range for spectral energy transfer can be expected for acoustic Reynolds numbers Re_{U_{max}}>100, based on the maximum acoustic velocity amplitude in the domain, by exploiting dimensionless scaling laws borrowed by Kolmogorov's theory of hydrodynamic turbulence.

Band structure and effective properties of one-dimensional thermoacoustic Bloch waves

We investigate the dispersion characteristics and the effective properties of acoustic waves propagating in a one-dimensional duct equipped with periodic thermoacoustic coupling elements. Each

Thermoacoustic effects on the propagation of non-planar sound in a circular duct

Abstract This paper examines thermoacoustic effects on the propagation of non-planar sound in a circular duct subjected to an axial temperature gradient. Of particular concern are thermoviscous

Underlying physics of limit-cycle, beating and quasi-periodic oscillations in thermoacoustic devices

Under certain circumstances, self-excited acoustic oscillations inside thermoacoustic systems exhibit beating and quasi-periodic patterns, in contrast to constant-amplitude limit-cycle oscillations



Linear and nonlinear modelling of a theoretical travelling-wave thermoacoustic heat engine

Abstract We have carried out three-dimensional Navier–Stokes simulations, from quiescent conditions to the limit cycle, of a theoretical travelling-wave thermoacoustic heat engine (TAE) composed of a

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

We have carried out wall-resolved unstructured fully compressible Navier–Stokes simulations of a complete standing-wave thermoacoustic–piezoelectric engine model inspired by the experimental work of

Weakly nonlinear propagation in thermoacoustic engines: a numerical study of higher harmonics generation up to the appearance of shock waves

Though thermoacoustic engines usually operate at high acoustic amplitude, they rarely exhibit strong deformation of the wavefront due to nonlinear propagation. It has however been demonstrated

Nonlinear theory for thermoacoustic waves in a narrow channel and pore subject to a temperature gradient

A nonlinear theory for thermoacoustic waves in a gas-filled, narrow channel and pore subject to an axial temperature gradient is developed based on the fluid dynamical equations for an ideal gas.

Observation of traveling thermoacoustic shock waves (L).

The results show that a periodic shock occurs in the traveling wave mode in a looped tube but not in the standing wave modes in a resonator, demonstrating a clear difference in the harmonic components of the acoustic intensity.

Observation of thermoacoustic shock waves in a resonance tube.

Measurements of the acoustic intensity show that the energy absorption in the stack region with the temperature gradient tends to prevent the nonlinear excitation of harmonic oscillations, which explains why the shock waves had been unfavorable in the resonance tube thermoacoustic systems.

Experimental and theoretical study of processes leading to steady-state sound in annular thermoacoustic engines.

It is demonstrated that the dynamical behavior observed in the experimental device is predominantly controlled by the effects of acoustic streaming and acoustically enhanced thermal conductivity tending not only to reduce the externally imposed temperature gradient along the stack, but also to change the shape of the temperature field.

A 3D investigation of thermoacoustic fields in a square stack

Thermally Driven Nonlinear Oscillations in a Pipe with Traveling Shock Waves

Nonlinear vibrations in a pipe closed at both ends with a plane heater in its midsection and containing a perfect gas are studied. When the frequency of a sinusoidal heat release is equal to twice

Non-Linear Growth and Limiting Amplitude of Acoustic Oscillations in Combustion Chambers

Due to non-linear loss or gain of energy, unstable oscillations in combustion chambers cannot grow indefinitely. Very often the limiting amplitudes are sufficiently low that the wave motions appear