Simplified account of Rayleigh streaming for the description of nonlinear processes leading to steady state sound in thermoacoustic engines

Abstract

a b s t r a c tThis paper focuses on the transient regime of wave amplitude growth and stabilization occuring in a standing wave thermoacoustic engine. Experiments are performed on a simple apparatus consisting of an open ended thermoacoustic oscillator with atmospheric air as working fluid. The results show that, even in that simple device, the transient regime leading to steady state sound exhibits complicated dynamics, like the systematic overshoot of wave amplitude before its final stabilization, and the spontaneous and periodic switch on/off of the thermoacoustic instability at constant heat power supply. A simplified model is then presented which describes wave amplitude growth from the coupled equations describing thermoacoustic amplification and unsteady heat transfer. In this model, the assumption of a one-dimensional and exponential temperature profile is retained and the equations describing heat transfer through the thermoacoustic core are substantially simplified into a set of ordinary differential equations. These equations include the description of two processes saturating wave amplitude growth, i.e. thermoacoustic heat pumping and heat convection by acoustic streaming. It is notably shown that accounting for the effect of acoustic streaming allows to reproduce qualitatively the overshoot process.

Measurement of density fluctuations using digital holographic interferometry in a standing wave thermoacoustic oscillator

“…For this configuration, the onset of self-sustained thermoacoustic oscillations occurs as soon as the heat power supplied by the Nichrome wire exceeds the critical value Q onset % 20 W (note that this value of Q onset depends on the stack position [31]). The frequency f % 171 Hz of acoustic oscillations corresponds to the quarter wavelength resonance, which means that f % c 0 =4L, where c 0 % 344 m=s stands for the adiabatic sound speed at room temperature.…”

“…The frequency f % 171 Hz of acoustic oscillations corresponds to the quarter wavelength resonance, which means that f % c 0 =4L, where c 0 % 344 m=s stands for the adiabatic sound speed at room temperature. Previous studies of the same device [30][31][32] have clearly shown that, despite of its very simple geometry, this thermoacoustic oscillator can exhibit complicated dynamics of wave amplitude growth/saturation which are not reliably reproduced by theoretical/numerical modeling. It is therefore the objective of this study to perform holographic interferometry to analyze the refractive index variations in a window localized near the stack, where the temperature gradients are the highest, and to gain further insight on the physical processes controlling the saturation of the thermoacoustic instability.…”

Experimental and theoretical study of the dynamics of self-sustained oscillations in a standing wave thermoacoustic engine

“…14 Other studies have described the transient regime under an assigned heat input (instead of a temperature difference) in different kinds of engines (e.g., annular engine, 7,15 standing-wave engine, 8 or thermoacoustic-Stirling engine 16 ): in these models, sound saturation occurs via the diminution of the temperature gradient due to heat transport by the thermoacoustic effect along the stack, while the propagation of acoustic waves is assumed linear, and it is described either by lumped elements 16 or by two-ports. 17 Attempts have also been made (in the above mentioned two-port models) to account for heat convection by acoustic streaming in an annular thermoacoustic a) engine, 7,15 or more recently in the standing wave thermoacoustic engine, 8 which will be studied in the following. It is also worth mentioning that a few papers dealt with the use of commercial computational fluid dynamics simulation tools to compute the transient regime in thermoacoustic devices of complicated geometry, 18,19 leading to results that are still quite different from experiments.…”

“…This device has already been studied recently in Ref. 8, in which both experimental data and a very simplified modeling of the transient regime are provided. However, contrarily to the works of Ref.…”

Active control of thermoacoustic amplification in a thermo-acousto-electric engine

“…5 The saturation of acoustic waves, and therefore the efficiency of thermoacoustic energy conversion, is controlled by several nonlinear effects. Among them is the thermoacoustic heat pumping, reducing the externally imposed temperature gradient, 2,9 as well as the generation of acoustic streaming [10][11][12][13][14][15] but also other nonlinear phenomena such as wave steepening, 16,17 minor losses, 18 or turbulence. 19 All of these phenomena contribute together to reducing the overall efficiency of the engine either by dissipating acoustic power or by modifying the temperature field in the heterogeneously heated part of the device.…”