Nonlinear saturation of the thermoacoustic instability

Карпов, С. В.; Prosperetti, Andréa

doi:10.1121/1.429342

Cited by 40 publications

(12 citation statements)

References 21 publications

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“…Karpov and Prosperetti [16] proposed a time-domain description of the evolution of thermoacoustic instability combined with a multiple time scales method to calculate the initial wave amplitude growth and its saturation due to higher harmonics generation in the case of a standing wave engine with a fixed temperature gradient. De Waele [17] presented a simplified model based on the lumped element description of thermoacoustic engines, and he performed calculations of the transient regime in a so-called traveling wave thermoacoustic Stirling engine [18], in which the effect saturating the wave amplitude growth is the cooling effect due to acoustic oscillations in the thermoacoustic core.…”

Section: Introductionmentioning

confidence: 99%

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

Pénelet

Guédra

Gusev

et al. 2012

International Journal of Heat and Mass Transfer

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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.

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Section: Introductionmentioning

confidence: 99%

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

Pénelet

Guédra

Gusev

et al. 2012

International Journal of Heat and Mass Transfer

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“…The growth rate calculated is based on the linear theory assuming infinitesimally small disturbance, whereas it was measured for the amplitude of p 0 =p 0 between 10 À3 and 10 À2 and the oscillations are within nonlinear regime. If Landau-Stuart equation is valid, 14) the growth rate measured should be lower than the linear one due to the effects of finite amplitude. However, on the contrary, the growth rate is greater than the linear one.…”

Section: Marginal Conditions For the Onset Of Instabilitymentioning

confidence: 99%

Experiments on Self-excited Thermoacoustic Oscillations in an Air-filled Looped Tube with a Pair of Stacks

Sugimoto

Minamigawa

2018

J. Phys. Soc. Jpn.

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This paper investigates experimentally the onset of thermoacoustic instability and ensuing emergence of self-excited oscillations of air in a looped tube with a pair of identical stacks installed inside on diametrically opposite positions. Each stack is sandwiched by hot and cold (ambient) heat exchangers so that a temperature gradient may be imposed on it in the same sense. The loop is circular except for two short straight sections in which the stack and the heat exchangers are housed. Four sets of stacks of 100, 300, 600, and 900 cells=in 2 are used to examine influences of stack's pore radius on the onset of instability and the steady state of oscillations. It is found that thermoacoustic self-excited oscillations emerge spontaneously for all sets of the stacks in a 1-wave mode where the loop length corresponds to one wavelength of oscillations. It is also found that for the stacks of 900 cells=in 2 , a 2-wave mode also emerges besides the 1-wave mode. Temperatures of the heaters are constantly monitored and excess pressures are measured at four positions. The onset of instability is examined in light of marginal conditions obtained theoretically and step-up behaviors are discussed in terms of the temperature ratio and the growth rate. It is revealed that the pressure profiles of oscillations at the steady state propagate along the loop in the same sense as the temperature gradient and that the peak-to-peak pressure takes a maximum near the stack. As it increases, emergence of acoustic shock waves is observed except for the case with the stacks of 100 cells=in 2. Physical mechanisms of shock formation are discussed in terms of eigenfrequencies of oscillations in higher modes.

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“…Latter, Karpov and Prosperetti [8] developed a one-dimensional theoretical model based on the perturbation theory. Growth, non-linear evolution and final saturation of thermoacoustic instabilities, in response of imposed temperature differences, were reported.…”

Section: Introductionmentioning

confidence: 99%

Characteristic-based non-linear simulation of large-scale standing-wave thermoacoustic engine

El-Rahman

Abdel‐Rahman

2014

The Journal of the Acoustical Society of America

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A few linear theories [Swift, J. Acoust. Soc. Am. 84(4), 1145-1180 (1988); Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and numerical models, based on low-Mach number analysis [Worlikar and Knio, J. Comput. Phys. 127(2), 424-451 (1996); Worlikar et al., J. Comput. Phys. 144(2), 199-324 (1996); Hireche et al., Canadian Acoust. 36(3), 164-165 (2008)], describe the flow dynamics of standing-wave thermoacoustic engines, but almost no simulation results are available that enable the prediction of the behavior of practical engines experiencing significant temperature gradient between the stack ends and thus producing large-amplitude oscillations. Here, a one-dimensional non-linear numerical simulation based on the method of characteristics to solve the unsteady compressible Euler equations is reported. Formulation of the governing equations, implementation of the numerical method, and application of the appropriate boundary conditions are presented. The calculation uses explicit time integration along with deduced relationships, expressing the friction coefficient and the Stanton number for oscillating flow inside circular ducts. Helium, a mixture of Helium and Argon, and Neon are used for system operation at mean pressures of 13.8, 9.9, and 7.0 bars, respectively. The self-induced pressure oscillations are accurately captured in the time domain, and then transferred into the frequency domain, distinguishing the pressure signals into fundamental and harmonic responses. The results obtained are compared with reported experimental works [Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and the linear theory, showing better agreement with the measured values, particularly in the non-linear regime of the dynamic pressure response.

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Nonlinear saturation of the thermoacoustic instability

Cited by 40 publications

References 21 publications

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

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

Experiments on Self-excited Thermoacoustic Oscillations in an Air-filled Looped Tube with a Pair of Stacks

Characteristic-based non-linear simulation of large-scale standing-wave thermoacoustic engine

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