Nonlinear saturation of thermoacoustic instability

Карпов, С. В.; Prosperetti, Andréa

doi:10.1121/1.424610

Cited by 3 publications

(5 citation statements)

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“…Multiple authors (Swift 1992;Karpov & Prosperetti 2000;Hamilton et al 2002;Penelet et al 2005) have discussed the higher harmonic generation in non-combustiondriven thermoacoustically unstable waves, restricting their analysis to only a first few overtones of the unstable mode. Biwa et al (2011) reported the first experimental observation of energy cascade in thermoacoustically sustained shock waves in a looped thermoacoustic resonator.…”

Section: Introductionmentioning

confidence: 99%

Spectral energy cascade in thermoacoustic shock waves

2017

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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• in the thermoacoustic core and not in pure travelling-wave phasing. High-order unstructured fully compressible Navier-Stokes simulations reveal three regimes: (i) Modal growth, governed by linear thermoacoustics; (ii) Hierarchical spectral broadening, resulting in a nonlinear inertial energy cascade; (iii) Shock-wave dominated limit cycle, where energy production is balanced by dissipation occurring at the captured shock-thickness scale. The acoustic energy budgets in regime (i) have been analytically derived, yielding an expression of the Rayleigh index in closed form and elucidating the effect of geometry and hot-to-cold temperature ratio on growth rates. A time-domain nonlinear dynamical model is formulated for regime (ii), highlighting the role of second-order interactions between pressure and heat-release fluctuations, causing asymmetry in the thermoacoustic energy production cycle and growth rate saturation. Moreover, energy cascade is inviscid due to steepening in regime (ii), with the k th harmonic growing at k/2-times the modal growth rate of the thermoacoustically sustained second harmonic. The frequency energy spectrum in regime (iii) is shown to scale with a −5/2 power law in the inertial range, rolling off at the captured shock-thickness scale in the dissipation range. We have thus shown the existence of equilibrium thermoacoustic energy cascade analogous to hydrodynamic turbulence.

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Section: Introductionmentioning

confidence: 99%

Spectral energy cascade in thermoacoustic shock waves

2017

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“…where p ref is the reference pressure (which is set when the system is initially filled with gas), and T ref is the reference temperature. Equation (35) guarantees that the total mass in the system is conserved. The necessity of this replacement is explained in Appendix A.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…For a finite volume scheme, we replace one local DC continuity equation with Eq. (35). Since closed thermoacoustic systems are often filled at room temperature, a beneficial effect of this global equation is the fact that we obtain the DC pressure increase in the system under operating conditions.…”

Section: Appendix A: Mass Balancementioning

confidence: 99%

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Modeling of thermoacoustic systems using the nonlinear frequency domain method

Jong

Wijnant

Wilcox

et al. 2015

The Journal of the Acoustical Society of America

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When modeling thermoacoustic (TA) devices at high amplitude, nonlinear effects such as time-average mass flows, and the generation of higher harmonics can no longer be neglected. Thus far, modeling these effects in TA devices required a generally computationally costly time integration of the nonlinear governing equations. In this paper, a fast one-dimensional nonlinear model for TA devices is presented, which omits this costly time integration by directly solving the periodic steady state. The model is defined in the frequency domain, which eases the implementation of phase delays due to viscous resistance and thermoacoustic heat exchange. As a demonstration, the model is used to solve an experimental standing wave thermoacoustic engine. The obtained results agree with experimental results, as well as with results from a nonlinear time domain model from the literature. The low computational cost of this model opens the possibility to do optimization studies using a nonlinear TA model.

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“…For the study of the standing wave thermoacoustic engines functioning in the start mode Karpov et.al. [2] applied a weakly non-linear theory of the thermoacoustic instability in a channel with temperature gradient. The motivation for this work was provided by the research results of the lumped thermal capacity model presented by Matveev [3].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model of acoustic thermal excitation for pulse tube engine

Zinovyev¹,

Dovgyallo²,

Nekrasova³

2015

Proceedings of the 3rd International Workshop on Thermoacoustics

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IntroductionThe most of works applied for the pulse tube converters contain the workflow description implemented through the use of mathematical models on stationary modes. However, the study of the thermoacoustic systems unsteady behavior in the start, stop, acoustic load changes modes is in the particular interest. Yuan et.al.[1] offered a simplified quasi-onedimensional model of a thermoacoustic engine that described the amplification of acoustic oscillations and their subsequent "saturation" at the launch phase. For the study of the standing wave thermoacoustic engines functioning in the start mode Karpov et.al.[2] applied a weakly non-linear theory of the thermoacoustic instability in a channel with temperature gradient. The motivation for this work was provided by the research results of the lumped thermal capacity model presented by Matveev [3]. The aim of the present study is to develop a mathematical thermal excitation model of acoustic oscillations in pulse the tube engine (PTE) (Figure1) in more general formulation of the mathematical description. A half-length cylindrical resonator length is 240 mm, resonator radius -10 mm, regenerator length -60 mm, porosity -0.89, piston mass -0.02 kg.

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Nonlinear saturation of thermoacoustic instability

Cited by 3 publications

References 0 publications

Spectral energy cascade in thermoacoustic shock waves

Spectral energy cascade in thermoacoustic shock waves

Modeling of thermoacoustic systems using the nonlinear frequency domain method

A mathematical model of acoustic thermal excitation for pulse tube engine

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