Spectral energy cascade in thermoacoustic  shock waves

Gupta, Prateek; Lodato, Guido; Scalo, Carlo

doi:10.1017/jfm.2017.635

Cited by 36 publications

(34 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, on the contrary, the growth rate is greater than the linear one. Recently Gupta et al 15) examined the step-up behavior in the experiment by Yazaki et al 4) in detail by the computational fluid dynamics. From their results, the range between 10 À3 and 10 À2 belongs to their second regime of hierarchial spectral broadening subsequent to the first regime of the modal growth predicted by the linear theory.…”

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.

View full text Add to dashboard Cite

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.

show abstract

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.

View full text Add to dashboard Cite

show abstract

“…In previous numerical investigations [9] -inspired by the experimental setups in [16,17] -the present authors have demonstrated the existence of an equilibrium spectral energy cascade in quasi-planar weak shock waves sustained by thermoacoustic instabilities in a resonator. The latter inject energy only at scales comparable to the resonator length (large scales); harmonic generation then takes place, leading to spectral broadening and progressive generation of smaller scales until viscous losses, occurring at the shock-thickness scale, dominate the energy cascade.…”

Section: Introductionmentioning

confidence: 80%

“…Nonlinear wave processes are observed in a variety of engineering and physics applications such as acoustics [1,2], combustion noise [3,4], jet noise [5][6][7], thermoacoustics [8,9], surface waves [10], and plasmaphysics [11], requiring nonlinear evolution equations to describe the dynamics of perturbations. In the case of high amplitude planar acoustic wave propagation, two main nonlinear effects are present: acoustic streaming [2,12] and wave steepening [1,13].…”

Section: Introductionmentioning

confidence: 99%

Spectral energy cascade and decay in nonlinear acoustic waves

Gupta

Scalo

2018

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

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 and pressure (STP). We analyze various one-dimensional canonical flow configurations: a propagating traveling wave (TW), a standing wave (SW), and randomly initialized Acoustic Wave Turbulence (AWT). Due to nonlinear wave propagation, energy at the large scales cascades down to smaller scales dominated by viscous dissipation, analogous to hydrodynamic turbulence. We use shock-resolved mesh-adaptive direct numerical simulations (DNS) of the fully compressible onedimensional Navier-Stokes equations to simulate the spectral energy cascade in nonlinear acoustic waves. The simulation parameter space for the TW, SW, and AWT cases spans three orders of magnitude in initial wave pressure amplitude and dynamic viscosity, thus covering a wide range of both spectral energy cascade and the viscous dissipation rates. The shock waves formed as a result of energy cascade are weak (M < 1.4), and hence we neglect thermodynamic non-equilibrium effects such as molecular vibrational relaxation in the current study. We also derive a new set of nonlinear acoustics equations truncated to second order and the corresponding perturbation energy corollary yielding the expression for a new perturbation energy norm E (2) . Its spatial average, satisfies the definition of a Lyapunov function, correctly capturing the inviscid (or lossless) broadening of spectral energy in the initial stages of evolution -analogous to the evolution of kinetic energy during the hydrodynamic break down of three-dimensional coherent vorticity -resulting in the formation of smaller scales. Upon saturation of the spectral energy cascade i.e. fully broadened energy spectrum, the onset of viscous losses causes a monotonic decay of in time. In this regime, the DNS results yield ∼ t −2 for TW and SW, and ∼ t −2/3 for AWT initialized with white noise. Using the perturbation energy corollary, we derive analytical expressions for the energy, energy flux, and dissipation rate in the wavenumber space. These yield the definitions of characteristic length scales such as the integral length scale (characteristic initial energy containing scale) and the Kolmogorov length scale η (shock thickness scale), analogous to K41 theory of hydrodynamic turbulence (A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30 , 9 (1941)). Finally, we show that the fully developed energy spectrum of the nonlinear acoustic waves scales as E k k 2 −2/3 1/3 ∼ C f (kη), with C ≈ 0.075 constant for TW and SW but decaying in time for AWT. arXiv:1809.02202v1 [physics.flu-dyn]

show abstract

“…2βẼ quantifies the rate of energy accumulation, dĨ/dx is the work source defined in the previous section,R is an energy redistribution term.P andD are the thermoacoustic production and dissipation, respectively. The energy redistribution term in the acoustic energy budgets of solid thermoacoustics cannot be found in the fluid counterpart of the same equations [19]. This term is absent in fluids because it is canceled in the algebraic derivations by expressing the variation of mean density according to the ideal gas law, as a function of the mean temperature gradient.…”

Section: Acoustic Energy Budgetsmentioning

confidence: 99%

Traveling and standing thermoacoustic waves in solid media

Hao

Scalo

Semperlotti

2019

Journal of Sound and Vibration

Self Cite

View full text Add to dashboard Cite

The most attractive application of fluid-based thermoacoustic (TA) energy conversion involves traveling wave devices due to their low onset temperature ratios and high growth rates. Recently, theoretical and numerical studies have shown that thermoacoustic effects can exist also in solids. However, these initial studies only focus on standing waves. This paper presents a numerical study investigating the existence of self-sustained thermoelastic oscillations associated with traveling wave modes in a looped solid rod under the effect of a localized thermal gradient. Configurations having different ratios of the rod radius R to the thermal penetration depth δ k were explored and the traveling wave component (TWC) was found to become dominant as R approaches δ k . The growth-rate-tofrequency ratio of the traveling TA wave is found to be significantly larger than that of the standing wave counterpart for the same wavelength. The perturbation energy budgets are analytically formulated and closed, shedding light onto the energy conversion processes of solid-state thermoacoustic (SSTA) engines and highlighting differences with fluids. Efficiency is also quantified based on the thermoacoustic production and dissipation rates evaluated from the energy budgets.

show abstract

Spectral energy cascade in thermoacoustic shock waves

Cited by 36 publications

References 47 publications

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

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

Spectral energy cascade and decay in nonlinear acoustic waves

Traveling and standing thermoacoustic waves in solid media

Contact Info

Product

Resources

About