Acoustic Energy Flux Research Articles

Stability analysis for the onset of thermoacoustic oscillations in a gas-filled looped tube

AbstractThis paper develops a stability analysis for the onset of thermoacoustic oscillations in a gas-filled looped tube with a stack inserted, subject to a temperature gradient. Analysis is carried out based on approximate theories for a thermoviscous diffusion layer derived from the thermoacoustic-wave equation taking account of the temperature dependence of the viscosity and the heat conductivity. Assuming that the stack consists of many pores axially and that the thickness of the diffusion layer is much thicker than the pore radius, the diffusion wave equation with higher-order terms included is applied for the gas in the pores of the stack. For the gas outside of the pores, the theory of a thin diffusion layer is applied. In a section called the buffer tube over which the temperature relaxes from that at the hot end of the stack to room temperature, the effects of the temperature gradient are taken into account. With plausible temperature distributions specified on the walls of the stack and the buffer tube, the solutions to the equations in both theories are obtained and a frequency equation is finally derived analytically by matching the conditions at the junctions between the various sections. Seeking a real solution to the frequency equation, marginal conditions of instability are obtained numerically not only for the one-wave mode but also for the two-wave mode, where the tube length corresponds to one wavelength and two wavelengths, respectively. It is revealed that the marginal conditions depend not only on the thickness of the diffusion layer but also on the porosity of the stack. Although the toroidal geometry allows waves to be propagated in both senses along the tube, it is found that the wave propagating in the sense from the cold to the hot end through the stack is always greater, so that a travelling wave in this sense emerges as a whole. The spatial and temporal variations of excess pressure and mean axial velocity averaged over the cross-section of a flow passage are displayed for the two modes of oscillations at the marginal state. The spatial distribution of mean acoustic energy flux (acoustic intensity) over one period is also shown. It is unveiled that the energy flux is generated only in the stack, and it decays slowly in the other sections by lossy effects due to a boundary layer. Mechanisms for the generation of the acoustic energy flux are also discussed.

3D numerical modeling of YSO accretion shocks

The dynamics of YSO accretion shocks is determined by radiative processes as well as the strength and structure of the magnetic field. A quasi-periodic emission signature is theoretically expected to be observed, but observations do not confirm any such pattern. In this work, we assume a uniform background field, in the regime of optically thin energy losses, and we study the multi-dimensional shock evolution in the presence of perturbations, i.e. clumps in the stream and an acoustic energy flux flowing at the base of the chromosphere. We perform 3D MHD simulations using the PLUTO code, modelling locally the impact of the infalling gas onto the chromosphere. We find that the structure and dynamics of the post-shock region is strongly dependent on the plasma-beta (thermal over magnetic pressure), different values of which may give distinguishable emission signatures, relevant for observations. In particular, a strong magnetic field effectively confines the plasma inside its flux tubes and leads to the formation of quasi-independent fibrils. The fibrils may oscillate out of phase and hence the sum of their contributions in the emission results in a smooth overall profile. On the contrary, a weak magnetic field is not found to have any significant effect on the shocked plasma and the turbulent hot slab that forms is found to retain its periodic signature.

Dynamics of the solar atmosphere above a pore with a light bridge

Context: Solar pores are small sunspots lacking a penumbra that have a prevailing vertical magnetic field component. They can include light bridges at places with locally reduced magnetic field. Like sunspots, they exhibit a wide range of oscillatory phenomena. Aims: A large isolated pore with a light bridge (NOAA 11005) is studied to obtain characteristics of a chromospheric filamentary structure around the pore, to analyse oscillations and waves in and around the pore, and to understand the structure and brightness of the light bridge. Methods: Spectral imaging observations in the line Ca II 854.2 nm and complementary spectropolarimetry in Fe I lines, obtained with the DST/IBIS spectrometer and HINODE/SOT spectropolarimeter, were used to measure photospheric and chromospheric velocity fields, oscillations, waves, the magnetic field in the photosphere, and acoustic energy flux and radiative losses in the chromosphere. Results: The chromospheric filamentary structure around the pore has all important characteristics of a superpenumbra: it shows an inverse Evershed effect and running waves, and has a similar morphology and oscillation character. The granular structure of the light bridge in the upper photosphere can be explained by radiative heating. Acoustic waves leaking up from the photosphere along the inclined magnetic field in the light bridge transfer enough energy flux to balance the total radiative losses of the light-bridge chromosphere. Conclusions: The presence of a penumbra is not a necessary condition for the formation of a superpenumbra. The light bridge is heated by radiation in the photosphere and by acoustic waves in the chromosphere.

3D YSO accretion shock simulations: a study of the magnetic, chromospheric and stochastic flow effects

AbstractThe structure and dynamics of young stellar object (YSO) accretion shocks depend strongly on the local magnetic field strength and configuration, as well as on the radiative transfer effects responsible for the energy losses. We present the first 3D YSO shock simulations of the interior of the stream, assuming a uniform background magnetic field, a clumpy infalling gas, and an acoustic energy flux flowing at the base of the chromosphere. We study the dynamical evolution and the post-shock structure as a function of the plasma-beta (thermal pressure over magnetic pressure). We find that a strong magnetic field (~hundreds of Gauss) leads to the formation of fibrils in the shocked gas due to the plasma confinement within flux tubes. The corresponding emission is smooth and fully distinguishable from the case of a weak magnetic field (~tenths of Gauss) where the hot slab demonstrates chaotic motion and oscillates periodically.

On the phase between pressure and heat release fluctuations for propane/hydrogen flames and its role in mode transitions

This paper presents an experimental investigation into mode-transitions observed in a 50-kW, atmospheric pressure, backward-facing step combustor burning lean premixed C3H8/H2 fuel mixtures over a range of equivalence ratios, fuel compositions and preheat temperatures. The combustor exhibits distinct acoustic response and dynamic flame shape (collectively referred to as “dynamic modes”) depending on the operating conditions. We simultaneously measure the dynamic pressure and flame chemiluminescence to examine the phase between pressure (p′) and heat release fluctuations (q′) in the observed dynamic modes. Results show that the heat release is in phase with the pressure oscillations (θqp≈0) at the onset of a dynamic mode, while as the operating conditions change within the mode, the phase grows until it reaches a critical value θqp=θc, at which the combustor switches to another dynamic mode. According to the classical Rayleigh criterion, this critical phase (θc) should be π/2, whereas our data show that the transition occurs well below this value. A linear acoustic energy balance shows that this critical phase marks the point where acoustic losses across the system boundaries equal the energy addition from the combustion process to the acoustic field. Based on the extended Rayleigh criterion in which the acoustic energy fluxes through the system boundaries as well as the typical Rayleigh source term (p′q′) are included, we derive an extended Rayleigh index defined as Re=θqp/θc, which varies between 0 and 1. This index, plotted against a density-weighted strained consumption speed, indicates that the impact of the operating parameters on the dynamic mode selection of the combustor collapses onto a family of curves, which quantify the state of the combustor within a dynamic mode. At Re=0, the combustor enters a mode, and switches to another as Re approaches 1. The results provide a metric for quantifying the instability margins of fuel-flexible combustors operating at a wide range of conditions.

Acoustic emission from magnetic flux tubes in the solar network

We present the results of three-dimensional numerical simulations to investigate the excitation of waves in the magnetic network of the Sun due to footpoint motions of a magnetic flux tube. We consider motions that typically mimic granular buffeting and vortex flows and implement them as driving motions at the base of the flux tube. The driving motions generates various MHD modes within the flux tube and acoustic waves in the ambient medium. The response of the upper atmosphere to the underlying photospheric motion and the role of the flux tube in channeling the waves is investigated. We compute the acoustic energy flux in the various wave modes across different boundary layers defined by the plasma and magnetic field parameters and examine the observational implications for chromospheric and coronal heating.

Influence of rough seabed surface on statistics of modal energy flux

When sound propagates through a random media, the wave properties of the acoustic field may be viewed as stochastic variables. It is thus natural to investigate the relationship between the statistical properties of the acoustic field and the random fluctuations of the waveguide. The interest here is a 2-D ocean waveguide with a rough seabed. Numerical solutions to the 2-way integral coupled mode equations (ICME), for random realizations of the roughness from a wavenumber power spectrum, provide the statistics of the modal intensity and cross-mode coherence with range. The roughness induces mode coupling within the trapped spectrum, between the trapped and the continuum spectrum, and to the back propagating modal spectrum. Instead of a master equation for the modal intensities to study the connection between the statistics of the acoustics and the fluctuations in the waveguide as has been advocated in previous studies, the conservation law for acoustic energy flux is used to develop an expression for the individual modal Poynting vectors. In addition to exact numerical computations of the range derivatives of the modal energy flux vectors for both forward and backward propagation, a Poynting vector master equation is derived for the case where the Born approximation is valid.

Modeling and optimization of an acoustic diode based on micro-bubble nonlinearity

The first acoustic diode (AD), which is composed by integrating a super lattice (SL) with a nonlinear medium (NLM), has recently been proposed to make a one-way street for the acoustic energy flux. This device prohibits the acoustic waves from one direction, but allows the transmission of the second harmonic wave (generated from the NLM) from the other direction. To improve its performance, it is crucial to transfer more acoustic energy from the stop-band of the acoustic filter (i.e., the SL) to its pass-band with the help of the NLM. In this work, a finite difference time domain model is developed to study the dynamic behaviors of the AD, in which a micro-bubble suspension takes the role of the NLM. Based on this model, the method of optimizing the nonlinearity-based AD is investigated by examining its performance with respect to several parameters, such as the periodicity number of the SL, the bubble size distribution, the bubble shell parameters, and the bubble concentration. It is also suggested that, instead of the rectification ratio, it might be more reasonable to characterize the performance of the AD with the energy attenuation coefficients (or transmission loss) for both incident directions.

Disturbance energy transport and sound production in gaseous combustion

AbstractThis paper presents an analysis of the energy transported by disturbances in gaseous combustion. It extends the previous work of Myers (J. Fluid Mech., vol. 226, 1991, 383–400) and so includes non-zero mean-flow quantities, large-amplitude disturbances, varying specific heats and chemical non-equilibrium. This extended form of Myers’ ‘disturbance energy’ then enables complete identification of the conditions under which the famous Rayleigh source term can be derived from the equations governing combusting gas motion. These are: small disturbances in an irrotational, homentropic, non-diffusive (in terms of species, momentum and energy) and stationary mean flow at chemical equilibrium. Under these assumptions, the Rayleigh source term becomes the sole source term in a conservation equation for the classical acoustic energy. It is also argued that the exact disturbance energy flux should become an acoustic energy flux in the far-field surrounding a (reacting or non-reacting) jet. In this case, the volume integral of the disturbance energy source terms are then directly related to the area-averaged far-field sound produced by the jet. This is demonstrated by closing the disturbance energy budget over a set of aeroacoustic, direct numerical simulations of a forced, low-Mach-number, laminar, premixed flame. These budgets show that several source terms are significant, including those involving the mean-flow and entropy fields. This demonstrates that the energetics of sound generation cannot be examined by considering the Rayleigh source term alone.

On the approximation of total absorption of the street open ceiling at low frequencies

This work deals with numerical modeling of sound propagation in street canyons with flat building facades. The street is seen as an open waveguide and two 3D wave models are used: a parabolic equation model and a modal expansion model. The comparison between the models shows a very good agreement. Then, the study focuses on the radiation condition at the opening of the street. In usual energetic approaches as ray tracing, the opening is assumed to be perfectly absorbing. This assumption is realistic at high frequencies, however the reflection phenomenon caused by the geometric discontinuity at the opening is still an open question at low frequencies. This possible reflection is investigated through three parametric studies of the acoustic longitudinal energy flux decay along the street. The first study shows that the approximation of total absorption at the street open ceiling is no longer valid when the ratio η between the street width and the wavelength is small. The second study shows that the effect of source height is weak except under restrictive conditions: when η is small and when the source height is not small compared to the wavelength, the approximation of total absorption is acceptable for an elevated source. At least, the results of the last study show that the error made by assuming a perfectly absorbing ceiling is not negligible compared to the error made by considering perfectly reflecting walls.

Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field

We present an analytical model that describes the linear interaction of a planar shock wave with an isotropic random sonic field. First, we study the interaction with a single-mode acoustic field. We present the exact evolution for the pressure, velocity, vorticity, and density field generated behind the shock wave, and we also calculate exact and closed analytical expressions for the asymptotic behavior of these modes. Applying superposition, we use the results obtained from the single-mode analysis in order to compute the interaction with 2D/3D isotropic random acoustic fields. We present analytical expressions for the average turbulent kinetic energy generated behind the shock, as well as the averaged vorticity and the density perturbations as a function of the shock strength M(1) and the gas compressibility γ. We also study the acoustic energy flux emitted by the shock front. Exact asymptotic analytical scaling laws are given for all the 3D averages downstream. A detailed comparison with previous works is shown.

NUMERICAL SIMULATIONS OF CONVERSION TO ALFVÉN WAVES IN SUNSPOTS

We study the conversion of fast magneto-acoustic waves to Alfven waves by means of 2.5D numerical simulations in a sunspot-like magnetic configuration. A fast, essentially acoustic, wave of a given frequency and wave number is generated below the surface and propagates upward though the Alfven/acoustic equipartition layer where it splits into upgoing slow (acoustic) and fast (magnetic) waves. The fast wave quickly reflects off the steep Alfven speed gradient, but around and above this reflection height it partially converts to Alfven waves, depending on the local relative inclinations of the background magnetic field and the wavevector. To measure the efficiency of this conversion to Alfven waves we calculate acoustic and magnetic energy fluxes. The particular amplitude and phase relations between the magnetic field and velocity oscillations help us to demonstrate that the waves produced are indeed Alfven waves. We find that the conversion to Alfven waves is particularly important for strongly inclined fields like those existing in sunspot penumbrae. Equally important is the magnetic field orientation with respect to the vertical plane of wave propagation, which we refer to as "field azimuth". For field azimuth less than 90 degrees the generated Alfven waves continue upwards, but above 90 degrees downgoing Alfven waves are preferentially produced. This yields negative Alfven energy flux for azimuths between 90 and 180 degrees. Alfven energy fluxes may be comparable to or exceed acoustic fluxes, depending upon geometry, though computational exigencies limit their magnitude in our simulations.

On acoustic and gravity waves in the solar photosphere and their energy transport

Aims. We study acoustic and atmospheric gravity waves in the quiet Sun to estimate their energy transport to the chromosphere. Methods. A two-dimensional time sequence from quiet Sun disc centre was analysed with simultaneous spectroscopic observations in Fe i 5576 A and Fe i 5434 A (both with Lande factor g = 0). We calculated response functions of the velocities for the line minimum shifts and atmospheric transmissions of waves for the two lines. For this, NLTE line formation in granular and intergranular model atmospheres from numerical simulations were performed. For the interpretation of the observed waves and for the estimates of energy fluxes, we assumed adiabatic propagation of plane waves in an isothermal model atmosphere. Fourier analyses of intensity and velocity fluctuations were carried out. They yield power, phase, and coherence as functions of frequency ν (from temporal Fourier transforms) and in thekh−ν plane (from three-dimensional transforms). The power spectra, together with the mass densities at velocity formation heights, give then the energy fluxes. Results. The rms velocities found here in the acoustic and gravity wave domains are lower by a factor ∼1.5 as in earlier work. We therefore admit a factor of 2 for an upward correction of the estimated fluxes. For acoustic waves we find: 1) upward propagating waves are present on the Sun with frequencies up to 14−15 mHz (periods U ≈ 70 s); 2) the approximation of plane adiabatic waves in an isothermal atmosphere appears adequate for estimating the energy fluxes; 3) the acoustic energy fluxes are in the same range as found in our earlier work from ground-based, two-dimensional spectroscopy, 1500−3100 W m −2 at an atmospheric height of ∼380 km and 1300−2700 W m −2 at 570 km. The energy flux carried by gravity waves is difficult to determine. We find: 1) phase and coherence spectra between continuum and velocity fluctuations show that convective overshoot and gravity waves are superimposed. We account for the convective flows using these coherence spectra. 2) At low frequencies, the vertical wavelength Λz can be short (� 300 km), yielding large corrections for atmospheric transmissions (factors >100). We thus exclude from the flux estimates waves with |kz| > 20 Mm −1 and with vertical group velocities υgr,z < 0. 3k m s −1 . They are likely to be strongly reduced in amplitude by radiative damping. 3) With these caveats, the energy fluxes carried by gravity waves are found in the range of 4000−8200 W m −2 at 380 km and 700−1400 W m −2 at 570 km. Gravity waves thus also contribute to the energy transport into the chromosphere.

Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic density field

We present an analytical linear model describing the interaction of a planar shock wave with an isotropic random pattern of density nonuniformities. This kind of interaction is important in inertial confinement fusion where shocks travel into weakly inhomogeneous cryogenic deuterium-wicked foams, and also in astrophysics, where shocks interact with interstellar density clumps. The model presented here is based on the exact theory of space and time evolution of the perturbed quantities generated by a corrugated shock wave traveling into a small-amplitude single-mode density field. Corresponding averages in both two and three dimensions are obtained as closed analytical expressions for the turbulent kinetic energy, acoustic energy flux, density amplification, and vorticity generation downstream. They are given as explicit functions of the two parameters (adiabatic exponent γ and shock strength M(1)) that govern the dynamics of the problem. In addition, these explicit formulas are simplified in the important asymptotic limits of weak and strong shocks and highly compressible fluids.

Acoustic waves in the solar atmosphere at high spatial resolution

Aims. We investigate the energy supply of the solar chromosphere by acoustic waves. Methods. A time sequence with high spatial and temporal resolution from the quiet Sun disc centre in Fe i 5434 A (Lande factor g = 0) is analysed. We used models from a numerical simulation of granular convection and apply NLTE spectral line transfer to determine the height of formation. For estimates of acoustic energy flux, we adopted wave propagation with inclinations of the wave vector with respect to the vertical of 0 ◦ ,3 0 ◦ , and 45 ◦ . For a granular and an intergranular model, the transmissions of the atmosphere to highfrequency waves were determined for the three inclination angles. Wavelet and Fourier analyses were performed and the resulting power spectra were corrected for atmospheric transmission. Results. We find waves with periods down to ∼40 s. They occur intermittently in space and time. The velocity signal is formed at a height of 500 km in the granular model and at 620 km in the intergranule. At periods shorter than the acoustic cutoff (∼190 s), ∼40% of the waves occur above granules and ∼60% above intergranules. By adopting vertical propagation, we estimate total fluxes above granules of 2750–3360 W m −2 , and of 910–1 000 W m −2 above intergranules. The weighted average is 1730–2 060 W m −2 .T he estimates of the total fluxes increase by 15% when inclined wave propagation of 45 ◦ is assumed.

Frequency-dependence of the acoustic rectifying efficiency of an acoustic diode model

For an acoustic diode (AD) model formed by coupling a superlattice with a nonlinear medium, the transmission of acoustic wave is investigated as a function of frequency in a numerical manner. The important phenomenon of rectifying effect of acoustic energy flux is identified in a series of frequency bands whose locations agree exactly with the analytical predictions. Within these frequency bands, the AD can exhibit extremely high rectifying efficiency and strong resistance to “reverse breakdown.” These results are particularly of practical significance for the potential design and application of ADs.

Numerical study of thermoacoustic Taconis oscillations

This paper studies quantitatively a thermoacoustic field by the Taconis oscillations with finite amplitude in a helium-filled, quarter-wavelength tube. Numerical simulations are performed based on the one-dimensional theory in the boundary-layer approximation developed in a previous paper [N. Sugimoto and D. Shimizu, Phys. Fluids 20, 104102 (2008)] by solving initial- and boundary-value problems for a smooth step temperature distribution. It is found that the variations in the density, temperature, and entropy are so significant that the mean values deviate from the respective values in quiescent state. The mean acoustic energy flux and mean heat flux are calculated not only in the main-flow region but also in the boundary layer. The mean convective heat flux appears locally in the main-flow region due to higher-order nonlinear effects. While the total heat flux into the gas vanishes per one period, the local heat flux flows into the gas over a middle part of the tube.

10.1007/s11486-008-1004-3

Retrospective data of monitoring under conditions of low seismic activity are used to identify free oscillations of the Earth, including the fundamental mode, the oscillation with a central period of 54 min (0 S 2 multiplet), split into five lines with azimuthal numbers m = −2, −1, 0, 1, 2. It is shown that some lines of this oscillation are also recorded in atmospheric pressure variation spectra and group in ensembles of observations around frequencies predicted by the 0 S 2 splitting theory. This phenomenon is discovered in data recorded both synchronously and in different time intervals. A causal relationship involved in the oscillation under study is determined on the basis of the examination of the direction of the acoustic energy flux. The energy flux in the region of the 0 S 2 multiplet is shown to be directed from the Earth toward the atmosphere. This suggests that deep processes in the Earth are capable of exciting its upper shells.

Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems

We numerically demonstrate a simple one-dimensional model of an acoustic diode formed by coupling a superlattice with a strongly nonlinear medium. The first numerical observation is presented of a significant rectifying effect on the acoustic energy flux within particular ranges of frequencies. By studying the underlying rectifying mechanism and the parameter dependence of the rectifying efficiency, the effectiveness of the acoustic diode is proved despite its simplicity. We also briefly discuss possible schemes of the experimental realization of this model as well as devising more efficient models.

The energy flow for a spherical acoustic lens: Ray and wave methods vs experiment.

A simple classroom demonstration consists of a weather balloon filled with carbon dioxide, a sound source, and a microphone. Since the speed of sound is slower in carbon dioxide than in air at room temperature and pressure, the balloon acts as a positive spherical acoustic lens. The accuracy of ray methods in locating the acoustic focus versus a full‐blown wave solution approach has been presented previously [Cleon E. Dean and James P. Braselton, “The energy flow for a spherical acoustic lens: ray vs. wave methods,” J. Acoust. Soc. Am. 123, 3520 (2008).] Theoretically, this problem presents particular difficulties if the sound source lies in the near field region. The sound emitter is treated as a dipole source equivalent to a rigid oscillating sphere of small size and amplitude of motion relative to the scatterer. The energy flux around the balloon has been visualized by both ray methods and by the acoustic energy flux vector field. The geometrical ray results and the energy flux vector field resulting from the wave solution are compared with experiment.