Jet engine combustion noise: Pressure,entropy and vorticity perturbations produced by unsteady combustion or heat addition

By idealizing combustion or heat addition processes to occur over a short distance in the flow direction it is possible to calculate the amplitude and phase of the disturbances corresponding to small amplitude fluctuations in the heat addition. The fluctuating heat input is assumed to vary sinusoidally with time and with distance along the direction normal to the flow. Pressure waves propagate away from the heat input region upstream and downstream, whilst on the downstream side waves of vorticity and entropy are convected away. Strong resonant peaks in the pressure and vorticity waves are present close to the cut-off condition of the pressure waves in two dimensions. Generally the wave amplitudes tend to be higher when the mean flow velocity into the region is close to sonic and to become smaller as the steady heat input is increased. For a simplified calculation in which the combustion chamber discharges directly into a multi-stage turbine the downstream noise was predominantly due to the interaction of the entropy with the turbine (i.e., “indirect” rather than “direct” combustion noise).     

Acoustic waves in random fields

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.     

Estimation of shear wave velocity in gelatin phantoms utilizing PhS-SSOCT

We report a method for measuring shear wave velocity in soft materials using phase stabilized swept source optical coherence tomography (PhS-SSOCT). Wave velocity was measured in phantoms with various concentrations of gelatin and therefore different stiffness. Mechanical waves of small amplitudes (??10 ??m) were induced by applying local mechanical excitation at the surface of the phantom. Using the phase-resolved method for displacement measurement described here, the wave velocity was measured at various spatially distributed points on the surface of the tissue-mimicking gelatin-based phantom. The measurements confirmed an anticipated increase in the shear wave velocity with an increase in the gelatin concentrations. Therefore, by combining the velocity measurements with previously reported measurements of the wave amplitude, viscoelastic mechanical properties of the tissue such as cornea and lens could potentially be measured.     

Wave propagation in 1D elastic solids in presence of long-range central interactions

In this paper wave propagation in non-local elastic solids is examined in the framework of the mechanically based non-local elasticity theory established by the author in previous papers. It is shown that such a model coincides with the well-known Kröner-Eringen integral model of non-local elasticity in unbounded domains. The appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the Cauchy stress. In fact, the long-range forces between different volume elements are modelled, in the body domain, as central body forces applied to the interacting elements. It is shown that the shape change of travelling disturbances coalesces with those predicted by the non-local integral theory of elasticity in unbounded domains, but several differences arise in the case of bounded domains. The wave propagation problem has been formulated by means of the Hamiltonian functional of the proposed mechanically based model of non-local elasticity, introducing an additional term to the elastic potential energy that accounts for elastic long-range interactions. In this way, the wave equation may be obtained in a weak formulation and be further used to provide approximate analytical solutions to the governing equation in the context of standing wave analysis. An equivalent discrete point-spring model, similar to lattice-type networks, has also been introduced to show the mechanical equivalence of the non-local elastic model as well as to provide a mechanical scheme suitable for the numerical treatment of pressure waves travelling in non-local bounded domains.     

Response to ‘On the orthogonality of the phase velocity and its feasibility for plane waves’

A recent theoretical study of plane waves with orthogonal phase velocity is premised on incorrect assumptions. The conclusion reached therein – namely, that “a plane wave with orthogonal phase velocity cannot possess linear momentum” and therefore “cannot propagate at all” – is incorrect in general.     

Wave Resonance in Media with Modular,Quadratic and Quadratically-Cubic Nonlinearities Described by Inhomogeneous Burgers-Type Equations

The phenomenon of “wave resonance” which occurs at excitation of traveling waves in dissipative media possessing modular, quadratic and quadratically-cubic nonlinearities is studied. The mathematical model of this phenomenon is the inhomogeneous (or “forced”) equation of Burgers type. Such nonlinearities are of interest because the corresponding equations admit exact linearization and describe real physical objects. The presence of “accompanying sources” (traveling with the wave) on the right-hand side of the inhomogeneous equations ensures the inflow of energy into the wave, which thereafter spreads throughout the wave profile, flows to emerging shock fronts, and then dissipates due to linear and nonlinear losses. As an introduction, the phenomenon of wave resonance in ideal and dissipative media is described and physical examples are given. Exact expressions for nonlinear steady-state wave profiles are derived. Non-stationary processes of wave generation, spatial “beating” of amplitudes with different relationship between the speed of motion of the sources and the natural wave velocity in the medium are studied. Resonance curves are constructed that contain a nonlinear shift of the absolute maxima to the “supersonic” region. The features of the resonance in each of the three types of nonlinearity are discussed.     

Scattering from non-overlapping potentials. I. General formulation

The problem of scattering from an assembly of non-overlapping spherical potentials is solved in partial-wave basis for each of the constituent potentials. The resulting scattering operator is a quotient of two infinite matrices and depends on “on-shell” partial wave amplitudes of the individual potentials. It suggests in general a truncation scheme which essentially considers only those partial waves effective for each collision at the given energy. The multiple-scattering series is recovered and limiting cases of low energy and high energy are considered. Applications to high-energy scattering of elementary particles on nuclei are briefly discussed.     

The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates

This study analytically investigates the propagation of shear waves (SH waves) in a coupled plate consisting of a piezoelectric layer and an elastic layer with initial stress. The piezoelectric material is polarized in z-axis direction and perfectly bonded to an elastic layer. The mechanical displacement and electrical potential function are derived for the piezoelectric coupled plates by solving the electromechanical field equations. The effects of the thickness ratio and the initial stress on the dispersion relations and the phase and group velocities are obtained for electrically open and mechanically free situations. The numerical examples are provided to illustrate graphically the variations of the phase and group velocities versus the wave number for the different layers comparatively. It is seen that the phase velocity of SH waves decreases with the increase of the magnitude of the initial compression stress, while it increases with the increase of the magnitude of the initial tensile stress. The initial stress has a great effect on the propagation of SH waves with the decrease of the thickness ratio. This research is theoretically useful for the design of surface acoustic wave (SAW) devices with high performance.     

Study of fully developed wind wave spectrum by application of quantum statistics

The spectrum of fully developed wind waves is studied by application of the method of quantum statistics. A particle picture of water waves is introduced as an analogy of wave–particle duality. “Water wave particles” are conceived which are similar to phonons for elastic waves in solids. However, due to the property of wave breaking, the number of “water wave particles” in a quantum state is restricted. The spectrum of fully developed wind waves is studied on the basis of the maximum entropy principle. The similarity law of fully developed wind wave spectrum is proved. In the high frequency range, the spectral form is in agreement with the result of observations. In the particle picture, a saturated spectrum is introduced which is in conceptual consistency with the saturated spectrum introduced by Phillips in the wave picture, and the form of which is the same as Phillips’. It is further shown that in the high frequency range the spectrum is only half saturated for fully developed wind waves. The frequency downshifting phenomenon which cannot be explained by wave theory is explained in the particle picture.     

Nature of dark matter and pancake mass

If dark matter is made of collisionless particles a relation holds between the mass m of such particles, the primordial spectral index n, and the “pancake” mass. The case of dark matter of two different particles is debated here; present calculations lead to stringent limits on “supersymmetrical” particle abundance and/or to the prediction of their masses from clustering analysis.     

Acoustic disturbance from gas non-uniformities convected through a nozzle

The non-steady flow generated by convection of gas containing non-uniform temperature regions or “entropy spots” through a nozzle is examined analytically as a source of acoustic disturbance. The first portion of the investigation treats the “compact nozzle”, the case where all wave lengths are much longer than the nozzle. Strengths of transmitted and reflected one-dimensional waves are given for supersonic and subsonic nozzles and for one configuration of supersonic nozzle with normal shock at the outlet. In addition to a wave reflected from the nozzle inlet, the supersonic nozzle discharges two waves, one facing upstream and the other facing downstream. For reasonable values of the nozzle inlet Mach number, the pressure amplitude of each wave increases directly as the discharge Mach number.The acoustic perturbations from a supercritical nozzle of finite length, in which the undisturbed gas velocity increases linearly through the nozzle, are analyzed for several inlet and discharge Mach number values and over a wide frequency range. The results which agree with the compact analysis for low frequency, deviate considerably as the frequency rises, achieving pressure fluctuation levels of several times the compact values. It is shown that this result originates in a phase shift between the two waves emitted downstream and that the pressure fluctuations for moderate frequencies may be approximated from the compact analysis with an appropriate phase shift.In all cases, the pressure fluctuations caused by a 2% fluctuation in absolute inlet temperature are large enough to require consideration in acoustic analysis of nozzles or turbine blade channels.     

Application of acoustic methods for a non-destructive evaluation of the elastic properties of several typologies of materials

In solid phase materials, differently from what happens in the fluid phase, elastic waves propagate both through longitudinal and transverse waves. From the speed of propagation of longitudinal and transverse waves, it is possible to evaluate important elastic properties of the solids under study, namely the Young’s modulus, the Poisson’s coefficient, the bulk modulus and the shear modulus. This work suggests an accurate method for measuring wave propagation speeds in homogeneous and non-homogeneous materials with the purpose to evaluate their mechanical properties and the associated uncertainty.First of all, to assess the performance of the proposed methodology, based on the “pulse-echo” technique, in terms of accuracy and precision, measurements of wave propagation speeds have been carried out, in atmospheric conditions, in well-known homogeneous and isotropic materials, such as copper, aluminum, stainless steel and also polymethyl methacrylate (Plexiglas®), Teflon® and optical glass BK7. These results were compared with the values reported in literature (if present), showing how published speed of sound data are very disperse and not so reliable owing to the lack of a precise uncertainty evaluation and of the temperature value associated to the measurement. Then, the same experimental apparatus was used for measuring speed of sound as a function of temperature (from 274.15 to 313.15 K) for 304 stainless steel and oxygen free copper, showing a good accuracy of the results also for temperature conditions far from ambient. Finally, the same procedure was applied to a non-homogeneous solid, obtaining some very preliminary results in typical mediterranean building material, as Carrara marble.     

Dynamics of Spiral Waves Induced by Periodic Mechanical Deformation with Phase Difference

The dynamics of spiral waves under the influences of periodic mechanical deformation are studied. Here, the mechanical deformation propagating along the medium with phase differences are considered. It is found that weak mechanical deformation may lead to resonant drift of spiral waves. The drift direction and velocity can be changed by the wave length of the deformation. Strong mechanical deformation may result in breakup of spiral waves. The characteristics of breakup are discussed. The critical amplitudes are determined by two factors, i.e. the wave length and frequency of the periodic mechanical deformation. When the wave length of mechanical deformation is comparable to the spiral wave, simulation shows that the critical amplitude is substantially increased. As the frequency of the mechanical deformation is around 1.5 times of the spiral wave, the critical amplitudes are minimal.     

Relation between the Grüneisen ratio and the pressure dependence of Poisson's ratio for metals

The Grüneisen ratio of crystalline solids is shown to be dependent on a parameter n whose values are characteristic of each solid, and can be determined by two independent ways: from experimental shock data and from the pressure derivative of Poisson's ratio. The determinations are made for several metals, using data on the pressure derivatives of polycrystalline elastic moduli or of the second order elastic constants measured on single crystals, and giving the pressure derivatives of Poisson's ratio by means of the Voigt-Reuss-Hill averaging procedure. The values of the parameter n deduced from shock data are found to be in good agreement with those deduced from the pressure derivatives of Poisson's ratio. Positive and negative values of parameter n correspond respectively to increasing and decreasing Poisson's ratio with increasing pressure. Discussion of the results is made using the linear and the quadratic relationships between shock velocity and particle velocity. It is shown that shock wave data cannot yield directly an accurate estimation of the derivative of the initial slope of the Hugoniot.     

Acoustics of shells

We discuss the physical phenomena that arise in the scattering of acoustic waves from fluid-immersed elastic (metal) shells which may be either evacuated or filled with the same or with a different fluid. The phenomena occurring here include the formation of circumferential (peripheral, or “surface”) waves that circumnavigate the shells, propagating either as elastic waves in the shell material or as fluid-borne waves of the Scholte-Stoneley type in the external or the internal fluid. By phase matching along a closed circuit, these waves may lead to prominent resonances in the acoustic scattering amplitude, and we demonstrate how the set of observed resonance frequencies is related to the dispersive phase velocities of the surface waves, so that one can be determined from the other. In addition, we discuss how the dispersion curves (phase velocity plotted vs. frequency) of the various types of surface waves show repulsion phenomena due to their coupling through the boundary conditions. The cases of spherical and cylindrical shells are investigated here as typical examples, and as an introductory topic we additionally mention surface waves on plates where related phenomena also occur. Both the theoretical and the experimental aspects of the present subject will be considered, including the experimental visualization of the surface waves.     

Decay instability of ion-acoustic wave train (or soliton) and formation of the shock profile

The stability of a periodic ion-acoustic wave of a finite amplitude propagating in a nonisothermal plasma is investigated. It is demonstrated that such a wave is unstable with respect to the splitting into a large number of satellite waves with effective wave numbers different from the wave number of the initial wave. The phase velocity of the satellite waves differs therefore from that of the initial pulse. Hence, the satellite waves with bigger phase velocity will “overtake” the initial pulse and turbulize the upstream plasma. The scattering of ions and electrons by the fluctuations of electric field of turbulent oscillations will cause the energy dissipation of the initial ion-acoustic wave translational motion and produce a collisionless shock wave.     

Pulsed magnetic resonance as a probe of longitudinal spin waves and magnetic second sound

Under appropriate conditions, longitudinal spin waves and spin wave second sound, a magnetic temperature wave, can be observed in quantum liquids and solid using pulsed magnetic resonance. A “hole-burning” experiment yields directly the spectrum ω(k) of the propagating magnetic wave.     

Extreme waves statistics for the Ablowitz-Ladik system

We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz-Ladik (AL) system. Modulation instability depends on one free parameter h that has the meaning of the coupling between the nodes on the lattice. For strong coupling h ? 1, the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical nonlinear Schrödinger equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak h ～ 1, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called “fat tails” when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical nonlinear Schrödinger equation.     

The free and forced waves on a fluid-loaded elastic plate

The often-studied problem of the response of a fluid-loaded thin elastic plate to external forcing is considered again, with the aim of determining those “free waves” of the coupled system which can actually be excited. General properties of the quintic equation whose roots yield the free wavenumbers can be used to establish the character of those roots, and a generalized “coincidence condition” can be given at which the nature of the roots changes. It is argued, however, and demonstrated, that in general no significance can be attached to this condition or to any of the roots except that relating to the undamped subsonic surface wave. The far field contributions associated with all other waves, including the so-called “leaky waves”, may be altered merely by change of integration path from the stationary phase contour to the steepest descent contour in the complex wavenumber plane, and thus these contributions, which are exponentially small with distance, do not represent physically meaningful free modes. It is shown, however, that if a second limit process, associated with small fluid loading, is considered simultaneously with the far field limit, then the leaky waves can be unambiguously identified over a large, but not too large, range of distances, and that for such distances these waves generate a conical or plane beam (in three or two dimensions, respectively).