Victor W. Sparrow

Simulation of ultrasonic pulse propagation through the abdominal wall

Ultrasonic pulse propagation through the abdominal wall has been simulated using a model for two-dimensional propagation through anatomically realistic tissue cross sections. The time-domain equations for wave propagation in a medium of variable sound speed and density were discretized to obtain a set of coupled finite-difference equations. These difference equations were solved numerically using a two-step MacCormack scheme that is fourth-order accurate in space and second-order accurate in time. The inhomogeneous tissue of the abdominal wall was represented by two-dimensional matrices of sound speed and density values. These values were determined by processing scanned images of abdominal wall cross sections stained to identify connective tissue, muscle, and fat, each of which was assumed to have a constant sound speed and density. The computational configuration was chosen to simulate that of wavefront distortion measurements performed on the same specimens. Qualitative agreement was found between those measurements and the results of the present computations, indicating that the computational model correctly depicts the salient characteristics of ultrasonic wavefront distortion in vivo. However, quantitative agreement was limited by the two-dimensionality of the computation and the absence of detailed tissue microstructure. Calculations performed using an asymptotic straight-ray approximation showed good agreement with time-shift aberrations predicted by the full-wave method, but did not explain the amplitude fluctuations and waveform distortion found in the experiments and the full-wave calculations. Visualization of computed wave propagation within tissue cross sections suggests that amplitude fluctuations and waveform distortion observed in ultrasonic propagation through the abdominal wall are associated with scattering from internal inhomogeneities such as septa within the subcutaneous fat. These observations, as well as statistical analysis of computed and observed amplitude fluctuations, suggest that weak fluctuation models do not fully describe ultrasonic wavefront distortion caused by the abdominal wall.

Fundamental Structural-Acoustic Idealizations for Structures with Fuzzy Internals

Fundamental issues relative to structural vibration and to scattering of sound from structures with imprecisely known internals are explored, with the master structure taken as a rectangular plate in a rigid baffle, which faces an unbounded fluid medium on the external side. On the internal side is a fuzzy structure, consisting of a random array of point-attached spring-mass systems. The theory predicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function m F (Ω) which gives a smoothed-out total mass, per unit plate area, of all those attached oscillators which have their natural frequencies less than a given value Ω. The theory also predicts that the exact value of the damping in the fuzzy structure is of little importance, because the structure, even in the limit of zero damping, actually absorbs energy with an apparent frequency-dependent damping constant proportional to dm F (ω)/dω incorporated into the dynamical description of the master structure. A small finite value of damping within the internals will cause little appreciable change to this limiting value.

The role of nonlinear effects in the propagation of noise from high-power jet aircraft

To address the question of the role of nonlinear effects in the propagation of noise radiated by high-power jet aircraft, extensive measurements were made of the F-22A Raptor during static engine run-ups. Data were acquired at low-, intermediate-, and high-thrust engine settings with microphones located 23-305 m from the aircraft along several angles. Comparisons between the results of a generalized-Burgers-equation-based nonlinear propagation model and the measurements yield favorable agreement, whereas application of a linear propagation model results in spectral predictions that are much too low at high frequencies. The results and analysis show that significant nonlinear propagation effects occur for even intermediate-thrust engine conditions and at angles well away from the peak radiation angle. This suggests that these effects are likely to be common in the propagation of noise radiated by high-power aircraft.

A numerical method for general finite amplitude wave propagation in two dimensions and its application to spark pulses

The general equations of finite amplitude acoustics, including classical absorption effects and second‐order nonlinear effects, are written in a form suitable for two‐dimensional numerical solution. A finite difference scheme then is applied to numerically solve the equations. To demonstrate the method, examples are given of spherical free‐field propagation, normal plane reflection from a hard surface, and oblique spherical reflection from a hard surface for spark pulses. This method has an advantage over Burgers’ equation methods, one‐way wave equation methods, and Pestorius type algorithms in that it can predict the interaction of multiple finite amplitude acoustic waves at arbitrary propagation angles.

On the Perception of Crackle in High-Amplitude Jet Noise

Crackle is a phenomenon sometimes found in supersonic jet noise and can comprise an annoying and dominant part of the overall perceived noise. In the past, crackle has been commonly quantified by the skewness of the tune waveform. In this investigation, a simulated waveform with a virtually identical probability density function and power spectrum as an actual F/A-18E afterburner recording has been created by nonlinearly transforming a statistically Gaussian waveform. Although the afterburner waveform crackles noticeably, playback of the non-Gaussian simulated waveform yields no perception of crackle at all, despite its relatively high skewness

Numerical simulation of finite amplitude wave propagation in air using a realistic atmospheric absorption modela)

A nonlinear system of fluid dynamic equations is modeled that accounts for the effects of classical absorption, nitrogen and oxygen molecular relaxation, and relative humidity. Total variables rather than acoustic variables are used, which allow for the inclusion of frequency-independent terms. This system of equations is then solved in two dimensions using a fourth-order Runge-Kutta scheme in time and a dispersion-relation-preserving scheme in space. It is shown that the model accurately simulates wave steepening for propagation up to one shock formation distance. For a source amplitude of 157dB re 20μPa, the Fourier component amplitudes of the analytical and computed waveforms differ by 0.21% at most for the first harmonic in a lossless medium and 0.16% at most for the first harmonic in a medium that includes thermoviscous losses. It is shown that the absorption due to classical effects and molecular relaxation demonstrated by the model is within 1% of the analytical model and the computed dispersion du...

Measurement and Prediction of Noise Propagation from a High-Power Jet Aircraft

Static engine run-up noise measurements have been made on the F-22 Raptor at low and high power settings. At afterburner, the propagation measurements reveal significant evidence of nonlinearity in that there is much greater high-frequency energy than is predicted by linear theory. The measurements have been compared against the results of a nonlinear numerical model based on the generalized Mendousse-Burgers equation. Although the model simplifies the propagation environment in that it neglects ground effects and atmospheric variability, agreement between the measured and nonlinearly predicted spectra is quite favorable. This comparison demonstrates that nonlinear effects can play a significant role in the propagation of high-amplitude noise and that prediction of these effects is possible with this type of numerical model.

The effect of supersonic aircraft speed on the penetration of sonic boom noise into the ocean

In 1968 Sawyers presented a theory which predicts the acoustic pressure underwater due to a supersonic aircraft’s sonic boom in the air. The theory has since been validated in laboratory experiments. In the present paper Sawyers’ theory is utilized to predict the effect of a supersonic aircraft’s speed on the penetration of the sonic boom into the water. By taking into account the variation in a sonic boom’s duration as a function of the aircraft Mach number, it is shown that higher aircraft speeds are associated with higher acoustic pressures in the water. For fixed depths of 10 m or less the peak SPL varies less than 6 dB over a wide range of Mach numbers. For greater depths, 100 m for example, increased Mach numbers may increase the SPL by 15 dB or more. The actual levels are always diminished for deeper depths. These observations may be important for evaluating the possible effects of sonic boom noise on marine mammals.

Preliminary Analysis of Nonlinearity in F/A-18E/F Noise Propagation

*† ‡ § Analyses of recent F/A-18E/F military power and afterburner measurements suggest that the noise propagation is nonlinear in the far field. Spectral broadening takes place as the radiated noise propagates from 18 to 150 m, the limits of the measurement range. This broadening phenomenon cannot be readily explained in terms of linear propagation effects. Calculation of a nonlinearity indicator derived by Howell and Morfey supports the assertion that nonlinear propagation effects are present. Furthermore, skewness and kurtosis calculations indicate that the noise data distributions are non-Gaussian over the propagation range at these engine settings. Finally, the measured spectra have been compared against predictions obtained with existing nonlinear spectral evolution methods. Even though the prediction results compare poorly with the actual measurements, this is attributable to limitations of the spectral evolution methods themselves. I. Introduction HIS paper contains a preliminary analysis of F/A-18E/F Super Hornet static engine run-up noise measurements made at NAVAIR Lakehurst, NJ on 15 April 2003. Results of the analysis show evidence of nonlinear acoustic propagation effects. These effects are typified by a spectral broadening in which energy is transferred from midfrequencies to the ends of the spectrum. The evolution of a finite-amplitude noise spectrum may be explained in terms of two time-domain phenomena. Waveform steeping is responsible for the transfer of energy from mid to high frequencies, whereas shock coalescence and a corresponding increase in time scale accounts for a relative increase of energy at low frequencies 1 . In this paper, the measurement setup and apparatus as well as analysis procedure are first described. Next, the probability density function (PDF) and related statistical quantities are calculated. The measured spectra are compared with linear predictions, which take into account spherical spreading and atmospheric absorption, as well as nonlinear predictions from two existing jet noise prediction schemes 2-4 . The assertion that the disparity between linear predictions and measurements are caused by nonlinear propagation is supported by calculation of a quantity derived by Howell and Morfey as a useful nonlinearity indicator 3 .

Nonlinear Modeling of F/A-18E Noise Propagation

*† ‡ § An algorithm has been developed to study the nonlinear propagation of high-amplitude jet noise. The hybrid time-frequency domain algorithm employs a split-step solution to a Mendousse-Burgers equation that includes the effects of quadratic nonlinearity, atmospheric absorption and dispersion, and geometrical spreading. Spectral predictions generated using the algorithm are compared to recent F/A-18E engine run-up noise measurements made at afterburner and military thrust conditions at distances of 74 and 150 m from the engine nozzles. The agreement between the predicted and measured spectra is such that the results help confirm that energy transfer is occurring to higher frequencies. However, the differences between the model and the measurement raise important issues regarding some of the physical phenomena likely associated with the measurement but not accounted for in the model. Among these are the substantial multipath interference effects in the measured spectra and the finite extent of the aeroacoustic sources within the jet.