Sonic Boom Propagation Research Articles

Nonlinear propagation of spark-generated N-waves in atmosphere: theoretical and experimental assessment of the shock front structure

Extensive outdoor and laboratory-scale experiments on sonic boom propagation in turbulent atmosphere have shown that shock wave amplitude and rise time are important parameters responsible for sonic boom annoyance. However, accurate measurement of the shock front structure with standard microphone remains a challenge due to the broadband spectrum of the N-wave shock front. In this work the experimental setup utilizing a spark source has been designed and built to investigate nonlinear N-wave propagation in homogeneous medium. Short duration (30μs) and high amplitude (1 kPa) spherically divergent N-waves were generated. In addition to acoustic measurements with 1/8" B&K microphones, the shadowgraphy method using short duration flash lamp (20 ns) and CCD camera was employed to assess the shock front structure at different distances from the spark. It is shown that the shock rise time measured by the shadowgraphy method was in a good agreement with the theoretical predictions and it was 10 times shorter than in microphone measurements. The widening of the shock in acoustic measurements was therefore due to the limited bandwidth of the microphone. The combination of modeling, acoustic and optical measurements provided an accurate calibration of the shock wave measuring system. [Work supported by RFBR and INTAS.]

Numerical modeling of sonic boom propagation from hypersonic aircraft

A numerical study of sonic boom propagation from hypersonic aircraft is performed including the effects of nonlinearity, atmospheric absorption and dispersion, and atmospheric stratification. A second-order split-step algorithm, which alternates application of nonlinearity in the time domain and complex absorption in the frequency domain, allows for a faster convergence of results with fewer range steps than with conventional first-order algorithms. Nonlinearity is calculated using the potential, the integral of the pressure, as proposed by Burgers and later applied to sonic booms by Hayes et al. This method, an alternative to Landau's law of equal areas, efficiently locates the shock position by selecting the maximum potential in multivalued regions. Definition of atmospheric absorption at high altitudes is important for modeling the propagation of sonic booms from hypersonic aircraft. Some aspects of an extended absorption model by Sutherland and Bass are adopted, therefore, which extend absorption predictions above the 20 km limit of the current ISO and ANSI standards. The study is completed using the meteorological conditions at two locations, Le Havre, France and Edwards Air Force Base, CA, USA, over the course of a year. [Work supported by European Union through ATLLAS AST5-CT-2006-030729, meteorological data provided by ECMWF.]

Modeling atmospheric turbulence as a filter for sonic boom propagation

Atmospheric turbulence is known to alter the pressure waveform created by supersonic flight. It is challenging to predict how a particular sonic boom waveform will be affected by a particular atmospheric realization without performing intense atmospheric modeling calculations. This paper attempts to approximate the effects of turbulence as a linear FIR filter. Such a filter is estimated from real sonic boom data measured on the ground and at altitude.

Extension of a sonic boom model to ellipsoidal Earth and 3‐D atmosphere

Sonic boom ray tracing models generally use flat‐earth geometry, with 3‐D ray propagation through a horizontally stratified atmosphere. There has been recent interest in long‐range sonic boom propagation, both for analysis of sonic boom carpet edges from high‐altitude flight and for analysis of over‐the‐top booms. The sonic boom program PCBoom4 has been extended to incorporate ellipsoidal earth and full 3‐D ray tracing through a three‐dimensional atmosphere. Ellipsoidal geometry of the Earth is handled by the method of Sofair [J. Guidance Control, 23(2)], which defines a local vertical at given coordinates. A tangent reference plane is defined, and ray tracing is performed using the 3‐D formulation of Schulten [NLR TP 97‐374], in Cartesian coordinates. Once rays are traced, ray tube areas, signature aging, and focal zones are computed in the traditional manner. When over the top booms are analyzed, a starting signature for propagation after the caustic passage is generated from the recent numeric calculations by Kandil [AIAA Paper No. 2005‐0013]. The new program, denoted PCBoom5, is expected to be available in 2007.

Sonic Boom Minimization Using Inverse Design and Probabilistic Acoustic Propagation

near-field signature is more accurately represented. The problem of F-function parameters’ estimation is reformulated as a gradient-based optimization problem and solved. Sonic boom propagation is carried out in a probabilistic fashion using parametric atmospheric models and statistical techniques. A bilevel pseudoinverse optimization is performed using coarse-grained parallel genetic algorithms to design aircraft that meet low sonic boom requirements under atmospheric uncertainty. The optimization analysis is split into two cycles with multiple conflicting objectives. Results are presented and discussed.

Model experiments to study sonic boom propagation through turbulence

The aim of this paper is to present data from laboratory‐scale experimental simulations of sonic boom propagation through a turbulent atmosphere. The source used to simulate sonic boom N waves is an electric spark source. In order to model turbulence, two setups have been used: a turbulent jet for kinematic turbulence and a heated grid for thermal turbulence. Acoustic measurements have been conducted for three configurations: free field; close to a plane surface in order to simulate ground effects; and close to a curved surface in order to investigate the propagation into a shadow zone. The surfaces were either smooth or rough. With turbulence, many waveforms have been recorded, then the statistics of various parameters, including the peak pressure and the rise time, have been analyzed. In the free field, data show that the increase of the mean rise time and the decrease of the mean peak pressure are linked to the probability of random focusing. The experiments have enabled separate assessment of the effects of turbulence and roughness in the shadow zone caused by the curved surface. Comparison with numerical simulations will be discussed. [This work was supported by European Commission Contract N:G4RD‐CT‐2000‐00398 and French Ministere de la Recherche (Decision 00T0116).]

Atmospheric effects on sonic boom loudness

The effects of sonic boom propagation through nonstandard atmospheres have been studied. Variations in atmospheric temperature, pressure, humidity, and winds can have significant impact on the structure of the shock waves in the boom signal, as well as the propagation path of the boom. In the study, a hybrid time‐frequency domain code was used to calculate finely resolved sonic boom signals for a variety of atmospheric conditions. Idealized near–field signals for low amplitude ‘‘N‐wave’’ and ‘‘shaped’’ booms were used to calculate ground level signals. The perceived level metric of Stevens [‘‘Perceived level of noise by Mark VII and decibels (E),’’ J. Acoust. Soc. Am. 51, 575–601 (1972)] was used to quantify the loudness of the calculated booms. Results of the study will be used to determine the impact of atmospheric variations on the acceptability of sonic booms from future supersonic cruise aircraft.

Atmospheric turbulence filter functions derived from high‐fidelity measurements

Efforts have been underway to develop filter functions suitable for adding turbulent atmospheric effects to theoretical low‐boom waveforms. Filter functions have been created based on a measured input‐output relationship. The input is a relatively clean sonic boom waveform measured at altitude by a glider, and the outputs are turbulized’ waveforms measured on the ground. One input waveform and multiple output waveforms are used to represent multiple realizations of the atmosphere. Work presented in 2005 [Locey and Sparrow, Innovations in Nonlinear Acoustics, 17th International Symposium on Nonlinear Acoustics (American Institute of Physics, Melville, NY, 2006)] yielded an initial set of filter functions using one particular algorithm and data collected during the Shaped Sonic Boom Experiment (SSBE) in January of 2004. In this talk new results will be presented based on high‐fidelity measurements made at NASA Dryden Flight Research Center in June of 2006 [T. Gabrielson et al., Proc. Internoise (2006)]. Time permitting, additional methods for obtaining filter functions will be discussed, including the use of existing sonic boom propagation codes modified to include atmospheric turbulence. [Work supported by the FAA/NASA/Transport‐Canada PARTNER Center of Excellence for Aircraft Noise and Aviation Emissions Mitigation.]

PARTNER Project 8: Sonic boom mitigation

Current U.S. and international laws prohibit commercial supersonic flight over land due to the impact of conventional sonic boom noise. Aircraft manufacturers, however, now have modern computational fluid dynamics and optimization tools, unavailable when those laws were enacted, that will allow them to design and build aircraft with boom signatures that are substantially smoothed compared with traditional N‐waves. One purpose of the FAA/NASA/Transport Canada PARTNER Center of Excellence Project 8 is to determine exactly which waveforms would be heard by the public if low‐boom supersonic aircraft are put into service. Another purpose is to ascertain the acceptability of those waveforms. The project involves the following universities, government, and industry partners: Penn State, Purdue, Stanford, the National Aeronautics and Space Administration, the Federal Aviation Administration, Boeing, Cessna, Gulfstream, Lockheed‐Martin, and Wyle Laboratories. Some of the initial project work includes studies on the propagation of sonic booms through atmospheric turbulence, on the mutual reproducibility of three sonic boom simulators, and on the realism of those simulators as determined by expert listeners. The results of all the studies are intended to provide the FAA with new data to reassess current regulations. [Work supported by NASA, the FAA, and the PARTNER industrial partners.]

Meteorologically induced variability of sonic-boom characteristics of supersonic aircraft in cruising flight

The influence of the meteorological variability on the characteristics of the primary sonic boom emerging from an aircraft in cruising flight is investigated. The sonic-boom propagation is calculated by means of an advanced ray-tracing algorithm which takes meteorological influences into account. Real meteorological situations are considered based on a full 10-year data set in 12- and/or 24-h resolution. Three different climate regions are studied: a mid-latitude coastal sea region, a tropical coastal sea area, and a subpolar land region. Frequency distributions of sonic-boom characteristics such as wave amplitude, rise time, and carpet width are shown for each area, all seasons, and opposing flight directions. It turns out that while variability is low at the ground track, it is high laterally for carpet width or boom amplitude at the outer carpet edges. A correlation analysis is applied which shows specific relationships between meteorological profile parameters and acoustical response. In addition, a meteorological classification is introduced and tested.

Propagation of spark generated N waves through turbulent media

It is generally accepted that turbulence plays a role in the propagation and the distortion of sonic booms generated by supersonic flights. This paper describes laboratory experiments in which acoustic shocks from electric sparks have been used to model the propagation of sonic booms [Ollivier et al., 10th AIAA/CEAS Conference, AIAA 2004-2921]. In order to study separately the influence of random fluctuations of temperature and velocity, the N-waves are propagated through a turbulent plane jet or over a heated grid. The recording of 1000 snapshots allows statistical analysis of the variation of the parameters used to describe N-waves, including the maximum and the minimum peak pressures, the rise time, the arrival times and the duration of the wave. In particular, the data show that the increase of the average rise time and the decrease of the average peak pressure with the increase of the rms value of the fluctuations or the increase of the propagation distance could be linked to the probability of occurence of random caustics as observed in numerical simulations [Blanc-Benon et al., J. Acoust. Soc. Am. 111, 487–498 (2002)]. [This work is partly supported by the European Community SOBER project, Contract No. G4RD-CT-2000-00398 and by the French Ministère de la Recherche et des Nouvelles Technologies.]

Modeling of secondary sonic booms: Influence of the variability of the atmosphere

The shock waves generated by a supersonic aircraft are reflected in the upper part of the atmosphere. Back to the ground, they are indirect sonic booms called secondary sonic booms. The recorded signals of secondary sonic booms show a low amplitude and a low frequency. They sound like rumbling noises due to amplitude bursts. These signals strongly depend on the atmospheric conditions, in particular to the amplitude and to the direction of the wind in the stratopause. The propagation of the secondary sonic boom is studied using atmospheric models up to the thermosphere. By solving temporal ray equations, the secondary carpet position is investigated. An amplitude equation including nonlinearity, absorption, and relaxation by various chemical species is coupled to the ray solver in order to get information on the amplitude and on the frequency of the sonic boom at the ground level. Using this propagation model and the atmospheric model, the seasonal dependencies of the secondary sonic boom are investigated. Multipath arrivals are directly linked to wind field or 3-D inhomogeneities. They have been of special concern as a way to explain the rumble noise as a summation over different ray contributions.

Extension of Crow’s paraboloid of dependence to spherical waves

Crow1 discussed the distortion of sonic booms in the presence of atmospheric turbulence. He showed that the scattering from a weak shock is given by a surface integral over a paraboloid of dependence. The paraboloid of dependence describes the two-dimensional surface that contains the scatterers that contribute to the scattered sound at a point behind the shock at a given time. In Crow’s analysis the sonic boom is treated as a plane wave. Lipkens et al.2,3 used electrical sparks that propagate through turbulence created by a plane jet to simulate sonic boom propagation through a turbulent atmosphere. Experiments were done with plane and spherical waves. An extension of Crow’s scattering surface for spherical wave propagation is presented. For spherical waves the two-dimensional scattering surface is an ellipsoid of dependence.

A model experiment to study sonic boom propagation through turbulence. Part III: validation of sonic boom propagation models.

In previous papers, we have shown that model experiments are successful in simulating the propagation of sonic booms through the atmospheric turbulent boundary layer. The results from the model experiment, pressure wave forms of spark-produced N waves and turbulence characteristics of the plane jet, are used to test various sonic boom models for propagation through turbulence. Both wave form distortion models and rise time prediction models are tested. Pierce's model [A. D. Pierce, "Statistical theory of atmospheric turbulence effects on sonic boom rise times," J. Acoust. Soc. Am. 49, 906-924 (1971)] based on the wave front folding mechanism at a caustic yields an accurate prediction for the rise time of the mean wave form after propagation through the turbulence.

Propagation of finite amplitude sound through turbulence: modeling with geometrical acoustics and the parabolic approximation.

Sonic boom propagation can be affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. Turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometrical acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results from numerical experiments that simulate the propagation of spark-produced N waves through turbulence are presented. It is observed that turbulence decreases, on average, the peak pressure of the N waves and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The effects of random vector fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wave front are also presented. These observations confirm the results from the model experiment in which spark-produced N waves are used to simulate sonic boom propagation through a turbulent atmosphere.

Atmospheric turbulence conditions leading to focused and folded sonic boom wave fronts.

The propagation and subsequent distortion of sonic booms with rippled wave fronts are investigated theoretically using a nonlinear time-domain finite-difference scheme. This work seeks to validate the rippled wave front approach as a method for explaining the significant effects of turbulence on sonic booms [A. S. Pierce and D. J. Maglieri, J. Acoust. Soc. Am. 51, 702-721 (1971)]. A very simple description of turbulence is employed in which velocity perturbations within a shallow layer of the atmosphere form strings of vortices characterized by their size and speed. Passage of a steady-state plane shock front through such a vortex layer produces a periodically rippled wave front which, for the purposes of the present investigation, serves as the initial condition for a finite-difference propagation scheme. Results show that shock strength and ripple curvature determine whether ensuing propagation leads to wave front folding. High resolution images of the computed full wave field provide insights into the spiked and rounded features seen in sonic booms that have propagated through turbulence.

Effect of molecular relaxation on the propagation of sonic booms through a stratified atmosphere

Nonlinear acoustic wave propagation through a stratified atmosphere is considered. The initial signal is taken to be an isolated N-wave, which is the disturbance that is generated some distance away from a supersonic body in horizontal flight. The effect of cylindrical spreading and exponential density stratification on the propagation of the disturbance is considered, with the shock structure controlled by molecular relaxation mechanisms and by thermoviscous diffusion. An augmented Burgers equation is obtained and asymptotic solutions are derived based on the limit of small dissipation and dispersion. For a single relaxation mode, the solution depends on whether relaxation alone can support the shock or whether a sub-shock arises controlled by other mechanisms. The resulting shock structures are known as fully dispersed and partly dispersed shocks, respectively. In this paper, the spatial location of the transition between fully dispersed and partly dispersed shocks is identified for shocks propagating above and below the horizontal. This phenomenon is important in understanding the character of sonic booms since the transition to a partly dispersed shock structure leads to the appearance of a shorter scale in the shock rise-time, associated with the embedded sub-shock.

Scattering of sonic booms by anisotropic turbulence in the atmosphere

An earlier paper [J. Acoust. Soc. Am. 98, 3412-3417 (1995)] reported on the comparison of rise times and overpressures of sonic booms calculated with a scattering center model of turbulence to measurements of sonic boom propagation through a well-characterized turbulent layer under moderately turbulent conditions. This detailed simulation used spherically symmetric scatterers to calculate the percentage of occurrence histograms of received overpressures and rise times. In this paper the calculation is extended to include distorted ellipsoidal turbules as scatterers and more accurately incorporates the meteorological data into a determination of the number of scatterers per unit volume. The scattering center calculation overpredicts the shifts in rise times for weak turbulence, and still underpredicts the shift under more turbulent conditions. This indicates that a single-scatter center-based model cannot completely describe sonic boom propagation through atmospheric turbulence.

Propagation of sonic booms through a water fog

Sonic boom propagation in a quiet, water–fog atmosphere is investigated. An evolutional equation that governs the development of sonic boom is derived. The interaction between sonic boom shock and droplet spectrum in fog (due to vaporization and liquefaction) is considered. The effect of nonlinearity, attenuation, and dispersion due to multiple relaxation and viscosity are also taken into account. A computer code is developed to solve the evolutional equation. From the numerical solutions of the equation, it is found that not only the relaxation and heat conduction increase the nonlinear distortion, but the droplet spectrum in fog greatly influences the development of sonic boom. The change of droplet spectrum affects the rise time of N wave and even causes sonic boom shock to degenerate to a series of waves.

Sonic boom propagation through turbulence: A geometric acoustics and a KZK approach

Sonic boom propagation is strongly affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. The turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometric acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results show that, on average, turbulence decreases the mean peak pressure and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The geometric acoustics results indicated that the effects of random vectorial fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wavefront are also presented. [Work supported by a grant from NASA.]