Three-dimensional linearised Euler model simulations of sound propagation in idealised urban situations with wind effects

A three-dimensional numerical time-domain model based on the linearised Euler equation is applied to idealised urban situations with elongated, isolated buildings beside a straight street with sound emissions. The paper aims at the investigation of principle relationships between the source-receiver geometry (street and building facades) and sound propagation under the consideration of ground and wind. By applying cyclic lateral boundary conditions for either one or both horizontal co-ordinates, two different idealised urban environments were considered: a single street and parallel streets. Numerical experiments were performed to elaborate the effects of different roof types, ground properties, wind flow, and turbulence in both urban environments with the focus on the back facades (‘quiet’ sides) of the buildings. As a result it was found that the back facades of flat-roof buildings are quieter than those of hip roof buildings despite equal cross-cut areas. The wind effect (resulting in quieter upwind and louder downwind facades) is more pronounced for hip-roof buildings. In the case of parallel streets upwind facades are slightly louder than downwind facades because they are simultaneously exposed to downwind propagating sound from the next parallel street.     

NUMERICAL MODELLING OF THE SOUND FIELDS IN URBAN STREETS WITH DIFFUSELY REFLECTING BOUNDARIES

A radiosity-based theoretical/computer model has been developed to study the fundamental characteristics of the sound fields in urban streets resulting from diffusely reflecting boundaries, and to investigate the effectiveness of architectural changes and urban design options on noise reduction. Comparison between the theoretical prediction and the measurement in a scale model of an urban street shows very good agreement. Computations using the model in hypothetical rectangular streets demonstrate that though the boundaries are diffusely reflective, the sound attenuation along the length is significant, typically at 20-30 dB/100 m. The sound distribution in a cross-section is generally even unless the cross-section is very close to the source. In terms of the effectiveness of architectural changes and urban design options, it has been shown that over 2-4 dB extra attenuation can be obtained either by increasing boundary absorption evenly or by adding absorbent patches on the façades or the ground. Reducing building height has a similar effect. A gap between buildings can provide about 2-3 dB extra sound attenuation, especially in the vicinity of the gap. The effectiveness of air absorption on increasing sound attenuation along the length could be 3-9 dB at high frequencies. If a treatment is effective with a single source, it is also effective with multiple sources. In addition, it has been demonstrated that if the façades in a street are diffusely reflective, the sound field of the street does not change significantly whether the ground is diffusely or geometrically reflective.     

A ray model for hard parallel noise barriers in high-rise cities

A ray model is developed and validated for prediction of the insertion loss of hard parallel noise barriers placed in an urban environment either in front of a row of tall buildings or in a street canyon. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the ground, barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and the near-side barrier. Comparisons of the ray model with a wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Results of scale model experimental studies are also presented. It is demonstrated that the ray model agrees tolerably well with the scale model experimental data.     

Numerical modeling of urban sound fields by a diffusion process

In this paper, we present the numerical implementation of a sound field model used in urban acoustics. The mathematical model being based on a classic diffusion equation for the sound energy, a simple finite difference scheme is applied. We give also some finite difference equations for simple boundary conditions, like absorption by a wall and at building edges. The two-dimensional numerical scheme is then compared to analytical solutions of the sound field propagation in a rectangular street with a good agreement, both in the steady state and in the time varying state. Finally it is suggested that the adjustment of usual softwares for heat transfer could be an interesting and low cost way to develop powerful acoustic softwares for the prediction of noise in urban areas.     

Efficient calculation of two-dimensional periodic and waveguide acoustic Green's functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.     

Line source and site characterizations for defining the sound transmission loss of building facades

An analytical model is presented for defining the sound transmission loss of building facades exposed to noise from line sources. The model describes the non-diffuse sound field incident upon the facade in terms of both source and site parameters. The effects of facade orientation relative to the line source and the sound propagation with distance are introduced as a single term in the definition of the facade sound transmission loss. This term defines a mean angle of incidence for the exterior sound field that is equivalent to a point source location relative to a point on the facade. Numerical results are presented illustrating the magnitudes of these effects and it is shown that alternative methods for conducting field measurements of building facade sound transmission loss may be related by using this model.     

Sound propagation in the vicinity of an isolated building: an experimental investigation

Recently, the study of acoustics in urban terrain has been concerned with the propagation of sound through street canyons typical of residential areas in large cities, while sparsely built suburban and rural areas have received little attention. An isolated building's effect on propagating sound is a fundamental case of suburban acoustics and urban acoustics in general. Its study is a necessity in order to determine the processes that might be required to model the sound field in the building's vicinity, e.g., diffraction and wind effects. The work herein presents the results of an experimental effort to characterize the interaction between propagating sound and a single story, gabled-roof building typical of some North American suburban and rural areas. Recorded data are found to reasonably compare to a common diffraction model in some instances.     

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.     

A linearized Eulerian sound propagation model for studies of complex meteorological effects

Outdoor sound propagation is significantly affected by the topography (including ground characteristics) and the state of the atmosphere. The atmosphere on its part is also influenced by the topography. A sound propagation model and a flow model based on a numerical integration of the linearized Euler equations have been developed to take these interactions into account. The output of the flow model enables the calculation of the sound propagation in a three-dimensionally inhomogeneous atmosphere. Rigid, partly reflective, or fully absorptive ground can be considered. The linearized Eulerian (LE) sound propagation model has been validated by means of four different scenarios. Calculations of sound fields above rigid and grass-covered ground including a homogeneous atmosphere deviate from analytic solutions by < or = 1 dB in most parts of the computed domain. Calculations of sound propagation including wind and temperature gradients above rigid ground agree well with measured scale model data. Calculations of sound propagation over a screen including ground of finite impedance show little deviations to measured scale model data which are probably caused by an insufficient representation of the complex ground impedance. Further calculations included the effect of wind on shading by a screen. The results agree well with the measured scale model data.     

Experimental and numerical study on the propagation of impulsive sound around buildings

Propagation of impulsive sound around buildings and induced structural loading are investigated experimentally and numerically. Experiments were conducted on a rectangular building at Virginia Tech using sonic booms generated by shaped charges with an explosive weight of 0.78 kg, constructed from detonation cord. These experiments were simulated with a three-dimensional numerical model, in the context of geometrical acoustics (GA), by combining the image source method for the reflected field (specular reflections) with an extension of the Biot–Tolstoy–Medwin (BTM) method for the diffracted field. In this model, it is assumed that the acoustic propagation is linear and that all surfaces are acoustically rigid. This numerical model is validated against a boundary element (BE) solution and experimental data, showing a good overall agreement. The key advantages of this GA modeling approach for this application include the ability to model large three-dimensional domains over a wide frequency range and also to decompose the sound field into direct, reflected, and diffracted components, thus providing a better understanding of the sound-propagation mechanisms. Finally, this validated numerical model is used to investigate sound propagation around a cluster of six rectangular buildings, for a range of elevated source positions simulating sonic booms from aircraft.     

Diffraction of sound from a dipole source near to a barrier or an impedance discontinuity

Pierce's formulation for the diffraction of spherical waves by a hard wedge has been extended to the case of the sound field due to a dipole source. The same approach is also used to extend a semiempirical model for sound propagation above an impedance discontinuity due to a dipole source. The resulting formulas have been validated by comparing their numerical solutions with that computed by summing the sound fields due to two closely spaced monopole sources of equal magnitude but opposite in phase. These new formulations are then used to develop a simple model for calculating the dipole sound field diffracted by a barrier above an impedance ground. Applications of these models relate to transportation noise prediction, particularly railway noise abatement, for which dipole sources are commonly used. The numerical predictions have been found to compare reasonably well with indoor measurements using piezoceramic transducers as dipole sources.     

A beam tracing method for interactive architectural acoustics

A difficult challenge in geometrical acoustic modeling is computing propagation paths from sound sources to receivers fast enough for interactive applications. This paper describes a beam tracing method that enables interactive updates of propagation paths from a stationary source to a moving receiver in large building interiors. During a precomputation phase, convex polyhedral beams traced from the location of each sound source are stored in a "beam tree" representing the regions of space reachable by potential sequences of transmissions, diffractions, and specular reflections at surfaces of a 3D polygonal model. Then, during an interactive phase, the precomputed beam tree(s) are used to generate propagation paths from the source(s) to any receiver location at interactive rates. The key features of this beam tracing method are (1) it scales to support large building environments, (2) it models propagation due to edge diffraction, (3) it finds all propagation paths up to a given termination criterion without exhaustive search or risk of under-sampling, and (4) it updates propagation paths at interactive rates. The method has been demonstrated to work effectively in interactive acoustic design and virtual walkthrough applications.     

Effect of the open roof on low frequency acoustic propagation in street canyons

This paper presents an experimental, numerical and analytical study of the open roof effect on acoustic propagation along a 3D urban canyon. The experimental study is led by means of a street scale model. The numerical results are performed with a 2D-Finite Difference in Time Domain approach adapted to take into account the acoustic radiation losses due to the street open roof. An analytical model, based on the modal decomposition of the pressure field in the street width mixed with a 2D image sources model including the reflection by the open roof, is also presented. Results are given for several frequencies in the low frequency domain. The comparison of these approaches shows a quite good agreement until f = 100 Hz at full scale. For higher frequency, experimental results show that the leakage, due to the street open roof, is not anymore uniformly distributed on all modes of the street. The notion of leaky modes must be introduced to model the acoustic propagation in a street canyon.     

Excess attenuation for sound propagation over an urban canyon

Because quiet areas in dense urban environments are important to well-being, the prediction of sound propagation to shielded urban areas is an ongoing research focus. Sound levels in shielded areas, such as canyons between rows of buildings, are strongly influenced by distant sources. Therefore, propagation factors such as metrology, screening, and intermediate canyons—as occur between a source canyon and a receiver canyon—must be addressed in an engineering propagation model. Though current models address many important propagation factors, engineering treatment of a closed urban canyon, subject to multiple internal reflections, remains difficult.A numerical investigation of sound propagation across the open tops of intermediate urban canyons has been performed, using the parabolic equation and equivalent sources methods. Results have been collected for various canyon geometries, and the influences of multiple canyons, canyon/rooftop absorption, variable rooftop height, wind gradient, and correlated versus uncorrelated source models have been investigated. Resulting wideband excess attenuation values ranged from −1 dB to −4 dB per canyon, and were fairly constant with frequency in many useful cases. By characterizing the excess attenuation of canyons intermediate to the source and receiver, the influence of these intermediate canyons could be addressed simply, without the overhead of a detailed numerical calculation.     

Predicted attenuation of sound in a rigid-porous ground from an airborne source

An approximate analytical formula has been derived for the prediction of sound fields in a semi-infinite rigid-porous ground due to an airborne source. The method starts by expressing the sound fields in an integral form, which can subsequently be evaluated by the method of steepest descents. The concept of effective impedance has been introduced by using a physically plausible assumption. The integral can then be simplified and evaluated analytically. The analytical solution can be expressed in a closed form analogous to the classical Weyl-Van der Pol formula that has been used for predicting sound fields above a rigid-porous ground. Extensive comparisons with the wave-based numerical solutions according to the fast field formulation and the direct evaluation of the integral have been conducted. It has been demonstrated that the analytical formula is sufficiently accurate to predict the penetration of sound into a wide range of outdoor ground surfaces.     

The extended Fourier pseudospectral time-domain method for atmospheric sound propagation

An extended Fourier pseudospectral time-domain (PSTD) method is presented to model atmospheric sound propagation by solving the linearized Euler equations. In this method, evaluation of spatial derivatives is based on an eigenfunction expansion. Evaluation on a spatial grid requires only two spatial points per wavelength. Time iteration is done using a low-storage optimized six-stage Runge-Kutta method. This method is applied to two-dimensional non-moving media models, one with screens and one for an urban canyon, with generally high accuracy in both amplitude and phase. For a moving atmosphere, accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen. The method has also been validated for three-dimensional sound propagation over a screen. For that application, the developed method is in the order of 100 times faster than the second-order-accurate FDTD solution to the linearized Euler equations. The method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated.     

Numerical modeling of the exterior-to-interior transmission of impulsive sound through three-dimensional,thin-walled elastic structures

Exterior propagation of impulsive sound and its transmission through three-dimensional, thin-walled elastic structures, into enclosed cavities, are investigated numerically in the framework of linear dynamics. A model was developed in the time domain by combining two numerical tools: (i) exterior sound propagation and induced structural loading are computed using the image-source method for the reflected field (specular reflections) combined with an extension of the Biot–Tolstoy–Medwin method for the diffracted field, (ii) the fully coupled vibro-acoustic response of the interior fluid–structure system is computed using a truncated modal-decomposition approach. In the model for exterior sound propagation, it is assumed that all surfaces are acoustically rigid. Since coupling between the structure and the exterior fluid is not enforced, the model is applicable to the case of a light exterior fluid and arbitrary interior fluid(s). The structural modes are computed with the finite-element method using shell elements. Acoustic modes are computed analytically assuming acoustically rigid boundaries and rectangular geometries of the enclosed cavities. This model is verified against finite-element solutions for the cases of rectangular structures containing one and two cavities, respectively.     

A topological pattern of urban street networks: Universality and peculiarity

In this paper, we derive a topological pattern of urban street networks using a large sample (the largest so far to the best of our knowledge) of 40 US cities and a few more from elsewhere of different sizes. It is found that all the topologies of urban street networks based on street-street intersection demonstrate a small world structure, and a scale-free property for both street length and connectivity degree. More specifically, for any street network, about 80% of its streets have length or degrees less than its average value, while 20% of streets have length or degrees greater than the average. Out of the 20%, there are less than 1% of streets which can form a backbone of the street network. Based on the finding, we conjecture that the 20% streets account for 80% of traffic flow, and the 1% streets constitute a cognitive map of the urban street network. We illustrate further a peculiarity about the scale-free property.     

The importance of roof shape for road traffic noise shielding in the urban environment

The influence of roof shape on sound propagation in a densely build-up city centre is evaluated. Road traffic noise propagation from a street canyon to an adjacent, non-directly exposed building façade is numerically studied by the finite-difference time-domain method. A large number of common and less common roof shapes were analyzed in an idealized city canyon configuration. Roof shape can be responsible for differences in road traffic noise shielding exceeding 10 dBA, averaged over the shielded façade. Therefore, roof shape can be considered as an important means to limit sound pressure levels at a quiet side; various researchers indicated that the presence of silent zones and façades may limit city noise annoyance. With increasing vehicle speed, the choice of roof shape becomes more important. The roof top height was shown to be a bad predictor of shielding efficiency in the equal-building-volume approach followed in this study.