Jens Forssén

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.

The 2.5-dimensional equivalent sources method for directly exposed and shielded urban canyons.

When a domain in outdoor acoustics is invariant in one direction, an inverse Fourier transform can be used to transform solutions of the two-dimensional Helmholtz equation to a solution of the three-dimensional Helmholtz equation for arbitrary source and observer positions, thereby reducing the computational costs. This previously published approach [D. Duhamel, J. Sound Vib. 197, 547-571 (1996)] is called a 2.5-dimensional method and has here been extended to the urban geometry of parallel canyons, thereby using the equivalent sources method to generate the two-dimensional solutions. No atmospheric effects are considered. To keep the error arising from the transform small, two-dimensional solutions with a very fine frequency resolution are necessary due to the multiple reflections in the canyons. Using the transform, the solution for an incoherent line source can be obtained much more efficiently than by using the three-dimensional solution. It is shown that the use of a coherent line source for shielded urban canyon observer positions leads mostly to an overprediction of levels and can yield erroneous results for noise abatement schemes. Moreover, the importance of multiple facade reflections in shielded urban areas is emphasized by vehicle pass-by calculations, where cases with absorptive and diffusive surfaces have been modeled.

A scale model study of parallel urban canyons

Shielded urban areas are of importance regarding urban citizens’ annoyance and adverse health effects related to road traffic noise. This work extends the existing knowledge of sound propagation to such areas by a scale model study, rather than by model calculations. The scale model study was executed for two parallel urban canyons at a 1 to 40 scale, with a point source located in one canyon. Cases with acoustically hard facades and absorption and diffusion facade treatments were in vestigated. To correct for excess air attenuation of the measurements, a wavelet-based method has been applied. The measurement results in the shielded canyon show that, in contrast to the directly exposed street canyon, the levels and the decay times are quite constant over the length of the canyon. The energy-time curve in the shielded canyon is characterized by a rise time, which can be related to the sound pressure level. The rise times and decays can be explained by separate reflection, diffraction and diffusion processes. A closed courtyard situation enlarges the level difference between acoustically hard facades and applied facade absorption or diffusion treatments at both the directly exposed and shielded side. A comparison between measurements with two different diffusion mechanisms, horizontal and vertical diffusion, reveals that vertical diffusion yields lower levels at the shielded side compared to horizontal diffusion for the investigated situations.

Thick barrier noise-reduction in the presence of atmospheric turbulence: measurements and numerical modelling

Atmospheric turbulence causes scattering of sound, which can reduce the performance of sound barriers. This is an important inclusion in prediction models to obtain a correct picture of the sound reduction at higher frequencies. Here a prediction method is applied that uses the strengths of the wind and temperature turbulence to estimate the scattered power into the shadow zone of a barrier. The predictions are compared to full-scale measurements on a thick barrier, where both acoustic and meteorological data were recorded simultaneously under both calm and windy conditions. Comparison between the measurements and the predictions indicate that the method gives reasonably accurate results for mid to high frequencies and a slight overestimation at very high frequencies.

Wind Turbine Noise Propagation over Flat Ground: Measurements and Predictions

Noise from wind turbines is of concern in the planning process of new wind farms, and accurate estimations of immission noise levels at residents nearby are required. Sound propagation from wind turbine to receiver could be modelled by a simplified standard model assuming constant meteorological conditions, by an engineering method taking atmospheric and ground propagation conditions into account, or by a more exact model. Epidemiological studies have found a higher frequency of annoyance due to wind turbine noise than to other community noise sources at equal noise levels, indicating that the often used simplified model is not sufficient. This paper evaluates the variation of immission sound levels under the influence of meteorological variation and explores if the prediction of levels could be improved by taking the effect of wind speed on sound propagation into account. Long-term sound recordings and measurements at a distance of 530 m from a wind turbine show that the simplified standard model predicts the average sound pressure levels satisfactorily under downwind conditions, and that a more complex propagation model might not be needed for wind turbine noise at a relatively short distance. Large variations of sound immission levels at the same wind speed were however present. Statistical analysis revealed that these variations were influenced by meteorological parameters, such as temperature, static pressure and deviation from ideal downwind direction. The overall results indicate that meteorological factors influence the noise generated by the wind turbine rather than the sound propagation.

Calculation of sound reduction by a screen in a turbulent atmosphere using the parabolic equation method

Results from applying a Crank–Nicholson parabolic equation method (CNPE) are presented in situations with a thin screen on a hard ground in a turbulent atmosphere, and with the acoustic source at ground level. The results are evaluated by comparison with Daigle’s model, which uses the sound scattering cross section by Tatarskii together with diffraction theory. The results show a fairly good agreement for situations where the receiver is above ground, thus indicating that both methods are applicable to the problem. When the receiver is at ground level the two methods lead to significant differences in insertion loss since only the PE method predicts that turbulence causes an increased sound level in the case without a screen. For the situations considered in the paper a turbulent atmosphere shows a significant influence on sound reduction by screens. [This work is financially supported by the Swedish Environmental Protection Agency (SNV) and the Swedish Transport and Communications Research Board (KFB).]

Urban background noise mapping: the general model

Surveys show that inhabitants of dwellings exposed to high noise levels benefit from having access to a quiet side. However, current practice in noise prediction often underestimates the noise levels at a shielded facade. Multiple reflections between facades in street canyons and inner yards are commonly neglected and facades are approximated as perfectly flat surfaces yielding only specular reflection. In addition, sources at distances much larger than normally taken into account in noise maps might still contribute significantly. Since one of the main reasons for this is computational burden, an efficient engineering model for the diffraction of the sound over the roof tops is proposed, which considers multiple reflections, variation in building height, canyon width, facade roughness and different roof shapes. The model is fitted on an extensive set of full-wave numerical calculations of canyon-to-canyon sound propagation with configurations matching the distribution of streets and building geometries in a typical historically grown European city. This model allows calculating the background noise in the shielded areas of a city, which could then efficiently be used to improve existing noise mapping calculations. The model was validated by comparison to long-term measurements at 9 building facades whereof 3 were at inner yards in the city of Ghent, Belgium. At shielded facades, a strong improvement in prediction accuracy is obtained.

Scattering by an array of perforated cylinders with a porous core

In this work multiple scattering by an array of perforated cylindrical shells with a porous core has been investigated. A semi-analytical model to predict scattering from such cylindrical units is presented in the context of the multiple scattering theory (MST), and validated against laboratory experiments. The suggested semi-analytical multiple scattering model uses an impedance expression to include the perforated shell in the scattering coefficients, which is a compact way to describe a composite scatterer in MST. Calculation results of a small array are shown to be in excellent agreement with measured data. Predictions and data show that perforated cylinders with empty cavities exhibit a strong and narrow insertion loss peak at resonance, though simultaneously suffer from amplification below resonance. By adding porous material in the core of the scatterer adverse effects below the resonance peak were suppressed. In addition, it was found that the reduction peak broadens, though at a cost of a reduced peak amplitude. Finally, it has been shown that adding porous material in a perforated shell will introduce partial absorption of the incoming field, which can be optimized by adjusting the perforation ratio of the shell.

A model of sound scattering by atmospheric turbulence for use in noise mapping calculations

Sound scattering due to atmospheric turbulence limits the noise reduction in shielded areas. An engineering model is presented, aimed to predict the scattered level for general noise mapping purposes including sound propagation between urban canyons. Energy based single scattering for homogeneous and isotropic turbulence following the Kolmogorov model is assumed as a starting point and a saturation based on the von Karman model is used as a first-order multiple scattering approximation. For a single shielding obstacle the scattering model is used to calculate a large dataset as function of the effective height of the shielding obstacle and its distances to source and receiver. A parameterisation of the dataset is used when calculating the influence of single or double canyons, including standardised air attenuation rates as well as facade absorption and Fresnel weighting of the multiple facade reflections. Assuming a single point source, an aver aging over three receiver positions and that each ground reflection causes energy doubling, the final engineering model is formulated as a scattered level for a shielding building without canyon plus a correction term for the effect of a single or a double canyon, assuming a flat rooftop of the shielding building. Input parameters are, in addition to geometry and sound frequency, the strengths of velocity and temperature turbulence.

The 2.5D MST for sound propagation through an array of acoustically rigid cylinders perpendicular to an impedance surface

In this work a study of sound propagation through arrays of semi-infinitely long cylinders placed perpendicular to an impedance surface has been carried out. The cross sections of the structures are assumed to be invariant along the main axis of the cylinders, and the cylinders are considered rigid. It is further assumed that the structures are insonified by a monopole source placed above the impedance surface. To study such configurations, we introduce the two-and-a-half-dimensional multiple scattering theory (2.5D MST), which essentially solves the pressure in a three-dimensional domain by post-processing a set of precomputed solutions obtained in a two-dimensional domain. The total pressure can then be obtained by complex addition of four contributions: source-to-receiver, source-to-array-to-receiver, image source-to-receiver, and image source-to-array-to-receiver. The proposed method is validated using both analytical and numerical tools, showing very good agreement for all studied cases. Among other things, we show that a cylinder array placed on top of flat rigid ground can deteriorate the ground interference dips that exist without the array. In addition, we show that the characteristic response of the cylinder array, i.e. in terms of pass and stop bands, may be shifted up in frequency due to a projection phenomenon, which happens when the source or receiver is elevated along the main axis of the cylinders.