Edinburgh, Scotland
EURONOISE 2009
October 26-28
NOISE BARRIERS AND THE HARMONOISE SOUND PROPAGATION MODEL
Erik Salomons[a]
TNO Built Environment and Geosciences, Van Mourik Broekmanweg 6, 2628 XE Delft, The Netherlands
Dirk van Maercke[b]
CSTB Grenoble, 24 rue Joseph Fourier, F-38400 Saint Martin d’Hères, France
Ando Randrianoelina
TNO Science and Industry, Stieltjesweg 1, 2628 CK Delft, The Netherlands
ABSTRACT
The Harmonoise sound propagation model (‘the Harmonoise engineering model’) was developed in the European project Harmonoise (2001-2004) for road and rail traffic noise. In 2008, CSTB Grenoble and TNO Delft have prepared a detailed description of the various steps involved in a calculation with the Harmonoise model. In the course of this joint project, some elements of the model were further improved. In 2009, test calculations were performed with the model, and results were compared to results of other models. In this paper calculation results are presented for situations with noise barriers. A basic approximation of the Harmonoise model is the linearization of the sound speed profile in the atmosphere. The effect of linearizing the complex wind profile near a noise barrier is investigated by comparison with numerical calculations with a parabolicequation wave propagation model. Comparisons with the Nord2000 model are also presented.
1. INTRODUCTION
The Harmonoise sound propagation model (‘the Harmonoise engineering model’)1 was developed in the European project Harmonoise (2001-2004) for road and rail traffic noise. Further developments of the model were performed in the European project Imagine (2004-2006), including extensions of the model to aircraft noise and industrial noise. In 2008, CSTB Grenoble and TNO Delft have prepared a detailed description of the various steps involved in a calculation with the Harmonoise model. In the course of this joint project, some elements of the model were further improved.
In 2009, test calculations were performed with the model, and results were compared to results of other models, both accurate reference models and the Scandinavian Nord2000 model.2,3This work was presented at the NAGDAGA meeting in March 2009.4 Spectral comparisons were presented for sixteen test cases, and in many cases good agreement was found between Harmonoise, Nord2000, and reference models. In some cases with complex wind profiles, however, Harmonoise and Nord2000 deviated from the reference solutions.
More recently we have performed additional test calculations for larger propagation distances. The results of these calculations are presented in this article. While the results in Reference4were presented in terms of 1/3octave band spectra of the propagation attenuation, here we present results in terms of broadband sound levels generated by a passenger car driving at a speed of 100km/h.
First we give a brief overview of the Harmonoise model, including salient features such as the convex hull approach, Fresnel weighting for irregular terrain, and ground curvature to account for the effect of atmospheric refraction.
2. HARMONOISE MODEL
A detailed description of the Harmonoise model has been presented by vanMaercke and Defrance.1 Here we present a brief overview.
As usual for the modelling of road or rail traffic noise, source lines are divided into segments and each segment is represented by a central source point for the calculation of the point-to-point excess attenuation. In this study we focus on pointtopoint model comparisons.
For a point-to-point calculation, a ground profile consisting of an arbitrary number of segments is assumed. Figure 1 shows an example with three diffraction points above the sourcereceiver line. The excess attenuation is calculated as a sum of diffraction attenuations and ground attenuations. In the example of Fig.1 there are three diffraction attenuations, and four ground attenuations corresponding to the ground sections between the diffraction points.
The diffraction attenuations are calculated with a theoretical formula for diffraction by a wedge. The ground attenuations are calculated with a theoretical formula that represents a weighted average between two solutions, one for relatively flat ground and one for valleyshaped terrain. The solutions contain a coherence factor accounting for various effects resulting in coherence loss; for the model comparisons presented here we included only coherence loss due to frequencyband averaging. The solutions are sums of contributions from different ground segments, with Fresnel weights as weighting factors. A Fresnel weight for a ground segment is basically equal to the fraction of the Fresnel ellipse (see Figure 2) that is covered by the segment. Thus, a Fresnel ellipse can be considered as a measure of the (frequencydependent) ‘thickness’ of the sound ray reflected at the ground surface.
The effect of atmospheric refraction due to vertical wind speed gradients in the atmosphere is taken into account by applying a coordinate transformation (conformal mapping) to the ground vertices. In the case of downward refraction, for example, a flat ground surface is transformed into a valleyshaped terrain, as illustrated in Figure 3. This approach assumes a linear sound speed profile c=c0+ az, where c0=340m/s is the sound speed at the ground, z is the height, and a is the sound speed gradient. The linear profile is considered as an approximation of the logarithmic profile c=c0+ bln(1+z/z0), with parameters b and z0=0.1m; for the calculations presented in this article a value of 1m/s was used for parameter b. The logarithmic and linear profiles are illustrated in Figure4. The logarithmic wind profile is a realistic representation for situations with a more or less flat ground surface (although thermal gradients in the atmosphere cause deviations from the logarithmic profile). For a situation with a noise barrier, however, large deviations from the logarithmic profile occur, in particular in the recirculation region on the downwind side of the barrier. This is illustrated in Figure 5. The effects on sound propagation, and the performance of the Harmonoise and Nord2000 models, is illustrated by calculation results presented in the next section.
A description of the Harmonoise linearization approach can be found in Ref. 5. Here we reproduce the formula for the gradient a of the linearized sound speed profile:, (1)
with , , and .
Here the following quantities are used: , , , , and, where hS is the source height, hR is the receiver height, and dSR is the horizontal distance between the source and the receiver.
3. MODEL COMPARISONS
Calculations were performed for two situations, one without barriers and one with a noise barrier.First the situations are described and next the calculation results are presented.
Figure 6 shows the situation without barriers. The noise source is a passenger car driving at a speed of 100km/h, which is represented by a point source at height 0.3m. The sound power spectrum of the source was calculated with the Harmonoise emission model for road vehicles,6and is given in Table 1 (for simplicity the two point sources of the Harmonoise model at heights 0.01m and 0.3m were represented by a single point source at height 0.3 m). The ground surface is hard for r30m and absorbing for r30m, where ris the horizontal range measured from the source. Thehard ground section represents a road surface. For the absorbing ground we assumed a flow resistivity of 100kPasm2 and used the Delany and Bazley impedance model. The receiver height is 5m, and calculations were performed for receivers up to r=600m.
Figure 7 shows the situation with the noise barrier, which differs from the situation without barriers only by the presence of a 6m high noise barrier at range r=30m. Reflections from the barrier were ignored.
For the calculation of the air absorption we assumed a temperature of 15oC and a relative humidity of 80%. A-weighted broadband sound levels were calculated from 1/3octave band spectra. The sound levels represent the noise from a single car. For a situation with 100cars concentrated in a small region, for example, distant sound levels are 20dB higher.
To assess the accuracy of Harmonoise and Nord2000 results, accurate ‘Reference solutions’ were calculated with a numerical parabolicequation model for atmospheric sound propagation.7Onethird octave band spectra of the excess attenuation were derived from narrowband calculations for four frequencies per 1/3octave band (the 1/12octave band center frequencies).
Figures 8 to 11 show the results of the calculations. Figures 8 and 9 are for the situation without barriers (see Figure 6), without and with wind, respectively. Figures 10 and 11 are for the situation with the noise barrier (see Figure 7), withoutand with wind, respectively. Each graph includes a curve representing the free-field sound level (in free field, sound waves are attenuated only by spherical spreading and air absorption). The curves calculated with Harmonoise, Nord2000, and the Reference model deviate from the freefield curve due to the effects of ground reflections, screening and diffraction by the barrier, and atmospheric refraction.
Figure 8 shows good agreement between Harmonoise, Nord2000, and the Reference solution. For ranges up to about 200m the sound level is higher than the freefield level, as a consequence of ground reflections. Beyond range 200m the sound level decreases below the freefield level, as a consequence of destructive interference between direct sound and sound reflected by the absorbing ground surface.
Figure 9 shows that under downwind conditions distant sound levels are up to about 20dB higher than without wind. Two Reference solutions are included, one for the logarithmic wind profile and one for the linearized profile that was also used for Harmonoise and Nord2000. The two Reference solutions deviate considerably from each other, which implies that the linearization of the wind profile may still need further improvement.Harmonoise shows a reasonable agreement with the Reference solution for the linearized profile, while Nord2000 shows larger deviations.
Figure 10 shows that without wind sound levels behind the barrier are about 20dB lower than the freefield level. Harmonoise and Nord2000 show good agreement in this case.
Figure 11 shows that under downwind conditions the sound levels behind the barrier are higher than without wind. Most striking is the Reference solution for the rangedependent wind profile (see Figure 5), with levels that are up to 15dB higher than the solutions for the logarithmic and linearized profiles. This illustrates that large barrierinduced wind speed gradients result in large reductions of the performance of noise barriers.8Harmonoise and Nord2000 show good agreement with the Reference solution for the linearized profile. The Reference solution for the logarithmic profile shows levels that are a bit lower.
Table 1.One-third octave band spectrum LW(f) of the A-weighted sound power level used for the calculations.
25 / 50 / 100 / 200 / 400 / 800 / 1600 / 3150 / 6300f / 31.5 / 63 / 125 / 250 / 500 / 1000 / 2000 / 4000 / 8000
(Hz) / 40 / 80 / 160 / 315 / 630 / 1250 / 2500 / 5000 / 10000
41.4 / 57.9 / 73.4 / 78.4 / 86.1 / 92.3 / 96.2 / 90.9 / 83.0
LW / 48.4 / 70.5 / 74.8 / 82.2 / 87.0 / 95.3 / 95.0 / 88.3 / 79.7
(dB) / 53.1 / 75.1 / 77.0 / 84.1 / 89.8 / 96.1 / 93.5 / 85.4 / 75.8
4. CONCLUDING REMARKS
The Harmonoise propagation model is an elegant engineering model for outdoor sound propagation, and is certainly a ‘step forward’ with respect to older engineering models. Harmonoise can be applied to arbitrary terrain profiles, employing a Fresnel weighting approach that was initially based on the Nord2000 approach and was further developed and finetuned by comparison with reference solutions.
The application of a point-to-point model such as Harmonoise or Nord2000 to full calculations for complex situations in an urban environment is not straightforward. The problem in an urban environment is that we have to deal with multiple reflections and diffractions by buildings. In principle this problem can be solved by introducing image sources and image receivers, and using Fresnel weighting to account for the reduction of reflection efficiency with increasing order of reflection (due to the finite ratio of building height over wavelength).9 The challenge is to implement these ideas while keeping the model practical and efficient.
REFERENCES
1.D. van Maercke and J. Defrance, “Development of an analytical model for outdoor sound propagation within the Harmonoise project”, Acta Acustica united with Acustica 93, pp.201212,(2007).
2.J. Kragh, B. Plovsing, S.Å. Storeheier, G. Taraldsen, and H.G. Jonasson, “Nordic environmental noise prediction method. Nord2000 summary report. General Nordic sound propagation model and applications in source-related prediction methods”, DELTA Acoustics & Vibration Report, 1719/01, 2002. Available from URL:
3.G.B. Jónsson and F. Jacobsen, “A comparison of two engineering models for outdoor sound propagation: Harmonoise and Nord2000”, Acta Acustica united with Acustica 94, pp.282289, (2008).
4.D. van Maercke and E. Salomons, “The Harmonoise sound propagation model: further developments and comparison with other models”, Proceedings NAG-DAGA Conference, 2326March 2009, Rotterdam, The Netherlands.
5.IMAGINE WP4 team, “IMAGINE – Reference and Engineering models for aircraft noise sources”, report of the EU project Imagine, IMA4DR-070323-EEC-10, 23 March 2007.
6.Hans Jonasson et al, “Source modelling of road vehicles”, report of the EU project Harmonoise, HAR11TR-041210-SP10, 17 December 2004.
7.E. Salomons, Computational atmospheric acoustics, Kluwer, Dordrecht, 2001.
8.E. Salomons, “Reduction of the performance of a noise screen due to screeninduced windspeed gradients. Numerical computations and windtunnel experiments”, J. Acoust. Soc. Am. 105, pp. 287-2293, (1999).
9.J. Forssén and M. Hornikx, “Statistics of A-weighted road traffic noise levels in shielded urban areas”, Acta Acustica united with Acustica 92, pp.998-1008, (2006).
Figure 1. The Harmonoise model can be applied to arbitrary ground profiles.
Figure 2. Fresnel weighting is employed for sound propagation over heterogeneous ground. An example is shown where the Fresnel ellipse covers 80% of ground type 1 and 20% of ground type 2.
Figure 3. Illustration of the coordinate transformation to take into account the effect of atmospheric refraction. In the original system (top), the wind profile is linearized and sound rays are curved. In the transformed system (bottom), there is no wind and sound rays are straight.
Figure 4. Logarithmic wind profile (left) and linearized wind profile (right).
Figure 5. A logarithmic wind profile is disturbed in the recirculation region near a noise barrier (top). This results in a rangedependent wind speed profile, with large wind speed gradients near the barrier top, which have a large effect on sound propagation over the barrier. For engineering calculations, one may adopt a (constant) logaritmic profile (middle), or a linear profile (bottom).
Figure 6. Situation without noise barriers.
Figure 7. Situation with a noise barrier.
Figure 8. A-weighted sound level as a function of range, calculated for the situation shown in Fig. 6 without wind. / Figure 9. As Fig. 8, for wind profiles shown in Fig. 4.Figure 10. A-weighted sound level as a function of range, calculated for the situation shown in Fig. 7 without wind. / Figure 11. As Figure 10, for wind profiles shown in Fig. 5.
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