NUMERICAL MODELS FOR NOISE PREDICTION NEAR AIRPORTS

Transcription

1 Philippe JEAN 1 NUMERICAL MODELS FOR NOISE PREDICTION NEAR AIRPORTS Abstract Ph. Jean, J.-F. Rondeau, D. Van Maercke Centre Scientifique et Technique du Bâtiment 24 rue Joseph Fourier St Martin d Hères, France jean@cstb.fr The problem of numerical prediction models for airport noise is addressed. Outdoor sound propagation can be studied with the ray tracing program MITHRA coupled to the INM database. An original approach; named GRIM, aims at the prediction of noise inside dwellings by means of the use of complex outdoor Green functions within a Rayleigh-like integral representation. INTRODUCTION The increase of air traffic leads to a greater concern for related noise problems. In France, for instance, a noise tax is collected for each aircraft mouvement and used to subsidize the protection of nearby dwellings. In order to use efficiently this money it is essential to develop new prediction methods, both for the outdoor propagation effects as for the estimation of sound insulation of facades. In order to optimise solutions, noise should be predicted not only in front of the facades but also inside the lodgings. Many effects that are neglected in conventionnal prediction models such as INM should be taken into account: ground effect, meteorological conditions, long distance propagation, multiple reflections and diffraction on facades. At CSTB, these effects have been studied for a long time using several distinct models. Research models include FFP (Fast Field Program), GFPE (Parabolic Equation) and METEO-BEM (Complex Green functions which include meteorological aspects). For engineering tasks, ray tracing algorithms are more appropriate because they need less computing power. Recently, the MITHRA software has been extended to include aircraft noise. This will be developed in the first part of this paper. In order to predict noise inside dwellings, an original integral representation coupled with geometrical estimations of the outdoor Green functions has been developed under the name GRIM (Green Ray Integral Method). Detailled information and results of this approach will be given in part two of this paper.

2 Philippe JEAN 2 PART I : MITHRA COUPLED WITH INM Conventional prediction models for aircraft noise INM can be considered a wordwide reference for the noise mapping around airports. On input, it used Noise Power Data (NPD) curves for the prediction of emission levels and propagation losses in the free field, lateral directivity and ground effects are calculated using the SAE-AIR 1751 [1] recommandation. For non straight file paths or changes in thrust, speed, climb, a segmented method is used and the contribution of each segment is estimated assuming a cos² directivity in the vertical plane [2]. INM is basically written for noise contour calculations. For the purpose of more detailled acoustic studies such as the prediction of real exposure levels, sound insulation prescription,etc.., the model is to simple and many implicit hypotheses are hidden from the user : the receiver is suposed to be at 1.2 m above an acoustical soft ground, the aircraft must be in view (no shielding), the NPD curves are derived from measurements without wind or temperature gradients, The INM model only produces global db(a) levels. Because SAE- AIR 1751 is based on measurements dating from the 80, a revision of the model is now being undertaken, taken into account more realistic spectral data for modern aircraft [3]. Mithra software and NMPB propagation model MITHRA software was first developed in the late 80 for the prediction of road and railway traffic noise [4,5]. From the start it was based on a clear physical separation of source emission, described in terms of sound power, directivity and spectral contents in octave bands and propagation attenuation. MITHRA uses an inverse ray-tracing technique : a 360 sweep of rays is emitted from the source and any combination of reflection and diffraction from vertical obstacles taken into account during propagation till a line source is hit. From this 2 dimensionnal path a three dimensionnal cross section is constructed for the acoustical part of the calculation, taken into account spherical divergence, air absorption, excess attenuation by diffraction, ground reflection, etc Meteorological conditions (wind and temperature gradients) were introduced from the middle of the 80 [6,7] and gave way to a new official prediction method used in France : NMPB (New French calculation method including meteorological effects), which is now being transformed to a National Standard [8,9]. The basis of the method is to calculate the sound propagation attenuation for two different meteorological conditions : neutral (no wind, nor temperature gradient) and favorable (moderate down wind or thermal inversion at night) ; unfavorable conditions (e.g. in the shadow zone) were considered too difficult to predict and assimilated to neutral conditions. For 50 different stations covering France, the frequency of occurrence p F (θ) of favorable conditions, as yearly averaged values, were established as a function of the direction of propagation. The long term averaged attenuation is then calculated as the weighted attenuation over favorable and neutral conditions ; the direction of propagation θ depending on each individual ray : av ATT /10 ATT /10 ( p (θ ) 10 F + (1 p (θ )) 10 H ) ATT = 10 log (1) F F

3 Philippe JEAN 3 Coupling of Mithra software with INM databases In 1999, DGAC (General Direction of Civil Aircraft) asked CSTB to introduce aircraft noise into the Mithra software. As there is a clear distinction between source emission and propagation, the only problem we had to tackle was the emission part. It was decided to use INM s database and flight path calculator to produce the necessary input data. Mithra reads in these data from the «flight.pth» file produced by INM and does the following operations : 1. For each ray that hits a flight segment INM s algorithm is applied : NPD interpolation, speed correction, lateral attenuation, etc In this calculation only distance to the segment and slant angle are used. This gives us the L p,inm value. Comparaisons showed that our ray model approach reproduced the same results as INM within a +/- 0.5 db(a) range. 2. The NMPB method is used to estimate the attenuation from the source to the receiver under the same circumstances as assumed in INM : flat ground, no obstacles, receiver at 1.2m above a soft ground, no wind nor temperature gradients. This calculation gives us ATT INM. 3.Then the real attenaution from the same source to the real receiver is calculated using the full NMPB method (true receiver height, reflections from surrounding buildings, masking by buildings and terrain, ground effect, meteorological effects, ) ; which gives us ATT NMPB. 4. Finally, the corrected sound level is obtained by : L p,nmpb = L p,inm + ATT INM ATT NMPB. Because of the lack of spectral information in the INM database, the calculation of ATT INM and ATT NMPB are carried out in db(a) for a hypothetical point source with a pink noise spectrum and a cos² directivity. This approach can easily be improved when INM s Technical Manual version 6.0 will become available. Many usefull tools are provided inside Mithra software to help airport authorities in their usual tasks : level versus time histories, SEL and L Amax levels can be calculated for each individual flight, different operating modes can be compared, noise mapping can be done in the horizontal or vertical plane or for individual receivers. Automatic placement of receiver areas around buildings provide immediate information for the calculation of exposed populations,etc Benefits and practical use Modern simulation techniques, based on physical modelling of sound emission and propagation effects, including screening, reflections, ground and meteorological effects have now become possible on low-price PC equipment within reasonable computation time (on average 1 sec/receiver on a Pentium III 800 MHz). For land use, zoning and strategical planning these models can take into account the relief, the effective receiver height, shielding by relief and the nature of the ground (from very hard surfaces like water to very soft ground in forest areas). For local problems, like the instruction of complaints or urban planning, excess levels due to extra reflections from hard ground and surrounding buildings can be taken into account, using the same model and the same input data. Coupling of Mithra-Air with GIS systems provide fast input of accurate terrain modelling and positionning of buildings and screens ( 1m precision). On output, GIS systems can be used for noise mapping presentations and for the estimation of the exposed poupulations at different levels of precision : from number of habitants per km² to number of habitants per m² of facade. Identification of the most exposed facade and the presence of a relatively quiet façade can easily be identified.

4 Philippe JEAN 4 Future resarch and improvements of the model CEAC and FAA have engaged cooperation on better prediction models and/or the use of true radar data for flight path simulation ; lateral dispersion of tracks seems to be a particuliar point of interest. It has been proposed to create a common database for european and american aircraft, under control of ICAO. Within this database, spectral data and more realistic 3 dimensional directivity patterns should be included. With this information the accuracy of the model can be drastically increased, as compared to the conventionnal NPD based methods. Separation of subsources for engine noise (as a function of thrust setting) and aerodynamic noise (mainly a function of speed) can provide an important improvement for the prediction model for landing and ground operations. Taking into account the combined effect of weather on aircraft performance and propagation conditions, an import increase of accuracy for the predicted long time averaged indicators such as L DEN and L NIGHT can be espexcted. PART II : THE GRIM APPROACH Geometrical approaches can deal efficiently with outdoor sound propagation problems whereas integral representations can represent coupled vibro-acoustic problems. The GRIM approach has been presented in several papers and conferences [10,11] and an original field of application is considered in this paper. Applying the GRIM method to sound insultation problems consists in using, in the integral representation of an acoustical field, a complex Green functions which is computed by means of a ray tracing program or the like. If we consider the case of an outdoor noise source at position S and a receiver point M inside a lodging we first consider the reciprocal problem and write that the pressure at S due to a source at M can be written as: P(M) = jρω V(Q).G (M,Q).dS(Q) t(m) (2) S V V + where V(Q) is the velocity of the outer window pane S V and G V (M,Q) is the Green solution between M and S V when S V is assumed perfectly rigid. G V includes all outdoor effects ; t(m) accounts for the contribution of other sources. It is also assumed that the velocity V can be obtained from a decoupled problem consisting only of a room and a window. This has been numerically verified. In practice, V can be measured, using a laser velocimeter. It can also be computed by means of a modal approach or by a finite element program, the former being more interesting in terms of computation time and the latter in terms of complex geometries. This approach renders possible the study of complex situations with reasonable computation times. The estimation of V needs only be carried once and a database consisting of sets of precollected spectra can be employed rapidly in different situations where only the estimation of G V needs to be done. An alternative consists in generalising the GRIM approach [12] where the sound pressure behind a transmitting structure, placed between domains 1 and 2, can be expressed as following :

5 Philippe JEAN 5 P( R) = jωρ G2 ( M, R) G1 ( Q, R) Y12 ( Q, M ) ds1 ( Q) ds ) 2 ( M (3) S2 S1 where G 1 and G 2 stand for Green functions on both sides of the partition (the window in our case) and Y 12 represents the transfer mechanical mobility across the structure. This formalism offers several advantages. Using a finite element model limited to the partition will permit computations to medium or high frequencies. The Y 12 functions must be computed for all pairs of points between both sides of the structure and the calculation of (3), can be optimised [12]. Also, there is no need to study the reciprocal source/receiver problem and G 1 can contain atmospheric information as well as geometrical reflection/diffraction effects. When dealing with double glazing, Y 12 must be evaluated for both sides of an isolated window. A first validation example is presented in Figure 1. It corresponds to a 2D problem where the sound pressure inside a room on top of a 4 story building if first computed by a fully coupled 2D BEM/FEM program [13,14] and then by means of equation (2) where the velocity is computed for an isolated room + window cell. The window is made of a 1 cm thick glass. Note that in this first example, the facade is plain without balconies. The agreement between reference and GRIM calculations if excellent in this simple situation. Note that all figures are represented as 1/12 octave spectra. Source positions S are given with reference to caption in Figure 1. Projected roof Figure 1. Pressure level inside the top room. S at (500,1500). Adding a projected roof appears to be equivalent to adding a noise barrier with the hope of shielding noise coming from above the building. Such a device has been found effective only for upper lodgings or houses when the aircraft is on the other side of the receiving room. It can be worth considering for rooms positioned on the quiet side of

6 Philippe JEAN 6 buildings with respect to flying trajectories. Figure 2 represents the reduction of noise that can be expected for such a situation, for a plane at an angle of 30 degrees relative to the ground, computed both with FEM/BEM and with GRIM. Reductions up to 10 db can be expected between 500 and 1000 Hz, for this type of projected roof. Above 1200 Hz (critical frequency of the window) the roof leads to an increase of pressure levels inside the room. Although the G.V product for a given point on the window and a given frequency is less with the roof, the integrated GV product is higher. The projected roof leads to less grazing incoming waves on the window, which if they were plane waves would lead to less transmission. However in this very particular case the edge of the roof acts as a close point source which generates irregular phase pattern on the window as produced by cylindrical waves. Balcony effect Figure 2. Efficiency of a 50 cm-long projected roof. S at (500,1500). The vibrating surface S V considered in (2) needs not be a proper vibrating structure but may be any vibrating surface such as an opening. When modelling a balcony with GRIM, the user may either include the balcony in the computation of the outside G V function or, which is simpler, estimate the velocity on the balcony opening and then replace the opening by a rigid surface to compute G V. However, in order do adopt the second approach, one needs to include the balcony in the model used to estimate the velocity on S V. The balcony + room problem is dealt with in two steps and consists in separating both parts of this geometry. First, the velocity of the window is computed, as previously, using either a finite element or a modal approach for the room + window system (or eventually measurements). The balcony is modelled by combining a modal description in the plane parallel to the window and a wave analysis across the balcony. Boundary conditions are then written, first on the window (known velocity), on the back wall or on the balcony (rigid or with a known impedance) and then on the opening itself by equating the internal pressure at selected points with the outer Rayleigh integral (similar to equation (2) expressed in terms of internal velocities. Figure 3 illustrates this approach. A comparison of a reference FEM/BEM calculation is made with a GRIM calculation for the three possible approaches (a) the Green function includes propagation inside the balcony, with mediocre agreement (b) with an exact velocity

7 Philippe JEAN 7 on the opening estimated with BEM/FEM, G V being evaluated outside the balcony and (c) where the outer velocity at the balcony opening is estimated as described above. Both Figures 3b and 3c show a good agreement with the exact calculation. Figure 3. Sound pressure level with balcony. Source S at (-200,200). Nearby building The next effect considered is the influence of a nearby building which can either acts as a barrier or as a reflector depending on the position of the aircraft. This effect is showed in Figure 4 for three different positions of an aircraft: (i) behind a pair of buildings (shielding effect), (ii) directly above, and (iii) in front of the receiving building (amplification effect) where the influence of the added building is plotted (level with level without the added building). In this last case (iii), adding five cm of mineral wool (iv) on the facade facing the window (thick curve) seems effective above 300 Hz. Similar noise reductions have been obtained when the aircraft is on the other side. Figure 4. Effect of a nearby building. Different source positions S.

8 Philippe JEAN 8 CONCLUSION New tools are required to efficiently predict noise around airports. A coupled MITHRA/INM program appears to be a significant improvement from the conventionnal INM approach since it includes both meteorological and building effects. The GRIM approach, on the other end, shows good promise for the assessment of noise inside dwellings and can therefore be considered as a new step towards a general prediction model. ACKNOWLEDGMENTS Part of this wok has been funded by ADEME (Agence de l Environnement et de la Maitrîse de l Energie), ADP (Aéroports de Paris) and by DGAC (Direction Générale de l Aviation Civile). REFERENCES 1. Society of Automotive Engineers, Prediction Method for Lateral Attenuation of Airplane Noise during Takeoff and Landing, SAE-AIR 1751, March Federal Aviation Administration, INM Version 5.2 Technical Manual, Annex D (1998). 3. G.G. Fleming, Updated lateral attenuation in FAA s Integrated Noise Model, Proceddings INTERNOISE Nice, (2000). 4. Y. Gabillet, M. Rosen, A simple algoritmh to determine Acoustic paths between a receiver and complex noise sources, Proceedings INTER-NOISE, Avignon, vol. 3, (1988). 5. Y. Gabillet, D. Van Maercke, Outdoor noise propagation in urban areas : principles and use of the Mithra Software, Proceedings EURO-NOISE, Lyon, vol 1, (1995). 6. Y. Gabillet, F. Bonfil, A. L Espérance, J. Colard, Traffic noise propagation under the influence of wind and temperature gradients, Proceedings INTER-NOISE, Leuven, (1993), 7. J. Defrance, Y. Gabillet, A new analytical method for the calculation of outdoor noise propagation., Applied Acoustics 57, (1999). 8. CERTU, CSTB, LCPC, SETRA, Road traffic noise, New French calculation method including meteorological effects, expermental version 1996, road noise (1997). 9. J. Defrance, Y. Gabillet, D. Van Maercke, C. Dine, P.E Gautier, A new french method for railway noise prediction. Proceddings INTER-NOISE, Nice (2000). 10. P. Jean, Coupling integral and geometrical representations for vibro-acoustical problems, Journal of Sound and Vibration 224, (1999). 11. P. Jean, The Green Ray Integral Method applied to indoor and outdoor problems, Proceedings INTERNOISE, 28-30, Nice. (2000). 12. P. Jean, J. Roland,. Application of the Green Ray Integral Method (GRIM) to sound transmission problems, to be published in Building Acoustic (2001). 13. P. Jean, A variational approach for the study of outdoor sound propagation and application to railway noise, Journal of sound and vibration 212, (1998). 14. P. Jean, The effect of structural elasticity in the efficiency of noise barriers Journal of Sound and Vibration 237,1-21 (2000).