Numerical simulations of sonic boom propagation over urban areas

Didier Dragna1 1 , Ariane Emmanuelli, Sébastien Ollivier, Philippe Blanc-Benon Univ Lyon, Ecole Centrale de Lyon, CNRS, UCB Lyon 1, INSA Lyon, LMFA, UMR5509, 36 Avenue Guy de Collongue, F-69134, Ecully, France

ABSTRACT Acceptability of supersonic transportation by population requires an accurate prediction of ground noise levels generated by sonic boom. This study aims at predicting sonic boom propagation over urban areas. For this purpose, numerical simulations are performed; the full 2D Euler equations are solved using high-order finite-di ff erence time-domain techniques. First, the case of an isolated building is considered. From a geometrical analysis, two characteristic zones are highlighted: an illuminated region in front of the building and a shadow zone at its rear. The sonic boom waveforms at the ground are composed of several arrivals, related to reflection at the building facades and di ff raction at the building corners. The evolution of the noise levels is then shown to follow closely the geometrical analysis, with an amplification in the illuminated region and a large reduction in the shadow zone. Second, the case of two identical buildings is investigated. The acoustic field inside the street canyon is examined. In particular, the boom waveforms exhibit low-frequency oscillations, in addition to the geometrical arrivals. They are related to resonant modes of the canyon. Finally, an urban geometry representative of European city centres is considered. The variability of the boom waveforms and the noise levels is shown.

1. INTRODUCTION

With the aim of designing quieter supersonic civil aircraft, research is underway on low-boom design. In addition, acceptability of low booms by the population should be investigated in a near future [1]. This motivates the improvement of prediction schemes for sonic boom at the ground. In particular, it is important to consider the modification of the boom signature in an urban environment. While sonic boom reflection over an isolated building has been studied analytically [2], experimentally [3, 4] or numerically [5,6], the case of multiple buildings has not been examined thoroughly. In order to investigate sonic boom reflection over urban areas, the authors have performed recent numerical studies. For that, based on the work of Emmanuelli et al. [7], the 2D Euler equations have been solved using high-order finite-di ff erence schemes [8]. In a first study [9], academic configurations have been examined. An isolated building has been first considered as the reference case. Then, reflection over two buildings and over a series of identical buildings has been analyzed. In a second study [10], sonic boom reflection over realistic urban configurations has been considered. For this purpose, ten urban geometries have been generated, based on the classification LCZ on urban forms [11]. Two main conclusions have been obtained. First, the main parameter at play is the aspect

1 didier.dragna@ec-lyon.fr

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ratio of the urban canyon, i.e. the ratio of the building height to the street width. Thus, for small aspect ratios, referred to as open geometries, the reflection of the boom over the urban area is similar to that over an isolated building. The noise levels are thus large in front of the building (with an increase of + 7 PLdB compared to the flat ground case) and significantly reduce in the shadow zone at their back. For large aspect ratios, referred to as compact geometries, multiple reflection occurs on the building facades in the street canyons. The noise levels tend to become more homogeneous. Second, oscillations, that slowly decay with time, are noticed at the tail of the waveforms in the street canyons. As a consequence, the duration of the boom signature is largely increased. These oscillations have been shown to be related to resonant modes of the street canyons. This paper presents some results for one of the ten urban geometries, considered in [10], namely LCZ 3 also referred to as "compact lowrise". This geometry corresponds to closely spaced buildings of 1 to 3 floors and can be found in densely populated urban areas. The paper is organized as follows. Sec. 2 summarizes the numerical methods used and details the configuration considered. Results for the urban geometry LCZ 3 are exemplified in Sec. 3. Concluding remarks are given in Sec. 4.

2. METHODS AND CONFIGURATION

2.1. Methods Numerical simulations are performed to study sonic boom reflection over urban areas. The 2D Euler equations are solved using high-order finite-di ff erence time-domain techniques [8]. A moving frame, that follows the aircraft, is implemented to reduce the computational cost. The solver including numerical methods and boundary conditions is described in details in Emmanuelli et al. [7]. Simulations have been carried out in [10] for a N-wave and a low-boom wave. For conciseness, results are shown thereafter only for the N-wave. Its peak overpressure is equal to 25 Pa and its duration is 0.15 s. The flight Mach number is M = 1 . 6.

2.2. Configuration The urban geometry has been defined, according to the LCZ (local climate zone) standard [11]. It aims to represent densely populated areas, with closely spaced buildings of 1 to 3 floors, which are labelled as LCZ 3. The urban geometry is made of 40 buildings, whose heights are between 3 and 10 m and widths between 10 and 15 m. The street widths are between 5 and 10 m. The aspect ratio, defined as the ratio of the mean building to the mean street width, is about 1. For the Mach number considered, this value corresponds to a compact geometry [10]. The geometry is sketched in Fig. 1. Note that the atmosphere is homogeneous and at rest.

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Figure 1: Urban geometry LCZ 3.

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2.3. Numerical specification The computational domain is 800 m long and 200 m high. The mesh is uniform in the x - and z - directions. The mesh size is set to 0.05 m in order to ensure that the noise levels are accurately calculated [7]. The number of points is equal to 64 millions. The Courant–Friedrichs–Lewy number is set to 0.31. 70 000 time iterations are performed, corresponding to a simulation time of 1.8 s. The total CPU time is about 8000 hours.

3. RESULTS

A snapshot of the acoustic pressure is shown in Fig. 2. The N-wave is propagating from the right boundary. The boom reflected on the ground appears di ff use, as di ff racted waves are generated each time that the boom impinges on a building.

Figure 2: Snapshot of the acoustic pressure, showing the reflection of an incident N-wave over the urban geometry. The color scales are between -50 and 50 Pa, from gray to red.

Figure 3: Examples of waveforms inside three canyons.

Examples of waveforms inside three canyons are shown in Fig. 3. They are plotted as a function of τ = t − t 0 , where t is the time and t 0 is the arrival time. The waveforms appear very di ff erent from each other. Thus, the peak overpressure is equal to 40 Pa in canyon A. This is smaller that the value obtained on a flat ground (the peak pressure would be equal to 50 Pa, because of the pressure doubling due to perfectly reflecting ground surface). On the contrary, the peak overpressure in C is of 60 Pa. Finally, in B, the peak overpressure is very large, with a value of 120 Pa. In addition, the signal after τ > 0 . 2 s is significantly di ff erent for the three canyons. In B, low frequency oscillations, which have a large amplitude (almost 10 Pa at τ = 1 s) and which decay slowly with time are observed. In C, oscillations are also noticed but their period is significantly smaller than for B and their amplitude

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0 0.2 04 0.6 Ts 08 12

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decreases much faster. Finally, in A, no clear pattern can be distinguished. The variability of the waveforms in the street canyons echoes the results obtained in [10] for another compact geometry, namely LCZ 2. Note that for an open geometry, it was exemplified in [10] that the variability is largely reduced. The variation of the peak pressure along the ground is examined using the intensity factor. It is defined as the ratio of the peak overpressure on the ground to that of the incident boom. The intensity factor is plotted along the ground in Fig. 4. It is equal to two su ffi ciently far from the buildings, which is the value expected above a flat perfectly reflecting surface. In most of the canyons, the intensity factor is larger than two and can reach locally values up to 5, as in canyon B. There are some canyons in which the intensity factor can be smaller than two, such as canyon A: this occurs when the left building of the canyon is su ffi ciently higher than the right building to create a shadow zone in the canyon [10].

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Figure 4: Evolution of the intensity factor along the ground.

Finally, the noise levels are plotted along the ground in Fig. 5. They are computed using the Stevens’ Mark VII perceived level (PL) [12]. For comparison, the noise levels are shown relative to the flat ground case. The noise levels are between -8 and + 8 PLdB. For most of the canyons, the noise levels are below those for a flat ground case in the left part of the canyon but higher in the right part (see canyon C). For some canyons, they are however everywhere smaller, such as canyon A, or mostly greater, such as canyon B.

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Figure 5: Evolution of the noise levels (relative to the flat ground case) along the ground.

4. CONCLUSIONS

Sonic boom reflection over an urban geometry has been exemplified for one of the ten configurations studied in [10]. More specifically, a compact urban geometry has been considered. It has been shown that the variability of the boom signature is significant for a compact geometry. Thus, the peak overpressure can vary with a factor of two and a half, depending on the position in the urban geometry. Similarly, the noise levels inside street canyons can increase or reduce, compared to the flat ground

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case. Finally, low frequency oscillations associated to the canyon resonances have been noticed in the waveforms. Their frequency, amplitude and time decay rate were shown to vary largely depending on the canyon considered. The detailed analysis for the ten representative urban geometries is presented in [10]. Future work will consider three-dimensional e ff ects, that can be important for buildings of finite size. In addition, micro-meteorological e ff ects on boom propagation inside street canyons will be investigated.

ACKNOWLEDGEMENTS

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement N ◦ 769896 (RUMBLE). This publication reflects only the author’s view and the Innovation and Networks Executive Agency (INEA) is not responsible for any use that may be made of the information it contains. It was performed within the framework of the LABEX CeLyA (ANR-10-LABX-0060) of Université de Lyon, within the program “Investissements d’Avenir" (ANR-16-IDEX-0005) operated by the French National Research Agency (ANR). This work was granted access to the HPC resources of PMCS2I (Pôle de Modélisation et de Calcul en Sciences de l’Ingénieur et de l’Information) of Ecole Centrale de Lyon, PSMN (Pôle Scientifique de Modélisation Numérique) of ENS de Lyon and P2CHPD (Pôle de Calcul Hautes Performances Dédiés) of Université Lyon I, members of FLMSN (Fédération Lyonnaise de Modélisation et Sciences Numériques), partner of EQUIPEX EQUIP@MESO and IDRIS (Institut du Développement et des Ressources en Informatique Scientifique) under the allocation 2020-02203 made by GENCI (Grand Equipement National de Calcul Intensif).

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