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Outdoor blast wave propagation in real environment:
statistical comparisons between simulations and
measurements
Olaf Gainville
To cite this version:
Olaf Gainville. Outdoor blast wave propagation in real environment: statistical comparisons
be-tween simulations and measurements.
Forum Acusticum, Dec 2020, Lyon, France.
pp.879-882,
�10.48465/fa.2020.0779�. �hal-03233752�
OUTDOOR BLAST WAVE PROPAGATION IN REAL ENVIRONMENTS:
STATISTICAL COMPARISONS BETWEEN SIMULATIONS AND
MEASUREMENTS
Olaf Gainville
CEA, DAM, DIF, France
olaf.gainville(at)cea.fr
ABSTRACT
Outdoor blast wave propagation is affected by numerous physical parameters such as source energy, topography, ground nature or atmospheric conditions. Part of these ef-fects are deterministic and well explained using numeri-cal simulation. A wide angle parabolic equation code with Arome meteorological data and IGN topography is used to model waveform signatures up to 20 km for 300 kg ex-plosion. These waveform signatures are uncertain due to random nature of the medium, which is not included in the model. To quantify this uncertainty and validate the model, comparisons between simulations and measurements are performed for numerous blast wave records of well cali-brated ground explosions. A metamodel of the maximum overpressure is proposed.
1. INTRODUCTION
The study of outdoor propagation of blast waves is mainly motivated by the evaluation of overpressure annoyance [1] and the characterization of explosions [2,3]. The character-ization of low frequency sources from measurements at lo-cal distance, typilo-cally up to few kilometers, is particularly important to validate the ability of yield estimation from long range infrasound detection [4]. For example, volcanic eruptions are repetitive infrasonic sources, for which en-ergy is unknown and can be evaluated from local acoustic records [5].
The outdoor propagation is affected by numerous phys-ical phenomena between the source and the receivers lo-cated few kilometers away. In the near field of the ex-plosion, where strong shock nonlinearities dominate, the blast wave signature mainly depends on the source energy and the topography. Due to the spherical divergence of the wavefront, the amplitude of the blast wave decreases rapidly to reach the weakly nonlinear and linear propaga-tion regime where topography, ground nature and atmo-spheric conditions effects dominate. For a repetitive source located in a given site, variations of the blast signatures be-tween explosions depend on atmospheric temperature and wind profiles. Despite the fact that all these phenomena are well known, quantitative relationship between blast wave signatures and local weather conditions are not well estab-lished. Moreover, the random nature of the atmosphere implies an uncertainty on the blast wave amplitude predic-tion.
In the literature, several experiments where performed to calibrate atmospheric effects on blast wave maximum overpressure. These experiments consist of single or few large explosions with yield higher than 200 kg [2, 4, 6] or large databases essentially composed of small explosions of a few kilograms [7, 8]. We built a database composed of 600 explosions, with yields ranging from 300 to 500 kg, over 3 years, uniformly sampled over weeks.
A simple propagation model of blast wave including to-pography, temperature and wind is used to perform com-parisons with measurements. After the description of the blast wave database, the main elements of the propagation model are presented. A comparison is performed for the station located at 4200 m away from the source.
2. BLAST WAVE RECORDS
The neighborhood of an industrial pyrotechnic site, where open-air explosions were performed, was instrumented during three years with acoustic microphones [9–11]. The source is generated by the explosion of Ammonium Nitrate Fuel Oil (ANFO) with equivalent TNT weight of 300 kg to 500 kg (eq. TNT). The ANFO weight of each explo-sion is known and blast wave measurements at 300 m al-low to check source variations. The database is composed of approximately 6000 acoustic signatures associated with 600 explosions and dispatched on 16 recorded sites. The source is located in a canyon of approximately 1500 m width, surrounded by hills of 300 m height, which shapes a natural acoustic screen against blast annoyance.
We focus this study on the MASR station located 4200 m eastward of the source [10]. The blast wave max-imum overpressure p2is both a standard annoyance
indi-cator and an explosion energy estimator when the distance to the source is known. To remove the main atmospheric pressure effect and the main source energy variation, the scaled maximum overpressure is defined as p2R/p0R0,
where p0is the sea level atmospheric pressure, R is the
re-ceiver distance and R0is the blast wave radius. This radius
is defined from the source energy E0in Joules by the
rela-tion R0 = (E0/p0)1/3. For a 300 kg explosion at ground
level at standard atmospheric pressure, the blast wave ra-dius R0 equals 29 m. Detailed analysis of the database
shows that scaled maximum overpressure is not correlated with the source energy [12]. In Fig. 1, the scaled maxi-mum overpressure measured at MASR for the 600
explo-sions is represented as a function of the zonal wind speed measured 2 m above the ground. The maximum ampli-tude significantly depends on the atmospheric condition. For the downwind propagation, when the wind blows at ground level in the propagation direction, the amplitude is generally higher than in the upwind case. The scattering of measured maximum overpressure is smaller for upwind propagation than for null and positive wind speed. Down-wind, blast waves mainly follow the ground, like creeping waves, with low dependency on wind profile variations. In the wind direction, blast wave amplitude significantly de-pends on the vertical wind gradients in altitude, indepen-dently of ground wind speed. Strongest recorded ampli-tudes are associated with both low ground wind speed and high wind speed in altitude. The planetary boundary layer rises during the morning and induce strong variation of the scaled maximum overpressure for a day. However, no sta-tistical correlation with the hour of the day is established. This is shown by the color on Fig. 1.
To forecast the annoyance around a pyrotechnic site, the ability of blast propagation model to reproduce strongest amplitudes should be analyzed. Additionally, to evaluate the source yield, the uncertainty of the propagation model should be quantified. These tasks are initiated using our measurements for the simple propagation model described below.
Figure 1. Scaled maximum overpressure p2R/p0R0 as
a function of the wind speed in the receiver direction for the recorded blast wave at the MASR station. The color indicates the hour of the day (UT).
3. SIMPLE BLAST WAVE PROPAGATION MODEL Blast wave propagation in the atmosphere is accurately modeled by direct numerical resolution of Euler’s equa-tions [10, 13, 14]. However, these methods have a compu-tational cost often not compatible with the statistical
analy-ses. The parabolic approximation allows to reduce this cost with an acceptable error [15]. We use a classical wide an-gle linear parabolic model taking topography into account as proposed in [15]. The transition between the nonlinear near field and the linear far field was studied in [15]. Due to nonlinear interaction with the topography, the error of the linear parabolic model may reach 30% compared to direct numerical solution used as reference.
The topography is given with a 25 m resolution step [16]. Two dimensional axi-symmetric propagation is also assumed. Additionally to the propagation model, the meteorological condition of each event should be de-fined. Arome model weather forecast are available for France [17]. However, the horizontal resolution is 0.025◦, approximately, 100 times lower than the 25 m topography resolution. The physical, topography compliant, interpola-tion method of meteorological data used in [10,15] is again too long for statistical studies. Here, the vertical temper-ature profiles and wind profiles obtained with the Arome model at the source are used over the entire domain. No surface wind layer corrections, nor flow circulation correc-tions are applied around hills.
The propagation is simulated up to 5 km at a frequency of 30 Hz for a signal duration of 8.5 s. The simulation of one event is less than 30 s@4PE. Each recorded event of the database where simulated using the closest hour of the meteorological Arome simulation.
4. FIRST COMPARISON BETWEEN MEASUREMENTS AND SIMULATIONS In Fig. 2, the scaled maximum overpressure simulated is compared with that measured. Despite large discrepan-cies of results, the mean dependence between measure-ments and simulations (red dashed line) is relatively unbi-ased. The statistic distribution of measured and simulated overpressures are relatively close, with means of 0.066 and standard deviations of 0.0009 and 0.0005 respectively. This shows that a simple model is enough to perform mean statistical blast wave annoyance studies.
However, the model is not able to forecast the maximum overpressure for a given hour. The scattering of the model error (cf. Fig. 3) has the same range as the data, with a vari-ance of 0.0005. The model error follows a normal distri-bution in contrast with the log-normal distridistri-bution of mod-eled and measured maximum overpressures. The model underestimates higher measured maximum overpressures (red squares on Fig. 3) and over estimate lower values (blue squares). This result can be explained, on one hand, by the lack of variance of the meteorological model which does not include small scale structures, on the other hand, by the low frequency used in the propagation model.
5. CONCLUSION
The simulation of blast wave propagation in a complex en-vironment remains a difficult task, mainly because of the interaction of the wind with the topography. First compar-ison between a fast and simple model and numerous
maxi-Figure 2. Scaled measured maximum overpressure p2R/p0R0as a function of the modeled one at the MASR
station. The color indicate the wind speed at ground level in the receiver direction.
mum overpressure measurements shows that the statistical distribution is well simulated, but the model error for each individual event can be large.
Accuracy of the model can be increased by taking into account nonlinear effects between the source and 500 m, improving temperature and wind interpolation and defin-ing a wind profile compliant with the topography. Finally, due to the topography of the instrumented site, three di-mensional effects should be investigated.
Uncertainty of the source, of the atmosphere (turbu-lence) and of the ground (small scales) will be established and included in the model. This will allow to quantify the uncertainty of the full model.
6. ACKNOWLEDGMENTS
Numerical part of this work contribute to the Pro-longe project supported by the French Agence Nationale de la Recherche (ANR) and the Direction G´en´erale de l’Armement (DGA) under reference ANR-12-ASTR-0026. Present results are obtained within the frame of LETMA (Laboratoire ETudes et Mod´elisation Acous-tique), Contractual Research Laboratory between CEA, CNRS, Ecole Centrale de Lyon, C-Innov and Sorbonne Universit´e.
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Figure 3. Model error for the scaled measured maximum overpressure p2R/p0R0at MASR. The difference between
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