# Numerical Modeling of Formation and Rise of Gas and Dust Cloud from Large Scale Commercial Blasting

^{*}

## Abstract

**:**

## 1. Introduction

^{3}[18]. At the same time, large-scale explosions are carried out once a month. A rough estimation of the annual blast out volume of rock mass at the Lebedinsky GOK gives a value of 34 × 10

^{6}m

^{3}, and an assessment of the mass of explosives used annually is ≈37.9 × 10

^{6}kg. According to statistical reports, the total emissions of particulate pollutants to the atmosphere from all registered sources at the Lebedinsky GOK were 6.28 × 10

^{6}kg in 2017, whereas, the total emissions were 7.05 × 10

^{6}kg in 2018 [19].

## 2. Numerical Models for Describing the Gas and Dust Cloud

#### 2.1. A numerical Model of Fireball Formation (Eulerian Model)

_{cr}, the energy value increases by an amount $Q{\rho}_{dm}^{0}/{\rho}_{exp}$, where ${\rho}_{dm}^{0}$ is initial density of the detonating mixture, ${\rho}_{exp}$ is current explosive density, which exceeds ${\rho}_{dm}^{0}$, due to compression in the shock wave, and Q is the heat of the reaction. Such operation ensures total energy conservation, correct detonation velocity, and parameters after the detonation wavefront.

^{5}–10

^{10}with proximate trajectories, and accordingly, having proximate velocities, dimensions, and other characteristics. The reference number of such markers in actual calculations is 10

^{4}–10

^{5}. Dust diffusion is calculated using the Monte Carlo method. At each time step τ, the particle movement δ

**r**is defined as $\mathsf{\delta}r=u\mathsf{\tau}+j\sqrt{D\mathsf{\tau}}$, where D is the diffusion coefficient,

**u**is the particle velocity, and

**j**is a unit vector, whose direction is selected randomly.

**g**is gravitational acceleration, ${C}_{d}$ is drag coefficient. The first and second term of the right-hand side of Equation (1) combine the Stokes drag force, the predominant effect of which is experienced by the mass at low Reynolds numbers, and the drag force at high Reynolds numbers [35]. A specially designed implicit algorithm for calculating the momentum transfer [26] ensures a proper solution for both large particles which follow ballistic trajectories largely unaffected by the ambient air, and for the case of microparticles that are frozen in the gas stream. The scheme also ensures a proper particle settling limiting velocity (depending on their size) under the influence of gravity force.

#### 2.2. Numerical Model of the Rising Thermal (Navier–Stokes LES Code)

## 3. Modeling the Gas and Dust Cloud Initiated by a 500 t TNT Explosion

^{3}placed on a smooth horizontal surface of quartz. The detonation was initiated in the center of the hemisphere at the boundary between explosive material and the rock. The simulations were run using Eulerian model on an axisymmetric, two-dimensional domain. The mesh consisted of 700 cells in both radial and vertical directions. The initial cell size was 10 cm. During the process of cloud extension, the cell size was increased to 3.2 m.

## 4. The Gas and Dust Cloud Rise Initiated by a TNT Explosion

#### 4.1. The Rise of the Thermal Initiated by a 500 t TNT Explosion

#### 4.2. The Gas and Dust Cloud Rise Initiated by 1–1000 t TNT Explosion

## 5. The Size Distribution of Dust Particles

_{p}(t) is defined as the maximum radius of the cloud of particles of considered size, and its center is on the axis at a distance R

_{p}(t) from the top cloud edge. Part of the cloud below the CDP will be called a stipe of dust particles (SDP). CDP and SDP are different for particles of different sizes. As follows from the calculations, the larger the particle size, the smaller the CDP radius. Let the CDP

^{*}be the CDP with the maximum radius. The size of CDP

^{*}is determined by the transfer of passive pollution (the smallest particles) at the time the cloud rise is complete. The upper-edge height and radius of the CDP

^{*}are determined by ratios (14) and (15).

^{*}has a radius of ~700 m. The lower boundary of this volume is marked with a dotted line in Figure 11b. The cloud of particles with ${r}_{p}$ = 0.3 cm (Figure 11b, curve 6) is partially included into the CDP

^{*}during the rise; it rises to its maximum height for 3 min after the detonation, then it starts to sink, and by the time the cloud rise is complete, the particles of the said size have fallen out of the CDP

^{*}. Thus, according to our estimation, the 500 t explosion cloud cap includes particles with dimensions not exceeding 0.1–0.3 cm at the time when the cloud rises to its maximum height.

## 6. Discussion of Results and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Trubetskoy, K.N.; Galchenko, Y.P. Methodology for estimating promising development paradigm for mineral mining and processing industry. J. Min. Sci.
**2015**, 51, 407–415. [Google Scholar] [CrossRef] - Viktorov, S.D. The explosive destruction of the rock is the basis of progress in mining. Min. Inf. Anal. Bull.
**2015**, 1, 63–75. (In Russian) [Google Scholar] - Patra, A.K.; Gautam, S.; Kumar, P. Emissions and human health impact of particulate matter from surface mining operation—A review. Environ. Technol. Innov.
**2016**, 5, 233–249. [Google Scholar] [CrossRef] - Ministry of Natural Resources of Russia. State Report: On the State and Protection of the Environment of the Russian Federation in 2018; NPP “Kadastr”, Ministry of Natural Resources of Russia: Moscow, Russia, 2019; p. 844. Available online: https://www.mnr.gov.ru/docs/o_sostoyanii_i_ob_okhrane_okruzhayushchey_sredy_rossiyskoy_federatsii/gosudarstvennyy_doklad_o_sostoyanii_i_ob_okhrane_okruzhayushchey_sredy_rossiyskoy_federatsii_v_2018_/ (accessed on 30 August 2020). (In Russian)
- Rout, T.K.; Masto, R.E.; Padhy, P.K.; Ram, L.C.; George, J.; Joshi, G. Heavy metals in dusts from commercial and residential areas of Jharia coal mining town. Environ. Earth Sci.
**2014**, 73, 347–359. [Google Scholar] [CrossRef] - Gautam, S.; Kumar, P.; Patra, A.K. Occupational exposure to particulate matter in three Indian opencast mines. Air Qual. Atmos. Health
**2014**, 9, 143–158. [Google Scholar] [CrossRef] - Csavina, J.; Field, J.; Taylor, M.P.; Gao, S.; Landázuri, A.; Betterton, E.A.; Sáez, A.E. A review on the importance of metals and metalloids in atmospheric dust and aerosol from mining operations. Sci. Total Environ.
**2012**, 433, 58–73. [Google Scholar] [CrossRef] [Green Version] - Barrows, A.; Cathey, S.; Petersen, C. Marine environment microfiber contamination: Global patterns and the diversity of microparticle origins. Environ. Pollut.
**2018**, 237, 275–284. [Google Scholar] [CrossRef] [Green Version] - Zhang, Z.X. Rock Fracture and Blasting. Theory and Applications; Elsevier, Butterworth-Heinemann: Amsterdam, The Netherlands, 2016; p. 528. [Google Scholar]
- Michailov, O.Y.; Tarasenko, J.V. Golden jubilee of the iron ore giant of Russia. Gorn. Zhurnal
**2017**, 5, 15–18. (In Russian) [Google Scholar] - Silva, J.; Worsey, T.; Lusk, B. Practical assessment of rock damage due to blasting. Int. J. Min. Sci. Technol.
**2018**, 29, 379–385. [Google Scholar] [CrossRef] - Beresnevich, P.V.; Mikhailov, V.A.; Filatov, S.S. Aerology Quarries: Reference Book; Nedra: Moscow, Russia, 1990; 280p. (In Russian) [Google Scholar]
- Roy, S.; Adhikari, G.R.; Singh, T.N. Development of emission factors for quantification of blasting dust at surface. J. Environ. Prot.
**2010**, 1, 346–361. [Google Scholar] [CrossRef] [Green Version] - Adushkin, V.V.; Spivak, A.A.; Soloviev, S.P.; Pernik, L.M.; Kishkina, S.B. Environmental consequences of mass chemical blasting in open pits. Geoekologiya
**2000**, 6, 554–563. (In Russian) [Google Scholar] - Monjezi, M.; Shahriar, K.; Dehghani, H.; Namin, F.S. Environmental impact assessment of open pit mining in Iran. Environ. Earth Sci.
**2008**, 58, 205–216. [Google Scholar] [CrossRef] - Fişne, A.; Kuzu, C.; Hüdaverdi, T. Prediction of environmental impacts of quarry blasting operation using fuzzy logic. Environ. Monit. Assess.
**2010**, 174, 461–470. [Google Scholar] [CrossRef] [PubMed] - Adushkin, V.V.; Weidler, P.G.; Dubovskoi, A.N.; Pernik, L.M.; Popel, S.I.; Friedrich, F. Properties of nano- and microparticles emitted into the environment from open-pit mining of iron deposits. Geol. Ore Depos.
**2010**, 52, 373–380. [Google Scholar] [CrossRef] - Ugarov, A.A.; Ismagilov, R.I.; Badtiev, B.; Borisov, I.I. State-of-the art and future considerations on drilling-and-blasting system at plants of Metalloinvest. Gorn. Zhurnal
**2017**, 5, 102–106. [Google Scholar] [CrossRef] - Zvyagintseva, A.V.; Sazonova, S.A.; Kulneva, V.V. Analytical monitoring of the harmful effects at the Lebedinsky Mining and Processing Plant (Lebedinsky GOK) on the environment and improvement of environmental protection measures. Inf. Technol. Build. Soc. Econ. Syst.
**2020**, 1, 92–99. (In Russian) [Google Scholar] - Sairanen, M.; Rinne, M.; Selonen, O. A review of dust emission dispersions in rock aggregate and natural stone quarries. Int. J. Min. Reclam. Environ.
**2017**, 32, 196–220. [Google Scholar] [CrossRef] - Silvester, S.; Lowndes, I.S.; Hargreaves, D. A computational study of particulate emissions from an open pit quarry under neutral atmospheric conditions. Atmos. Environ.
**2009**, 43, 6415–6424. [Google Scholar] [CrossRef] - Joseph, G.; Lowndes, I.S.; Hargreaves, D. A computational study of particulate emissions from Old Moor Quarry, UK. J. Wind. Eng. Ind. Aerodyn.
**2018**, 172, 68–84. [Google Scholar] [CrossRef] - Torno, S.; Toraño, J.; Menendez, M.; Gent, M. CFD simulation of blasting dust for the design of physical barriers. Environ. Earth Sci.
**2010**, 64, 73–83. [Google Scholar] [CrossRef] - Reed, W.R. Significant Dust Dispersion Models for Mining Operations; NIOSH-Publications Disseminations: Cincinnati, OH, USA, 2005; p. 27. [Google Scholar]
- Belotserkovskiy, O.M.; Andrushchenko, V.A.; Shevelev, Y.D. Dynamics of Spatial Vortex Flows in an Inhomogeneous Atmosphere: Computational Experiment; Yanus: Moscow, Russia, 2000; p. 456. (In Russian) [Google Scholar]
- Shuvalov, V. Multi-dimensional hydrodynamic code SOVA for interfacial flows: Application to the thermal layer effect. Shock Waves
**1999**, 9, 381–390. [Google Scholar] [CrossRef] - Shuvalov, V.; Artem’Eva, N.; Kosarev, I. 3D hydrodynamic code sova for multimaterial flows, application to Shoemakerlevy 9 comet impact problem. Int. J. Impact Eng.
**1999**, 23, 847–858. [Google Scholar] [CrossRef] - Andreyev, S.G.; Babkin, A.V.; Baum, F.A.; Imkhovik, N.A.; Kobylkin, I.F.; Kolpakov, V.I.; Ladov, S.V.; Odintsov, V.A.; Orlenko, L.P.; Okhitin, V.N.; et al. Explosion Physics, 3rd ed.; Fizmatlit: Moscow, Russia, 2004; Volume 1, p. 823. (In Russian) [Google Scholar]
- Andreyev, S.G.; Babkin, A.V.; Baum, F.A.; Imkhovik, N.A.; Kobylkin, I.F.; Kolpakov, V.I.; Ladov, S.V.; Odintsov, V.A.; Orlenko, L.P.; Okhitin, V.N.; et al. Explosion Physics, 3rd ed.; Fizmatlit: Moscow, Russia, 2004; Volume 2, p. 648. (In Russian) [Google Scholar]
- Vasil’yev, A.A.; Zhdan, S.A. Parameters of a shock wave in the explosion of a cylindrical explosive charge in air. Fiz. Goreniya Vzryva
**1981**, 17, 99–105. (In Russian) [Google Scholar] - Kuznetsov, N.M. Thermodynamic Functions and Shock Adiabats of Air at High Temperatures; Mashinostroyeniye: Moscow, Russia, 1965; p. 465. (In Russian) [Google Scholar]
- Tompson, S.L.; Lauson, H.S. Improvements in the Chart D Radiation-Hydrodynamic CODE III: Revised Analytic Equation of State; Report SC-RR-71 0714; Sandia National Laboratory: Albuquerque, NM, USA, 1974; p. 121.
- Teterev, A.V. Cratering model of asteroid and comet impact on a planetary surface. Int. J. Impact Eng.
**1999**, 23, 921–932. [Google Scholar] [CrossRef] - Nigmatulin, R.I. Dynamics of Multiphase Media; Hemisphere Publishing Corporation: New York, NY, USA, 1990; Volume 2, p. 507. [Google Scholar]
- Landau, L.D.; Lifshitz, E.M. Course of theoretical physics. In Fluid Mechanics, 2nd ed.; Pergamon Press: Oxford, UK, 1987; Volume 6, p. 554. [Google Scholar]
- Zatevakhin, M.A.; Kuznetcov, A.E.; Nikulin, D.A.; Strelets, M.K. Numerical simulation of the process of levitation of a system of high-temperature turbulent thermals in an inhomogeneous compressible atmosphere. High Temp.
**1994**, 32, 42–55. [Google Scholar] - Harlow, F.H.; Welch, J.E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids
**1965**, 8, 2182. [Google Scholar] [CrossRef] - Viecelly, J.A. A computing method for incompressible flows bounded by moving walls. J. Comp. Phys.
**1971**, 8, 119–143. [Google Scholar] [CrossRef] - Lesier, M.; Metais, O. New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech.
**1996**, 28, 45–82. [Google Scholar] [CrossRef] - Hazins, V.M. Approach in Problems on floating up of high temperature thermals in stratified atmosphere. High Temp.
**2010**, 48, 402–410. [Google Scholar] [CrossRef] - Launder, B.E.; Spalding, D.B. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng.
**1974**, 3, 269–289. [Google Scholar] [CrossRef] - Anderson, D.A.; Tannehill, J.C.; Pletcher, R.H. Computational Fluid Mechanics and Heat Transfer; Hemisphere Publishing Corporation: New York, NY, USA, 1984; p. 599. [Google Scholar]
- Sreekantha, B.; Anand, S.; Ikkurthi, V.R.; Chaudhury, P.; Sapra, B.K.; Mayya, Y.S.; Chaturvedi, S. Evolution of particle metrics in a buoyant aerosol cloud from explosive releases. Aerosol Sci. Technol.
**2020**, 54, 656–667. [Google Scholar] [CrossRef] - Ivanov, B.A.; Bazilevskiy, A.T. On the fragment-size distribution of ejecta of impact craters. In Proceedings of the Lunar and Planetary Science XIV, Houston, TX, USA, 14–18 March 1983; pp. 345–346. [Google Scholar]
- Brode, H.L. The Blast Wave in Air Resulting from a High Temperature, High Pressure Sphere of Air (U); RAND Corporation: Santa Monica, CA, USA, 1956; Available online: https://www.rand.org/pubs/research_memoranda/RM1825.html (accessed on 30 August 2020).
- Rozhdestvenskiy, V.B.; Khristoforov, B.D.; Yur’yev, V.L. Influence of the Rayleigh-Taylor instability on the radiation characteristics of an explosive explosion in air. Prikl. Mekhanika Tekhnicheskaya Fiz.
**1989**, 5, 107–114. (In Russian) [Google Scholar] [CrossRef] - State Standard 4401-81: Standart Atmosphere: Parameters; Izdatel’stvo Standartov: Moscow, Russia, 1982; p. 181. Available online: https://files.stroyinf.ru/Data2/1/4294823/4294823872.pdf (accessed on 30 August 2020). (In Russian)
- Church, H. Cloud Rise from High-Explosives Detonations; Office of Scientific and Technical Information (OSTI): Albuquerque, NM, USA, 1969. [Google Scholar]
- Kansa, E.J. Time-Dependent Buoyant Puff Model for Explosive Sources; Technical Report UCRL-ID-128733; Lawrence Livermore National Laboratory: Livermore, CA, USA, 1997.
- Spidell, M.T.; Gordon, J.M.; Pitz, J.; Gross, K.C.; Perram, G.P. High speed radiometric measurements of IED detonation fireballs. SPIE Def. Secur. Sens.
**2010**, 7668, 76680. [Google Scholar] [CrossRef] - Morton, B.R.; Taylor, G.I.; Turner, J.S. Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1956**, 234, 1–23. [Google Scholar] [CrossRef] - Gualtieri, C.; Angeloudis, A.; Bombardelli, F.; Jha, S.; Stoesser, T. On the values for the turbulent Schmidt number in environmental flows. Fluids
**2017**, 2, 17. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Density isolines. The black-filled areas correspond to rock. The grey-colored areas mark the products of detonation. The dots show the distribution of dust particles. Distance in kilometers is plotted on the axes. Time after the detonation of explosive: (

**a**) 10 ms, (

**b**) 30 ms, (

**c**) 100 ms, (

**d**) 300 ms.

**Figure 2.**Temperature distribution at the initial stage of the explosion. The lighter shade corresponds to a higher temperature; white corresponds to values: (

**a**) 5300 K, (

**b**) 3300 K, (

**c**) 1900 K, (

**d**) 1200 K Distance in kilometers is plotted on both axes. Time periods corresponding to each image are the same as in Figure 1.

**Figure 3.**Dependence of the gas and dust cloud radius on time. The grey color line depicts the experimental data, black color line—the calculated data.

**Figure 4.**Time dependency of the position of the upper edge of the gas-dust cloud: 1—experimental dependence for the explosion in 1985; 2—experimental dependence of explosion in 1987; yellow rectangles show a numerical simulation of the Euler equations; yellow circles show a numerical simulation of the Euler equations in the case of additional 30% of energy release; curves 3 and 4 describe the numerical simulation by the Navier–Stokes LES code with different values of the Smagorinsky coefficient (see Section 4.1).

**Figure 5.**(

**a**) The photo of the gas-dust cloud at 15 s after detonation. (

**b**) The calculated data and the isolines of the density of the explosion products (gray lines on the left part) and the dust (dots on the right part) at the same timepoint. The distances in kilometers are plotted along the axes.

**Figure 6.**The predicted time dependency of the relative rock particles mass (i.e., divided by the explosive mass) remaining in the atmosphere.

**Figure 7.**The distributions of the relative density of pollution compared to the velocity field (

**a**,

**c**) and buoyancy (

**b**,

**d**) shown in the radial section of the gas and dust cloud at 2 and 4 min (panels (

**a**,

**b**) and (

**c**,

**d**), respectively). Brown shades (panels (

**a**,

**c**)) indicate changes in the relative dust concentration (divided by the initial concentration). Dust concentration values are given in color bars. Shades of color (panels (

**b**,

**d**)) indicate changes in buoyancy values. The buoyancy values are given in color bars. The maximum values of velocities are given in rectangles on panels (

**a**,

**c**). Distance in kilometers is plotted on both axes.

**Figure 8.**The distributions of the relative density of particles with a size of 0.4 mm (panels (

**a**,

**b**)) and 0.8 mm (panels (

**c**,

**d**)), at 2 min (panels (

**a**,

**c**)) and 4 min (panels (

**b**,

**d**)), respectively. Shades of color are the same as in Figure 7a. Distance in kilometers is plotted on both axes.

**Figure 9.**The distributions of the relative density of pollution particles are similar to those shown in Figure 8 (panels (

**a**,

**b**)) and 0.8 mm (panels (

**c**,

**d**)), at 2 min (panels (

**a**,

**c**)) and 4 min (panels (

**b**,

**d**)), but these do not account for diffusion. Shades of color are the same as in Figure 7a. Distance in kilometers is plotted on both axes.

**Figure 10.**(

**a**) The dependence of the Smagorinsky parameter ${\mathrm{C}}_{\mathrm{sm}}$ on the charge mass W, the charge-mass dependent maximum height ${\mathrm{H}}_{\mathrm{m}}/{\mathrm{r}}_{\mathrm{T}}$ of the cloud upper edge, and charge-mass dependent maximum radius ${\mathrm{R}}_{\mathrm{m}}/{\mathrm{r}}_{\mathrm{T}}$ of the gas and dust cloud cap. The two latter are obtained for this dependence ${\mathrm{C}}_{\mathrm{sm}}$ (W). (

**b**,

**c**) The time dependences of the upper-edge height $\mathrm{H}/{\mathrm{r}}_{\mathrm{T}}$ and the cloud cap radius $\mathrm{R}/{\mathrm{r}}_{\mathrm{T}}$ for 3-, 30-, and 500-t TNT explosions (curves 1, 2, 3, respectively).

**Figure 11.**A 500 t TNT explosion: (

**a**) The time dependence of the mass fraction of particles with radius ${r}_{p}$ in CDP (related to the mass of particles with this radius in CDP and SDP); (

**b**) the upper edge height of the cloud of particles with radius ${r}_{p}$; (

**c**) the radius of CDP of particles with radius ${r}_{p}$. Curves 1–6 correspond to ${r}_{p}$ = 1.5 × 10

^{−4}, 9.5 × 10

^{−3}, 0.019, 0.075, 0.15, 0.3 cm.

**Figure 12.**The curves for the one-tonne TNT explosion: (

**a**) The time dependence of the mass fraction of particles with radius ${r}_{p}$ in CDP (related to the mass of particles with this radius in CDP and SDP); (

**b**) the upper edge height of the cloud of particles with radius ${r}_{p}$; (

**c**) the radius of CDP of particles with radius ${r}_{p}$. Curves 1–4 correspond to ${r}_{p}=$ 1.5 × 10

^{−4}, 4.75 × 10

^{−3}, 9.5 × 10

^{−3}, 0.019 cm.

**Figure 13.**A 500 t TNT explosion: The distribution of dust particles mass by size at the initial moment of time (black squares), at 30 s (blue dots), and at 5 min (red triangles) after the detonation.

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**MDPI and ACS Style**

Khazins, V.M.; Shuvalov, V.V.; Soloviev, S.P.
Numerical Modeling of Formation and Rise of Gas and Dust Cloud from Large Scale Commercial Blasting. *Atmosphere* **2020**, *11*, 1112.
https://doi.org/10.3390/atmos11101112

**AMA Style**

Khazins VM, Shuvalov VV, Soloviev SP.
Numerical Modeling of Formation and Rise of Gas and Dust Cloud from Large Scale Commercial Blasting. *Atmosphere*. 2020; 11(10):1112.
https://doi.org/10.3390/atmos11101112

**Chicago/Turabian Style**

Khazins, Valery M., Valery V. Shuvalov, and Sergey P. Soloviev.
2020. "Numerical Modeling of Formation and Rise of Gas and Dust Cloud from Large Scale Commercial Blasting" *Atmosphere* 11, no. 10: 1112.
https://doi.org/10.3390/atmos11101112