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Dynamics of rapidly depressurized multiphase shock tubes

Published online by Cambridge University Press:  09 October 2019

D. Zwick
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
S. Balachandar
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
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Rapid depressurization is a fluid phenomenon that occurs in many industrial and natural applications. Its behaviour is often complicated by the formation, propagation and interaction of waves. In this work, we perform computer simulations of the rapid depressurization of a gas–solid mixture in a shock tube. Our problem set-up mimics previously performed experiments, which have been historically used as a laboratory surrogate for volcanic eruptions. The simulations are carried out with a discontinuous Galerkin compressible fluid solver with four-way coupled Lagrangian particle tracking capabilities. The results give an unprecedented look into the complex multiphase physics at work in this problem. Different regimes have been characterized in a regime map that highlights the key observations. While the mean flow behaviour is in good agreement with experiments, the simulations show unexpected accelerations of the particle front as it expands. Additionally, a new lifting mechanism for gas bubble (void) growth inside the gas–solid mixture is detailed.

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Alatorre-Ibargüengoitia, M. A., Scheu, B., Dingwell, D. B., Delgado-Granados, H. & Taddeucci, J. 2010 Energy consumption by magmatic fragmentation and pyroclast ejection during vulcanian eruptions. Earth Planet. Sci. Lett. 291 (1–4), 6069.CrossRefGoogle Scholar
Anilkumar, A. V.1989 Experimental studies of high-speed dense dusty gases. PhD thesis, California Institute of Technology, Pasadena, CA.Google Scholar
Anilkumar, A. V., Sparks, R. S. J. & Sturtevant, B. 1993 Geological implications and applications of high-velocity two-phase flow experiments. J. Volcanol. Geotherm. Res. 56 (1–2), 145160.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.CrossRefGoogle Scholar
Berrut, J. P. & Trefethen, L. N. 2004 Barycentric Lagrange interpolation. SIAM Rev. 46 (3), 501517.CrossRefGoogle Scholar
Beyer, W. H. 1987 CRC Standard Mathematcial Tables, 28th edn. CRC Press.Google Scholar
Cagnoli, B., Barmin, A., Melnik, O. & Sparks, R. S. J. 2002 Depressurization of fine powders in a shock tube and dynamics of fragmented magma in volcanic conduits. Earth Planet. Sci. Lett. 204 (1–2), 101113.CrossRefGoogle Scholar
Cerminara, M., Ongaro, T. E. & Neri, A. 2016 Large eddy simulation of gas–particle kinematic decoupling and turbulent entrainment in volcanic plumes. J. Volcanol. Geotherm. Res. 326, 143171.CrossRefGoogle Scholar
Chojnicki, K., Clarke, A. B. & Phillips, J. C. 2006 A shock-tube investigation of the dynamics of gas–particle mixtures: implications for explosive volcanic eruptions. Geophys. Res. Lett. 33 (15), L15309.CrossRefGoogle Scholar
Costa, A., Suzuki, Y. J., Cerminara, M., Devenish, B. J., Ongaro, T. E., Herzog, M., Van Eaton, A. R., Denby, L. C., Bursik, M., de’ Michieli Vitturi, M. et al. 2016 Results of the eruptive column model inter-comparison study. J. Volcanol. Geotherm. Res. 326, 225.CrossRefGoogle Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Géotechnique 29 (1), 4765.CrossRefGoogle Scholar
Deville, M. O., Fischer, P. F. & Mund, E. H. 2002 High-order Methods for Incompressible Fluid Flow. Cambridge University Press.CrossRefGoogle Scholar
Fortes, A. F., Joseph, D. D. & Lundgren, T. S. 1987 Nonlinear mechanics of fluidization of beds of spherical particles. J. Fluid Mech. 177, 467483.CrossRefGoogle Scholar
Fowler, A. C., Scheu, B., Lee, W. T. & McGuinness, M. J. 2010 A theoretical model of the explosive fragmentation of vesicular magma. Proc. R. Soc. Lond. A 466 (2115), 731752.CrossRefGoogle Scholar
Gidaspow, D. 1994 Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press.Google Scholar
Gonnermann, H. M. 2015 Magma fragmentation. Annu. Rev. Earth Planet. Sci. 43 (1), 431458.CrossRefGoogle Scholar
Hackl, J. F., Shringarpure, M. S., Koneru, R. B., Delchini, M. G. & Balachandar, S.A shock capturing discontinuous Galerkin spectral element method for curved geometry using entropy viscosity. Comput. Fluids (submitted).Google Scholar
Haselbacher, A. C., Balachandar, S. & Kieffer, S. W. 2007 Open-ended shock tube flows: influence of pressure ratio and diaphragm position. AIAA J. 45 (8), 19171929.CrossRefGoogle Scholar
Hesthaven, J. S. & Warburton, T. 2008 Nodal Discontinuous Galerkin Methods. Springer.CrossRefGoogle Scholar
Kieffer, S. W. & Sturtevant, B. 1984 Laboratory studies of volcanic jets. J. Geophys. Res. 89 (B10), 82538268.CrossRefGoogle Scholar
La Spina, G., de’ Michieli Vitturi, M. & Clarke, A. B. 2017 Transient numerical model of magma ascent dynamics: application to the explosive eruptions at the Soufrière Hills Volcano. J. Volcanol. Geotherm. Res. 336, 118139.CrossRefGoogle Scholar
Ling, Y., Balachandar, S. & Parmar, M. 2016 Inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows. Phys. Fluids 28 (3), 033304.CrossRefGoogle Scholar
Ling, Y., Wagner, J. L., Beresh, S. J., Kearney, S. P. & Balachandar, S. 2012 Interaction of a planar shock wave with a dense particle curtain: modeling and experiments. Phys. Fluids 24 (11), 113301.CrossRefGoogle Scholar
Marjanovic, G., Hackl, J., Shringarpure, M., Annamalai, S., Jackson, T. L. & Balachandar, S. 2018 Inviscid simulations of expansion waves propagating into structured particle beds at low volume fractions. Phys. Rev. Fluids 3 (9), 094301.CrossRefGoogle Scholar
McGuinness, M. J., Scheu, B. & Fowler, A. C. 2012 Explosive fragmentation criteria and velocities for vesicular magma. J. Volcanol. Geotherm. Res. 237–238, 8196.CrossRefGoogle Scholar
McGuinness, M. J. & Singh, H. 2015 Modelling the initiation of dust eruptions. J. Volcanol. Geotherm. Res. 299, 5467.CrossRefGoogle Scholar
de’ Michieli Vitturi, M., Neri, A., Ongaro, T. E., Lo Savio, S. & Boschi, E. 2010 Lagrangian modeling of large volcanic particles: application to vulcanian explosions. J. Geophys. Res. 115 (B8), B08206.CrossRefGoogle Scholar
Ongaro, T. E., Clarke, A. B., Voight, B., Neri, A. & Widiwijayanti, C. 2012 Multiphase flow dynamics of pyroclastic density currents during the May 18, 1980 lateral blast of Mount St. Helens. J. Geophys. Res. 117 (B6), B06208.Google Scholar
Ongaro, T. E., Neri, A., Menconi, G., de’ Michieli Vitturi, M., Marianelli, P., Cavazzoni, C., Erbacci, G. & Baxter, P. J. 2008 Transient 3D numerical simulations of column collapse and pyroclastic density current scenarios at Vesuvius. J. Volcanol. Geotherm. Res. 178 (3), 378396.CrossRefGoogle Scholar
Oosthuizen, P. H. & Carscallen, W. E. 2013 Introduction to Compressible Fluid Flow, 2nd edn. CRC Press.Google Scholar
Rudinger, G. 1980 Fundamentals of Gas–Particle Flow, vol. 2. Elsevier.Google Scholar
Shallcross, G. S. & Capecelatro, J. 2018 A parametric study of particle-laden shock tubes using an Eulerian–Lagrangian framework. In 2018 AIAA Aerospace Sciences Meeting. AIAA.Google Scholar
Stever, H. G. & Bisplinghoff, R. L. 1954 The shock tube in aerodynamic and structural research. Proc. Natl Acad. Sci. USA 40 (7), 557565.CrossRefGoogle ScholarPubMed
Tasissa, A. F., Hautefeuille, M., Fitek, J. H. & Radovitzky, R. A. 2016 On the formation of Friedlander waves in a compressed-gas-driven shock tube. Proc. R. Soc. A 472 (2186), 20150611.Google Scholar
Toro, E. F.1999 NUMERICA, a library of source codes for teaching, research and applications. NUMERITEK Ltd.Google Scholar
Turcotte, D. L., Ockendon, H., Ockendon, J. R. & Cowley, S. J. 1990 A mathematical model of vulcanian eruptions. Geophys. J. Intl 103 (1), 211217.CrossRefGoogle Scholar
Woods, A. W. 1995 A model of vulcanian explosions. Nucl. Engng Des. 155 (1–2), 345357.CrossRefGoogle Scholar
Zwick, D. 2019a ppiclF: a parallel particle-in-cell library in Fortran. J. Open Source Softw. 4 (37), 1400.CrossRefGoogle Scholar
Zwick, D.2019b Scalable highly-resolved Euler–Lagrange multiphase flow simulation with applications to shock tubes. PhD thesis, University of Florida, Gainesville, FL.Google Scholar
Zwick, D. & Balachandar, S. 2019 An Eulerian–Lagrangian approach for multiphase flow simulation on spectral elements. Intl J. High Performance Comput. Appl. doi:10.1177/1094342019867756.CrossRefGoogle Scholar

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