Research Papers: Fundamental Issues and Canonical Flows

Evaporation Effects in Shock-Driven Multiphase Instabilities

[+] Author and Article Information
Wolfgang J. Black

Department of Mechanical Engineering,
University of Missouri,
Columbia, MO 65202
e-mail: wjbvg5@missouri.com

Nicholas A. Denissen

Department of Computational Physics,
Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: Denissen@lanl.gov

Jacob A. McFarland

Department of Mechanical Engineering,
University of Missouri,
Columbia, MO 65202
e-mail: mcfarlandja@missouri.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 19, 2016; final manuscript received February 13, 2017; published online April 26, 2017. Assoc. Editor: Daniel Livescu.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Fluids Eng 139(7), 071204 (Apr 26, 2017) (15 pages) Paper No: FE-16-1528; doi: 10.1115/1.4036162 History: Received August 19, 2016; Revised February 13, 2017

This paper considers the effects of multiphase parameters on a shock-driven particle-laden hydrodynamic instability using simulations performed with the hydrocode FLAG, developed at Los Alamos National Laboratory. The classic sinusoidal interface common in instability literature is created using water particles seeded in a nitrogen–water vapor mixture. The simulations model a shock tube environment as the computational domain, to guide future experimentation. Multiphase physics in FLAG include momentum and energy coupling, with this paper discussing the addition of mass coupling through evaporation. The multiphase effects are compared to a dusty gas approximation, which ignores multiphase components, as well as to a multiphase case which ignores evaporation. Evaporation is then further explored by artificially changing parameters which effect the rate of evaporation as well as the amount of total evaporation. Among all these experiments, the driving force of the hydrodynamic instability is a shock wave with a Mach number of 1.5 and a system Atwood number of 0.11 across the interface. The analysis is continued into late time for select cases to highlight the effects of evaporation during complex accelerations, presented here as a reshock phenomenon. It was found that evaporation increases the circulation over nonevaporating particles postshock. Evaporation was also shown to change the postshock Atwood number. Reshock showed that the multiphase instabilities exhibited additional circulation deposition over the dusty gas approximation. Mixing measures were found to be affected by evaporation, with the most significant effects occurring after reshock.

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Wohletz, K. H. , 1983, “ Mechanisms of Hydrovolcanic Pyroclast Formation: Grain-Size, Scanning Electron Microscopy, and Experimental Studies,” J. Volcanol. Geotherm. Res., 17(1–4), pp. 31–63. [CrossRef]
Wróblewski, W. , Dykas, S. , Gardzilewicz, A. , and Kolovratnik, M. , 2009, “ Numerical and Experimental Investigations of Steam Condensation in LP Part of a Large Power Turbine,” ASME J. Fluids Eng., 131(4), p. 041301. [CrossRef]
Colarossi, M. , Trask, N. , Schmidt, D. P. , and Bergander, M. J. , 2012, “ Multidimensional Modeling of Condensing Two-Phase Ejector Flow,” Int. J. Refrig., 35(2), pp. 290–299. [CrossRef]
Silvia, D. W. , Smith, B. D. , and Shull, J. M. , 2012, “ Numerical Simulations of Supernova Dust Destruction. II. Metal-Enriched Ejecta Knots,” Astrophys. J., 748(1), pp. 12–21. [CrossRef]
Cherchneff, I. , 2014, “ Dust Production in Supernovae,” preprint arXiv:1405.1216.
McFarland, J. A. , Black, W. J. , Dahal, J. , and Morgan, B. E. , 2016, “ Computational Study of the Shock Driven Instability of a Multiphase Particle-Gas System,” Phys. Fluids, 28(2), p. 024105. [CrossRef]
Richtmyer, R. D. , 1960, “ Taylor Instability in Shock Acceleration of Compressible Fluids,” Commun. Pure Appl. Math., 13(2), pp. 297–319. [CrossRef]
Meshkov, E. E. , 1969, “ Instability of the Interface of Two Gases Accelerated by a Shock Wave,” Fluid Dyn., 4(5), pp. 101–104. [CrossRef]
Marble, F. E. , 1970, “ Dynamics of Dusty Gases,” Annu. Rev. Fluid Mech., 2(1), pp. 397–446. [CrossRef]
Vorobieff, P. , Anderson, M. , Conroy, J. , White, R. , Truman, C. R. , and Kumar, S. , 2011, “ Vortex Formation in a Shock-Accelerated Gas Induced by Particle Seeding,” Phys. Rev. Lett., 106(18), p. 184503. [CrossRef] [PubMed]
Anderson, M. , Vorobieff, P. , Truman, C. R. , Corbin, C. , Kuehner, G. , Wayne, P. , Conroy, J. , White, R. , and Kuman, S. , 2015, “ An Experimental and Numerical Study of Shock Interaction With a Gas Column Seeded With Droplets,” Shock Waves, 25(2), pp. 107–125. [CrossRef]
Ukai, S. , Balakrishnan, K. , and Menon, S. , 2010, “ On Richtmyer–Meshkov Instability in Dilute Gas-Particle Mixtures,” Phys. Fluids, 22(10), p. 104103. [CrossRef]
Schulz, J. C. , Gottiparthi, K. C. , and Menon, S. , 2013, “ Richtmyer–Meshkov Instability in Dilute Gas-Particle Mixtures With Re-Shock,” Phys. Fluids, 25(11), p. 114105. [CrossRef]
Balakumar, B. J. , Orlicz, G. C. , Ristorcelli, J. R. , Balasubramanian, S. , Prestridge, K. P. , and Tomkins, C. D. , 2012, “ Turbulent Mixing in a Richtmyer–Meshkov Fluid Layer After Reshock: Velocity and Density Statistics,” J. Fluid Mech., 696, pp. 67–93. [CrossRef]
McFarland, J. A. , Greenough, J. A. , and Ranjan, D. , 2011, “ Computational Parametric Study of a Richtmyer–Meshkov Instability for an Inclined Interface,” Phys. Rev. E, 84(2), p. 026303. [CrossRef]
Chapman, P. R. , and Jacobs, J. W. , 2006, “ Experiments on the Three-Dimensional Incompressible Richtmyer–Meshkov Instability,” Phys. Fluids, 18(7), p. 074101. [CrossRef]
Robey, H. F. , Kane, J. O. , Remington, B. A. , Drake, R. P. , Hurricane, O. A. , Louis, H. , Wallace, R. J. , Knauer, J. , Keiter, P. , Arnett, D. , and Ryutov, D. D. , 2001, “ An Experimental Testbed for the Study of Hydrodynamic Issues in Supernovae,” Phys. Plasmas, 8(5), pp. 2446–2453. [CrossRef]
Ranjan, D. , Oakley, J. , and Bonazza, R. , 2011, “ Shock-Bubble Interactions,” Annu. Rev. Fluid Mech., 43(1), pp. 117–140. [CrossRef]
Tomkins, C. D. , Balakumar, B. J. , Orlicz, G. , Prestridge, K. P. , and Ristorcelli, J. R. , 2013, “ Evolution of the Density Self-Correlation in Developing Richtmyer–Meshkov Turbulence,” J. Fluid Mech., 735, pp. 288–306. [CrossRef]
Motl, B. , Oakley, J. , Ranjan, D. , Weber, C. , Anderson, M. , and Bonazza, R. , 2009, “ Experimental Validation of a Richtmyer–Meshkov Scaling Law Over Large Density Ratio and Shock Strength Ranges,” Phys. Fluids, 21(12), p. 126102. [CrossRef]
Long, C. C. , Krivets, V. V. , Greenough, J. A. , and Jacobs, J. W. , 2009, “ Shock Tube Experiments and Numerical Simulation of the Single-Mode Three-Dimensional Richtmyer–Meshkov Instability,” Phys. Fluids, 21(11), p. 114104. [CrossRef]
McFarland, J. , Greenough, J. A. , and Ranjan, D. , 2013, “ Investigation of the Initial Perturbation Amplitude for the Inclined Interface Richtmyer–Meshkov Instability,” Phys. Scr., T155, p. 014014.
McFarland, J. , Reilly, D. , Creel, S. , McDonald, C. , Finn, T. , and Ranjan, D. , 2014, “ Experimental Investigation of the Inclined Interface Richtmyer–Meshkov Instability Before and After Reshock,” Exp. Fluids, 55(1), pp. 1640–1674. [CrossRef]
McFarland, J. A. , Greenough, J. A. , and Ranjan, D. , 2014, “ Simulations and Analysis of the Reshocked Inclined Interface Richtmyer–Meshkov Instability for Linear and Nonlinear Interface Perturbations,” ASME J. Fluids Eng., 136(7), p. 071203. [CrossRef]
Bernard, T. , Truman, C. R. , Vorobieff, P. , Corbin, C. , Wayne, P. J. , Kuehner, G. , Anderson, M. , and Kumar, S. , 2014, “ Observation of the Development of Secondary Features in a Richtmyer–Meshkov Instability Driven Flow,” ASME J. Fluids Eng., 137(1), p. 011206. [CrossRef]
Wilson, B. M. , Mejia-Alvarez, R. , and Prestridge, K. P. , 2016, “ Single-Interface Richtmyer–Meshkov Turbulent Mixing at the Los Alamos Vertical Shock Tube,” ASME J. Fluids Eng., 138(7), p. 070901. [CrossRef]
Shilling, O. , Latini, M. , and Don, W. S. , 2007, “ Physics of Reshock and Mixing in Single-Mode Richtmyer–Meshkov Instability,” Phys. Rev. E, 76(2), p. 026319. [CrossRef]
Cook, A. W. , Cabot, W. , and Miller, P. L. , 2004, “ The Mixing Transition in Rayleigh–Taylor Instability,” J. Fluid Mech., 511, pp. 332–362. [CrossRef]
Zabusky, N. J. , Kotelnikov, A. D. , Gulak, Y. , and Peng, G. , 2003, “ Amplitude Growth Rate of a Richtmyer–Meshkov Unstable Two-Dimensional Interface to Intermediate Times,” J. Fluid Mech., 475, pp. 147–162. [CrossRef]
Olson, B. J. , and Greenough, J. A. , 2014, “ Comparison of Two- and Three-Dimensional Simulations of Miscible Richtmyer–Meshkov Instability With Multimode Initial Conditions,” Phys. Fluids, 26(10), p. 101702. [CrossRef]
Miles, R. , Blue, B. , Edwards, M. J. , Greenough, J. A. , Hansen, J. F. , Robey, H. F. , Drake, R. P. , Kuranz, C. , and Leibrandt, D. R. , 2005, “ Transition to Turbulence and Effect of Initial Conditions on Three-Dimensional Compressible Mixing in Planar Blast-Wave-Driven-Systems,” Phys. Plasmas, 12(5), p. 056317. [CrossRef]
McFarland, J. A. , Reilly, D. , Black, W. , Greenough, J. A. , and Ranjan, D. , 2015, “ Modal Interactions Between a Large Wave-Length Inclined Interface and Small-Wavelength Multimode Perturbations in a Richtmyer–Meshkov Instability,” Phys. Rev. E, 92(1), p. 013023. [CrossRef]
Reilly, D. , McFarland, J. A. , Mohaghar, M. , and Ranjan, D. , 2015, “ The Effects of Initial Conditions and Circulation Deposition on the Inclined-Interface Reshocked Richtmyer–Meshkov Instability,” Exp. Fluids, 56(8), pp. 168–184. [CrossRef]
Kane, J. , Drake, R. P. , and Remington, B. A. , 1999, “ An Evaluation of the Richtmyer–Meshkov Instability in Supernova Remnant Formation,” Astrophys. J., 511(1), pp. 335–340. [CrossRef]
Taylor, G. , 1950, “ The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes,” Proc. R. Soc. London, Ser. A, 201(1065), pp. 192–196. [CrossRef]
Burton, D. E. , 1992, “ Connectivity Structures and Differencing Techniques for Staggered-Grid Free-Lagrange Hydrodynamics,” 7th International Association of Mathematics and Computer Simulation (IMACS PDE7), Rutgers University, New Brunswick, NJ, June 22–24, Paper No. UCRL-JC-110555.
Burton, D. E. , 1994, “ Consistent Finite-Volume Discretization of Hydrodynamic Conservation Laws for Unstructured Grids,” Lawrence Livermore National Laboratory, Livermore, CA, Contract No. W-7405-ENG-48.
Boris, J. P. , and Book, D. L. , 1973, “ Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works,” J. Comput. Phys., 11(1), pp. 38–69. [CrossRef]
Fung, J. , Harrison, A. K. , Chitanvis, S. , and Margulies, J. , 2012, “ Ejecta Source and Transport Modeling in the FLAG Hydrocode,” Los Alamos National Laboratory, Los Alamos, NM, Technical Report No. LA-UR-11-04992.
Harrison, A. , and Fung, J. , 2009, “ Ejecta in the FLAG Hydrocode,” Numerical Methods for Multi-Material Fluids and Structures, Pavia.
Zalesak, S. T. , 1979, “ Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids,” J. Comput. Phys., 31(3), pp. 335–362. [CrossRef]
Barth, T. J. , and Jespersen, D. C. , 1989, “ The Design and Application of Upwind Schemes on Unstructured Meshes,” 27th Aerospace Sciences Meeting, Reno, NV, Jan. 9–12.
Youngs, D. L. , 1982, “ Time-Dependent Multi-Material Flow With Large Fluid Distortion,” Numerical Methods For Fluid Dynamics, K. W. Morton and M. J. Baines, Eds., Academic Press, New York, pp. 273–285.
Andrews, M. , and O’Rourke, P. , 1996, “ The Multiphase Particle-in-Cell (MP-PIC) Method for Dense Particle Flows,” Int. J. Multiphase Flow, 22(2), pp. 379–402. [CrossRef]
Fuks, N. A. , 1955, “ The Mechanics of Aerosols,” Chemical Warfare Labs Army Chemical Center, MD, Standard No. CWL-SP-4-12.
Ranz, W. E. , and Marshall, W. R. , Jr., 1952, “ Evaporation From Drops,” Chem. Eng. Prog., 48(3), pp. 141–146.
Cloutman, L. D. , 1988, “ Analytical Solutions for the Trajectories and Thermal Histories of Unforced Particulates,” Am. J. Phys., 56(7), pp. 643–645. [CrossRef]
Crowe, C. T. , Schwarzkopf, J. D. , Sommerfeld, M. , and Tsuji, Y. , 2011, Multiphase Flows With Droplets and Particles, 2nd ed., CRC Press, Salem, MA.


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Fig. 1

Analytical solutions versus FLAG simulations for nonevaporating particles: particle velocity (left) and particle temperature (right)

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Fig. 2

Two-axis plot validation of the saturation temperature and vapor concentration for the evaporation model

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Fig. 3

(a) The initial particle field and (b) the initial gas field. Note: This shows how the seeded and nonseeded phase are initialized separately despite being the same gas. This also can be used to show the DG case initial conditions.

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Fig. 4

Evolution of the dusty gas and evaporation particles instabilities with respect to nondimensional time, τ

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Fig. 5

The qualitative scalar fields for the physical cases at τ = 200

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Fig. 6

Circulation over time for the physical cases

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Fig. 7

Integral mixed width over time for the physical cases

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Fig. 8

The qualitative scalar fields for the diffusion modifier cases at τ = 200

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Fig. 9

The circulation over time for the diffusion modifier cases

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Fig. 10

Integral mixed width over time for the diffusion modifier cases

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Fig. 11

The qualitative scalar fields for the saturation pressure modifier cases at τ = 200

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Fig. 12

Circulation over time for the saturation pressure modifier cases

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Fig. 13

Integral mixed width over time for the saturation pressure modifier cases

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Fig. 14

Evolution of the post-reshock interface with respect to nondimensional time, τR. Like Fig. 4, the particle cases are represented by the exemplar case.

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Fig. 15

Density of the reshock cases with respect to τR

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Fig. 16

Temperatures of the reshock cases with respect to τR

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Fig. 17

Particle temperatures of the reshock cases with respect to τR

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Fig. 18

Vorticity fields of the reshock cases with respect to τR

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Fig. 19

Circulation over time for the reshock cases

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Fig. 20

Integral mixed width over time for the reshock cases




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