## A numerical study of bubble and spike velocities in shock-driven liquid metals

## Abstract

In this study, we use detailed continuum hydrodynamics and molecular dynamics simulations to investigate the dynamics of ejecta that are initialized with large amplitude perturbations and non-sinusoidal shapes. Insights from the simulations are used to suggest a modified expression for the velocity associated with ejected spike structures, whereas a recently suggested model explains the observed bubble velocities. Specifically, we find the asymptotic bubble velocity prediction given by Mikaelian is in excellent agreement with the simulations, when a nonlinear correction for finite amplitudes is used in that model. In contrast, existing models can overpredict observed spike velocities if they do not include the modification of the initial spike growth rates due to nonlinearities. Instead, we find that when potential flow models are corrected with a suitable nonlinear prefactor, this leads to predictions in close agreement with our simulation data. We also propose a simple empirical expression for the nonlinear correction for spike velocities which is able to reproduce results from our simulations and published experimental and simulation data over a wide range of initial conditions and Mach numbers. We discuss extensions of these models to initial interfaces with arbitrary shapes. In particular, for non-sinusoidal shapes, the bubble and spike velocities aremore »

- Authors:

- University of North Carolina, Charlotte, NC (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E)

- OSTI Identifier:
- 1479928

- Alternate Identifier(s):
- OSTI ID: 1416841

- Report Number(s):
- LA-UR-17-28876

Journal ID: ISSN 0021-8979

- Grant/Contract Number:
- AC52-06NA25396; AC52-06NA2-5396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Journal Volume: 123; Journal Issue: 2; Journal ID: ISSN 0021-8979

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ejecta; Richtmeyer-Meshkov Instability; ejecta models; numerical simulation

### Citation Formats

```
Karkhanis, V., Ramaprabhu, P., Cherne, Frank Joseph, Hammerberg, James Edward, and Andrews, Malcolm John. A numerical study of bubble and spike velocities in shock-driven liquid metals. United States: N. p., 2018.
Web. doi:10.1063/1.5008495.
```

```
Karkhanis, V., Ramaprabhu, P., Cherne, Frank Joseph, Hammerberg, James Edward, & Andrews, Malcolm John. A numerical study of bubble and spike velocities in shock-driven liquid metals. United States. doi:10.1063/1.5008495.
```

```
Karkhanis, V., Ramaprabhu, P., Cherne, Frank Joseph, Hammerberg, James Edward, and Andrews, Malcolm John. Fri .
"A numerical study of bubble and spike velocities in shock-driven liquid metals". United States. doi:10.1063/1.5008495. https://www.osti.gov/servlets/purl/1479928.
```

```
@article{osti_1479928,
```

title = {A numerical study of bubble and spike velocities in shock-driven liquid metals},

author = {Karkhanis, V. and Ramaprabhu, P. and Cherne, Frank Joseph and Hammerberg, James Edward and Andrews, Malcolm John},

abstractNote = {In this study, we use detailed continuum hydrodynamics and molecular dynamics simulations to investigate the dynamics of ejecta that are initialized with large amplitude perturbations and non-sinusoidal shapes. Insights from the simulations are used to suggest a modified expression for the velocity associated with ejected spike structures, whereas a recently suggested model explains the observed bubble velocities. Specifically, we find the asymptotic bubble velocity prediction given by Mikaelian is in excellent agreement with the simulations, when a nonlinear correction for finite amplitudes is used in that model. In contrast, existing models can overpredict observed spike velocities if they do not include the modification of the initial spike growth rates due to nonlinearities. Instead, we find that when potential flow models are corrected with a suitable nonlinear prefactor, this leads to predictions in close agreement with our simulation data. We also propose a simple empirical expression for the nonlinear correction for spike velocities which is able to reproduce results from our simulations and published experimental and simulation data over a wide range of initial conditions and Mach numbers. We discuss extensions of these models to initial interfaces with arbitrary shapes. In particular, for non-sinusoidal shapes, the bubble and spike velocities are still predicted by these models provided we use an effective wavelength λeff which is the wavelength of an equivalent sinusoid that has the same missing area. Lastly, the issues of nonlinearity, non-standard shapes and shock Mach number addressed in this work are relevant to recent experimental campaigns involving twice-shocked targets.},

doi = {10.1063/1.5008495},

journal = {Journal of Applied Physics},

number = 2,

volume = 123,

place = {United States},

year = {2018},

month = {1}

}

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