# Relaxation drag history of shock accelerated microparticles

## Abstract

Experimental measurements of the displacements of shock accelerated microparticles from shortly after shock interaction to the particle relaxation time show time-dependent drag coefficients ($$C_{D}$$) that are much higher than those predicted by quasi-steady and unsteady drag models. Nylon particles with mean diameter of $$4~\unicode[STIX]{x03BC}\text{m}$$, accelerated by one-dimensional normal shocks (Mach number$$M_{s}=1.2$$, 1.3 and 1.4), have measured$$C_{D}$$values that follow a power-law behaviour. The drag is a function of the time-dependent Knudsen number,$$Kn^{\ast }=M_{s}/Re_{p}$$, where the particle Reynolds number ($$Re_{p}$$) is calculated using the time-dependent slip velocity. Also, some portion of the drag can be attributed to quasi-steady forces, but the total drag cannot be predicted by current unsteady force models that are based on the Basset–Boussinesq–Oseen equation and pressure drag. The largest contribution to the total drag is the unsteady component ($$C_{D,us}$$) until the particle attains$$Kn^{\ast }\approx 0.5{-}1.0$$, then the unsteady contribution decays. The quasi-steady component ($$C_{D,qs}$$) increases almost linearly with$$Kn^{\ast }$$, intersects the$$C_{D,us}$$at$$Kn^{\ast }\approx 2$$and becomes the primary contributor to the drag towards the end of the relaxation zone as$$Re_{p}\rightarrow 0$$. Finally, there are currently no analytical models that are able to predict the nonlinear behaviour of the shock accelerated particles during the relaxation phase of the flow.

- Authors:

- 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 National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10)

- OSTI Identifier:
- 1369203

- Report Number(s):
- LA-UR-17-22125

Journal ID: ISSN 0022-1120

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 823; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; high-speed flow; multiphase and particle-laden flows; shock waves

### Citation Formats

```
Bordoloi, Ankur D., Martinez, Adam A., and Prestridge, Katherine.
```*Relaxation drag history of shock accelerated microparticles*. United States: N. p., 2017.
Web. doi:10.1017/jfm.2017.389.

```
Bordoloi, Ankur D., Martinez, Adam A., & Prestridge, Katherine.
```*Relaxation drag history of shock accelerated microparticles*. United States. doi:10.1017/jfm.2017.389.

```
Bordoloi, Ankur D., Martinez, Adam A., and Prestridge, Katherine. Wed .
"Relaxation drag history of shock accelerated microparticles". United States.
doi:10.1017/jfm.2017.389. https://www.osti.gov/servlets/purl/1369203.
```

```
@article{osti_1369203,
```

title = {Relaxation drag history of shock accelerated microparticles},

author = {Bordoloi, Ankur D. and Martinez, Adam A. and Prestridge, Katherine},

abstractNote = {Experimental measurements of the displacements of shock accelerated microparticles from shortly after shock interaction to the particle relaxation time show time-dependent drag coefficients ($C_{D}$) that are much higher than those predicted by quasi-steady and unsteady drag models. Nylon particles with mean diameter of $4~\unicode[STIX]{x03BC}\text{m}$, accelerated by one-dimensional normal shocks (Mach number$M_{s}=1.2$, 1.3 and 1.4), have measured$C_{D}$values that follow a power-law behaviour. The drag is a function of the time-dependent Knudsen number,$Kn^{\ast }=M_{s}/Re_{p}$, where the particle Reynolds number ($Re_{p}$) is calculated using the time-dependent slip velocity. Also, some portion of the drag can be attributed to quasi-steady forces, but the total drag cannot be predicted by current unsteady force models that are based on the Basset–Boussinesq–Oseen equation and pressure drag. The largest contribution to the total drag is the unsteady component ($C_{D,us}$) until the particle attains$Kn^{\ast }\approx 0.5{-}1.0$, then the unsteady contribution decays. The quasi-steady component ($C_{D,qs}$) increases almost linearly with$Kn^{\ast }$, intersects the$C_{D,us}$at$Kn^{\ast }\approx 2$and becomes the primary contributor to the drag towards the end of the relaxation zone as$Re_{p}\rightarrow 0$. Finally, there are currently no analytical models that are able to predict the nonlinear behaviour of the shock accelerated particles during the relaxation phase of the flow.},

doi = {10.1017/jfm.2017.389},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 823,

place = {United States},

year = {Wed Jun 21 00:00:00 EDT 2017},

month = {Wed Jun 21 00:00:00 EDT 2017}

}

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