# A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow

## Abstract

In this paper, we introduce a new method (piecewise integrated dynamics equation fit, PIDEF) that uses the particle dynamics equation to determine unsteady kinematics and drag coefficient (C _{D}) for a particle in subsonic post-shock flow. The uncertainty of this method is assessed based on simulated trajectories for both quasi-steady and unsteady flow conditions. Traditional piecewise polynomial fitting (PPF) shows high sensitivity to measurement error and the function used to describe C _{D}, creating high levels of relative error (>>1) when applied to unsteady shock-accelerated flows. The PIDEF method provides reduced uncertainty in calculations of unsteady acceleration and drag coefficient for both quasi-steady and unsteady flows. This makes PIDEF a preferable method over PPF for complex flows where the temporal response of C _{D} is unknown. Finally, we apply PIDEF to experimental measurements of particle trajectories from 8-pulse particle tracking and determine the effect of incident Mach number on relaxation kinematics and drag coefficient of micron-sized particles.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Arizona State Univ., Tempe, AZ (United States). School for Engineering of Matter, Transport and Energy

- Publication Date:

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

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1440444

- Report Number(s):
- LA-UR-17-31279

Journal ID: ISSN 0957-0233

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Measurement Science and Technology

- Additional Journal Information:
- Journal Volume: 29; Journal Issue: 7; Journal ID: ISSN 0957-0233

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; particle tracking accelerometry; kinematics measurement; shock-particle interaction; unsteady drag

### Citation Formats

```
Bordoloi, Ankur D., Ding, Liuyang, Martinez, Adam A., Prestridge, Katherine, and Adrian, Ronald J..
```*A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow*. United States: N. p., 2018.
Web. doi:10.1088/1361-6501/aac076.

```
Bordoloi, Ankur D., Ding, Liuyang, Martinez, Adam A., Prestridge, Katherine, & Adrian, Ronald J..
```*A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow*. United States. doi:10.1088/1361-6501/aac076.

```
Bordoloi, Ankur D., Ding, Liuyang, Martinez, Adam A., Prestridge, Katherine, and Adrian, Ronald J.. Thu .
"A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow". United States.
doi:10.1088/1361-6501/aac076.
```

```
@article{osti_1440444,
```

title = {A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow},

author = {Bordoloi, Ankur D. and Ding, Liuyang and Martinez, Adam A. and Prestridge, Katherine and Adrian, Ronald J.},

abstractNote = {In this paper, we introduce a new method (piecewise integrated dynamics equation fit, PIDEF) that uses the particle dynamics equation to determine unsteady kinematics and drag coefficient (C D) for a particle in subsonic post-shock flow. The uncertainty of this method is assessed based on simulated trajectories for both quasi-steady and unsteady flow conditions. Traditional piecewise polynomial fitting (PPF) shows high sensitivity to measurement error and the function used to describe C D, creating high levels of relative error (>>1) when applied to unsteady shock-accelerated flows. The PIDEF method provides reduced uncertainty in calculations of unsteady acceleration and drag coefficient for both quasi-steady and unsteady flows. This makes PIDEF a preferable method over PPF for complex flows where the temporal response of C D is unknown. Finally, we apply PIDEF to experimental measurements of particle trajectories from 8-pulse particle tracking and determine the effect of incident Mach number on relaxation kinematics and drag coefficient of micron-sized particles.},

doi = {10.1088/1361-6501/aac076},

journal = {Measurement Science and Technology},

number = 7,

volume = 29,

place = {United States},

year = {Thu Apr 26 00:00:00 EDT 2018},

month = {Thu Apr 26 00:00:00 EDT 2018}

}