# Active attenuation of a trailing vortex inspired by a parabolized stability analysis

## Abstract

Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Often, intuitive control strategies lead to suboptimal control. To navigate the control space, we use a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack $$\unicode[STIX]{x1D6FC}=5^{\circ }$$ and a chord-based Reynolds number $Re=1000$. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode does not. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Furthermore, relative to the uncontrolled case, the controlled flows show increased attenuation of circulation and peak streamwise vorticity, with the fifth-mode-based control set-up outperforming the principal-mode-based set-up. From these results, we conclude that a rudimentary linear stability analysis can provide key insights into the underlying physics and help engineers design effective physics-based flow control strategies.

- Authors:

- Florida State Univ., Tallahassee, FL (United States)
- Imperial College London, London, (United Kingdom)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- ONR; USDOE

- OSTI Identifier:
- 1477439

- Report Number(s):
- SAND-2018-6492J

Journal ID: ISSN 0022-1120; 664491

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 855; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING

### Citation Formats

```
Edstrand, Adam M., Sun, Yiyang, Schmid, Peter J., Taira, Kunihiko, and Cattafesta, Louis N. Active attenuation of a trailing vortex inspired by a parabolized stability analysis. United States: N. p., 2018.
Web. doi:10.1017/jfm.2018.701.
```

```
Edstrand, Adam M., Sun, Yiyang, Schmid, Peter J., Taira, Kunihiko, & Cattafesta, Louis N. Active attenuation of a trailing vortex inspired by a parabolized stability analysis. United States. doi:10.1017/jfm.2018.701.
```

```
Edstrand, Adam M., Sun, Yiyang, Schmid, Peter J., Taira, Kunihiko, and Cattafesta, Louis N. Wed .
"Active attenuation of a trailing vortex inspired by a parabolized stability analysis". United States. doi:10.1017/jfm.2018.701. https://www.osti.gov/servlets/purl/1477439.
```

```
@article{osti_1477439,
```

title = {Active attenuation of a trailing vortex inspired by a parabolized stability analysis},

author = {Edstrand, Adam M. and Sun, Yiyang and Schmid, Peter J. and Taira, Kunihiko and Cattafesta, Louis N.},

abstractNote = {Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Often, intuitive control strategies lead to suboptimal control. To navigate the control space, we use a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack $\unicode[STIX]{x1D6FC}=5^{\circ }$ and a chord-based Reynolds number $Re=1000$. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode does not. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Furthermore, relative to the uncontrolled case, the controlled flows show increased attenuation of circulation and peak streamwise vorticity, with the fifth-mode-based control set-up outperforming the principal-mode-based set-up. From these results, we conclude that a rudimentary linear stability analysis can provide key insights into the underlying physics and help engineers design effective physics-based flow control strategies.},

doi = {10.1017/jfm.2018.701},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 855,

place = {United States},

year = {2018},

month = {9}

}

#### Figures / Tables:

_{$x$}= —0.8 (transparent gray) and streamwise velocity perturbation (blue and red) of body force are visualized.

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*