## Subgrid-scale effects in compressible variable-density decaying turbulence

## Abstract

We present that many turbulent flows are characterized by complex scale interactions and vorticity generation caused by compressibility and variable-density effects. In the large-eddy simulation of variable-density flows, these processes manifest themselves as subgrid-scale (SGS) terms that interact with the resolved-scale flow. This paper studies the effect of the variable-density SGS terms and quantifies their relative importance. We consider the SGS terms appearing in the density-weighted Favre-filtered equations and in the unweighted Reynolds-filtered equations. The conventional form of the Reynolds-filtered momentum equation is complicated by a temporal SGS term; therefore, we derive a new form of the Reynolds-filtered governing equations that does not contain this term and has only double-correlation SGS terms. The new form of the filtered equations has terms that represent the SGS mass flux, pressure-gradient acceleration and velocity-dilatation correlation. To evaluate the dynamical significance of the variable-density SGS effects, we carry out direct numerical simulations of compressible decaying turbulence at a turbulent Mach number of 0.3. Two different initial thermodynamic conditions are investigated: homentropic and a thermally inhomogeneous gas with regions of differing densities. The simulated flow fields are explicitly filtered to evaluate the SGS terms. The importance of the variable-density SGS terms is quantified relative tomore »

- Authors:

- Univ. of Minnesota, Minneapolis, MN (United States). Aerospace Engineering and Mechanics

- Publication Date:

- Research Org.:
- California Inst. of Technology (CalTech), Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10); US Air Force Office of Scientific Research (AFOSR)

- OSTI Identifier:
- 1436961

- Grant/Contract Number:
- NA0002382; FA9550-12-1-0461; FA9550-17-1-0250

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 846; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; compressible turbulence; isotropic turbulence; turbulent mixing

### Citation Formats

```
GS, Sidharth, and Candler, Graham V. Subgrid-scale effects in compressible variable-density decaying turbulence. United States: N. p., 2018.
Web. doi:10.1017/jfm.2018.281.
```

```
GS, Sidharth, & Candler, Graham V. Subgrid-scale effects in compressible variable-density decaying turbulence. United States. doi:10.1017/jfm.2018.281.
```

```
GS, Sidharth, and Candler, Graham V. Tue .
"Subgrid-scale effects in compressible variable-density decaying turbulence". United States. doi:10.1017/jfm.2018.281. https://www.osti.gov/servlets/purl/1436961.
```

```
@article{osti_1436961,
```

title = {Subgrid-scale effects in compressible variable-density decaying turbulence},

author = {GS, Sidharth and Candler, Graham V.},

abstractNote = {We present that many turbulent flows are characterized by complex scale interactions and vorticity generation caused by compressibility and variable-density effects. In the large-eddy simulation of variable-density flows, these processes manifest themselves as subgrid-scale (SGS) terms that interact with the resolved-scale flow. This paper studies the effect of the variable-density SGS terms and quantifies their relative importance. We consider the SGS terms appearing in the density-weighted Favre-filtered equations and in the unweighted Reynolds-filtered equations. The conventional form of the Reynolds-filtered momentum equation is complicated by a temporal SGS term; therefore, we derive a new form of the Reynolds-filtered governing equations that does not contain this term and has only double-correlation SGS terms. The new form of the filtered equations has terms that represent the SGS mass flux, pressure-gradient acceleration and velocity-dilatation correlation. To evaluate the dynamical significance of the variable-density SGS effects, we carry out direct numerical simulations of compressible decaying turbulence at a turbulent Mach number of 0.3. Two different initial thermodynamic conditions are investigated: homentropic and a thermally inhomogeneous gas with regions of differing densities. The simulated flow fields are explicitly filtered to evaluate the SGS terms. The importance of the variable-density SGS terms is quantified relative to the SGS specific stress, which is the only SGS term active in incompressible constant-density turbulence. It is found that while the variable-density SGS terms in the homentropic case are negligible, they are dynamically significant in the thermally inhomogeneous flows. Investigation of the variable-density SGS terms is therefore important, not only to develop variable-density closures but also to improve the understanding of scale interactions in variable-density flows.},

doi = {10.1017/jfm.2018.281},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 846,

place = {United States},

year = {2018},

month = {5}

}