## A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing

## Abstract

A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and showsmore »

- 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

- OSTI Identifier:
- 1239104

- Report Number(s):
- LA-UR-14-27431

Journal ID: ISSN 1386-6184; PII: 9643

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Flow, Turbulence and Combustion

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 1386-6184

- Publisher:
- European Research Community on Flow, Turbulence and Combustion (ERCOFTAC)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 04 OIL SHALES AND TAR SANDS; 24 POWER TRANSMISSION AND DISTRIBUTION; Turbulence; mixing; variable density; Reynolds stress; closure model; shear flow; Rayleigh-Taylor; Richtmyer-Meshkov; direct numerical simulation; shocks; Favre average; compressible flows; density fl

### Citation Formats

```
Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A., and Ristorcelli, J. R. A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing. United States: N. p., 2015.
Web. doi:10.1007/s10494-015-9643-z.
```

```
Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A., & Ristorcelli, J. R. A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing. United States. doi:10.1007/s10494-015-9643-z.
```

```
Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A., and Ristorcelli, J. R. Tue .
"A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing". United States. doi:10.1007/s10494-015-9643-z. https://www.osti.gov/servlets/purl/1239104.
```

```
@article{osti_1239104,
```

title = {A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing},

author = {Schwarzkopf, J. D. and Livescu, D. and Baltzer, J. R. and Gore, R. A. and Ristorcelli, J. R.},

abstractNote = {A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. Additionally, the importance of using DNS to calibrate and assess RANS type turbulence models is highlighted.},

doi = {10.1007/s10494-015-9643-z},

journal = {Flow, Turbulence and Combustion},

number = 1,

volume = 96,

place = {United States},

year = {2015},

month = {9}

}

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