# Reaction analogy based forcing for incompressible scalar turbulence

## Abstract

Here, we present a novel reaction analogy (RA) based forcing method for generating statistically stationary scalar fields in incompressible turbulence. The new method can produce more general scalar probability density functions (PDFs), for example, quasi-double- $\delta $ PDF, than current methods, while ensuring that scalar fields remain bounded, unlike existent forcing methodologies that can potentially violate naturally existing bounds. Such features are useful for generating initial fields in nonpremixed combustion, inlet conditions for spatially developing flows, or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived such that the reaction term is smooth in scalar space and is consistent with mass conservation. For large values of the scalar forcing rate, the method produces statistically stationary quasi-double- $\delta $ scalar PDFs. Quasiuniform, Gaussian, and stretched exponential scalar statistics are recovered for smaller values of the scalar forcing rate. The shape of the scalar PDF can be further controlled by changing the stoichiometric coefficients of the reaction. Finally, the ability of the new method to produce fully developed passive scalar fields with quasi-Gaussian PDFs is also investigated, by exploring the convergence of the scalar variance spectrum to the Obukhov-Corrsin scaling and of the third-order mixed structure function to the “four-thirds” Yaglom's law.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Chung-Ang Univ., Seoul (Korea, Republic of). School of Mechanical Engineering

- Publication Date:

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

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

- OSTI Identifier:
- 1477698

- Alternate Identifier(s):
- OSTI ID: 1468870

- Report Number(s):
- LA-UR-18-22664

Journal ID: ISSN 2469-990X

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Fluids

- Additional Journal Information:
- Journal Volume: 3; Journal Issue: 9; Journal ID: ISSN 2469-990X

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; mixing; turbulence

### Citation Formats

```
Daniel, Don, Livescu, Daniel, and Ryu, Jaiyoung. Reaction analogy based forcing for incompressible scalar turbulence. United States: N. p., 2018.
Web. doi:10.1103/PhysRevFluids.3.094602.
```

```
Daniel, Don, Livescu, Daniel, & Ryu, Jaiyoung. Reaction analogy based forcing for incompressible scalar turbulence. United States. doi:10.1103/PhysRevFluids.3.094602.
```

```
Daniel, Don, Livescu, Daniel, and Ryu, Jaiyoung. Thu .
"Reaction analogy based forcing for incompressible scalar turbulence". United States. doi:10.1103/PhysRevFluids.3.094602. https://www.osti.gov/servlets/purl/1477698.
```

```
@article{osti_1477698,
```

title = {Reaction analogy based forcing for incompressible scalar turbulence},

author = {Daniel, Don and Livescu, Daniel and Ryu, Jaiyoung},

abstractNote = {Here, we present a novel reaction analogy (RA) based forcing method for generating statistically stationary scalar fields in incompressible turbulence. The new method can produce more general scalar probability density functions (PDFs), for example, quasi-double-δ PDF, than current methods, while ensuring that scalar fields remain bounded, unlike existent forcing methodologies that can potentially violate naturally existing bounds. Such features are useful for generating initial fields in nonpremixed combustion, inlet conditions for spatially developing flows, or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived such that the reaction term is smooth in scalar space and is consistent with mass conservation. For large values of the scalar forcing rate, the method produces statistically stationary quasi-double-δ scalar PDFs. Quasiuniform, Gaussian, and stretched exponential scalar statistics are recovered for smaller values of the scalar forcing rate. The shape of the scalar PDF can be further controlled by changing the stoichiometric coefficients of the reaction. Finally, the ability of the new method to produce fully developed passive scalar fields with quasi-Gaussian PDFs is also investigated, by exploring the convergence of the scalar variance spectrum to the Obukhov-Corrsin scaling and of the third-order mixed structure function to the “four-thirds” Yaglom's law.},

doi = {10.1103/PhysRevFluids.3.094602},

journal = {Physical Review Fluids},

number = 9,

volume = 3,

place = {United States},

year = {2018},

month = {9}

}

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Figures / Tables found in this record:

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