## Linear stability analysis of a premixed flame with transverse shear

## Abstract

One-dimensional planar premixed flames propagating in a uniform flow are susceptible to hydrodynamic instabilities known (generically) as Darrieus–Landau instabilities. Here, we extend that hydrodynamic linear stability analysis to include a lateral shear. This generalization is a situation of interest for laminar and turbulent flames when they travel into a region of shear (such as a jet or shear layer). It is shown that the problem can be formulated and solved analytically and a dispersion relation can be determined. The solution depends on a shear parameter in addition to the wavenumber, thermal expansion ratio, and Markstein lengths. The study of the dispersion relation shows that perturbations have two types of behaviour as wavenumber increases. First, for small shear, we recover the Darrieus–Landau results except for a region at small wavenumbers, large wavelengths, that is stable. Initially, increasing shear has a stabilizing effect. But, for sufficiently high shear, the flame becomes unstable again and its most unstable wavelength can be much smaller than the Markstein length of the zero-shear flame. Lastly, the stabilizing effect of low shear can make flames with negative Markstein numbers stable within a band of wavenumbers.

- Authors:

- Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)

- 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)

- OSTI Identifier:
- 1343118

- Grant/Contract Number:
- NA0002382

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 765; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; flames; instability; reacting flows

### Citation Formats

```
Lu, Xiaoyi, and Pantano, Carlos. Linear stability analysis of a premixed flame with transverse shear. United States: N. p., 2015.
Web. doi:10.1017/jfm.2014.728.
```

```
Lu, Xiaoyi, & Pantano, Carlos. Linear stability analysis of a premixed flame with transverse shear. United States. doi:10.1017/jfm.2014.728.
```

```
Lu, Xiaoyi, and Pantano, Carlos. Mon .
"Linear stability analysis of a premixed flame with transverse shear". United States. doi:10.1017/jfm.2014.728. https://www.osti.gov/servlets/purl/1343118.
```

```
@article{osti_1343118,
```

title = {Linear stability analysis of a premixed flame with transverse shear},

author = {Lu, Xiaoyi and Pantano, Carlos},

abstractNote = {One-dimensional planar premixed flames propagating in a uniform flow are susceptible to hydrodynamic instabilities known (generically) as Darrieus–Landau instabilities. Here, we extend that hydrodynamic linear stability analysis to include a lateral shear. This generalization is a situation of interest for laminar and turbulent flames when they travel into a region of shear (such as a jet or shear layer). It is shown that the problem can be formulated and solved analytically and a dispersion relation can be determined. The solution depends on a shear parameter in addition to the wavenumber, thermal expansion ratio, and Markstein lengths. The study of the dispersion relation shows that perturbations have two types of behaviour as wavenumber increases. First, for small shear, we recover the Darrieus–Landau results except for a region at small wavenumbers, large wavelengths, that is stable. Initially, increasing shear has a stabilizing effect. But, for sufficiently high shear, the flame becomes unstable again and its most unstable wavelength can be much smaller than the Markstein length of the zero-shear flame. Lastly, the stabilizing effect of low shear can make flames with negative Markstein numbers stable within a band of wavenumbers.},

doi = {10.1017/jfm.2014.728},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 765,

place = {United States},

year = {2015},

month = {1}

}

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