# Oscillatory response of an idealized two-dimensional diffusion flame: Analytical and numerical study

## Abstract

The heat release response of a two-dimensional (2-D) co-flow diffusion flame is theoretically investigated for the mass fraction fluctuations of reactant concentration at the inlet boundary and for time-varying spatially uniform flow velocity field in the domain. The present work is an extension of the Burke-Schumann steady flame model to an oscillatory situation, but in a 2-D framework. The governing equation of the problem is the scalar advection equation for the Schwab-Zel'dovich variable. An exact solution is found in terms of an infinite series for the case of mixture fraction fluctuations at the inlet boundary. The cases of time-varying uniform flow velocity field and a combination of velocity and mixture fraction fluctuations are investigated numerically. The temperature and heat release rate of the flame are thermodynamically calculated utilizing the mixed-is-burnt approach. The main results of the paper are the response functions. The nonlinearity in the calculation of the heat release rate and the convective nonlinearity due to velocity fluctuations result in the generation of higher harmonics in the response function for a given sinusoidal excitation. Therefore, the response function is decomposed and obtained for each of the significant harmonics. The results show that, in general, the response function decreases withmore »

- Authors:

- Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036 (India)
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036 (India)

- Publication Date:

- OSTI Identifier:
- 20880663

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Combustion and Flame; Journal Volume: 149; Journal Issue: 3; Other Information: Elsevier Ltd. All rights reserved

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; RESPONSE FUNCTIONS; FLUCTUATIONS; FLAMES; MIXTURES; NUMERICAL SOLUTION; DIFFUSION; VELOCITY; HARMONICS; EXCITATION; HEAT; TWO-DIMENSIONAL CALCULATIONS; NONLINEAR PROBLEMS; EXACT SOLUTIONS; EQUATIONS; ADVECTION; SCALARS; SHAPE; SERIES EXPANSION; MASS; OSCILLATIONS; COMBUSTION KINETICS; FREQUENCY DEPENDENCE

### Citation Formats

```
Tyagi, Manav, Jamadar, Nachiket, and Chakravarthy, S.R.
```*Oscillatory response of an idealized two-dimensional diffusion flame: Analytical and numerical study*. United States: N. p., 2007.
Web. doi:10.1016/J.COMBUSTFLAME.2006.12.020.

```
Tyagi, Manav, Jamadar, Nachiket, & Chakravarthy, S.R.
```*Oscillatory response of an idealized two-dimensional diffusion flame: Analytical and numerical study*. United States. doi:10.1016/J.COMBUSTFLAME.2006.12.020.

```
Tyagi, Manav, Jamadar, Nachiket, and Chakravarthy, S.R. Tue .
"Oscillatory response of an idealized two-dimensional diffusion flame: Analytical and numerical study". United States.
doi:10.1016/J.COMBUSTFLAME.2006.12.020.
```

```
@article{osti_20880663,
```

title = {Oscillatory response of an idealized two-dimensional diffusion flame: Analytical and numerical study},

author = {Tyagi, Manav and Jamadar, Nachiket and Chakravarthy, S.R.},

abstractNote = {The heat release response of a two-dimensional (2-D) co-flow diffusion flame is theoretically investigated for the mass fraction fluctuations of reactant concentration at the inlet boundary and for time-varying spatially uniform flow velocity field in the domain. The present work is an extension of the Burke-Schumann steady flame model to an oscillatory situation, but in a 2-D framework. The governing equation of the problem is the scalar advection equation for the Schwab-Zel'dovich variable. An exact solution is found in terms of an infinite series for the case of mixture fraction fluctuations at the inlet boundary. The cases of time-varying uniform flow velocity field and a combination of velocity and mixture fraction fluctuations are investigated numerically. The temperature and heat release rate of the flame are thermodynamically calculated utilizing the mixed-is-burnt approach. The main results of the paper are the response functions. The nonlinearity in the calculation of the heat release rate and the convective nonlinearity due to velocity fluctuations result in the generation of higher harmonics in the response function for a given sinusoidal excitation. Therefore, the response function is decomposed and obtained for each of the significant harmonics. The results show that, in general, the response function decreases with increase in the excitation frequency as reported with premixed flames in the literature. However, in the present case, the decrease occurs when the excitation time-scale is less than the diffusion time-scale. Interesting flame shape variations such as flame clip-off, flipping between overexpanded and underexpanded conditions, and flame wrinkling are observed in the case of mixture fraction oscillations. (author)},

doi = {10.1016/J.COMBUSTFLAME.2006.12.020},

journal = {Combustion and Flame},

number = 3,

volume = 149,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}