Session: 04-27 Combustion Dynamics - Modeling

Paper Number: 153134

Modeling the Response of a Forced Turbulent Premixed Flame Using Resolvent Analysis 

Flows in practical gas turbine combustors operating in the lean premixed regime are composed of multiple shear layers and recirculation zones. These flow features arise from combustion design strategies implemented to achieve flame stabilisation, good fuel-air mixing and reduction in emissions. However, these flow features can result in hydrodynamic instabilities, and the resulting velocity oscillations can interact with the premixed flame, leading to heat release oscillations. The heat release oscillations can couple favourably with the natural acoustic modes of the combustor, resulting in thermoacoustic oscillations, which can be detrimental to the combustor operation. Therefore, understanding the coupling between heat release and velocity oscillations can provide useful insight into efficient combustor nozzle design. We seek to understand the heat release response to harmonic velocity disturbance forcing using a resolvent analysis (RA) framework in this study. 

The flow configuration analysed in this paper is a turbulent premixed methane-air round jet flame at an equivalence ratio of 0.8 and unburnt gas temperature of 800.0 K. We study this flame in two configurations: unforced and forced. The forcing is in the form of low amplitude, harmonic velocity disturbances at the jet inlet. We vary the forcing frequency to evaluate it's impact on the heat release response. Time resolved flow dynamics are computed using an explicit filtering large eddy simulation (EFLES) method for all the cases analyzed in this study.

For constructing the resolvent operator, we first linearize the fully compressible reacting flow governing equations in the low Mach number limit, around a turbulent axi-symmetric time-averaged flow state. Then, we introduce a normal mode form for the perturbation quantities in the time and azimuthal directions. The resolvent operator is then constructed for a given azimuthal wavenumber, m component of the perturbation vector. For the terms that capture turbulent transport of coherently fluctuating momentum in the linearized governing equations, a linear eddy viscosity, ν_T, is used as the closure model. For the source terms arising due to chemical reactions, we compute results using two approaches. In the first method, the source terms arising from the chemical reactions are neglected. In the second method, the source terms are modeled using a linearized Eddy Breakup (EBU) model.

The optimal resolvent input-output mode pairs are computed for the unforced flame case. In the final paper, we will present a formal approach to construct the heat release response of the forced flame. We expect to show in the final paper, that the flame response to low amplitude harmonic forcing for this reacting flow configuration with an arbitrary spatial structure can be constructed using a reduced subset of resolvent modes of the unforced state. 

Presenting Author: Satyam Chauhan Indian Institute of Science

Presenting Author Biography: Satyam Chauhan is a M.Tech (Res.) student in the Aerospace Engineering Department at Indian Institute of Science. His research interests include LES of swirling flows, hydrodynamic stability and resolvent analysis.

Authors:

Satyam Chauhan Indian Institute of Science
Saarthak Gupta Indian Institute of Science
Anindya Datta Indian Institute of Science
Anagha Madhusudanan Indian Institute of Science
Santosh Hemchandra Indian Institute of Science