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research-article

Quantification and Propagation of Uncertainties in Identification of Flame Impulse Response For Thermoacoustic Stability Analysis

[+] Author and Article Information
Shuai Guo

Research Assistant, Student Member of ASME, Professur für Thermofluiddynamik, Technische Universität München, Boltzmannstr. 15, D-85748, Garching, Germany
guo@tfd.mw.tum.de

Camilo F. Silva

Ph.D., Professur für Thermofluiddynamik, Technische Universität München, Boltzmannstr. 15, D-85748, Garching, Germany
silva@tfd.mw.tum.de

Abdulla Ghani

Ph.D., Professur für Thermofluiddynamik, Technische Universität München, Boltzmannstr. 15, D-85748, Garching, Germany
ghani@tfd.mw.tum.de

Wolfgang Polifke

Professor, Ph.D., Professur für Thermofluiddynamik, Technische Universität München, Boltzmannstr. 15, D-85748, Garching, Germany
polifke@tfd.mw.tum.de

1Corresponding author.

ASME doi:10.1115/1.4041652 History: Received August 28, 2018; Revised September 14, 2018

Abstract

Thermoacoustic behavior of a combustion system can be determined numerically via acoustic tools coupled with a model for the flame dynamic response. Within such a framework, the flame dynamics can be described by a Finite Impulse Response (FIR) model, which can be derived from LES time series via system identification. However, the estimated FIR model will inevitably contain uncertainties due to low signal-to-noise ratio or finite length of time series. Thus, a necessary step towards reliable thermoacoustic stability analysis is to quantify the impact of uncertainties in FIR model on the growth rate of thermoacoustic modes. There are two practical considerations involved in this topic. First, how to efficiently propagate uncertainties from the FIR model to the modal growth rate of the system, considering it is a high dimensional uncertainty quantification (UQ) problem? Second, since longer CFD simulation time generally leads to less uncertain FIR model identification, how to determine the length of the CFD simulation required to obtain satisfactory confidence? To address these two issues, a dimensional reduction UQ methodology called "Active Subspace'' is employed in the present study. For the first question, Active Subspace is applied to exploit a low-dimensional approximation of the original system, which allows accelerated UQ analysis. Good agreement with Monte Carlo analysis demonstrates the accuracy of the method. For the second question, a procedure based on Active Subspace is proposed, which can serve as an indicator for terminating CFD simulation. The effectiveness of the procedure is verified in the paper.

Copyright (c) 2018 by ASME
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