Uncertainty Quantification in Spray Combustion Dynamics

Motivation

Liquid spray combustion is widely employed in aircraft propulsion system. Compared with gaseous combustion, dynamics of the spray combustion, shown as the coupling between the unsteady heat release and the acoustic oscillations, exhibit a much higher level of complexity, due to additionally involved physical phenomena, e.g., droplet atomization and collision, heating and evaporation, gas-liquid turbulence interaction, etc. As a result of its multi-phase, multi-scale, multi-interaction nature, the thermoacoustic behaviors as well as their predictions of the spray combustion are highly sensitive to small variations in configuration geometries, boundary and initial conditions, operating conditions and parameters adopted in various computational models. Therefore, uncertainty quantification (UQ) analysis, which focuses on identifying the uncertainty sources in the system inputs and quantifying the impact of the uncertain system inputs on the system outputs, constitutes a critical step towards a more reliable thermoacoustic stability analysis, and paves the way for developing robust active control schemes to ensure a stable operation of the gas turbine combustor.

Objectives and Strategy

This project will cover three aspects of uncertainty quantification in thermoacoustic instability analysis of turbulent spray combustion:

Forward uncertainty quantification: The goal here is to quantify the impact of uncertain system inputs on the variations of system outputs. The sources of the inputs’ uncertainties which are considered in the current project include variations in configuration geometries, boundary and initial conditions, operating conditions as well as various parameters adopted in physical-describing analytical models implemented in numerical thermoacoustic-behavior-prediction routines. Considering the limitation of standard Monte Carlo approach when one-time system evaluation is computational intensive, various surrogate modeling techniques (e.g., Active Subspace approach, non-intrusive/intrusive polynomial chaos expansion, Kriging-based response surface method, etc.) will be employed to achieve accurate and efficient uncertainty propagation. The obtained results are expected to provide an “error-bar” for the thermoacoustic instability prediction of the turbulent spray combustion.

Inverse uncertainty quantification: The goal here is to derive the uncertainty information on two different levels: (1) on the parameter level, calibrations will be performed to extract full statistical descriptions of the parameters embedded in target physical-describing model from noisy training data (experimental or computational). The obtained results are expected to inform practitioner regarding how much more resources (experimental or computational) need to be allocated to lower the parameter uncertainty to a satisfactory level. (2) on the model level, a model selection analysis will be performed to determine which model, among a set of plausible models, is the optimal in terms of generating predictions aligning better with the training data. The obtained results are expected to reveal physical insights of the associated phenomenon, which are already embedded in the determined optimal model. Advanced Monte Carlo Markov Chain approach, which is based on Bayesian inference methodology, will be employed to address the above two problems.

Global sensitivity analysis: The goal here is to determine the sensitivity of the output against each input parameter by looking at the entire input parameter space. Approaches based on variance-decomposing methodology will be employed to address this problem. The obtained results are expected to (1) identify the group of parameters responsible for driving the variations of the output and reveal the physical mechanisms represented by these parameters; (2) identify the unimportant parameters which can lead to model order reduction; (3) identify the critical parameters that drive the thermoacoustic system goes unstable.

Acknowledgement

Financial support has been provided by the doctoral scholarship of Chinese Scholarship Council (No. 201606830045), whose support is gratefully acknowledged.