Bayesian Data Assimilation for CFD Modeling of Turbulent Combustion

Abstract

Achieving accurate CFD prediction of turbulent combustion is challenging due to the multiscale nature of the dynamical system and the need to understand the effect of the small-scale physical features. Since direct numerical simulation (DNS) is still not feasible even for today’s computing power, Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES) is commonly used as the practical approach for turbulent combustion modeling. Nevertheless, physical models employed by RANS or LES for describing the interactions between the turbulence, chemical kinetics, and thermodynamic properties of the fluid are often inadequate because of the uncertainties in the dynamical system, including those in the model parameters, initial and boundary conditions, and numerical methods. Understanding and reducing these uncertainties are critical to the CFD prediction of turbulence and chemical reactions. To achieve this, this dissertation is focused on the development of a Bayesian computational framework for the uncertainty estimation of the dynamical system. In the framework, a data assimilation (DA) algorithm is integrated to obtain a more accurate solution by combining the CFD model and available data.

This research details the development, verification, and validation of a multi-algorithm system (referred to as DA+CFD system) that aims to increase the predictability of CFD modeling of turbulent and combusting flows. Specifically, in this research, we develop and apply a Bayesian computational framework by integrating our high-order CFD algorithm, Chord, with the maximum likelihood ensemble filter to improve the CFD prediction of turbulent combustion in complex geometry. The verified and validated system is applied to a time-evolving, reacting shear-layer mixing problem and turbulent flows in a bluff-body combustor with and without C$_3$H$_8$-air combustion. Results demonstrate the powerful capability of the DA+CFD system in improving our understanding of the uncertainties in model and data and the impact of data on the model.

This research makes novel contributions, including (i) the development of a new alternative approach to improve the predictability of CFD modeling of turbulent combustion by applying data assimilation, (ii) the derivation of new insights on factors, such as where, what, and when data should be assimilated and thus providing potential guidance to experimental design, and (iii) the demonstration of data assimilation as a potentially powerful approach to improve CFD modeling of turbulent combustion in engineering applications and reduce the uncertainties with data. Future work will focus on a performance study of the present DA+CFD system for turbulent combustion of high Reynolds numbers and understanding the uncertainty in model parameters for developing and assessing physical models based on available information.