Reduced Order Modeling of Turbulence-Chemistry Interactions using Dynamically Bi-Orthonormal Decomposition

The performance of the dynamically bi-orthogonal (DBO) decomposition for the reduced order modeling of turbulence-chemistry interactions is assessed. DBO is an on-the-fly low-rank approximation technique, in which the instantaneous composition matrix of the reactive flow field is decomposed into a set of orthonormal spatial modes, a set of orthonormal vectors in the composition space, and a factorization of the low-rank correlation matrix. Two factors which distinguish between DBO and the reduced order models (ROMs) based on the principal component analysis (PCA) are: (i) DBO does not require any offline data generation; and (ii) in DBO the low-rank composition subspace is time-dependent as opposed to static subspaces in PCA. Because of these features, DBO can adapt on-the-fly to intrinsic and externally excited transient changes in state of the transport variables. For demonstration, simulations are conducted of a non-premixed CO/H2 flame in a temporally evolving jet. The GRI-Mech 3.0 model with 53 species is used for chemical kinetics modeling. The results are appraised via a posteriori comparisons against data generated via full-rank direct numerical simulation (DNS) of the same flame, and the PCA reduction of the DNS data. The DBO also yields excellent predictions of various statistics of the thermo-chemical variables.