Low-Dimensional Manifold Simulation of Turbulent Reacting Flows Using Linear and Nonlinear Principal Components Analysis

Moment based simulation of the turbulent reacting flows have been based on the transport of the moments that parameterize the composition space in a given reactive system. These moments characterize the progress of a chemical system. Traditionally, these moments have been problem-specific, e.g. mixture fraction and progress variable for non-pre-mixed flames. The statistics of the reactive scalars, e.g. temperature and species mass fractions, can be derived from the moments' solution. On the other word, these moments parameterize the composition space. Moments' methods have been reasonably successful in predicting combustion flows in a broad range of applications. However, the validity of a given set of moments and their required number to parameterize the composition space depend on the complexity of the problem. Refinements of such moments' approaches invariably require the addition of more moments, and the inherent need for more closure models associated with the additional moments' transport equations. An alternative strategy within the moments' methods concept has gained increased attention in recent years. It is based on the construction of optimum moments that parameterize the composition space starting from numerical or experimental high fidelity data using principal component analysis (PCA). The present study falls under this framework and another framework of stand-alone one dimensional turbulent (ODT) modeling based on the mechanistic distinction between molecular processes including reaction and diffusion, and turbulent advection. Different versions of PCA are investigated: Linear (classical) PCA, Kernel PCA, and bottleneck neural network (BNN) PCA. First, an a priori validation of the proposed approach is carried out. The PCs' transport equations are constructed. Principal components (PCs) are derived from the high fidelity data based on a canonical problem that reproduces important features in composition space of the desired problem. Then, the composition space and the transport terms in the PC's transport equation are tabulated and reconstructed using artificial neural network (ANN) approach. It is shown that the ANN is capable of making up for the loss of information contained in the removed moments by adjusting the weight connection matrices between the input-retained set of PCs, and the scalars values.;After successful implementation of the a priori step, the a posteriori validation of the proposed PCA-ANN approach is performed, in the context of stand-alone ODT solution of methane-air jet flame, called Sandia Flame F. The solution of this flame is performed by transporting the retained set of PCs as well as transporting the original thermochemical scalars. The successful validation of the proposed PCA-ANN approach is shown through the 1D profile of the streamwise velocity and the thermochemical scalars including the temperature, major and intermediate species, and also the minor species that are not participating in the reduction step.