Improving combustion simulations through a novel principal component analysis-based reduction technique and a new pressure projection algorithm
Creators: name: Biglari, Amir
Publisher: name: University of Utah
Year: 2016
Subjects: Dimension Reduction Techniques
Pressure Projection
Principal Component Analysis
Reacting Flows
State-Space Parameterization
Turbulent Combustion

description: Turbulent combustion modeling is a complex computational problem. Several factors including the large number of unknowns and equations, stiffness in the chemical source terms, and turbulence-chemistry interaction combine to make simulation of turbulent combustion a grand-challenge problem. Direct Numerical Simulation (DNS) is the most accurate approach to simulate turbulent combustion processes. This approach solves for the full set of chemical variables in the system and is fully resolved in space and time; therefore, it is computationally expensive. There are several models trying to increase the efficiency of turbulent combustion modeling with reducing the number of unknowns, reducing the stiffness of the problem, or decreasing the resolution with the least error possible. In this research, two novel models are introduced to increase the efficiency of turbulent combustion modeling in the Large Eddy Simulation (LES) context. Each method tries to make the modeling more efficient in a different aspect. The first one is a method to reduce the number of species equations that must be solved, via application of Principal Component Analysis (PCA). This technique provides a robust methodology to reduce the number of species equations by identifying correlations in state-space and defining new variables that are linear combinations of the original variables. Here we first present results from \emph{a priori} studies to show the strengths and weaknesses of such a modeling approach. Results suggest that the PCA-based model can identify manifolds that exist in state space which are insensitive to filtering, suggesting that the model is directly applicable for use in Large Eddy Simulation.  Second, we explore the invariance of the manifolds identified by PCA with respect to the problem's parameters. In order to simulate a turbulent process using a PCA-based model, the PCA mapping should be trained using an empirical dataset. This \emph{a priori} study clarifies the important factors for choosing a training dataset. Results indicate that, for given reactant compositions and temperatures, over modest ranges of Reynolds number where the combustion regime does not change dramatically, PCA-derived manifolds are invariant with respect to Reynolds number. It also further confirms PCA manifolds invariance to the filter width, which is an interesting result that suggests the applicability of the model in LES. Finally, an \emph{a posteriori} study of PCA is presented as a combustion model applied to a nonpremixed CO/H$_2$ temporally evolving jet flame with extinction and reignition. As a basis for comparison, results from detailed chemistry calculations are compared with the PCA-transport results to verify the model and evaluate its performance. Invariance of the model's error to the Reynolds number, the number of retained PCs, the PCA scaling factor, and the training dataset is evaluated in this research. The second proposed method is a new explicit variable-density pressure projection method  with a focus on transient low-Mach-number reacting flows in order to avoid implicitness and iterative schemes. The method is based on solving the pressure Poisson equation and is suitable for implementation in fully explicit codes. It has been verified against novel closed-form analytical solutions as well as manufactured solutions for time-varying, variable-density test cases. These cases range from predominantly diffusive to purely convective conditions, and are suitable for use in verification of transient, variable-density flow codes such as those employed in low-Mach-number turbulent combustion simulations. Finally, the algorithm has been used to simulate an annular nonpremixed, nonreacting, variable-density jet flow to qualitatively demonstrate its performance on a practical case.