Accuracy Improvement of Flamelet Generated Manifold (FGM) Model in Modeling Partially Premixed Combustion Systems by Combining Machine Learning
Authors: Shrivastava Sourabh , Gohel Shitanshu , Srinivasa Mohan , Patil Hemesh , Nakod Pravin 
Published: February 2024

Abstract
Reducing the cost of reacting flow modeling is at the core of combustion modeling research. The Flamelet Generated Manifold approach (FGM) is one of the popular modeling methods developed to meet such requirements. The FGM model decouples the reaction zone from the bulk flow and reduces the dimension of reaction space by defining reaction scalars as functions of fewer parameters, like the mixture fraction, progress variable, and variances. The chemistry is pre-tabulated as flamelets and a probability density function (PDF) table. During the simulation, data for reaction scalars is accessed from the PDF table for each finite volume cell, based on controlling parameter values reducing the need for repeated calculations. Flamelet equations used for deriving reaction space are partial differential equations and require the solution of computationally expensive reaction source terms. Flamelets are classified as premixed or diffusion flamelets based on the underlying assumptions of the flow configurations used to derive and solve the flamelet equations.
Most real-world combustion systems operate in partially premixed states. Using the FGM model derived from the flamelets of either one of the families (premixed or diffusion) may limit accuracy under extreme scenarios. Researchers have proposed different parameters to differentiate the dominant local mode — premixed or diffusion of combustion. Such parameters can be clubbed with FGM model to call premixed or diffusion flamelet-based PDF tables, depending upon the local condition, and hence can improve accuracy. However, such workflow requires adding capabilities in Computational Fluid Dynamic (CFD) code to generate the two types of PDF tables, keeping them in the memory during the execution of the run and fetching values from corresponding tables based on calls from each cell. With the increase in the size of PDF tables, the whole process becomes computationally prohibitive from memory and speed requirements.
This work explores the possibility of using the flame index to identify local dominant modes, with the Machine Learning (ML) framework to access the corresponding chemical states through Artificial Neural Networks (ANN). ANNs are explored as an alternative to a PDF table to reduce the memory requirement. The ANNs are trained using premixed and diffusion flamelet-based PDF table test points. They are then used instead of PDF tables during the calculation to reduce the overall memory requirement. The approach is developed to implement flame index calculation and call different ANNs based on the local conditions at the cell level. The methodology is then tested against the experimental data available for Sydney-piloted partially premixed flames. Data of temperature and mixture fraction distribution at different axial locations are used to compare the accuracy improvement by the proposed methodology against the default FGM model results (based on either premixed or diffusion flamelets). ANN model-based approach is found to predict results much closer to test data and maintain the RAM requirement much lower than the PDF tables.