An Efficient Machine-Learning Approach for PDF Tabulation in Turbulent Combustion Closure

Abstract

Probability density function (PDF) based turbulent combustion modelling is limited by the need to store multi-dimensional PDF tables that can take up large amounts of memory. A significant saving in storage can be achieved by using various machine-learning techniques that represent the thermo-chemical quantities of a PDF table using mathematical functions. These functions can be computationally more expensive than the existing interpolation methods used for thermo-chemical quantities. More importantly, the training time can amount to a considerable portion of the simulation time. In this work, we address these issues by introducing an adaptive training algorithm that relies on multi-layer perception (MLP) neural networks for regression and self-organizing maps (SOMs) for clustering data to tabulate using different networks. The algorithm is designed to address both the multi-dimensionality of the PDF table as well as the computational efficiency of the proposed algorithm. SOM clustering divides the PDF table into several parts based on similarities in data. Each cluster of data is trained using an MLP algorithm on simple network architectures to generate 'local' functions for thermo-chemical quantities. The algorithm is validated for the socalled DLR-A turbulent jet diffusion flame using both RANS and LES simulations and the results of the PDF tabulation are compared to the standard linear interpolation method. The comparison yields a very good agreement between the two tabulation techniques and establishes the MLP-SOM approach as a viable method for PDF tabulation.

Progress in the Application of Machine Learning in Combustion Studies

“…[22] ML seems to be able to solve problems where the dependencies are nonlinear relationships between inputs and outputs or insufficiently known to be programmed in a traditional and rigid manner. [22] The advantages make ML play an important role in studies related to combustion theory, such as Computational Fluid Dynamics (CFD) simulation of combustion, [23][24][25] prediction of combustion phenomenon [26][27][28][29] and fuels. [30][31][32][33][34][35] ML can help to reduce mechanism scales, [23] optimize probability density function (PDF) [24] and Large Eddy Simulation (LES) [25] method in combustion simulation.…”

“…[22] The advantages make ML play an important role in studies related to combustion theory, such as Computational Fluid Dynamics (CFD) simulation of combustion, [23][24][25] prediction of combustion phenomenon [26][27][28][29] and fuels. [30][31][32][33][34][35] ML can help to reduce mechanism scales, [23] optimize probability density function (PDF) [24] and Large Eddy Simulation (LES) [25] method in combustion simulation. When investigating combustion phenomenon, ML algorithms were used to detect thermoacoustic combustion oscillations, [26,27] distinguish donation and ignition [28] and reconstruct the detonation surface.…”

“…Some scholars have used ML algorithms to solve problems involving combustion in CFD simulation. [23][24][25] Detailed kinetic model is the key factor to simulate laminar and turbulent flames. The computing cost of coupling detailed mechanism with CFD is too high, because detailed models contain too many species and elementary reactions, which recall the simplification of kinetic models.…”

“…Nonetheless, previous ANN tabulation studies need too much training time and have too many nonlinear activation functions to solve, which enlarge the computational costs and time, offsetting the advantage of memory saving. In combination with multi-layer perception (MLP) neural networks for regression and self-organizing maps (SOM) for clustering data, Ranade et al [24] developed a small and compact ANN, which is more accurate and costsaving in training and computation compared to previous ANN. The advantage of MLP-SOM is to find optimum number of neurons and subsequently construct a simpler network that can reduce training and interpolation time.…”

“…Compared to linear PDF interpolation approach, MLP-SOM method owns the advantage of easily accommodating more parameterized quantities due to 1000 times smaller memory requirements. [24] ).…”