Efficient Kinetic Uncertainty Quantification Framework for Turbulent Combustion Simulations

Outlined below is a highly efficient flamelet-based reduction method for turbulent combustion kinetic uncertainty quantification developed in the DENG lab at MIT. Key novelties of this kinetic reduction process include its applicability to the entire computational domain of a turbulent flame, remarkable efficiency when quantifying the kinetic uncertainty effects of high-dimensional kinetic models, and verified accuracy when compared against brute force sampling methods. Its performance is enabled through use of the active subspace methodology, as well as a specialized neural network response surface (shown below).

An initial study [1] found that, in the high strain regions of certain premixed flamelets, the kinetic sensitivity directions were largely independent of strain rate. That is, as the strain rate changes, the temperature and species responses of certain flames to perturbed kinetic models remained one-dimensional, and the dominant one-dimensional kinetic sensitivity direction remained largely consistent.

A later study [2] investigated the mixture fraction dependence of such kinetic sensitivities in nonpremixed flamelets. It similarly found that a one-dimensional kinetic subspace dominates the uncertainty response at each individual mixture fraction location sampled within a methane flamelet. However, when assessing these directions across the entire mixture fraction domain, significant breakdown of kinetic similarity was observed, requiring an increase to a four-dimensional subspace in order to capture the kinetic uncertainty across the entire flamelet.

A turbulent combustion demonstration [3] was finally carried out, using the insights and results from the above studies to inform the developed methodology and perform high-accuracy kinetic uncertainty quantification on a Reynolds averaged, flamelet-based simulation of the turbulent Sandia Flame D. This study demonstrated an active subspace and neural network powered methodology that was able to capture the uncertainty response of the turbulent combustion simulation with just seven perturbed samples of the greatly reduced subspace, compared to the thousands needed when using brute force sampling. Such significant computational savings along with the ~75-85% accuracy seen when compared against the brute force uncertainty ranges demonstrate promise for the application of this method in uncertainty quantification for computationally expensive turbulent combustion simulations.

Below are a few key figures demonstrating the process and results of this methodology.

Sample pipeline from the study carried out in [3]. Starting from the laminar nonpremixed flamelets, which have 217 reactions, a neural network is trained as a kinetic response surface (top middle, green) in which active subspace evaluation takes place. The multi-stage subspace reduction results in just three kinetic perturbation directions (top right, green) that capture a large amount of the kinetic uncertainty in the flamelets. By perturbing the kinetic model along these three directions, it is possible to construct temperature uncertainty profiles across the entire 2-D turbulent Sandia Flame D profile using just seven forward solves of the simulation (bottom, grey). When compared to the much more expensive fully perturbed samples (bottom left, blue), it is seen that this greatly reduced subspace-based sampling retains high accuracy.

A specialized neural network was developed based on recent advances in the scientific machine learning community in order to learn flame profiles across both the mixture fraction and strain rate spaces of a flamelet table. The split architecture here provides the network with inductive bias related to the physics-based split between the mixture fraction sampling location and underlying chemistry and flow properties. Additionally, the inclusion of mixture fraction and strain rate as network inputs allows for grid-independent training and application. This neural network was first introduced in [2], and then later expanded in [3] to include strain rate as an input node.

Temperature and CO mass fraction uncertainty range comparisons (3σ) of the Sandia Flame D between 2,000 brute force samples of the GRI-Mech 3.0 mechanism (blue) and 7 Latin Hypercube samples of the three kinetic subspace directions (green). Left figures (a, c) are measured at the centerline of the simulated flame, while right figures (b, d) are measured at the x/D=30 axial slice. Further discussion available in [3].