Forward propagation of kinetic uncertainty in combustion simulations usually adopts response surface techniques to accelerate Monte Carlo sampling. Yet it is computationally challenging to build response surfaces for high-dimensional input parameters and expensive combustion models. This study uses the active subspace method to identify low-dimensional subspace of the input space, within which response surfaces can be built. Active subspace methods have previously been developed only for single (scalar) model outputs,

however. This paper introduces a new method that can simultaneously approximate the marginal probability density functions of multiple outputs using a single low-dimensional shared subspace. We identify the shared subspace by solving a least-squares system to compute an appropriate combination of single-output active subspaces. Because the identification of the active subspace for each individual output may require a significant number of samples, this process may be computationally intractable for expensive models such as turbulent combustion simulations. Instead, we propose a heuristic approach that learns the relevant subspaces from cheaper combustion models. The performance of the active subspace for a single output, and of the shared subspace for multiple outputs, is first demonstrated with the ignition delay times and laminar flame speeds of hydrogen/air, methane/air, and dimethyl ether (DME)/air mixtures. Then we demonstrate extrapolatory performance of the shared subspace: using a shared subspace trained on the ignition delays at constant volume, we perform forward propagation of kinetic uncertainties through zero-dimensional HCCI simulations – in particular, single-stage ignition of a natural gas/air mixture and two-stage ignition of a DME/air mixture. We show that the shared subspace can accurately reproduce the probability of ignition failure and the probability density of ignition crank angle conditioned on successful ignition, given uncertainty in the kinetics.

Transported probability density function (TPDF) methods are attractive for modeling turbulent flames as the highly nonlinear chemical reactions appear in closed form.  The ability of the TPDF methods to capture complex phenomena such as extinction and re-ignition has been well demonstrated for turbulent non-premixed flames. However challenges remain when applying the TPDF methods to turbulent premixed flames, for which modeling molecular diffusion is difficult because the local species gradients may be strongly influenced by chemical reactions. The specification of a constant mechanical-to-scalar timescale ratio to relate the scalar mixing timescale to the turbulence timescale is questionable for premixed flames in the flamelet regime.

A new mixing timescale model is proposed to account for both flamelet-controlled and turbulence-controlled mixing to more accurately model scalar mixing rates [1,2]. In the limit of passive scalar mixing, the mixing timescale is proportional to the turbulence timescale according to the classical expression. Conversely, in the limit of laminar flamelets embedded in a turbulent flow field, the scalar mixing rate is expected to depend on the laminar flame structure, where the conditional scalar dissipation rate can be obtained from 1D laminar premixed reference flames.

A priori assessment using the DNS datasets of the H2-air premixed flames, as well as a posteriori tests in CH4-air Slot Bunsen flames, both demonstrate the model potential to better predict scalar dissipation and flame characteristics.

[1] Zhou, Z., Li, S., Wang, H., and Ren, Z. 2015. An investigation of a hybrid mixing model for PDF simulations of turbulent premixed flames. 68th Annual Meeting of the APS Division of Fluid Dynamics.

[2] Kuron, M., Ren, Z., Hawkes, E.R., Zhou, H., Kolla, H., Chen, J.H., and Lu, T. 2017. A mixing timescale model for TPDF simulations of turbulent premixed flames, Combust. Flame, 177, 171-183

In numerical simulations of combustion processes, the use of dimension reduction to simplify the description of the chemical system has the advantage of reducing the computational cost, but it is important also to retain accuracy and adequate detail. In current research, dimension reduction of combustion chemistry is performed by using the ICE-PIC method. The ICE-PIC method is developed based on three major ingredients: constrained equilibrium; trajectory-generated manifolds; and, the pre-image curve method. The low-dimensional manifold identified, the ICE manifold, is invariant, continuous and piecewise smooth. The ICE-PIC method achieves local species reconstruction based on the constrained-equilibrium pre-image curve. In comparison to other existing methods such as QSSA, RCCE and ILDM, this method is the first approach that locally determines compositions on a low-dimensional invariant manifold.

The accuracy of the ICE-PIC method has been examined in autoignition and in one-dimensional laminar flames of hydrogen/air and methane/air mixtures. Studies demonstrate that the local errors incurred by ICE-PIC (e.g., the errors in the reconstructed composition) are well controlled. The capability of the ICE-PIC method for the reduced description of reactive flows is demonstrated through the calculation of the oxidation of CO/H2 in a CSTR. The reduced description provided by the ICE-PIC method is capable of quantitatively reproducing the complex dynamics.

The final goal is to develop an efficient and accurate algorithm - In Situ Adaptive Tabulation with Dimension Reduction (the ICE-PIC method) to incorporate detailed chemistry in turbulent combustion simulations.