A Novel Hybrid Scheme for Large Eddy Simulation of Turbulent Combustion Based on the One-Dimensional Turbulence Model

Abstract

A hybrid numerical scheme based on large eddy simulation (LES) and the one-dimensional turbulence (ODT) model for turbulent combustion is developed and validated. The ODT model resolves, both temporally and spatially, subgrid scale processes such as mixing, molecular transport, and chemistry. This model addresses the limitations of traditional models in representing strong local and transient phenomena such as ignition or extinction and processes strongly dependent on cross-correlations of different scalars.

The ODT model formulation and numerical implementation involves the treatment of different processes governing the transport and chemistry for scalars and momentum through a combination of stochastic and deterministic solutions, which are implemented in parallel on the ODT domains. These domains are embedded in the LES computational domain. The ODT-based and the LES solutions provide a coupled set of solutions for scalars and momentum with redundancy in the way these quantities can be computed. The key processes included in the proposed formulation are: molecular processes consisting of reaction and diffusion, turbulent stirring, and filtered convection. In the present study, turbulent stirring is represented by random, instantaneous rearrangements of the fields of transported variables along a one-dimensional line via 'triplet maps', which emulate the rotational folding effects of turbulent eddies. Molecular diffusion and chemistry are solved deterministically through finite-difference solutions of the unsteady reaction-diffusion transport equation along the 1D domain. A novel method to incorporate 3D convection in ODT, denoted as 'node convection' combined with 'intra-node relaxation', is implemented. The Smagorinsky model is used as a subgrid stress closure model for LES. The coupling of LES and ODT is accomplished spatially by interpolating velocity information from LES to ODT and temporally at each LES time step.

The problem of non-homogeneous autoignition in isotropic turbulence is used to validate the proposed model. This problem offers a stringent test for the proposed model because it exhibits different modes of combustion (from ignition kernels to premixed and non-premixed flames) and a complex coupling between turbulent transport and molecular processes, diffusion and reaction, under highly transient conditions. The validation is carried out in comparison of the LES-ODT results with results from Direct Numerical Simulations (DNS). Both low and high turbulence conditions are considered, with three Lewis number cases carried out for the high turbulence condition. Both volume-averaged statistics and mixture fraction-conditioned statistics show that LES-ODT is able to accurately predict not only the flame ignition and extinction, kernel propagation, transition between different burning modes, but also the turbulence and Lewis number effects. LES-ODT simulation results are in excellent agreement with DNS results. This is achieved with a significantly reduced computational cost compared to DNS.