A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations

Abstract

Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast, efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. As an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption lead to a 15 % under-prediction of the normalized turbulent flame speed for premixed hydrogen air flames. This large difference in the turbulent flame speed raises questions on the appropriateness of using the mixture-averaged diffusion assumption for DNS of moderate to high Karlovitz number flames.

Assessing diffusion model impacts on enstrophy and flame structure in turbulent lean premixed flames

“…The diffusion fluxes are calculated using the semi-implicit scheme developed by Fillo et al 20 with either mixture-averaged 4 or multicomponent 21 models, both of which are based on Boltzmann's equation for the kinetic theory of gases 21,22 . We neglect both baro-diffusion and thermal diffusion (i.e., Soret and Dufour effects).…”

“…Chemical reactions in the hydrogen-air mixture are solved using the nine species, 54 reaction chemistry model from Hong et al [28][29][30] (forward and backward reactions are counted separately). The 3D turbulent flames are simulated using an identical flow configuration as in previous studies 14,20,26,31,32 , and therefore we only provide a brief description here. The computational domain consists of inflow and convective outflow boundary conditions in the streamwise (i.e., x) direction.…”

Assessing the impact of multicomponent diffusion in direct numerical simulations of premixed, high-Karlovitz, turbulent flames

“…However, modeling full multicomponent mass diffusion transport in a di-rect numerical simulation (DNS) can be computationally expensive, caused both by the cost of calculating the diffusion coefficients and the memory required to store the multicomponent diffusion coefficient matrix at every location [14]. As a result, researchers typically use simplified diffusion models to reduce the computational costs associated with calculating the diffusion coefficients [15,16].…”

“…Both methods reduce the computational cost of inverting the dense matrix associated with the Stefan-Maxwell equations [1,31,32]. Most recently, Fillo et al [14] proposed a fast, semi-implicit, low-memory algorithm for implementing multicomponent mass diffusion, which we use here with the DNS code NGA. As a preliminary demonstration of their method, Fillo et al [14] simulated lean, premixed, three-dimensional turbulent hydrogen/air flames at moderate-to-high Karlovitz numbers using the mixture-averaged and multicomponent diffusion models.…”

“…Most recently, Fillo et al [14] proposed a fast, semi-implicit, low-memory algorithm for implementing multicomponent mass diffusion, which we use here with the DNS code NGA. As a preliminary demonstration of their method, Fillo et al [14] simulated lean, premixed, three-dimensional turbulent hydrogen/air flames at moderate-to-high Karlovitz numbers using the mixture-averaged and multicomponent diffusion models. In these flames, the mixture-averaged diffusion model underpredicts the peak mean source term and normalized turbulent flame speed by 5.5 % and 15 %, respectively [14].…”