A quantitative method for a priori evaluation of combustion reaction models

Abstract

In recent years, direct numerical simulations have been used increasingly to evaluate the validity and performance of combustion reaction models. This study presents a new, quantitative method to determine the ideal model performance attainable by a given parameterization of the state variables. Data from direct numerical simulation (DNS) of unsteady CO/H₂–air jet flames is analysed to determine how well various parameterizations represent the data, and how well specific models based on those parameterizations perform. Results show that the equilibrium model performs poorly relative to an ideal model parameterized by the mixture fraction. The steady laminar flamelet model performs quite well relative to an ideal model parameterized by mixture fraction and dissipation rate in some cases. However, at low dissipation rates or at dissipation rates exceeding the steady extinction limit, the steady flamelet model performs poorly. Interestingly, even in many cases where the steady flamelet model fails (particularly at low dissipation rate), the DNS data suggests that the state may be parameterized well by the mixture fraction and dissipation rate. A progress variable based on the CO₂ mass fraction is proposed, together with a new model based on the CO₂ progress variable. This model performs nearly ideally, and demonstrates the ability to capture extinction with remarkable accuracy for the CO/H₂ flames considered.

Keywords:

• Combustion modelling
• direct numerical simulation
• manifold
• progress variable

Acknowledgements

This work is supported by the Division of Chemical Sciences, Geosciences, and Biosciences, the Office of Basic Energy Sciences, the US Department of Energy. We also gratefully acknowledge the Scalable Computing Research and Development department at Sandia National Laboratories, the National Energy Research Scientific Computing Center, and the Center for Computational Sciences at Oak Ridge National Laboratory, which provided computational resources for the calculations described herein.

Notes

¹Sometimes χ_st (dissipation rate at f _st) is used rather than χ_max (which occurs at f = 0.5 in equation (7)). These are easily related through equation (7) as χ_max F(0.5) = χ_st F(f _st).