A reacting jet direct numerical simulation for assessing combustion model error
The simulation of turbulent combustion systems is a vital tool in the design and development of new technologies for power generation, transportation, defense applications, and industrial heating. In an engineering design cycle, modeling realistic device configurations in a cost- and time-effective manner is required. Due to their flexibility and computational tractability, Reynolds-Averaged Navier-Stokes (RANS)-based models are most commonly used for these purposes. However, these models are known to be inadequate. Turbulent combustion is the coupling of two multiscale, nonlinear phenomena which individually have many modeling challenges. Hence, it is unsurprising that the modeling ansatzes and simplifying assumptions which lead to these practical RANS-based models are suspect. Since RANS-based models will continue to be the dominant tool for turbulent combustion simulation, it is necessary to improve their predictivity through a better understanding of their deficiencies.
The are three main modeling issues for turbulent combustion: modeling the turbulent flow, representing the chemical reactions, and capturing the interaction between the turbulence and the chemistry. Model errors can easily be conflated when attempting to quantify deficiencies in this multiphysics context where many individual models are coupled. This work introduces a new technique for isolating these errors through the creation of a flamelet-based direct numerical simulation (DNS) of a nonpremixed, temporally-evolving, planar, reacting jet. DNS is a technique which resolves all lengthscales and timescales of the turbulent flow, providing high-quality data for model development but at a significant computational cost. In the turbulent combustion context, the turbulence-chemistry interaction is also fully resolved. By closing the DNS with a steady laminar flamelet representation, a typical chemical reactions model for RANS-based simulations, RANS turbulence closures and turbulence-chemistry interaction models can be evaluated in isolation through a priori testing. Conversely, by comparing the flamelet DNS to a second DNS employing a higher-fidelity chemistry model, the flamelet closure and its impact on the flame's evolution can be interrogated directly. To obtain the DNS data, a novel algorithm for solving the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser for incompressible flow is detailed here. It is a pseudospectral Fourier/B-spline collocation approach which obtains second order accuracy in time and numerical stability for large density ratios with an efficient, matrix-free, iterative treatment of the scalar equations.
The a posteriori comparisons of the flamelet DNS and the complex chemistry DNS suggest the flamelet model can significantly alter the evolution of the mean state of the reacting jet; however, violations of global conservation were identified in the complex chemistry DNS. Therefore, no strong conclusions can be made about the chemical reactions model from the comparisons. Significant shortcomings have been identified in the a priori evaluations of the aforementioned RANS closures for turbulent transport, scalar mixing, and turbulence-chemistry interaction, where the flamelet model is taken to be exact. Finally, a flawed assumption in the steady laminar flamelet approach has been directly linked to nonphysical behavior of the density for small values of the scalar dissipation rate.