A systematic approach to high-fidelity modeling and efficient simulation of supercritical fluid mixing and combustion

Advances in fluid-flow modeling and simulation techniques over the past two decades have improved understanding of the intricate flow physics and combustion dynamics in the supercritical regime. However, there remain many numerical issues to be addressed, including turbulence closure modeling, combustion modeling, and the evaluation of real-fluid thermodynamic and transport properties. The challenges can be broadly categorized into two areas: (1) achieving highly accurate simulation through inclusion of all the necessary physics and (2) developing a computationally efficient framework to achieve simulation results in a reasonable turnaround time. This paper investigates these challenges and presents a systematic approach to achieve high-fidelity and efficient simulation of supercritical fluid mixing and combustion using large-eddy simulation (LES) techniques. The unresolved subgrid-scale (SGS) term in the filtered equation of state (EOS), which is generally neglected for ideal gases, becomes significant for real fluids, especially in regions of strong property gradients at supercritical conditions. The relative error for the filtered density can reach up to 40%, and this uncertainty can propagate and contaminate calculations of the conservation equations. Two closure models for the SGS term in the EOS are proposed: a gradient-based and a mixing-based approach. Both approaches reduce the modeling error considerably. Flamelet-based combustion models are also examined at supercritical conditions. The probability density functions (PDFs) for mixture fraction and scalar dissipation rate are evaluated using a data-driven approach. The presumed beta-function distribution accurately describes the PDF of the mixture fraction at low mixture fraction variance, but deviates at high variance (> 0.01). The lognormal distribution can capture the shape of the extracted PDF of the scalar dissipation rate but underestimates the peak value. An alternative combustion model using finite-rate chemistry integrated with dynamic adaptive chemistry and correlated transport is developed, rendering a computationally efficient and affordable framework. The efficiency of evaluating real-fluid thermodynamic and transport properties, a computationally expensive procedure, is dramatically enhanced using tabulation and correlated dynamic evaluation techniques. Finally, suggestions are provided regarding opportunities for future research.