A Comparison of Two Low-Dimension Manifold Combustion Models for Nonpremixed Supersonic Combustion

Hypersonic air-breathing propulsion systems can greatly be advanced if high fidelity simulation tools are increasingly used in the design process. Conventional design approaches for high speed propulsion systems have mainly relied on low fidelity tools and/or empirical models. Accurate computational fluid dynamics (CFD) methods tend to be extremely costly when applied to practical high-speed turbulent combustion problems. The scramjet combustor environment is plagued with complex interaction between turbulence, compressibility, and combustion physics. The presence of a wide range of spatiotemporal scales makes the problem too expensive to simulate with high fidelity simulation tools. However, with the development of more robust computational resources and the emergence of novel and resourceful simulation approaches, there is an increase in interest to reexamine the methodologies that simulate high speed reacting turbulent flows. With that in mind, the goal of this research project was to conduct a comparative investigation between two supersonic turbulent combustion modeling methodologies within the Large Eddy Simulation (LES) framework. These modeling approaches rely on the use of tabulated chemistry. Tabulated chemistry models are perceived to be more computationally cost effective. Turbulent combustion models of this type tend to assume that there is a separation of scales between turbulence and chemical reaction scales. As such, the turbulent combustion problem can be decomposed into two smaller problems. The first problem involves solving a mixing and transport problem and the second problem involves solving the flame structure. This decomposition allows the mapping of complex chemistry onto a set of tracking variables. The two main tracking variables are the mixture fraction and the progress variable. The mixture fraction is a conserved scalar that tracks the mixing between the fuel and oxidizer. The progress variable is a non-conserved variable that tracks how far the chemical reactions have progressed towards equilibrium. The complex mapping between the tracking variables and chemistry can then be stored on a low dimensional manifold, which will then be used to describe the chemical state. The first model that is examined in this research project is the Flamelet/Progress Variable (FPV). The basic assumption in most flamelet type models is that the chemical time scales are significantly shorter than the convective time scales. The assumption implies that turbulent combustion is made up of a collection of steady laminar predominantly one-dimensional flames. The complex flame structure is simplified to a one-dimensional steady-state reaction-diffusion problem. The flamelet type models were designed for incompressible flow. In a compressible flow environment, pressure can vary significantly. To account for these compressibility effects, the production rate for the progress variables is altered to be a function of pressure and temperature. The second model is the evolution-variable manifold (EVM) model. This turbulent combustion model assumes that combustion mainly occurs in the distributed reaction-zone (DRZ) regime. In this regime, the turbulent scales are smaller than the chemical scales, which is opposite from the flamelet assumptions. This leads to rapid turbulent mixing of scalars prior to the reaction process. The flame structure problem is simplified to solving a zero-dimensional unsteady reaction problem. The EVM approach represents the combustion process as being an interaction of Lagrangian chemically evolving fluid elements that are being transported with the flow. The heart of this investigation involves the development of a CFD solver that can simulate supersonic combustion flows using the investigated LES combustion models. The combustion models were implemented in a well-established CFD solver, US3D. The US3D code is an unstructured finite volume CFD solver that was developed at the University of Minnesota. The solver has the capability to simulate highly compressible and complex flows. Additionally, external solvers that build the tabulated chemistry libraries had to be developed for this project. For comparison, the FPV and EVM models were used to simulate a reacting transverse jet in a supersonic crossflow (JISCF) experiment. This experiment was conducted by M. Gamba and M.G. Mungal. The complex flow features that are present in the flowfield makes this experiment a relevant choice for a validation study. Features such as shocks, recirculation regions, shear layers, expansion regions, and compression regions can be observed in a typical scramjet combustor. In the current research project, we compared the hydroxyl radical planar laser-induced fluorescence (OH-PLIF) measurements of Gamba and Mungal to the FPV and EVM results. The OH-PLIF signals were not calibrated to match specific temperatures; therefore, the comparisons are qualitative in nature. In the experiment, . three regions of combustion are observed. These regions can be described as the recirculation region, the shear layer on the windward side of the jet, and the near wall region behind the jet. Both models were able capture these burning regions. However, the FPV simulation had weaker flames compared to the EVM simulation. The OH-PLIF signal comparison indicated that the EVM captured similar shear layer flow structures as the experiment. From the preliminary results, the EVM model outperformed the FPV model. We also observed that improving the compressibility correction procedure can have a significant effect on the performance of the FPV model. To this end, a new compressibility correction approach was proposed for the FPV model. This new form of the FPV model uses a more generic compressibility correction approach. Instead of scaling the progress variable production rate, the individual reaction rates of progress are scaled, which combine to form the progress variable production rate. Future work will focus on conducting a comparative study of this new form of the FPV model.