Improvements in Analyzing High-Speed Fuel/Air Mixing Problems Using Scalar Fluctuation Modeling

Abstract

A scalar fluctuation model (SFM) that solves partial differential equations for energy/species variance and corresponding dissipation rates is presented, along with several applications to high-speed fuel/air mixing problems. The model is implemented in a k- epsilon turbulence model framework with unified compressibility and low Re extensions, specialized for high speed aero-propulsive flow applications. It is used to predict the spatial variation of turbulent Prandtl and Schmidt numbers using time-scale relations, providing more accurate and reliable solutions than those based on user-specified average-values. Over the past several years, the authors and coworkers have systematically upgraded the SFM to treat flows of increasing complexity, using a approach to ensure that modifications made to improve the analysis of more complex cases will not degrade the model performance in analyzing fundamental cases. A GUI-driven building-block data base (BBDB) tool has been developed to facilitate the validation/calibration process, which contains the various data sets we are working with (experimental and LES) along with grids and solution files, and scripts to take CFD output and put it into the format required to compare with the data. This paper will describe the latest version of the SFM, its application to select fundamental cases in the BBDB, and a detailed description of its analysis of the SCHOLAR fuel/air mixing/combustion data in which we have examined grid resolution sensitivities and compared results using the SFM with those using different values of constant turbulent Prandtl and Schmidt numbers. I. INTRODUCTION Accurate modeling of scalar transport, such as internal energy and species concentration, is needed to properly predict the temperature and fuel/air distribution in high-speed aero-propulsive devices, and thus to predict combustion efficiency and overall performance. The effect of turbulence plays a dominant role in scalar transport and is accounted for in a RANS framework through the application of a turbulent Prandtl (Prt) and turbulent Schmidt (Sct) number for thermal and species mixing, respectively. It is now well recognized that the application of constant-average values of these numbers for complex flows is inadequate since: different values apply to different very basic flows (e.g., 0.7 is used for round jets, 0.9 is used for boundary layers); these numbers vary widely in complex flows; and, the values differ with varying levels of compressibility in the flow. Turbulence predictions for high speed flows are complicated by compressibility effects which have a first-order influence on fundamental