Numerical Simulations of High Speed Turbulent Jets in Crossflow

This dissertation studies high speed jets in crossflow using numerical simulations. The complexity of this flow makes detailed measurements difficult, and only limited information is provided by past experimental studies. Traditional engineering simulation tools also have difficulties in simulating such flows. Therefore, the current study: 1) develops Large-Eddy Simulation (LES) capability and novel subgrid-scale (SGS) models for high speed flows in complex geometries; 2) realizes multiple methods to generate realistic turbulent boundary layer inflow condition for unstructured compressible flow solver; 3) explores the detailed physics of high speed jets in crossflow; 4) investigates the jet trajectory, entrainment and coherent vortical motions.;Large-eddy simulation capability is developed for the base numerical scheme developed by Park & Mahesh (2007) for solving the compressible Navier-Stokes equations on unstructured grids. Large-eddy simulations are performed to study an under-expanded sonic jet injected into a supersonic crossflow and an over-expanded supersonic jet injected into a subsonic crossflow, where the flow conditions are based on Santiago et al.'s (1997) and Beresh et al.'s (2005) experiments, respectively. The simulations successfully reproduce experimentally observed shock systems and vortical structures. The time averaged flow fields are compared to the experimental results, and reasonable agreement is observed. The behavior of the flow is discussed, and the similarities and differences between the two regimes are studied. The trajectory and entrainment of the transverse jet is investigated. A modification to Schetz & Billig's theory (1966) theory is proposed, which yields good prediction of the jet trajectories in the current simulations in the near field. Along the jet center streamline, the jet entrainment grow faster compared to turbulent free jets. In the very far field, the growth rates of jet entrainment decrease to values that are close to those for turbulent free jets. The Strouhal numbers of relevant flow structures are computed from power spectral densities. Many flow motions are observed to be correlated in sonic jet in supersonic crossflow. The frequencies in supersonic injection are observed to be higher than those in sonic injection.;A novel eddy-viscosity model, "dynamic k-equation model'', is proposed for the LES of compressible flows with complex flow geometries, where the transport equation for sub-grid scale (SGS) kinetic energy is introduced to predict SGS kinetic energy, instead of using Yoshizawa's model as in standard Dynamic Smagorinsky Model (DSM). The exact SGS kinetic energy transport equation for compressible flows is derived formally. Each of the unclosed terms in the SGS kinetic energy equation is modeled separately and dynamically closed, instead of being grouped into production and dissipation terms, as in the Reynolds Averaged Navier-Stokes (RANS) equations. A priori test using Direct Numerical Simulation (DNS) of decaying isotropic turbulence shows that for Smagorinsky type eddy viscosity model, the correlation between SGS stress and the model is comparable to that from the original model. Also, the suggested model for pressure dilatation term in the SGS kinetic energy equation is found to have high correlation with its actual value. In a posteriori tests, the proposed dynamic k-equation model is applied to decaying isotropic turbulence and normal shock/isotropic turbulence interaction, and yields good agreement with available experimental and DNS data. Compared with the results of Dynamic Smagorinsky Model (DSM), the k-equation model predicts better energy spectra at high wave numbers, similar kinetic energy decay and fluctuations of thermodynamic quantities for decaying isotropic turbulence. For shock/turbulent interaction, k-equation model and DSM predict similar evolution of turbulent intensities across shocks, due to the dominant effect of linear interaction. The proposed k-equation model is more robust in that local averaging over neighboring control volumes (CV) is sufficient to regularize the dynamic procedure. The behavior of pressure dilation and dilatational dissipation is discussed through the budgets of SGS kinetic energy equation, and the importance of dilatational dissipation term is addressed.;The proposed dynamic k-equation model is then applied to Mach 2.9 supersonic turbulent boundary layer, where a recycling-rescaling method for turbulent boundary layer generation on fully unstructured meshes is developed and applied. Good agreement is observed between the LES results and available DNS and experimental results.