Executive Summary : | Computational fluid dynamics has become increasingly important in engineering research and development over the past three decades. However, direct numerical simulations (DNS) of turbulent flows have not yet become a reality due to the computational demand. Instead, methods like Reynolds-averaged Navier-Stokes (RANS), large-eddy simulation (LES), partially-averaged Navier-Stokes (PANS), and probability density function (PDF) methods are widely used. These methods face the problem of mathematical closure, requiring high-fidelity turbulence closure models. Understanding the underlying physics of turbulence processes is crucial, especially in highly compressible flow fields like hypersonic flows. These fields have more flow complexities than low-speed incompressible flows, including significant levels of divergence in the velocity field, altered thermodynamic nature of pressure evolution, vibrational excitations of air molecules, and dissociation of air molecules and chemical reactions. This proposal aims to improve our understanding of the influence of vibrational and chemical non-equilibrium on non-linear turbulence processes. The non-linear processes are examined following the evolution of the velocity gradient tensor in a compressible flow field, with the pressure Hessian tensor being a key process in the evolution equation. |