A Numerical Investigation of a Spatially Developing Compressible Plane Free Shear Layer

The present dissertation investigates the turbulence transition and energy exchange mechanisms, assesses some commonly-used turbulence models, and examines the compressibility effects on them. The investigation and assessment are based on the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional (3D), spatially-developing plane free shear layer (FSL) flow. The plane FSL is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is carried out using a high-order discontinuous spectral element method (DSEM) for three convective Mach numbers of 0.3, 0.5, and 0.7. The laminar-turbulent transition region is predicted by analyzing vorticities, Reynolds stresses, and turbulent dissipation rates in the entire flow domain. The FSL flow's energy exchange mechanisms are examined based on the budget terms of the turbulent kinetic energy (TKE), mean kinetic energy (MKE), and mean internal energy (MIE) transport equations. The DNS results show that the mean velocity, momentum thickness, and Reynolds stress profiles compare well with published numerical and experimental data. The two-point correlation functions of velocity components, the one-dimensional (1D) spanwise energy spectrum, and the balance of the TKE transport equation validate the domain size and resolution of the adopted grid for turbulence simulations in this work. It is found that the onset of turbulence transition and the location where the transition completes shift downstream, while the transition region's length increases with increasing convective Mach number. The turbulent production, turbulent viscous dissipation, mean viscous dissipation, pressure-dilatation, and enthalpic production are the main mechanisms responsible for energy exchange among different energy forms in the FSL flow. The primary budget terms evolve differently in the transition and turbulent regions and change significantly for varying compressibility. In the transition region, the shear layer center slightly shifts to the high-speed side due to the appearance of the velocity deficit. The velocity deficit presence distance (VDPD) becomes longer as compressibility increases. In the turbulent region, the primary budget terms' cross-stream profiles significantly shift to the low-speed side because of the asymmetric mass entrainment and shift even further as convective Mach number increases. The present DNS results are also utilized to provide insights into turbulence modeling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy (SRA) models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy (ESRA) models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure-dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure-strain correlation models perform excellently for most pressure-strain correlation components, while the compressibility modification model gives poor predictions. The results of a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modeled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.