Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Member

Dr. Richard S. Miller, Committee Chair

Committee Member

Dr. Donald E. Beasley

Committee Member

Dr. Xiangchun Xuan

Committee Member

Dr. John R. Wagner


A database of direct numerical simulation (DNS) of spatially evolving turbulent mixing slot jets of Heptane-Air and Heptane-Oxygen is developed. The formulation includes the compressible form of the governing equations, a generalized multicomponent diffusion model with Soret and Dufour effects, a cubic real gas equation of state and realistic property models. Simulations are conducted over a wide range of initial pressures (1 atm < P0 < 100 atm) and jet width based Reynolds numbers of 850 and 1300. High order explicit finite difference schemes in combination with low order boundary closures and Runge-Kutta time integration schemes are used to approximate the spatial and temporal derivatives. Non-reflecting inflow and outflow boundary conditions in combination with absorbing zones are applied for proper convection of flow structures and acoustic waves with minimal reflection of numerical waves. Low level disturbances are imposed on the laminar inflow near the nozzle to initiate instability for development of turbulence. The simulations are run until a statistically stationary state of the flow is achieved. The mean velocity, variance, centerline velocity excess decay, and downstream growth of normal Reynolds stresses are calculated and compared with various experimental results. For subgrid analysis, a spatial filtering operation is applied to the DNS. The filtered mass density function (FMDF) of mixture fraction at various filter widths is obtained from the simulation at several spatial locations within the flow. The conditional scalar diffusion (CSD) term in the exact transport equation of FMDF is calculated from the DNS. A parametric study of variation of CSD with time, spatial location, Reynolds number, pressure and diffusion models is conducted. An a priori analysis of Interaction by Exchange of Mean (IEM), Modified Curl (MC) and Mapping Closure (MAPPING) mixing models for CSD is conducted. Performance of mixing models at various pressures with the generalized and Fickian diffusion models, with real and ideal gas equations of state is evaluated. The significance of mixing frequency used in the models and the errors associated with calculation of mixing frequency in simulations with the generalized diffusion model is studied. A parametric study of variation of the mixing frequency and its parameters with pressures, diffusion models and Reynolds number is performed. New model constants for mixing frequency applicable to the LES with generalized diffusion models at various pressures are proposed. Conditionally averaged mixing frequency for the IEM model is determined and compared with the conditionally averaged second invariant of the strain tensor to study the effects of flow physics (viscous dissipation) on the mixing time. Mean turbulent kinetic energy and mean dissipation rates are calculated from the DNS and their ratios are compared with mixing frequencies at various pressures. The model constants for various pressures are determined and an alternative expression for determination of mixing frequency in LES with generalized diffusion models is proposed. The budget equation for the Reynolds stress tensor in the compressible RANS momentum equation is derived. The terms of the budget equation (convection, diffusion, pressure-strain, production, dissipation and compressibility) are calculated directly from the DNS at various pressures. The most significant terms in the budget that require modeling are determined to be diffusion and pressure-strain terms. Existing models for diffusion and pressure-strain terms are evaluated over a large range of pressures with the DNS data. At fixed Mach and Reynolds numbers, the models are determined to be dependent on the ambient pressure. New modeling constants for various models over a large range of pressures are proposed.