Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering


Miller, Richard S.

Committee Member

Figliola , Richard S.

Committee Member

Beasley , Donald E.


A Direct Numerical Simulation (DNS) database of supercritical, transitional H2/O2 mixing and reacting shear layers is analyzed in an a priori manner to obtain subgrid statistics relevant to Large Eddy Simulation (LES) engineering modeling. The DNS employs a real gas state equation, detailed chemistry, accurate property models, multicomponent, differential, and cross diffusion. The parallel simulations were conducted using eighth order central finite differencing in conjunction with a fourth order accurate Runge-Kutta time integration, on resolutions up to 135 million grid points, and used up to 2,016 processing cores. All simulations are for an ambient pressure of 100 atm and are relevant to rocket engine conditions. The particular focus of the study is on analyzing the subgrid heat flux vector which has thus far been nearly universally ignored in the literature. DNS provides a near 'exact' description of all of the scales of the flow. For this study the DNS database is filtered over a range of filter widths to provide the exact LES governing equations; including those terms requiring modeling. The filtered heat flux vector is extensively compared with the heat flux vector calculated as a function of the filtered primitive variables (ie. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid heat flux vector. The subgrid heat flux vector is found to be insignificant for pure mixing cases, however, even for mixing cases the divergence of the subgrid heat flux vector is of the same order as
the actual heat flux vector, other subgrid terms in the LES energy equation. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows due to the associated large temperature gradients. The analysis is done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid
temperature variance, flame temperature, etc. These results highlight specific regions of the flame where modeling errors may occur in an actual LES if the subgrid heat flux vector is neglected. The dynamic/similarity modeling approach is therefore derived
and tested for use in modeling the subgrid heat flux vector. An analysis of the model performance indicates that although the model improves the prediction of the filtered heat flux vector in both mixing and reacting flows, it nevertheless requires improvement. In particular, the model performance deteriorates with increasing filter
width, and retains substantial errors when the divergence of the heat flux vector is considered. However, the model shows improved results for the higher Reynolds number simulation.