Fundamental aspects of turbulence and turbulent mixing are investigated using direct numerical simulations (DNS) of stationary isotropic turbulence, with Taylor-scale Reynolds numbers ranging from 8 to 650 and Schmidt numbers from 1/8 to 1024. The primary emphasis is on important scaling issues that arise in the study of intermittency, mixing and turbulence under solid-body rotation. Simulations up to 2048^3 in size have been performed using large resource allocations on Terascale computers at leading supercomputing centers. Substantial efforts in algorithmic development have also been undertaken and resulted in a new code based on a two-dimensional domain decomposition which allows the use of very large number of processors.Benchmark tests indicate very good parallel performance for resolutions up to 4096^3 on up to 32768 processors. Investigation of intermittency through the statistics of dissipation and enstrophy in a series of simulations at the same Reynolds number but different resolution indicate that accurate results in high-order moments require a higher degree of fine-scale resolution than commonly practiced. At the highest Reynolds number in our simulations (400 and 650) dissipation and enstrophy exhibit extreme fluctuations of O(1000) the mean which have not been studied in the literature before and suggest a universal scaling of small scales. Simulations at Reynolds number of 650 on 2048^3 grids with scalars at Sc=1/8 and 1 have allowed us to obtain the clearest evidence of attainment of inertial-convective scaling in the scalar spectrum in numerical simulations to date whereas results at high Sc support k^{-1} viscous-convective scaling. Intermittency for scalars as measured by the tail of the PDF of scalar dissipation and moments of scalar gradient fluctuations is found to saturate at high Sc. Persistent departures from isotropy are observed as the Reynolds number increases. However, results suggest a return to isotropy at high Schmidt numbers, a tendency that appears to be stronger at high Reynolds numbers. The effects of the Coriolis force on turbulence under solid-body rotation are investigated using simulations on enlarged solution domains which reduce the effects of periodic boundary conditions.

Drastic changes in aircraft operational requirements and the emergence of new enabling technologies often occur symbiotically with advances in technology inducing new requirements and vice versa. These changes sometimes lead to the design of vehicle concepts for which no prior art exists. They lead to revolutionary concepts. In such cases the basic form of the vehicle geometry can no longer be determined through an ex ante survey of prior art as depicted by aircraft concepts in the historical domain. Ideally, baseline geometries for revolutionary concepts would be the result of exhaustive configuration space exploration and optimization. Numerous component layouts and their implications for the minimum external dimensions of the resultant vehicle would be evaluated. The dimensions of the minimum enclosing envelope for the best component layout(s) (as per the design need) would then be used as a basis for the selection of a baseline geometry. Unfortunately layout design spaces are inherently large and the key contributing analysis i.e. collision detection, can be very expensive as well. Even when an appropriate baseline geometry has been identified, another hurdle i.e. vehicle scaling has to be overcome. Through the design of a notional Cessna C-172R powered by a liquid hydrogen Proton Exchange Membrane (PEM) fuel cell, it has been demonstrated that the various forms of vehicle scaling i.e. photographic and historical-data-based scaling can result in highly sub-optimal results even for very small O(10-3) scale factors. There is therefore a need for higher fidelity vehicle scaling laws especially since emergent technologies tend to be volumetrically and/or gravimetrically constrained when compared to incumbents. The Configuration-space Exploration and Scaling Methodology (CESM) is postulated herein as a solution to the above-mentioned challenges. This bottom-up methodology entails the representation of component or sub-system geometries as matrices of points in 3D space. These typically large matrices are reduced using minimal convex sets or convex hulls. This reduction leads to significant gains in collision detection speed at minimal approximation expense. (The Gilbert-Johnson-Keerthi algorithm is used for collision detection purposes in this methodology.) Once the components are laid out, their collective convex hull (from here on out referred to as the super-hull) is used to approximate the inner mold line of the minimum enclosing envelope of the vehicle concept. A sectional slicing algorithm is used to extract the sectional dimensions of this envelope. An offset is added to these dimensions in order to come up with the sectional fuselage dimensions. Once the lift and control surfaces are added, vehicle level objective functions can be evaluated and compared to other designs. For each design, changes in the super-hull dimensions in response to perturbations in requirements can be tracked and regressed to create custom geometric scaling laws. The regressions are based on dimensionally consistent parameter groups in order to come up with dimensionally consistent and thus physically meaningful laws. CESM enables the designer to maintain design freedom by portably carrying multiple designs deeper into the design process. Also since CESM is a bottom-up approach, all proposed baseline concepts are implicitly volumetrically feasible. Furthermore the scaling laws developed from custom data for each concept are subject to less design noise than say, regression based approaches. Through these laws, key physics-based characteristics of vehicle subsystems such as energy density can be mapped onto key system level metrics such as fuselage volume or take-off gross weight. These laws can then substitute some historical-data based analyses thereby improving the fidelity of the analyses and reducing design time.