Empirical and Analytical Eigenfunctions as Bases for Reduced Order Methods in Heat Transfer
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Monte Carlo criticality calculations for nuclear reactors have typically only been able to find the primary eigenvalue and eigenmode. With the new fission matrix capability in MCNP6, it becomes possible to solve for higher modes, which are useful in wide variety of analyses. As a test case of this new capability, two reactor models in both a base configuration and a perturbed configuration were simulated in MCNP to generate fission matrices. Tools were written to find a relatively small number of eigenpairs of the resulting matrices, whereupon it was found that the implicitly restarted Arnoldi method outperformed the previously used power iteration as an eigenvalue algorithm by a factor of 1500 for a 3600 × 3600 sparse matrix.
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Three dimensional thermospheric model developed from solar XUV radiation and corpuscular heating during geomagnetic storms of atmospheric system
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A rational foundation is presented for the application of the linear shear flows to transition prediction, and an explicit method is given for carrying out the necessary calculations. The expansions used are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbances in the inner boundary layer, near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer in that the amplitudes of the discrete Tollmien-Schlicting waves are an extremely small fraction of the amplitude of the disturbance.
A rational foundation is provided for the application of the linear stability theory of parallel shear flows to transition prediction. An explicit method is given for carrying out the necessary calculations. The expansions are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbance in the inner boundary layer near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer, in that the amplitudes of the discrete Tollmein-Schlichting waves are an extremely small fraction of the amplitude of the disturbance.
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Analytical approximations for the acoustic modes in a duct carrying a uniform core flow with a thin shear layer at the walls are developed using the Method of Matched Asymptotic Expansions. Both two-dimensional and cylindrical duct propagation are considered. Numerical results for eigenvalues calculated using the theory are presented for the two dimensional problem and compared with results from earlier analyses. It is found that the new approximations yield a significant increase in accuracy.
Solar oscillations are manifested in the solar atmosphere as spatial and temporal perturbations in the local thermodynamical and mechanical properties. When measuring the solar radius/diameter, these perturbations enter the observation through changes in the radiative source function and opacity at the extreme limb. When compared to the disk center, the observable portion of these perturbations is changed in spatial character by projection effects and oblique optical depth geometry. The time varying solar radius signal at SCLERA (Santa Catalina Laboratory for Experimental Relativity) is produced by an edge definition sensitive to the resultant changes in the spatial shape of the limb intensity profile. An attempt is made to further determine the shape and properties of the limb signals which display global solar oscillations.
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A two-dimensional (one space and time) scalar adaptation of the proper orthogonal decomposition was applied to streamwise velocity data obtained in a lobed mixer flowfield, using a rake of 15 single-component hot wires. Through the application of the proper orthogonal decomposition, the amount of streamwise turbulent kinetic energy contained in the various proper orthogonal modes was examined for two different downstream locations (z/h = 2.6 and 3.9). The large eddy or dominant mode was shown to have a measurable decrease in the relative streamwise component of the kinetic energy between these two downstream locations. This indicates that the large eddy, as defined by the proper orthogonal decomposition, breaks down, and the flow becomes more homogeneous. A pseudoflow visualization technique was then employed to help visualize this process.
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