Applications of Finite Energy Methods to Transient, Random, and Shock Predictions
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Daniel Kaufman↗
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Nonlinear stability of the Boussinesq equations by the method of energy.
Energy method applied to stability of flows governed by nonlinear Boussinesq equations, establishing universal stability region in Reynolds-Rayleigh number plane
REYNOLDS NUMBER↗
A method for producing monoenergetic neutrons at kilovolt energies
Method for producing neutrons in keV energy region utilizing gamma rays from radioactive decay to induce photoneutron reaction in beryllium
Amster, H.↗
Compatible thermal and structural elements for the analysis of beam and plate structures
Energy methods are used to formulate steady-state thermal elements which are compatible with structural beam and plate elements. Comparisons of energy method results with finite element results indicate that the energy methods achieve similar accuracy with fewer degrees of freedom. Limitations of energy methods with regard to discontinuous functions and computational overflow are noted. Thermal stress calculations are simplified by the use of similar formulations for the thermal and structural elements. The advantages that these energy-based elements offer to high-temperature structural optimization are discussed.
Vause, R. F.↗
Energy addition methods for hyper-velocity true flight simulation
Arc heating and magnetohydrodynamic acceleration energy addition methods for wind tunnel hypervelocity flow true flight simulation
FLIGHT SIMULATION↗
A comparison of internal energy calculation methods for diatomic molecules
Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.
Liu, Yen↗
Grain size reduction in granular flows of spheres - The effects of critical impact energy
Methods employed to derive recent kinetic theories for rapid noncomminuting granular flows are extended to homogeneous flows in which a fraction of the repeated collisions produce tiny fractures on the particles' peripheries and gradually reduce their effective diameters. The theory consists of balance equations for mass, momentum, and energy, as well as constitutive relations for the presence tensor and collisional rates of mass and energy lost. The work of Richman and Chou (1989) is improved by incorporating into the constitutive theory the critical impact energy below which no mass loss occurs in a binary collision. The theory is applied to granular shear flows and, for fixed shear rates, predicts the time variations of the solid fraction granular temperature, and induced stresses, as well as their extreme sensitivities to small changes in the critical impact energy.
Richman, M. W.↗
Energy Analysis Method for Hidden Damage Detection
A method of detecting internal defects in composites or other multilayer materials includes generating a wavefield on a surface of the material. Wavefield data is collected from the wavefield on the surface, and the measured wavefield data is processed to provide measured energy data. The method may include generating simulated or predicted energy data for the multilayer material that is compared to the simulated energy data to determine if the multilayer material has internal defects or damage below the surface. The method can be utilized to detect and/or quantify damage or other defects that are "hidden" by damage that is closer to the surface of the material.
Campbell Leckey, Cara A.↗
Multidimensional Programming Methods for Energy Facility Siting: Alternative Approaches
The use of multidimensional optimization methods in solving power plant siting problems, which are characterized by several conflicting, noncommensurable objectives is addressed. After a discussion of data requirements and exclusionary site screening methods for bounding the decision space, classes of multiobjective and goal programming models are discussed in the context of finite site selection. Advantages and limitations of these approaches are highlighted and the linkage of multidimensional methods with the subjective, behavioral components of the power plant siting process is emphasized.
Solomon, B. D.↗
A liquid drop model for embedded atom method cluster energies
Minimum energy configurations for homonuclear clusters containing from two to twenty-two atoms of six metals, Ag, Au, Cu, Ni, Pd, and Pt have been calculated using the Embedded Atom Method (EAM). The average energy per atom as a function of cluster size has been fit to a liquid drop model, giving estimates of the surface and curvature energies. The liquid drop model gives a good representation of the relationship between average energy and cluster size. As a test the resulting surface energies are compared to EAM surface energy calculations for various low-index crystal faces with reasonable agreement.
Finley, C. W.↗
Real Gas Computation Using an Energy Relaxation Method and High-Order WENO Schemes
In this paper, we use a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition into two parts: one part is associated with a simpler pressure law and the other part (the nonlinear deviation) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the first part. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.
Montarnal, Philippe↗
Encircled energy correction method for raytrace programs
Program adjustments to increase the accuracy of the diffraction-based encircled energy analysis algorithms of the optical design computer programs ACCOS-V and SYNOPSYS are proposed. It is noted that the erroneous algorithms are based on the incorrect assumption that all the energy in a diffraction point spread function is contained within a circle of finite radius. Using these adjustments, more accurate encircled energy results are obtained for circles of radii less than or equal to the 100 percent boundary.
Dantzler, Andrew A.↗
An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled-cluster wave function - Application to Cl2O2
The analytic energy gradient for the single and double excitation coupled-cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented.
Rendell, Alistair P.↗
Probabilistic Structural Analysis Theory Development
The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.
Burnside, O. H.↗
Stability of structural rings under uniformly distributed radial loads
Energy method analysis establishes parameters governing stability of circular rings acted upon by constant, uniformly distributed loads. Energy method is used so that nonlinear behavior of structure before buckling can be accounted for. Method affords conceptually superior basis for analyzing the axisymmetric deviation mode.
Williams, H. E.↗
Optimization of a Remote Sensing Energy Balance Method over Different Canopy Applied at Global Scale
Parameterization methods which calculate turbulent heat and water fluxes with thermal remote sensing data were evaluated in the revised remote sensing surface energy balance system (SEBS) model (Chen et al., 2013). The model calculates sensible heat (H) based on the Monin-Obukhov similarity theory (MOST) and determines latent heat (LE) as the residual of energy balance. We examined the uncertainties of H and LE in the SEBS model due to five key parameters at the local station point scale. Observations at 27 flux towers located in seven land cover types (needle-leaf forest, broad leaf forest, shrub, savanna, grassland, cropland, and sparsely vegetated land) and an artificial intelligence particle swarm optimization (PSO) algorithm was combined to calibrate the five parameters (leaf drag coefficient, leaf heat transfer coefficients, roughness length for soil, and two parameters for ground heat calculation) in the SEBS model. The root-mean-square error at the site scale was reduced by 9 W/sq.m for H, and 92 W/sq.m for LE, and their correlation coefficients were increased by 0.07 (H) and 0.11 (LE) after using the calibrated parameters. The updated model validation was further conducted globally for the remotely sensed evapotranspiration (ET) calculations. Overestimation of SEBS global ET was significantly improved by using the optimized values of the parameters. The results suggested PSO was able to consistently locate the global optimum of the SEBS model, and appears to be capable of solving the ET model optimization problem.
Chen, Xuelong↗
Multiple large-scale coherent mode interactions in a developing round jet
The integral energy method has been used to study the nonlinear interactions of the large-scale coherent structure in a spatially developing round jet. The streamwise development of a jet is obtained in terms of the mean flow shear-layer momentum thickness, the wave-mode kinetic energy and the wave-mode phase angle. With the energy method, a system of partial differential equations is reduced to a system of ordinary differential equations. The nonlinear differential equations are solved with initial conditions which are given at the nozzle exit. It is shown that the initial wave-mode energy densities as well as the initial phase angles play a significant role in the streamwise evolution of the large-scale coherent wave modes and the mean flow.
Lee, Sang S.↗