Composite load spectra for select space propulsion structural components

The objective of the Composite Load Spectra (CLS) project is to build a knowledge based system to synthesize probabilistic loads for selected space propulsion engine components. The knowledge based system has a load expert system module and a load calculation module. The load expert system provides load information and the load calculation module generates the probabilistic load distributions. The engine loads are divided into 4 broad classes: the engine independent loads, the engine system dependent load, the component local independent loads and the component loads. These classes are defined and illustrated

The composite load spectra project

Probabilistic methods and generic load models capable of simulating the load spectra that are induced in space propulsion system components are being developed. Four engine component types (the transfer ducts, the turbine blades, the liquid oxygen posts and the turbopump oxidizer discharge duct) were selected as representative hardware examples. The composite load spectra that simulate the probabilistic loads for these components are typically used as the input loads for a probabilistic structural analysis. The knowledge-based system approach used for the composite load spectra project provides an ideal environment for incremental development. The intelligent database paradigm employed in developing the expert system provides a smooth coupling between the numerical processing and the symbolic (information) processing. Large volumes of engine load information and engineering data are stored in database format and managed by a database management system. Numerical procedures for probabilistic load simulation and database management functions are controlled by rule modules. Rules were hard-wired as decision trees into rule modules to perform process control tasks. There are modules to retrieve load information and models. There are modules to select loads and models to carry out quick load calculations or make an input file for full duty-cycle time dependent load simulation. The composite load spectra load expert system implemented today is capable of performing intelligent rocket engine load spectra simulation. Further development of the expert system will provide tutorial capability for users to learn from it

Time dependent transport phenomena

The aim of this review is to give a pedagogical introduction to our recently proposed ab initio theory of quantum transport.Comment: 28 pages, 18 figure

Orbital currents in the Colle-Salvetti correlation energy functional and the degeneracy problem

Popular density functionals for the exchange-correlation energy typically fail to reproduce the degeneracy of different ground states of open-shell atoms. As a remedy, functionals which explicitly depend on the current density have been suggested. We present an analysis of this problem by investigating functionals that explicitly depend on the Kohn-Sham orbitals. Going beyond the exact-exchange approximation by adding correlation in the form of the Colle-Salvetti functional we show how current-dependent terms enter the Colle-Salvetti expression and their relevance is evaluated. A very good description of the degeneracy of ground-states for atoms of the first and second row of the periodic table is obtained

Optimized Effective Potential Method in Current-Spin Density Functional Theory

Current-spin density functional theory (CSDFT) provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin- and orbital-degrees of freedom. Unlike in usual (spin-) density functional theory, approximations to the exchange-correlation energy based on the model of the uniform electron gas face problems in practical applications. In this work, explicitly orbital-dependent functionals are used and a generalization of the Optimized Effective Potential (OEP) method to the CSDFT framework is presented. A simplifying approximation to the resulting integral equations for the exchange-correlation potentials is suggested. A detailed analysis of these equations is carried out for the case of open-shell atoms and numerical results are given using the exact-exchange energy functional. For zero external magnetic field, a small systematic lowering of the total energy for current-carrying states is observed due to the inclusion of the current in the Kohn-Sham scheme. For states without current, CSDFT results coincide with those of spin density functional theory.Comment: 11 pages, 3 figure

Dimensional crossover of the exchange-correlation energy at the semilocal level

Commonly used semilocal density functional approximations for the exchange-correlation energy fail badly when the true two dimensional limit is approached. We show, using a quasi-two-dimensional uniform electron gas in the infinite barrier model, that the semilocal level can correctly recover the exchange-correlation energy of the two-dimensional uniform electron gas. We derive new exact constraints at the semilocal level for the dimensional crossover of the exchange-correlation energy and we propose a method to incorporate them in any exchange-correlation density functional approximation.Comment: 6 pages, 5 figure

Composite load spectra for select space propulsion structural components

The objective of this program is to develop generic load models with multiple levels of progressive sophistication to simulate the composite load spectra that are induced in space propulsion system components, representative of Space Shuttle Main Engines (SSME), such as transfer ducts, turbine blades, and liquid oxygen (LOX) posts and system ducting. These models will be developed using two independent approaches. The first approach consists of using state-of-the-art probabilistic methods to describe the individual loading conditions and combinations of these loading conditions to synthesize the composite load spectra simulation. The methodology required to combine the various individual load simulation models (hot-gas dynamic, vibrations, instantaneous position, centrifugal field, etc.) into composite load spectra simulation models will be developed under this program. A computer code incorporating the various individual and composite load spectra models will be developed to construct the specific load model desired. The second approach, which is covered under the options portion of the contract, will consist of developing coupled models for composite load spectra simulation which combine the (deterministic) models for composite load dynamic, acoustic, high-pressure and high rotational speed, etc., load simulation using statistically varying coefficients. These coefficients will then be determined using advanced probabilistic simulation methods with and without strategically selected experimental data. This report covers the efforts of the third year of the contract. The overall program status is that the turbine blade loads have been completed and implemented. The transfer duct loads are defined and are being implemented. The thermal loads for all components are defined and coding is being developed. A dynamic pressure load model is under development. The parallel work on the probabilistic methodology is essentially completed. The overall effort is being integrated in an expert system code specifically developed for this project

Non-collinear spin-spiral phase for the uniform electron gas within Reduced-Density-Matrix-Functional Theory

The non-collinear spin-spiral density wave of the uniform electron gas is studied in the framework of Reduced-Density-Matrix-Functional Theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of Reduced-Density-Matrix-Functional Theory, Overhauser showed a long time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge or spin density waves. Here we not only present a detailed numerical investigation of the spin-spiral density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral density wave instability by means of a recently proposed density-matrix functional.Comment: 9 pages, 10 figure

Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields

The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional theory. As a case study, a two-dimensional quantum dot in external magnetic fields is investigated. Excellent agreement with quantum Monte Carlo results is obtained when self-interaction corrected correlation energies from the standard local spin-density approximation are added to exact-exchange results. Full self-consistency within the complete current-spin-density-functional framework is found to be of minor importance.Comment: 5 pages, 2 figures, submitted to PR

A time-dependent approach to electron pumping in open quantum systems

We propose a time-dependent approach to investigate the motion of electrons in quantum pump device configurations. The occupied one-particle states are propagated in real time and used to calculate the local electron density and current. An advantage of the present computational scheme is that the same computational effort is required to simulate monochromatic, polychromatic and nonperiodic drivings. Furthermore, initial state dependence and history effects are naturally accounted for. This approach can also be embedded in the framework of time-dependent density functional theory to include electron-electron interactions. In the special case of periodic drivings we combine the Floquet theory with nonequilibrium Green's functions and obtain a general expression for the pumped current in terms of inelastic transmission probabilities. This latter result is used for benchmarking our propagation scheme in the long-time limit. Finally, we discuss the limitations of Floquet-based schemes and suggest our approach as a possible way to go beyond them.Comment: 14 pages, 8 figure