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At least 1,207 records · Page 67

Torque equilibrium attitudes for the Space Station

All spacecraft orbiting in a low earth orbit (LEO) experience external torques due to environmental effects. Examples of these torques include those induced by aerodynamic, gravity-gradient, and solar forces. It is the gravity-gradient and aerodynamic torques that produce the greatest disturbances to the attitude of a spacecraft in LEO, and large asymmetric spacecraft, such as the space station, are affected to a greater degree because the magnitude of the torques will, in general, be larger in proportion to the moments of inertia. If left unchecked, these torques would cause the attitude of the space station to oscillate in a complex manner and the resulting motion would destroy the micro-gravity environment as well as prohibit the orbiter from docking. The application of control torques will maintain the proper attitude, but the controllers have limited momentum capacity. When any controller reaches its limit, propellant must then be used while the device is reset to a zero or negatively-biased momentum state. Consequently, the rate at which momentum is accumulated is a significant factor in the amount of propellant used and the frequency of resupply necessary to operate the station. A torque profile in which the area curve for a positive torque is not equal to the area under the curve for a negative torque is 'biased,' and the consequent momentum build-up about that axis is defined as secular momentum because it continues to grow with time. Conversely, when the areas are equal, the momentum is cyclic and bounded. A Torque Equilibrium Attitude (TEA) is thus defined as an attitude at which the external torques 'balance' each other as much as possible, and which will result in lower momentum growth in the controllers. Ideally, the positive and negative external moments experienced by a spacecraft at the TEA would exactly cancel each other out and small cyclic control torques would be required only for precise attitude control. Over time, the only momentum build-up in the controllers would be due to electro-mechanical losses within the device. However, the atmospheric torques are proportional to the density of the atmosphere and the density varies with the orbital position, time of day, time of year, and the solar cycle. In addition, there are unmodeled disturbances and uncertainties in the mass and inertias. Therefore, there is no constant attitude that will completely balance the environmental torques and the dynamic TEA cannot be solved in closed form. The objective of this research was to determine a method to calculate a dynamic TEA such that the rate of momentum build-up in the controllers would be minimized and to implement this method in the MATRIX(x) simulation software by Integrated Systems, Inc.

Thompson, Roger C.↗

Theory and computation of optimal low- and medium-thrust transfers

This report describes the current state of development of methods for calculating optimal orbital transfers with large numbers of burns. Reported on first is the homotopy-motivated and so-called direction correction method. So far this method has been partially tested with one solver; the final step has yet to be implemented. Second is the patched transfer method. This method is rooted in some simplifying approximations made on the original optimal control problem. The transfer is broken up into single-burn segments, each single-burn solved as a predictor step and the whole problem then solved with a corrector step.

Chuang, C.-H.↗

Infinitesimal Conical Supersonic Flow

The calculation of infinitesimal conical supersonic flow has been applied first to the simplest examples that have also been calculated in another way. Except for the discovery of a miscalculation in an older report, there was found the expected conformity. The new method of calculation is limited more definitely to the conical case.

Busemann, Adolf↗

Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions

A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

Navier-Stokes calculations with a coupled strongly implicit method. II Spline deferred-corrector solutions

The coupled strongly implicit (CSIP) method described previously is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equations. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered (equal to or less than 1000). In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗

Equilibrium shape and location of a liquid drop acoustically positioned in a resonant rectangular chamber

The effect of a standing wave field in a rectangular chamber on the shape and location of an acoustically positioned drop or bubble is calculated. The sample deformation and equilibrium position are obtained from an analysis of the spherical harmonic projections of the total surface stress tensor. The method of calculation relies on the assumed condition that the sample is only slightly distorted from a spherical form. The equilibrium location of a levitated drop is combined with a formula introduced by Hasegawa (1979) to calcualte the ka dependence of the radiation force function. The present theory is valid for large as well as small ka values. Calculations in the small ka limit agree with previous theories and experimental results. Examples are presented for nonplane-wave modes as well as plane-wave rectangular modes.

Jackson, H. W.↗

Multigrid method for stability problems

The problem of calculating the stability of steady state solutions of differential equations is addressed. Leading eigenvalues of large matrices that arise from discretization are calculated, and an efficient multigrid method for solving these problems is presented. The resulting grid functions are used as initial approximations for appropriate eigenvalue problems. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a nonstandard way in which the right-hand side of the coarse grid equations involves unknown parameters to be solved on the coarse grid. This leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem are presented which demonstrate the effectiveness of the method.

Ta'asan, Shlomo↗

Calculation of flight vibration levels of the AH-1G helicopter and correlation with existing flight vibration measurements

NASA-Langley is sponsoring a rotorcraft structural dynamics program with the objective to establish in the U.S. a superior capability to utilize finite element analysis models for calculations to support industrial design of helicopter airframe structures. In the initial phase of the program, teams from the major U.S. manufacturers of helicopter airframes will apply extant finite element analysis methods to calculate loads and vibrations of helicopter airframes, and perform correlations between analysis and measurements. The aforementioned rotorcraft structural dynamics program was given the acronym DAMVIBS (Design Analysis Method for Vibrations). Sikorsky's RDYNE Rotorcraft Dynamics Analysis used for the correlation study, the specifics of the application of RDYNE to the AH-1G, and comparisons of the predictions of the method with flight data for loads and vibrations on the AH-1G are described. RDYNE was able to predict trends of variations of loads and vibrations with airspeed, but in some instances magnitudes differed from measured results by factors of two or three to one. Sensitivities were studied of predictions to rotor inflow modeling, effects of torsional modes, number of blade bending modes, fuselage structural damping, and hub modal content.

Sopher, R.↗

An improved method for direct incident solar radiation calculation from hourly solar insolation data in building energy simulation

Solar radiation considerably influences the energy consumption of buildings and the power production of building integrated photovoltaic (BIPV) systems. Hourly solar insolation (Wh/m 2 ), represented as the amount of solar irradiance collected on the ground during a 1-h period, is the most common solar radiation data available and widely used in weather files applied in building energy modeling programs (BEMPs). Because the solar beam and position vary over time, the use of hourly insolation data as the input might result in errors in the estimation of the direct incident solar radiation on a particular surface. In this study, methods used in BEMPs for direct incident solar radiation calculations are first analyzed, and an improved method adopting a new algorithm for estimating the solar irradiance is proposed. Furthermore, the algorithm assumes that the solar irradiance changes linearly within a 1-h period and can be estimated based on the solar irradiance at the half clock and slope. The collected direct normal solar irradiance data of 2016 from eight solar radiation stations in China were used to demonstrate the proposed method and evaluate its performance by comparing the results with those from three conventional methods used in BEMPs along with the ground truth measurements. In addition, in this study, factors affecting the accuracy of the calculation results are explored. The results of the estimated direct incident solar radiation show that the proposed method achieves the best accuracy, followed by the methods used in DOE-2, EnergyPlus, and DeST. The proposed method guarantees that the hourly direct solar insolation will remain the same and reflects the variation in the direct solar irradiance across a 1-h time frame. The proposed method can be adopted in BEMPs to improve the accuracy of the solar radiation calculation, thereby improving the accuracy of the simulated building performance and the BIPV production.

14 SOLAR ENERGY↗

Predicting Device Parameters for Dye-Sensitized Solar Cells from Electronic Structure Calculations to Reproduce Experiment.

Given that improvements to the power-conversion efficiency (PCE) of dye-sensitized solar cells (DSSCs) have slowed in recent years, a means to accurately predict the device parameters yielded by trial dyes in silico, without having to synthesize them, would be extremely valuable to speed up the design process. Currently, the best-performing methods of calculating device parameters rely on a set of experimentally determined kinetic coefficients. In practice, it is very difficult to measure these kinetic parameters accurately, limiting the overall accuracy of such predictive methods. This work proposes a model to obtain key parameters such as J(SC), V-OC, and PCE using only the results from density functional theory (DFT) and time-dependent DFT calculations, noting that rates of electron-transfer steps are ultimately linked to the electronic structure of the dye center dot center dot center dot TiO2 working electrode. Six organic DSSC dyes from dissimilar chemical classes (L0, L1, L2, WS-2, WS-92, and C281) were chosen to demonstrate the power of this approach. Their a priori known experimentally determined device performance metrics served to validate our predictions. The greatest absolute error in our predicted PCE values was 0.36% relative to the experiment, while the greatest fractional error was 0.042. This indicates that the proposed model offers a dramatic improvement on previous predictive methods for DSSC device parameters, both in accuracy and in consistency. Moreover, such a predictive model has great potential to be applied to other photovoltaic applications, further enabling the design of novel, highly efficient photoactive materials.

density functional theory↗

Method to determine the electron–ion temperature relaxation rate from test particle distributions

Here a method to calculate the electron–ion energy exchange rate from the forces on and velocities of an ensemble of test particles is described. The essence of the method is that the energy exchange rate is related to the covariance between the distribution of velocities of test particles and the forces acting on them. The energy exchange rate is related to the electron–ion temperature relaxation rate in the limit of a low test particle speed. A proof of concept is conducted with first-principles molecular dynamics simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical calculation of turbulent boundary layers including suction or injection with binary diffusion.

The modelling of turbulent transport processes with an eddy viscosity representation of the inner, wall region for cases with suction or injection is considered in detail. It is shown how the van Driest solid wall model can be logically extended for such cases. Further, a new inductive model is developed. Finite difference calculations using the new inductive model are shown to be in good agreement with experimental data over a wide range of conditions. Lastly, a new method for calculating the wall shear within a finite difference solution is developed. This procedure greatly relaxes the requirement for fine grid spacing in the vertical direction.

Schetz, J. A.↗

Methods of galactic heavy ion transport

Two methods of calculating the transition of galactic heavy ions in the earth's atmosphere are compared with respect to accuracy, generality, and computer efficiency. The most general method is shown to have the highest accuracy and is a simple numerical procedure.

Wilson, John W.↗

A New Method for Simulating Photoprocesses in Astrochemical Models

We propose a new model for treating solid-phase photoprocesses in interstellar ice analogues. In this approach, photoionization and photoexcitation are included in more detail, and the production of electronically-excited (suprathermal) species is explic- itly considered. In addition, we have included non-thermal, non-diffusive chemistry to account for the low-temperature characteristic of cold cores. As an initial test of our method, we have simulated two previous experimental studies involving the UV irradiation of pure solid O2. In contrast to previous solid-state astrochemical model calculations which have used gas-phase photoabsorption cross-sections, we have em- ployed solid-state cross-sections in our calculations. This method allows the model to be tested using well-constrained experiments rather than poorly constrained gas-phase abundances in ISM regions. Our results indicate that inclusion of non-thermal reac- tions and suprathermal species allows for reproduction of low-temperature solid-phase photoprocessing that simulate interstellar ices within cold ( 10 K) dense cores such as TMC-1.

astrochemical modeling↗

Chemomechanics in alloy phase stability

We describe a first-principles statistical mechanics method to calculate the free energies of crystalline alloys that depend on temperature, composition, and strain. The approach relies on an extension of the alloy cluster expansion to include an explicit dependence on homogeneous strain in addition to site occupation variables that track the degree of chemical ordering. The method is applied to the Si-Ge binary alloy and is used to calculate free energies that describe phase stability under arbitrary epitaxial constraints. We find that while the incoherent phase diagram (in which coexisting phases are not affected by coherency constraints) hosts a miscibility gap, coherent phase equilibrium predicts ordering and negative enthalpies of mixing. Instead of chemical instability, the chemomechanical free energy exhibits instabilities along directions that couple the composition of the alloy with a volumetric strain order parameter. Furthermore, this has fundamental implications for phase field models of spinodal decomposition as it indicates the importance of gradient energy coefficients that couple gradients in composition with gradients in strain.

Materials Science↗

Time-dependent orbital-free density functional theory: Background and Pauli kernel approximations

Time-dependent orbital-free density functional theory (DFT) is an efficient method for calculating the dynamic properties of large-scale quantum systems due to the low computational cost compared to standard time-dependent DFT. In this work, we formalize this method by mapping the real system of interacting fermions onto a fictitious system of noninteracting bosons. The dynamic Pauli potential and associated kernel emerge as key ingredients of time-dependent orbital-free DFT. Using the uniform electron gas as a model system, we derive an approximate frequency-dependent Pauli kernel. Pilot calculations suggest that space nonlocality is a key feature for this kernel. Nonlocal terms arise already in the second-order expansion with respect to unitless frequency and reciprocal space variable ($\frac{ω}{qk_F}$ and $\frac{q}{2k_F}$, respectively). Given the encouraging performance of the proposed kernel, we expect it will lead to more accurate orbital-free DFT simulations of nanoscale systems out of equilibrium. Additionally, the proposed path to formulate nonadiabatic Pauli kernels presents several avenues for further improvements which can be exploited in future work to improve the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The interaction of helium with alpha-quartz

A detailed method of calculating the three-dimensional interaction of gas atoms with solid surfaces has been developed in order to provide a quantitative means of determining atmospheric evolution and global distribution on exospheric planetary bodies. The computational method involves accurate structural models of the surface and subsurface, and numerical solution of 60-dimensional differential equations of motion in a Monte Carlo calculation of the collision process. Preliminary results for the He-alpha-quartz system are described.

Kunc, J. A.↗