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At least 1,027 records · Page 57

Multigrid method for stability problems

The problem of calculating the stability of steady state solutions of differential equations is treated. Leading eigenvalues (i.e., having maximal real part) of large matrices that arise from discretization are to be calculated. An efficient multigrid method for solving these problems is presented. The method begins by obtaining an initial approximation for the dominant subspace on a coarse level using a damped Jacobi relaxation. This proceeds until enough accuracy for the dominant subspace has been obtained. The resulting grid functions are then used as an initial approximation for appropriate eigenvalue problems. These problems are being solved first on coarse levels, followed by refinement until a desired accuracy for the eigenvalues has been achieved. 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 non-standard way in which the right hand side of the coarse grid equations involves unknown parameters to be solved for on the coarse grid. This in particular leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem demonstrate the effectiveness of the method proposed. Using an FMG algorithm a solution to the level of discretization errors is obtained in just a few work units (less than 10), where a work unit is the work involved in one Jacobi relization on the finest level.

Taasan, Shlomo↗

Computer program for calculating and fitting thermodynamic functions

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Mcbride, Bonnie J.↗

Methods for determining the internal thrust of scramjet engine modules from experimental data

Methods for calculating zero-fuel internal drag of scramjet engine modules from experimental measurements are presented. These methods include two control-volume approaches, and a pressure and skin-friction integration. The three calculation techniques are applied to experimental data taken during tests of a version of the NASA parametric scramjet. The methods agree to within seven percent of the mean value of zero-fuel internal drag even though several simplifying assumptions are made in the analysis. The mean zero-fuel internal drag coefficient for this particular engine is calculated to be 0.150. The zero-fuel internal drag coefficient when combined with the change in engine axial force with and without fuel defines the internal thrust of an engine.

Voland, Randall T.↗

Practical theories for service life prediction of critical aerospace structural components

A new second-order theory was developed for predicting the service lives of aerospace structural components. The predictions based on this new theory were compared with those based on the Ko first-order theory and the classical theory of service life predictions. The new theory gives very accurate service life predictions. An equivalent constant-amplitude stress cycle method was proposed for representing the random load spectrum for crack growth calculations. This method predicts the most conservative service life. The proposed use of minimum detectable crack size, instead of proof load established crack size as an initial crack size for crack growth calculations, could give a more realistic service life.

Ko, William L.↗

A recursive technique for adaptive vector quantization

Vector Quantization (VQ) is fast becoming an accepted, if not preferred method for image compression. The VQ performs well when compressing all types of imagery including Video, Electro-Optical (EO), Infrared (IR), Synthetic Aperture Radar (SAR), Multi-Spectral (MS), and digital map data. The only requirement is to change the codebook to switch the compressor from one image sensor to another. There are several approaches for designing codebooks for a vector quantizer. Adaptive Vector Quantization is a procedure that simultaneously designs codebooks as the data is being encoded or quantized. This is done by computing the centroid as a recursive moving average where the centroids move after every vector is encoded. When computing the centroid of a fixed set of vectors the resultant centroid is identical to the previous centroid calculation. This method of centroid calculation can be easily combined with VQ encoding techniques. The defined quantizer changes after every encoded vector by recursively updating the centroid of minimum distance which is the selected by the encoder. Since the quantizer is changing definition or states after every encoded vector, the decoder must now receive updates to the codebook. This is done as side information by multiplexing bits into the compressed source data.

Lindsay, Robert A.↗

Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

In this note we compute the 1-loop partition function of spin- s s fields on Euclidean de Sitter space S^{2n+1} S 2 n + 1 using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription L_{\text{AdS}}\to iL_{\text{dS}} L AdS → i L dS , appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal \text{AdS}_{2n+1} AdS 2 n + 1 into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal \text{AdS}_{2n+1} AdS 2 n + 1 can be generalized to calculating 1-loop partition functions on the thermal spherical quotients S^{2n+1}/\mathbb{Z}_{p} S 2 n + 1 / ℤ p . We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the analysis made for thermal AdS in [1-3] .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NORTH DAKOTA CARBONSAFE PHASE III: SITE CHARACTERIZATION AND PERMITTING OF GEOLOGIC STORAGE OF CARBON DIOXIDE

The Energy & Environmental Research Center (EERC), in partnership with Minnkota Power Cooperative Inc. (Minnkota), SLB, and Computer Modelling Group Ltd. (CMG), supported wide-scale deployment of carbon capture and storage (CCS) as part of the U.S. Department of Energy (DOE) National Energy Technology Laboratory Carbon Storage Assurance Facility Enterprise (CarbonSAFE) Initiative Phase III. This phase included the acquisition, analysis, and development of information to fully characterize two storage complexes to demonstrate viable storage resources for commercial volumes of CO2 (defined by DOE as a minimum of 50 million tonnes [MMt] of CO2 within a 30-year period) (National Energy Technology Laboratory, 2024). Phase III also involved the preparation, submission, and approval of North Dakota underground injection control (UIC) Class VI storage facility permits (SFPs)—required precursors to applications for Class VI injection well permits. The presumed viability of commercial-scale CCS, situated adjacent to Minnkota’s Milton R. Young Station (MRYS), is validated by Minnkota’s continued pursuit of Project Tundra—an initiative to build the world’s largest lignite-based CCS project in central North Dakota (www.projecttundrand.com). Project Tundra comprises two scopes of work, Tundra Capture (installation of postcombustion CO2 capture at MRYS) and Tundra SGS (secure geologic storage). The efforts of North Dakota CarbonSAFE Phase III, Site Characterization and Permitting, supported Tundra SGS. Extensive site-specific characterization activities included a successful multimeasurement geophysical approach and drilling a stratigraphic test well (J-ROC 1, subsequently renamed Liberty-1) adjacent to MRYS. Core collection and analyses, downhole testing and fluid sampling, and geophysical logging were performed on J-ROC 1 and on a nearby stratigraphic test well (known as J-LOC 1), which was drilled, cored, and tested under a complementary project funded by the North Dakota Lignite Research Program. The injection tests performed on J-LOC 1 positively impacted the CarbonSAFE project, resulting in fewer proposed injection wells and significant construction, operations, and monitoring cost savings. The characterization data collected and analyses performed were integrated into geologic models, and successive numerical simulations were run to determine CO2 plume extent and subsurface pressure buildup associated with the planned CO2 injection rate of nearly 4 MMt per year. The latter doubles the CarbonSAFE Initiative goal with an estimated 100 MMt of CO2 stored in 20 years. Application of the U.S. Environmental Protection Agency’s (EPA’s) method for estimating the Class VI Rule area of review (AOR) to the overpressurized Broom Creek Formation inspired an alternative method of calculation, called risk-based AOR delineation. This peer-reviewed method was applied for the first time during the storage facility-permitting process. The two SFP applications submitted in 2021 successfully resulted in North Dakota Industrial Commission (NDIC) orders in 2022 authorizing the creation of the storage facility areas and amalgamation of pore space as well as establishing financial responsibility requirements. After approval of the SFPs, Minnkota filed in 2022 applications for permits to reenter the J-ROC 1 well and to drill two new wells—all with the intended purpose to become Class VI injection wells. To establish eligibility under the Internal Revenue Code for Section 45Q tax incentives, a monitoring, reporting, and verification (MRV) plan was prepared and submitted by Minnkota to EPA in 2022, resulting in the first such plan approved in North Dakota. Also in 2022, under the National Environmental Policy Act (NEPA), Minnkota prepared and submitted an environmental information volume (EIV) describing the proposed CCS project and associated potential environmental impacts. Based on the EIV, DOE determined that the proposed construction project required an environmental assessment, and Minnkota submitted the first draft in 2023 and a revised draft in 2024. Both submissions were followed by a public comment period. Subsequently, DOE issued a finding of no significant impact (FONSI) on September 13, 2024. A successful outreach program, strongly based in the production, presentation, and dissemination of informational material, fostered an environment to aid stakeholders in making informed decisions regarding the planned project. Opportunities for public input were provided at various steps along the way, including at county planning and zoning meetings, before and during the SFP administrative hearing, and during environmental assessment public comment periods. In addition, land/pore space owners and mineral owners had various points of contact, including granting access rights, securing pore space leasing, and mineral owner notifications. Based upon the successful storage facility permitting issued by NDIC, approval of the MRV plan by EPA, and receipt of a FONSI under the NEPA, Minnkota is continuing its pursuit of Project Tundra. In December 2023, the Office of Clean Energy Demonstrations under its Carbon Capture Demonstrations Projects Program announced funding for the capture system (Office of Clean Energy Demonstrations, 2023) and a proposal for CarbonSAFE Phase IV: Construction funding was submitted in March 2024 for the storage project. A go/no-go decision to proceed with construction and operations in the Broom Creek Formation is anticipated in 2024. References National Energy Technology Laboratory, CarbonSafe Initiative, https://netl.doe.gov/carbon-management/carbon-storage/carbonsafe (accessed August 2024). Office of Clean Energy Demonstrations, 2023, OCED selects three projects in CA, ND, and TX to reduce harmful carbon pollution, create new economic opportunities, and advance carbon reducing technologies, December, www.energy.gov/oced/articles/oced-selects-three-projects-ca-nd-and-tx-reduce-harmful-carbon-pollution-create-new (accessed August 2024).

Peck, Wesley↗

Surface energy and radiation balance systems - General description and improvements

Surface evaluation of sensible and latent heat flux densities and the components of the radiation balance were desired for various vegetative surfaces during the ASCOT84 experiment to compare with modeled results and to relate these values to drainage winds. Five battery operated data systems equipped with sensors to determine the above values were operated for 105 station days during the ASCOT84 experiment. The Bowen ratio energy balance technique was used to partition the available energy into the sensible and latent heat flux densities. A description of the sensors and battery operated equipment used to collect and process the data is presented. In addition, improvements and modifications made since the 1984 experiment are given. Details of calculations of soil heat flow at the surface and an alternate method to calculate sensible and latent heat flux densities are provided.

Fritschen, Leo J.↗

Comparisons of one- and two- interface methods for tunnel wall interference calculation

Tunnel wall interference in two-dimensional subsonic flow can be analytically calculated on the basis of the one- or two-interface method. The application of numerical integration by means of matrix multiplication to both methods has been found to significantly reduce CPU time in on-line operation. An investigation of the sensitivity of these methods to random velocity-measurement disturbances shows the one-interface method to be less sensitive to measurement errors, and therefore to be preferable for practical applications.

Lo, C. F.↗

Accuracy Of The Correlated-k Method

Report discusses accuracy of correlated-k method of calculating spectral radiances of vertically nonhomogeneous atmospheres. Presents brief description of method. Discusses some theoretical considerations, showing method correct when applied to weak spectral lines, strong pressure-broadened spectral lines, spectral lines affected by Doppler shifts at constant temperatures, and overlapping spectral bands.

Goody, Richard↗

Analytical methods for computing the polar curves of airplanes

This report presents a method of calculating polar curves which is at least as precise as graphical methods, but it more rapid. Knowing the wind tunnel test of a wing and the performances of an airplane of the same profile, it is easy to verify the characteristic coefficients and, at the same time, the methods determining induced resistances.

LE SUEUR↗

Polarization from scattering in blobs

We describe a Monte Carlo method for calculating polarization due to scattering in various geometries. We apply the method in this paper to the case of scattering in a spherical cloud illuminated by parallel rays. The polarization is largest in small optical depth blobs, where single scattering dominates. The polarization decreases as optical depth increases until a limit is reached where scattering occurs on the surface, and increasing optical depth has little effect on the results. For a given optical depth, decreasing the albedo leads to an increase of the degree of polarization of the scattered light because single scattering increases relative to multiple scattering. As the optical depth of the blob increases, the scattered flux becomes increasingly backward throwing. In the high albedo blobs, the maximum polarization becomes skewed towards the illuminated hemisphere at high optical depths. We discuss the applications to polarization in supergiants and R CrB stars, and scattering in a clumpy interstellar medium.

Code, Arthur D.↗

Effects of nonlinear aerodynamics and static aeroelasticity on mission performance calculations for a fighter aircraft

During conceptual design studies of advanced aircraft, the usual practice is to use linear theory to calculate the aerodynamic characteristics of candidate rigid (nonflexible) geometric external shapes. Recent developments and improvements in computational methods, especially computational fluid dynamics (CFD), provide significantly improved capability to generate detailed analysis data for the use of all disciplines involved in the evaluation of a proposed aircraft design. A multidisciplinary application of such analysis methods to calculate the effects of nonlinear aerodynamics and static aeroelasticity on the mission performance of a fighter aircraft concept is described. The aircraft configuration selected for study was defined in a previous study using linear aerodynamics and rigid geometry. The results from the previous study are used as a basis of comparison for the data generated herein. Aerodynamic characteristics are calculated using two different nonlinear theories, potential flow and rotational (Euler) flow. The aerodynamic calculations are performed in an iterative procedure with an equivalent plate structural analysis method to obtain lift and drag data for a flexible (nonrigid) aircraft. These static aeroelastic data are then used in calculating the combat and mission performance characteristics of the aircraft.

Giles, Gary L.↗

A simplified application of the method of operators to the calculation disturbed motions of an airplane

A simplified treatment of the application of Heaviside's operational methods to problems of airplane dynamics is given. Certain graphical methods and logarithmic formulas that lessen the amount of computation involved are explained. The problem of representing a gust disturbance or control manipulation is taken up and it is pointed out that in certain cases arbitrary control manipulations may be dealt with as though they imposed specific constraints on the airplane, thus avoiding the necessity of any integration whatever.

Jones, R. T.↗

Calculations of axisymmetric vortex sheet roll-up using a panel and a filament model

A method for calculating the self-induced motion of a vortex sheet using discrete vortex elements is presented. Vortex panels and vortex filaments are used to simulate two-dimensional and axisymmetric vortex sheet roll-up. A straight forward application using vortex elements to simulate the motion of a disk of vorticity with an elliptic circulation distribution yields unsatisfactroy results where the vortex elements move in a chaotic manner. The difficulty is assumed to be due to the inability of a finite number of discrete vortex elements to model the singularity at the sheet edge and due to large velocity calculation errors which result from uneven sheet stretching. A model of the inner portion of the spiral is introduced to eliminate the difficulty with the sheet edge singularity. The model replaces the outermost portion of the sheet with a single vortex of equivalent circulation and a number of higher order terms which account for the asymmetry of the spiral. The resulting discrete vortex model is applied to both two-dimensional and axisymmetric sheets. The two-dimensional roll-up is compared to the solution for a semi-infinite sheet with good results.

Kantelis, J. P.↗

Preconditioned Conjugate Gradient methods for low speed flow calculations

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Ajmani, Kumud↗

Summary of AH-1G flight vibration data for validation of coupled rotor-fuselage analyses

Under a NASA research program designated DAMVIBS (Design Analysis Methods for VIBrationS), four U. S. helicopter industry participants (Bell Helicopter, Boeing Vertol, McDonnell Douglas Helicopter, and Sikorsky Aircraft) are to apply existing analytical methods for calculating coupled rotor-fuselage vibrations of the AH-1G helicopter for correlation with flight test data from an AH-1G Operational Load Survey (OLS) test program. Bell Helicopter, as the manufacturer of the AH-1G, was asked to provide pertinent rotor data and to collect the OLS flight vibration data needed to perform the correlations. The analytical representation of the fuselage structure is based on a NASTRAN finite element model (FEM) developed by Bell which has been extensively documented and correlated with ground vibration tests.The AH-1G FEM was provided to each of the participants for use in their coupled rotor-fuselage analyses. This report describes the AH-1G OLS flight test program and provides the flight conditions and measured vibration data to be used by each participant in their correlation effort. In addition, the mechanical, structural, inertial and aerodynamic data for the AH-1G two-bladed teetering main rotor system are presented. Furthermore, modifications to the NASTRAN FEM of the fuselage structure that are necessary to make it compatible with the OLS test article are described. The AH-1G OLS flight test data was found to be well documented and provide a sound basis for evaluating currently existing analysis methods used for calculation of coupled rotor-fuselage vibrations.

Dompka, R. V.↗

Increasing the volumetric efficiency of Diesel engines by intake pipes

Development of a method for calculating the volumetric efficiency of piston engines with intake pipes. Application of this method to the scavenging pumps of two-stroke-cycle engines with crankcase scavenging and to four-stroke-cycle engines. The utility of the method is demonstrated by volumetric-efficiency tests of the two-stroke-cycle engines with crankcase scavenging. Its practical application to the calculation of intake pipes is illustrated by example.

List, Hans↗