Search NASA⌕ Search

SEARCH · Search NASA

Results for “Sample Calculations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

A new method for transonic static aeroelasticity problems

A new method has been developed to calculate the steady flow and structural deformations for fluid/structure interaction problems. The discretized fluid dynamic and structural equations are regarded as a single set of coupled, nonlinear, algebraic equations. The equilibrium solution is directly obtained using Newton's method. The governing equations used for the fluid flow are the two-dimensional Navier-Stokes equations, and a finite-element model is used to represent the structure. This paper describes the analytical method and presents sample calculations demonstrating the technique. The results show rapid convergence and good agreement with experimental data.

Felker, Fort F.↗

X-alpha calculation of transition energies in multiply ionized atoms

It is shown that the accuracy of calculations can be improved if appropriate (different) values of alpha are used for each configuration. Alternatively, the Slater Transition state can be used, wherein a total energy difference is related to a difference in single electron eigenvalues. By a series expansion, the value of alpha for an excited configuration can be related to its value for the ground state configuration. The terms Delta alpha (delta Epsilon/delta alpha) exhibit a similar dependence on atomic number as the ground state values of alpha. Results of sample calculations are reported and compared with experiment.

Ringers, D. A.↗

SOLPRO: A computer code to calculate probabilistic energetic solar proton fluences

A code was developed for the calculation of interplanetary solar proton fluences at 1 AU for the active years 1977 to 1983. The fluences are presented as functions of mission duration tau, energy threshold E, and confidence level Q. For a given combination of tau and Q, the routine determines whether ordinary or anomalously large events are to be considered, and in the latter case, the number of anomalously large events that are predicted by probabilistic theory for the specified mission duration. The code is described in detail. A listing and sample calculations are included.

Stassinopoulos, E. G.↗

Improved sonic-box computer program for calculating transonic aerodynamic loads on oscillating wings with thickness

A computer program was developed to account approximately for the effects of finite wing thickness in transonic potential flow over an oscillation wing of finite span. The program is based on the original sonic box computer program for planar wing which was extended to account for the effect of wing thickness. Computational efficiency and accuracy were improved and swept trailing edges were accounted for. Account for the nonuniform flow caused by finite thickness was made by application of the local linearization concept with appropriate coordinate transformation. A brief description of each computer routine and the applications of cubic spline and spline surface data fitting techniques used in the program are given, and the method of input was shown in detail. Sample calculations as well as a complete listing of the computer program listing are presented.

Ruo, S. Y.↗

The Low-Noise Potential of Distributed Propulsion on a Catamaran Aircraft

The noise shielding potential of an inboard-wing catamaran aircraft when coupled with distributed propulsion is examined. Here, only low-frequency jet noise from mid-wing-mounted engines is considered. Because low frequencies are the most difficult to shield, these calculations put a lower bound on the potential shielding benefit. In this proof-of-concept study, simple physical models are used to describe the 3-D scattering of jet noise by conceptualized catamaran aircraft. The Fast Scattering Code is used to predict noise levels on and about the aircraft. Shielding results are presented for several catamaran type geometries and simple noise source configurations representative of distributed propulsion radiation. Computational analyses are presented that demonstrate the shielding benefits of distributed propulsion and of increasing the width of the inboard wing. Also, sample calculations using the FSC are presented that demonstrate additional noise reduction on the aircraft fuselage by the use of acoustic liners on the inboard wing trailing edge. A full conceptual aircraft design would have to be analyzed over a complete mission to more accurately quantify community noise levels and aircraft performance, but the present shielding calculations show that a large acoustic benefit could be achieved by combining distributed propulsion and liner technology with a twin-fuselage planform.

Posey, Joe W.↗

Evaluation of B and W UO{sub 2}/ThO{sub 2} VIII Experimental Core: Criticality and Thermal Disadvantage Factor Analysis

In the framework of the OECD/NEA International Reactor Physics Experiment (IRPHE) Project, an evaluation of core VIII of the Babcock and Wilcox (B and W) Spectral Shift Control Reactor (SSCR), critical experiment program was performed. The SSCR concept, moderated and cooled by a variable mixture of heavy and light water, envisaged changing of the thermal neutron spectrum during the operation to encourage breeding and to sustain the core criticality. Core VIII contained 2188 fuel rods with 93% enriched UO{sub 2}-ThO{sub 2} fuel in a moderator mixture of heavy and light water. The criticality experiment and measurements of the thermal disadvantage factor were evaluated. Benchmark criticality results using different cross-section libraries are reported. ENDF/B-VI.6 calculation was run using the S(α, β) model based on ENDF/B-VI.3 data while ENDF/B-VII.0 and ENDF/BVII.1 used an S(α, β) model based on ENDF/B-VII.0 data. JEFF calculations were run using the S(α, β) model based on JEFF 3.1.1 data except for the aluminum isotope, for which the S(α, β) model was missing. The maximum absolute deviation from the benchmark model was obtained using the JEFF-3.1.1 cross sections while closer results were obtained using ENDF/ B-VII.0 and ENDF/B-VII.1. Only ENDF/B-VII.1 and ENDF/B-VII.0 results are inside the 3σ uncertainty band (+2.8σ and 2.4σ, respectively), having deviations on the order of 300 pcm. The maximum deviation is -827 pcm (-6.1σ), using JEFF.3.1.1. Sample calculations of the TDF benchmark were also performed, studying the effects of the main nuclear data libraries. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Comparison of 2-D and 3-D models of grid erosion in an ion thruster

Numerical results of particle-in-cell/Monte Carlo calculations of accelerator grid erosion in an ion thruster are presented. Specifically, it is shown that a three-dimensional model is required to account for the experimentally observed pitting of the accelerator grid between grid apertures. Some comparisons with earlier two-dimensional, axisymmetric model are made, and it is shown that, for identical operating conditions of the thruster, the wear-through time in the three-dimensional model is about two to three times higher than that obtained previously with the two-dimensional model, namely on the order of 10,000 hours for sample calculation.

Peng, Xiaohang↗

A Multi-Stage Wear Model for Grid-to-Rod Fretting of Nuclear Fuel Rods

The wear of fuel rod cladding against the supporting structures in the cores of pressurized water nuclear reactors (PWRs) is an important and potentially costly tribological issue. Grid-to-rod fretting (GTRF), as it is known, involves not only time-varying contact conditions, but also elevated temperatures, flowing hot water, aqueous tribo-corrosion, and the embrittling effects of neutron fluences. The multi-stage, closed-form analytical model described in this paper relies on published out-of-reactor wear and corrosion data and a set of simplifying assumptions to portray the conversion of frictional work into wear depth. The cladding material of interest is a zirconium-based alloy called Zircaloy-4, and the grid support is made of a harder and more wear-resistant material. Focus is on the wear of the cladding. The model involves an incubation stage, a surface oxide wear stage, and a base alloy wear stage. The wear coefficient, which is a measure of the efficiency of conversion of frictional work into wear damage, can change to reflect the evolving metallurgical condition of the alloy. Wear coefficients for Zircaloy-4 and for a polyphase zirconia layer were back-calculated for a range of times required to wear to a critical depth. Inputs for the model, like the friction coefficient, are taken from the tribology literature in lieu of in-reactor tribological data. Concepts of classical fretting were used as a basis, but are modified to enable the model to accommodate the complexities of the PWR environment. Factors like grid spring relaxation, pre-oxidation of the cladding, multiple oxide phases, gap formation, impact, and hydrogen embrittlement are part of the problem definition but uncertainties in their relative roles limits the ability to validate the model. Sample calculations of wear depth versus time in the cladding illustrate how GTRF wear might occur in a discontinuous fashion during months-long reactor operating cycles. A means to account for grid/rod gaps and repetitive impact effects on GTRF wear is proposed

fretting↗

Residual entropy of ice III from Monte Carlo simulation

We calculated the residual entropy of ice III as a function of the occupation probabilities of hydrogen positions α and β assuming equal energies of all configurations. To do this, a discrete ice model with Bjerrum defect energy penalty and harmonic terms to constrain the occupation probabilities was simulated by the Metropolis Monte Carlo method for a range of temperatures and sizes followed by thermodynamic integration and extrapolation to N = ∞. Similarly as for other ices, the residual entropies are slightly higher than the mean-field (no-loop) approximation. However, the corrections caused by fluctuation of energies of ice samples calculated using molecular models of water are too large for accurate determination of the chemical potential and phase equilibria.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level

An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r{sup −2} instead of r{sup −1}. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Computer method for design of acoustic liners for turbofan engines

A design package is presented for the specification of acoustic liners for turbofans. An estimate of the noise generation was made based on modifications of existing noise correlations, for which the inputs are basic fan aerodynamic design variables. The method does not predict multiple pure tones. A target attenuation spectrum was calculated which was the difference between the estimated generation spectrum and a flat annoyance-weighted goal attenuated spectrum. The target spectrum was combined with a knowledge of acoustic liner performance as a function of the liner design variables to specify the acoustic design. The liner design method at present is limited to annular duct configurations. The detailed structure of the liner was specified by combining the required impedance (which is a result of the previous step) with a mathematical model relating impedance to the detailed structure. The design procedure was developed for a liner constructed of perforated sheet placed over honeycomb backing cavities. A sample calculation was carried through in order to demonstrate the design procedure, and experimental results presented show good agreement with the calculated results of the method.

Minner, G. L.↗

Predicted aboveground biomass of Typha angustifolia in an upland brackish tidal marsh, PIE LTER, Byfield, MA (2022-2024)

This dataset contains predicted monthly aboveground Typha angustifolia biomass per sample and per square meter in a brackish tidal marsh site dominated by Typha angustifolia near the Parker River in the upper estuary of the Plum Island Sound, Massachusetts (MA) during the growing seasons (May-September) of 2022, 2023, and 2024. This site is also located within the Plum Island Ecosystems Long Term Ecological Research Station (PIE LTER). Allometric equations were developed from dry weight data and associated maximum heights collected in 2022 and 2023. The goal of this study was to investigate the difference in aboveground biomass between the site’s marsh interior (MI) and the creek bank (CB). Metadata files (Typha_biomass_predictions_dd.csv and Typha_biomass_predictions_flmd.csv) contain detailed information on variable definitions, calculations, sampling methods, and the location of the site.

DATE↗

Application of two creep fatigue life models for the prediction of elevated temperature crack initiation of a nickel base alloy

Cyclic Damage Accumulation (CDA) and Total Strain-Strain Range Partitioning (TS-SRP) models for predicting the creep-fatigue crack initiation life of high temperature alloys are presented. The models differ in their fundamental assumptions regarding the controlling parameters for fatigue crack initiation and in the amount of data required to determine model constants. The CDA model represents a ductility exhaustion approach and uses stress quantities to calculate the cyclic fatigue damage. The TS-SRP model is based on the use of total mechanical strain and earlier concepts of the Strain Range Partitioning Method. Both models were applied to a well controlled fatigue data set at a high temperature nickel base alloy, B1900 + Hf, tested at 1600 F and 1800 F. The tests were divided into a baseline data set required to determine model constants and a verification data set for evaluation of the predictive capability of the models. Both models correlated the baseline data set to within factors of two in life, and predicted the verification data set to within a factor of three or better. In addition, sample calculations to demonstrate the application of each model and discusions of the predictive capabilities and areas requiring further development are presented.

Moreno, V.↗

Computer Programs for Calculating the Isentropic Flow Properties for Mixtures of R-134a and Air

Three computer programs for calculating the isentropic flow properties of R-134a/air mixtures which were developed in support of the heavy gas conversion of the Langley Transonic Dynamics Tunnel (TDT) from dichlorodifluoromethane (R-12) to 1,1,1,2 tetrafluoroethane (R-134a) are described. The first program calculates the Mach number and the corresponding flow properties when the total temperature, total pressure, static pressure, and mole fraction of R-134a in the mixture are given. The second program calculates tables of isentropic flow properties for a specified set of free-stream Mach numbers given the total pressure, total temperature, and mole fraction of R-134a. Real-gas effects are accounted for in these programs by treating the gases comprising the mixture as both thermally and calorically imperfect. The third program is a specialized version of the first program in which the gases are thermally perfect. It was written to provide a simpler computational alternative to the first program in those cases where real-gas effects are not important. The theory and computational procedures underlying the programs are summarized, the equations used to compute the flow quantities of interest are given, and sample calculated results that encompass the operating conditions of the TDT are shown.

Kvaternik, Raymond G.↗

Riding and handling qualities of light aircraft: A review and analysis

Design procedures and supporting data necessary for configuring light aircraft to obtain desired responses to pilot commands and gusts are presented. The procedures employ specializations of modern military and jet transport practice where these provide an improvement over earlier practice. General criteria for riding and handling qualities are discussed in terms of the airframe dynamics. Methods available in the literature for calculating the coefficients required for a linearized analysis of the airframe dynamics are reviewed in detail. The review also treats the relation of spin and stall to airframe geometry. Root locus analysis is used to indicate the sensitivity of airframe dynamics to variations in individual stability derivatives and to variations in geometric parameters. Computer programs are given for finding the frequencies, damping ratios, and time constants of all rigid body modes and for generating time histories of aircraft motions in response to control inputs. Appendices are included presenting the derivation of the linearized equations of motion; the stability derivatives; the transfer functions; approximate solutions for the frequency, damping ratio, and time constants; an indication of methods to be used when linear analysis is inadequate; sample calculations; and an explanation of the use of root locus diagrams and Bode plots.

Smetana, F. O.↗

DEVELOPMENT OF AN ANTIFOAM TRACKING SYSTEM AS AN OPTION TO SUPPORT THE MELTER OFF-GAS FLAMMABILITY CONTROL STRATEGY AT THE DWPF

The Savannah River National Laboratory (SRNL) has been working with the Savannah River Remediation (SRR) Defense Waste Processing Facility (DWPF) in the development and implementation of an additional strategy for confidently satisfying the flammability controls for DWPF’s melter operation. An initial strategy for implementing the operational constraints associated with flammability control in DWPF was based upon an analytically determined carbon concentration from antifoam. Due to the conservative error structure associated with the analytical approach, its implementation has significantly reduced the operating window for processing and has led to recurrent Slurry Mix Evaporator (SME) and Melter Feed Tank (MFT) remediation. To address the adverse operating impact of the current implementation strategy, SRR issued a Technical Task Request (TTR) to SRNL requesting the development and documentation of an alternate strategy for evaluating the carbon contribution from antifoam. The proposed strategy presented in this report was developed under the guidance of a Task Technical and Quality Assurance Plan (TTQAP) and involves calculating the carbon concentration from antifoam based upon the actual mass of antifoam added to the process assuming 100% retention. The mass of antifoam in the Additive Mix Feed Tank (AMFT), in the Sludge Receipt and Adjustment Tank (SRAT), and in the SME is tracked by mass balance as part of this strategy. As these quantities are monitored, the random and bias uncertainties affecting their values are also maintained and accounted for. This report documents: 1) the development of an alternate implementation strategy and associated equations describing the carbon concentration from antifoam in each SME batch derived from the actual amount of antifoam introduced into the AMFT, SRAT, and SME during the processing of the batch. 2) the equations and error structure for incorporating the proposed strategy into melter off-gas flammability assessments. Sample calculations of the system are also included in this report. Please note that the system developed and documented in this report is intended as an alternative to the current, analytically-driven system being utilized by DWPF; the proposed system is not intended to eliminate the current system. Also note that the system developed in this report to track antifoam mass in the AMFT, SRAT, and SME will be applicable beyond just Sludge Batch 8. While the model used to determine acceptability of the SME product with respect to melter off-gas flammability controls must be reassessed for each change in sludge batch, the antifoam mass tracking methodology is independent of sludge batch composition and as such will be transferable to future sludge batches.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Flutter of a uniform wing with an arbitrarily placed mass according to a differential-equation analysis and a comparison with experiment

A method is presented for the calculation of the flutter speed of a uniform wing carrying an arbitrarily placed concentrated mass. The method, an extension of recently published work by Goland and Luke, involves the solution of the differential equations of motion of the wing at flutter speed and therefore does not require the assumption of specific normal modes of vibration. The order of the flutter determinant to be solved by this method depends upon the order of the system of differential equations and not upon the number of modes of vibration involved. The differential equations are solved by operational methods, and a brief discussion of operational methods as applied to boundary-value problems is included in one of two appendixes. A comparison is made with experiment for a wing with a large eccentrically mounted weight and good agreement is obtained. Sample calculations are presented to illustrate the method; and curves of amplitudes of displacement, torque, and shear for a particular case are compared with corresponding curves computed from the first uncoupled normal modes.

Runyan, Harry L↗

Linearized Theory of Wind-tunnel Jet-boundary Corrections and Ground Effect for VTOL-STOL Aircraft

A linearized theory is developed to obtain interference factors for wind tunnels and ground effect. The calculated results, presented in tabular form in NASA Technical Notes D-933, D-934, D-935, and D-936, indicate that the degree to which the wake is deflected downward has a primary effect on the magnitude of the interference. When the wake is undeflected the corrections are essentially the same as those of classical theory. When the wake is deflected severely downward, the corrections are primarily determined by the floor of the wind tunnel. Under these conditions, the corrections are, in general, much larger than those given by previously available results. Because of deformations at the lower boundary of the jet, the corrections for an open wind tunnel are uncertain. Testing at low speeds and high lift coefficients in open wind tunnels, therefore, is not recommended. Although the theory is developed expressly for single-element, vanishingly small models, methods, with sample calculations, are given for extending the results to multielement and finite span models. The theory is at least partially verified by available test data; however, complete verification would require a substantially more detailed experimental study.

V/STOL aircraft↗