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NASA NTRS1984

Unsteady aerodynamics in time and frequency domains for finite time arbitrary motion of rotary wings in hover and forward flight

Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories, discussed in the paper, are obtained by developing finite state models using the Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a helicopter typical rotor blade section, are presented.

Dinyavari, M. A. H.↗

NASA NTRS1985

Postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression

Results of an experimental and analytical study of the postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression are presented. The postbuckling response and failure characteristics of the panels are described. Each panel had four equally-spaced I-shaped stiffeners and 16-ply quasi-isotropic skins. Panels with three different stiffener spacings were tested. Failure of all panels initiated in a skin-stiffener interface region. Analytical results from a nonlinear general shell finite element analysis computer code correlate well with typical postbuckling test results up to failure. The analytical modeling detail necessary to predict accurately the response of the panel is described. Measured initial geometric imperfections were included in the postbuckling analysis.

Knight, N. F., Jr.↗

NASA NTRS1988

Properties of finite difference models of non-linear conservative oscillators

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

Mickens, R. E.↗

NASA NTRS1990

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Chakravarthy, Sukumar R.↗

NASA NTRS1994

Deflections of anisotropic sandwich beams with variable face sheets and core thicknesses

A sandwich construction consists of a low-density core material with high strength face sheets bounded to the top and bottom surfaces. The construction has been widely used in the aerospace and marine industries due to its outstanding characteristics such as noise absorption, weight minimization, heat insulation, and better bending stiffness. In sandwich structures used in high-performance aircraft, the face sheets are often made of fiber-reinforced composite materials and the core is made of honeycomb. The structures may also have variable thickness so as to satisfy aerodynamic requirements. In the stress analysis, the constant-thickness face sheets are usually considered as membrane and the core is assumed to be inextensible but deformable in the thickness direction. The static behavior of variable-thickness, isotropic and homogeneous sandwich beams was successfully studied by employing a constant-thickness theory but allowing stiffnesses to vary in accordance with local thickness variations. It has been recently found in a refined theory that the analyses based on the constant thickness theory locally can lead to significant errors in structural responses if the sandwich beam is thickness-tapered and the cores are deformable in transverse shear. The errors arise mainly from two factors: (1) the transverse shear components of the membrane forces in the face sheets alter the transverse shears carried by the core; and (2) the face-sheet membrane strains arise from transverse shear deformation of the core. In practice the variable thickness may not only exist in core but also in face sheets. The thickness-variations may even be a type of step function. In this case the transverse shear stress in the face sheets and bending stress in the core should be taken into account in the refined theory mentioned. In the present study, energy principles are employed in deriving governing equations for general bending of anisotropic sandwich beams with variable thickness in both face sheets and cores. Solutions to these equations are based on a finite difference scheme. As an example in application, a simply supported thickness-tapered sandwich beam subject to a concentrated load at its center is considered. Let W' be the maximum deflection of the beam in which face sheets are considered as membrane, while W'' is that based on using the modified refined theory. It is found that W' is always larger than W'', however, the magnitude of (W'- W'') appears to be insensitive to the change of the taper of the beam.

Lu, Chu-Ho↗

NASA NTRS1995

Femtolensing: Beyond the semiclassical approximation

Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.

Ulmer, Andrew↗

DOE OSTI2018

Occupancy-Based HVAC Control with Short-Term Occupancy Prediction Algorithms for Energy-Efficient Buildings

This study aims to develop a concrete occupancy prediction as well as an optimal occupancy-based control solution for improving the efficiency of Heating, Ventilation, and Air-Conditioning (HVAC) systems. Accurate occupancy prediction is a key enabler for demand-based HVAC control so as to ensure HVAC is not run needlessly when when a room/zone is unoccupied. In this paper, we propose simple yet effective algorithms to predict occupancy alongside an algorithm for automatically assigning temperature set-points. Utilizing past occupancy observations, we introduce three different techniques for occupancy prediction. Firstly, we propose an identification-based approach, which identifies the model via Expectation Maximization (EM) algorithm. Secondly, we study a novel finite state automata (FSA) which can be reconstructed by a general systems problem solver (GSPS). Thirdly, we introduce an alternative stochastic model based on uncertain basis functions. The results show that all the proposed occupancy prediction techniques could achieve around 70% accuracy. Then, we have proposed a scheme to adaptively adjust the temperature set-points according to a novel temperature set algorithm with customers’ different discomfort tolerance indexes. By cooperating with the temperature set algorithm, our occupancy-based HVAC control shows 20% energy saving while still maintaining building comfort requirements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

Ensemble density functional theory (EDFT) is a generalization of ground-state DFT, which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional 'particle in a box' systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and local spin density approximation exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Geometric Mapping of Tasks to Processors on Parallel Computers with Mesh or Torus Networks

We present a new method for reducing parallel applications' communication time by mapping their MPI tasks to processors in a way that lowers the distance messages travel and the amount of congestion in the network. Assuming geometric proximity among the tasks is a good approximation of their communication interdependence, we use a geometric partitioning algorithm to order both the tasks and the processors, assigning task parts to the corresponding processor parts. In this way, interdependent tasks are assigned to “nearby” cores in the network. We also present a number of algorithmic optimizations that exploit specific features of the network or application to further improve the quality of the mapping. We specifically address the case of sparse node allocation, where the nodes assigned to a job are not necessarily located in a contiguous block nor within close proximity to each other in the network. Furthermore, our methods generalize to contiguous allocations as well, and results are shown for both contiguous and non-contiguous allocations. We show that, for the structured finite difference mini-application MiniGhost, our mapping methods reduced communication time up to 75% relative to MiniGhost's default mapping on 128K cores of a Cray XK7 with sparse allocation. For the atmospheric modeling code E3SM/HOMME, our methods reduced communication time up to 31% on 16K cores of an IBM BlueGene/Q with contiguous allocation.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Thermoluminescence: Potential Applications in Forensic Science

In crime laboratories one of the most difficult operations is to determine unequivocally whether or not two samples of evidence of the same type were originally part of the same thing or were from the same source. It has been found that high temperature thermoluminescence (room temperature to 723 K) can be used for comparisons of this type, although work to date indicates that there is generally a finite probability for coincidental matching of glass or soil samples. Further work is required to determine and attempt to minimize these probabilities for different types of materials, and to define more clearly the scope of applicability of thermoluminescence to actual forensic situations.

Ingham, J. D.↗

NASA NTRS1981

Numerical analysis of the scramjet-inlet flow field by using two-dimensional Navier-Stokes equations

A computer code was developed to solve the full two dimensional Navier-Stokes equations in a supersonic combustion ramjet (scramjet) inlet. In order to be able to consider a general inlet geometry with embedded bodies, a numerical coordinate transformation is used which generates a set of boundary-fitted curvilinear coordinates. The explicit finite difference algorithm of MacCormack is used to solve the governing equations. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with no strut, one strut, or multiple struts in the flow field. The application of the two dimensional analysis in the preliminary parametric design studies of a scramjet inlet is discussed. Detailed results are presented for one model problem and for several actual scramjet-inlet configurations.

Kumar, A.↗

NASA NTRS1991

Performance optimization of helicopter rotor blades

As part of a center-wide activity at NASA Langley Research Center to develop multidisciplinary design procedures by accounting for discipline interactions, a performance design optimization procedure is developed. The procedure optimizes the aerodynamic performance of rotor blades by selecting the point of taper initiation, root chord, taper ratio, and maximum twist which minimize hover horsepower while not degrading forward flight performance. The procedure uses HOVT (a strip theory momentum analysis) to compute the horse power required for hover and the comprehensive helicopter analysis program CAMRAD to compute the horsepower required for forward flight and maneuver. The optimization algorithm consists of the general purpose optimization program CONMIN and approximate analyses. Sensitivity analyses consisting of derivatives of the objective function and constraints are carried out by forward finite differences. The procedure is applied to a test problem which is an analytical model of a wind tunnel model of a utility rotor blade.

Walsh, Joanne L.↗

NASA NTRS1991

Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics

A prescription is given for conservatively integrating generalized hydromagnetic equations using flux-corrected transport (FCT) techniques. By placing the magnetic-field components at the interface locations of the finite-difference grid, the field is kept divergence-free to within machine roundoff error. The use of FCT techniques allows an integration scheme of high accuracy to be employed, while the numerical ripples associated with large dispersion errors are avoided. The method is particularly well suited for problems involving magnetohydrodynamic shocks and other discontinuities.

Devore, C. Richard↗

NASA NTRS1992

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗

NASA NTRS1993

Numerical investigation of receptivity to freestream vorticity

The receptivity to freestream vorticity of the boundary layer over a flat plate with an elliptic leading edge is studied numerically. A finite-difference scheme that is second-order accurate in both time and space is utilized to solve the incompressible Navier-Stokes system in general curvilinear coordinates with the vorticity and stream function as dependent variables. Simulations show, for the conditions considered, a linear variation in the Tollmien-Schlichting response with forcing amplitude for perturbations of freestream velocity that are either symmetrical or asymmetrical with respect to the basic state stagnation streamline.

Buter, Thomas A.↗

DOE OSTI2020

Rupture Dynamics Simulations of Shallow Crustal Earthquakes on Reverse Slip Faults

The main goal of this study was to perform dynamic rupture simulations in order constrain the characterization of kinematic rupture models implemented in techniques for simulating strong ground motion for crustal earthquakes. First, we investigated the rupture process of the 2008 Iwate-Miyagi Nairiku earthquake by developing a dynamic rupture model on a reverse fault using a trial-and-error technique that produced a slip distribution and near-fault ground motion that matched the recorded ones. The simulations were performed in the frequency range 0-2 Hz, using a 3D staggered grid finite-difference method and a linear slip weakening friction law. Constrained by the observed slip distribution and consistent with dynamic rupture models, the derived kinematic rupture model of the Iwate-Miyagi Nairiku earthquake contains areas with relatively large slip rate, representing strong motion generation areas, set against lower amplitude heterogeneous background slip, and a relatively low slip rate in the weak zone of the top-most crust (upper 3km). Second, we performed rupture dynamics modeling to constrain shallow slip characterization in rupture models for strike-slip crustal earthquakes. The objective was to establish general rules about the characterization of slip rate function and slip at shallow depths and in the strong motion generation areas (SMGAs). The simulations of spontaneous rupture were performed in the frequency range 0-2.0Hz, using a 3D staggered-grid finite-difference method and a layer over half-space 1D crustal velocity model with a minimum shear-wave velocity of 2.8 km/s. In order to account for changes in material ductility and reduction of stress drop, observed in the shallow crust (upper 3-5 km), and the transition from ductile state to brittle state in the upper seismogenic zone, in our stress models we included a shallow weak zone (<4km). In this zone the stress drop was set to zero at the free surface and gradually increased with depth, while the slip weakening distance was set to 75 cm at the free surface and decreased to 50 cm at the base of the weak zone. As in the case of reverse faulting during the Iwate-Miyagi Nairiku earthquake, from these computations we found a systematic change in the shape of the slip-rate function, from Kostrov-type in the deeper part of the fault to a more symmetric cosine-type in the upper few kilometers, near the free-surface. Moreover, the average slip duration in the weak zone, with respect to slip duration in the deeper parts of the fault, increases by at most a factor of 1.5. We found a systematic and gradual change in the shape of the slip-rate function from Kostrov-type in the asperity areas (SMGAs), to more symmetric cosine-type in the upper few km near the free-surface, on the long period motion generation area (LMGA). The effective rise time in the LMGA, with respect to that in the SMGAs, increases by at most a factor of 2. Effective rise time is the time difference between the time at which the slip rate drops to a level that is equal to 25% of its peak and the onset time of the signal. In addition, the slip in the LMGA located above the SMGAs is almost the same as the one in the SMGAs, and about 1.5 times larger than the average slip.

58 GEOSCIENCES↗

DOE OSTI2023

Towards Realistic and High Fidelity Models for Nuclear Reactor Power Synthesis Simulation with Self-Powered Neutron Detectors

As presented in this report, a weighting function–based inferencing method is being applied to synthesize the power distribution in next-generation and university research reactors based on simulated self power neutron detector (SPND) responses. The overall goal is to assess the impacts of sensor uncertainty and true power distribution perturbations on the error in the synthesized power distribution. Regarding sensor uncertainty, the NuScale Small Modular Reactor (SMR) and the Westinghouse AP1000 serve as testbeds for analyzing the impact of varying the sensor uncertainty, as well as varying the number of sensors per sensor string in the reactor core. The reactor models are informed by Monte Carlo N-Particle (MCNP) neutron flux tallies. For the NuScale SMR and Westinghouse AP1000, the SPND response functions (i.e., the response of the SPNDs to individual segments of fuel) were determined homogeneously. Regarding an analysis of power distribution perturbation detection, the Texas A&M Testing, Research, Isotopes, General Atomics Reactor (TAMU TRIGA) reactor was used as a demonstration case with one particular arrangement of SPNDs; the response functions for this reactor model were determined heterogeneously, making this a uniquely high-fidelity demonstration of perturbation detection. Finally, SPND models generated in the Geometry and Tracking 4 (Geant4) code have been generated and tested for comparison with traditionally implemented analytical SPND models, with the intent for Geant4 integration with the full methodological framework. SPND current outputs as a function of distance from some fuel assembly segment in the NuScale SMR are compared with the analytically determined currents. Results from the sensor uncertainty simulations for the NuScale SMR and AP1000 indicate that the average error in the inferred power distribution on the fuel assembly segment level is reasonably low, being slightly less than the random uncertainty applied to all respective SPNDs in both cores. For example, if all SPNDs in the core have a random uncertainty of 5%, then the corresponding fuel assembly segment level error (i.e. difference between the true and inferred local power) is ~2–3%. However, the maximum error in the inferred power distribution on the fuel assembly segment level can be considerably high (>15%) when SPND random uncertainties start to exceed ~3%. In general, the average and maximum errors in the inferred power distribution were slightly higher in the AP1000 as opposed to the NuScale SMR for the sensor string configurations considered herein. Another result determined from analysis of the sensor uncertainty simulations was that increasing the number of SPNDs per string does not clearly reduce inferred power distribution error and can in fact make the error large in some cases; however, this assessment may skewed due to imposed iteration limits. Results from the perturbation detection demonstration using the high-fidelity TAMU TRIGA model indicate that, given the arrangement of 17 SPND strings and 4 SPNDs per string considered herein, there is a clear, provable ability to infer a localized Gaussian-type peak perturbation in the 3D power distribution. Such a perturbation was detected with an average fuel assembly segment level error of 0.19%, and the general visualization of the detected perturbation clearly indicates that the magnitude and shape were appropriately resolved. Finally, the electrical current output generated by the Geant4 modeled SPND indicates significant magnitude differences than the analytically modeled SPND, demonstrating the need for accurate SPND models which account for finite sensor geometry effects to inform the power synthesis work described herein.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Calibrating constitutive models with full‐field data via physics informed neural networks

Abstract The calibration of solid constitutive models with full‐field experimental data is a long‐standing challenge, especially in materials that undergo large deformations. In this paper, we propose a physics‐informed deep‐learning framework for the discovery of hyperelastic constitutive model parameterizations given full‐field surface displacement data and global force‐displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic material models suitable for different material classes is considered including the Neo–Hookean, Gent, and Blatz–Ko constitutive models as exemplars for general non‐linear elastic behaviour, elastomer behaviour with finite strain lock‐up, and compressible foam behaviour, respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full‐field experimental data are utilized to calibrate constitutive models under finite deformations.

Hamel, Craig M.↗