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NASA NTRS1984

Numerical simulation of boundary-layer transition

The transition to turbulence in boundary layers was investigated by direct numerical solution of the nonlinear, three-dimensional, incompressible Navier-Stokes equations in the half-infinite domain over a flat plate. Periodicity was imposed in the streamwise and spanwise directions. A body force was applied to approximate the effect of a nonparallel mean flow. The numerical method was spectra, based on Fourier series and Jacobi polynomials, and used divergence-free basis functions. Extremely rapid convergence was obtained when solving the linear Orr-Sommerfeld equation. The early nonlinear and three-dimensional stages of transition, in a boundary layer disturbed by a vibrating ribbon, were successfully simulated. Excellent qualitative agreement was observed with either experiments or weakly nonlinear theories. In particular, the breakdown pattern was staggered or nonstaggered depending on the disturbance amplitude.

Spalart, P. R.↗

NASA NTRS2007

Generative Representations for Automated Design of Robots

A method of automated design of complex, modular robots involves an evolutionary process in which generative representations of designs are used. The term generative representations as used here signifies, loosely, representations that consist of or include algorithms, computer programs, and the like, wherein encoded designs can reuse elements of their encoding and thereby evolve toward greater complexity. Automated design of robots through synthetic evolutionary processes has already been demonstrated, but it is not clear whether genetically inspired search algorithms can yield designs that are sufficiently complex for practical engineering. The ultimate success of such algorithms as tools for automation of design depends on the scaling properties of representations of designs. A nongenerative representation (one in which each element of the encoded design is used at most once in translating to the design) scales linearly with the number of elements. Search algorithms that use nongenerative representations quickly become intractable (search times vary approximately exponentially with numbers of design elements), and thus are not amenable to scaling to complex designs. Generative representations are compact representations and were devised as means to circumvent the above-mentioned fundamental restriction on scalability. In the present method, a robot is defined by a compact programmatic form (its generative representation) and the evolutionary variation takes place on this form. The evolutionary process is an iterative one, wherein each cycle consists of the following steps: 1. Generative representations are generated in an evolutionary subprocess. 2. Each generative representation is a program that, when compiled, produces an assembly procedure. 3. In a computational simulation, a constructor executes an assembly procedure to generate a robot. 4. A physical-simulation program tests the performance of a simulated constructed robot, evaluating the performance according to a fitness criterion to yield a figure of merit that is fed back into the evolutionary subprocess of the next iteration. In comparison with prior approaches to automated evolutionary design of robots, the use of generative representations offers two advantages: First, a generative representation enables the reuse of components in regular and hierarchical ways and thereby serves a systematic means of creating more complex modules out of simpler ones. Second, the evolved generative representation may capture intrinsic properties of the design problem, so that variations in the representations move through the design space more effectively than do equivalent variations in a nongenerative representation. This method has been demonstrated by using it to design some robots that move, variously, by walking, rolling, or sliding. Some of the robots were built (see figure). Although these robots are very simple, in comparison with robots designed by humans, their structures are more regular, modular, hierarchical, and complex than are those of evolved designs of comparable functionality synthesized by use of nongenerative representations.

Homby, Gregory S.↗

NASA NTRS1994

Suboptimal schemes for atmospheric data assimilation based on the Kalman filter

This work is directed toward approximating the evolution of forecast error covariances for data assimilation. The performance of different algorithms based on simplification of the standard Kalman filter (KF) is studied. These are suboptimal schemes (SOSs) when compared to the KF, which is optimal for linear problems with known statistics. The SOSs considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. To employ a methodology for exact comparison among these schemes, a linear environment is maintained, in which a beta-plane shallow-water model linearized about a constant zonal flow is chosen for the test-bed dynamics. The results show that constructing dynamically balanced forecast error covariances rather than using conventional geostrophically balanced ones is essential for successful performance of any SOS. A posteriori initialization of SOSs to compensate for model - data imbalance sometimes results in poor performance. Instead, properly constructed dynamically balanced forecast error covariances eliminate the need for initialization. When the SOSs studied here make use of dynamically balanced forecast error covariances, the difference among their performances progresses naturally from conventional OI to the KF. In fact, the results suggest that even modest enhancements of OI, such as including an approximate dynamical equation for height error variances while leaving height error correlation structure homogeneous, go a long way toward achieving the performance of the KF, provided that dynamically balanced cross-covariances are constructed and that model errors are accounted for properly. The results indicate that such enhancements are necessary if unconventional data are to have a positive impact.

Todling, Ricardo↗

DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗

DOE OSTI2020

Tight-binding study of beryllium

In this work, we have applied the Naval Research Laboratory Tight-binding (NRL-TB) Method to the hcp alkaline-earth metal Beryllium. This approach consists of fitting to energy band and total energy data generated by the Linearized Augmented Plane Wave (LAPW) for the fcc, bcc, sc, and hcp structures as a function of volume. First, we found that using the Generalized Gradient Approximation (GGA) for the input data secures a better agreement to experimental volumes than the LDA. Second, we found that including small volumes to the fit is needed to get TB parameters that are transferable enough to successfully predict the energies of structures that were not fitted, and to perform molecular dynamics (MD) simulations. The non-orthogonal Hamiltonian obtained, is successful in correctly predicting the hcp lattice as the ground state of Be and finding eight other structures, that were not fitted to LAPW, positioned at higher energies. In addition, the NRL-TB produces accurate energy bands, densities of states, elastic constants, the Bain path and several quantities derived from MD simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Achieving High-Resolution Hard X-ray Microscopy using Monolithic 2D Multilayer Laue Lenses

This article introduces the 2D multilayer Laue lens (MLL) nanofocusing optics recently developed for high-resolution hard X-ray microscopy. The new optics utilized a micro-electro-mechanical-system (MEMS)-based template to accommodate two linear MLL optics in a pre-aligned configuration. Angular misalignment between the two lenses was controlled in tens of millidegrees, and the lateral position error was on a micrometer scale. Using the developed 2D MLLs, an astigmatism-free point focus of approximately 14 nm by 13 nm in horizontal and vertical directions, respectively, at 13.6 keV photon energy was obtained. In conclusion, the success of 2D MLL optics with an approaching 10 nm resolution is a significant step forward for the development of high-resolution hard X-ray microscopy and applications of MLL optics in the hard X-ray community.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2002

Structural Modeling of a Five-Meter Thin Film Inflatable Antenna/Concentrator

Inflatable structures have been the subject of renewed interest in recent years for space applications such as communications antennas, solar thermal propulsion, and space solar power. A major advantage of using inflatable structures in space is their extremely light weight. An obvious second advantage is on-orbit deployability and related space savings in the launch configuration. A recent technology demonstrator flight for inflatable structures was the Inflatable Antenna Experiment (IAE) that was deployed on orbit from the Shuttle Orbiter. Although difficulty was encountered in the inflation/deployment phase, the flight was successful overall and provided valuable experience in the use of such structures. Several papers on static structural analysis of inflated cylinders have been written, describing different techniques such as linear shell theory, and nonlinear and variational methods, but very little work had been done in dynamics of inflatable structures until recent years. In 1988 Leonard indicated that elastic beam bending modes could be utilized in approximating lower-order frequencies of inflatable beams. Main, et al. wrote a very significant 1995 paper describing results of modal tests of inflated cantilever beams and the determination of effective material properties. Changes in material properties for different pressures were also discussed, and the beam model was used in a more complex structure. The paper demonstrated that conventional finite element analysis packages could be very useful in the analysis of complex inflatable structures. The purposes of this paper are to discuss the methodology for dynamically characterizing a large 5-meter thin film inflatable reflector, and to discuss the test arrangement and results. Nonlinear finite element modal results are compared to modal test data. The work is significant and of considerable interest to researchers because of 1) the large size of the structure, making it useful for scaling studies, and 2) application of commercially available finite element software for modeling pressurized thin-film structures.

Smalley, Kurt B.↗

DOE OSTI2025

Adsorptive denitrogenation of model aviation fuel using mesoporous silica in a packed bed adsorption system

This study aims to understand the effects of system process parameters such as flow rate, adsorbent particle size, and use of recycled adsorbent on denitrogenation performance of a model fuel using mesoporous silica gel. The goal is to reduce the nitrogen content of the model fuel from 1500 parts per million to single-digit ppm to meet ASTM specifications for drop-in fuels. This work was done with the intent of applying adsorptive denitrogenation to sustainable aviation fuel (SAF) product fractions produced via hydrothermal liquefaction (HTL). The adsorption performance of the silica is evaluated via packed column breakthrough data, with data generated from collecting from the column outlet and quantifying nitrogen content via gas chromatography. Select experiments use a significantly larger (2.5x column diameter and length) column to demonstrate linear scalability of the process. Thermogravimetric analysis data is collected to evaluate the effects of thermal calcination as a sorbent regeneration method. Effects of a more complex feed are also investigated using a known reference fuel with additional added nitrogen containing compounds. The results presented in this work successfully demonstrate up to 99.8 % removal of NCCs from a model fuel fraction at an original NCC concentration of approximately 1500 ppm to single-digit parts per million after treatment. We also examine calcination of sorbent materials to remove the adsorbed species to enable sorbent reuse and minimize waste generation and show that the calcined material can be reused up to 5 cycles with reduced adsorption capacity. Overall, this work indicates that adsorptive denitrogenation using silica gel is a viable solution to enable the integration of HTL-derived aviation fuels into existing fuel infrastructure.

Adsorption techniques↗

NASA NTRS1987

Mass flow meter using the triboelectric effect for measurement in cryogenics

The use of triboelectric charge to measure the mass flow rate of cryogens for the Space Shuttle Main Engine was investigated. Cross correlation of the triboelectric charge signals was used to determine the transit time of the cryogen between two sensor locations in a .75-in tube. The ring electrode sensors were mounted in a removable spool piece. Three spool pieces were constructed for delivery, each with a different design. One set of electronics for implementation of the cross correlation and flow calculation was constructed for delivery. Tests were made using a laboratory flow loop using liquid freon and transformer oil. The measured flow precision was 1 percent and the response was linear. The natural frequency distribution of the triboelectric signal was approximately 1/f. The sensor electrodes should have an axial length less than approximately one/tenth pipe diameter. The electrode spacing should be less than approximately one pipe diameter. Tests using liquid nitrogen demonstrated poor tribo-signal to noise ratio. Most of the noise was microphonic and common to both electrode systems. The common noise rejection facility of the correlator was successful in compensating for this noise but the signal was too small to enable reliable demonstration of the technique in liquid nitrogen.

Bernatowicz, Henry↗

DOE OSTI2020

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗

NASA NTRS1993

Multigrid direct numerical simulation of the whole process of flow transition in 3-D boundary layers

A new technology was developed in this study which provides a successful numerical simulation of the whole process of flow transition in 3-D boundary layers, including linear growth, secondary instability, breakdown, and transition at relatively low CPU cost. Most other spatial numerical simulations require high CPU cost and blow up at the stage of flow breakdown. A fourth-order finite difference scheme on stretched and staggered grids, a fully implicit time marching technique, a semi-coarsening multigrid based on the so-called approximate line-box relaxation, and a buffer domain for the outflow boundary conditions were all used for high-order accuracy, good stability, and fast convergence. A new fine-coarse-fine grid mapping technique was developed to keep the code running after the laminar flow breaks down. The computational results are in good agreement with linear stability theory, secondary instability theory, and some experiments. The cost for a typical case with 162 x 34 x 34 grid is around 2 CRAY-YMP CPU hours for 10 T-S periods.

Liu, Chaoqun↗

NASA NTRS1984

A comparative look at sunspot cycles

On the basis of cycles 8 through 20, spanning about 143 years, observations of sunspot number, smoothed sunspot number, and their temporal properties were used to compute means, standard deviations, ranges, and frequency of occurrence histograms for a number of sunspot cycle parameters. The resultant schematic sunspot cycle was contrasted with the mean sunspot cycle, obtained by averaging smoothed sunspot number as a function of time, tying all cycles (8 through 20) to their minimum occurence date. A relatively good approximation of the time variation of smoothed sunspot number for a given cycle is possible if sunspot cycles are regarded in terms of being either HIGH- or LOW-R(MAX) cycles or LONG- or SHORT-PERIOD cycles, especially the latter. Linear regression analyses were performed comparing late cycle parameters with early cycle parameters and solar cycle number. The early occurring cycle parameters can be used to estimate later occurring cycle parameters with relatively good success, based on cycle 21 as an example. The sunspot cycle record clearly shows that the trend for both R(MIN) and R(MAX) was toward decreasing value between cycles 8 through 14 and toward increasing value between cycles 14 through 20. Linear regression equations were also obtained for several measures of solar activity.

Wilson, R. M.↗

DOE OSTI2022

Time dependent supervisory control update with FARM using rolling window

This report describes improvements to the Feasible Actuator Range Modifier (FARM) component of the RAVEN-based HYBRID framework for analysis of Integrated Energy Systems (IES). FARM supports the HERON plug-in that solves the power dispatch problem. The solution to the dispatch problem involves economically optimal dispatches that satisfy limits on production variables and their rates of variation (explicit constraints) as well as process variables tied to the service life of equipment (implicit constraints). FARM serves to validate or confirm that a HERON solution for explicit constraints also satisfies the implicit constraints. FARM-alpha was released by Argonne National Laboratory in January 2021 followed by FARM-Beta in January 2022 with the latter providing increased flexibility for the user. In this report, FARM-Gamma, the latest version of the code, is described. The major improvement is the implementation of a system identification algorithm based on the Dynamic Mode Decomposition with Control (DMDc) coupled with a “Rolling Window” scheme that allows obtaining linear time-varying state-space models. This feature equips FARM with the most accurate approximation of system dynamics, and it relieves the user from the burden of performing an exhaustive off-line characterization of the dynamics. FARM-Gamma capabilities are assessed by solving the power dispatch problem for a representative IES unit. The simulation times corresponding to the different releases are estimated and compared. These values capture the increasing computational burden of the successively higher fidelity state-space models adopted by FARM-Alpha, FARM-Beta and FARM-Gamma. The code implementation provides significant flexibility, i.e., the user can always select the most suitable version of FARM according to the problem to be solved and the available computational resources. It is anticipated that FARM will play a role in addressing several future IES applications. We outline how it can support the coordinated management and safe operation of a nuclear plant coupled to industrial processes to produce hydrogen and synfuels.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS2013

An Update on the Effectiveness of Postmission Disposal in LEO

The commonly‐adopted orbital debris mitigation measures were developed to reduce the growth of the future debris population. A major component in debris mitigation is post-mission disposal (PMD). The key PMD element for LEO satellites is the 25‐year rule. It is intended to limit the long‐term presence of rocket bodies (R/Bs) and spacecraft (S/C), as well as mission-related debris, in the environment. The effectiveness of PMD has been demonstrated and documented since the development of mitigation measures began in the 1990s. This paper summarizes an updated study, based on the current environment, using the NASA LEGEND model. The study focused on the > or = 10 cm population in LEO. The historical simulation covered 1957 through 2011 and followed the recorded launches and known breakup events. The future projection was carried out for 200 years. An eight‐year launch traffic, 2004 - 2011, was repeated during the projection period. An eight‐year mission lifetime was assumed for future S/C. No stationkeeping and no collision avoidance maneuver were implemented. Only objects 10 cm and larger were included in collision consideration. No explosion was allowed for R/Bs and S/C launched after 2011. The 25‐year PMD rule success rates were set at 0%, 10%, 50%, 75%, and 95%, respectively, for the 5 study scenarios. Results of the simulations were analyzed to quantify the differences among the different compliance rates. As expected, the 0% PMD projection followed a rapid and non‐linear increase in the next 200 years. The LEO population, on average, more than tripled at the end of the simulations. With a 50% compliance of the 25‐year rule, the population growth was reduced approximately by half. However, even with a 95% compliance of the 25‐year rule, the LEO debris population would still increase by an average of more than 50% in 200 years. These simulation results provide an updated assessment of the effectiveness of the 25‐year rule. It is the first and the most cost‐effective defense against future population growth. In addition, the results also confirm the instability of the LEO population and lay the foundation for the need to consider environment remediation in the future.

Liou, J.-C.↗

DOE OSTI2026

Higher-order LaSDI: Reduced order modeling with multiple time derivatives

Solving complex partial differential equations (PDEs) is essential across scientific disciplines but often requires numerical models that can be prohibitively expensive in time-sensitive applications. Reduced-order models (ROMs) address this challenge by exploiting low-dimensional structure to create fast approximations. The Latent Space Dynamics Identification (LaSDI) framework has demonstrated success in learning ROMs for parameterized PDE families, but remains limited to first-order systems. Here, in this paper, we propose Higher-Order LaSDI (HLaSDI), which extends the LaSDI framework to PDEs with arbitrary order of time derivatives. This generalization significantly expands the applicability of LaSDI-based methods to systems previously outside their scope, including hyperbolic PDEs. We demonstrate HLaSDI’s accuracy and efficiency on several linear and nonlinear benchmark problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Geometrical acoustics and transonic helicopter sound

A new method is presented for predicting the impulsive noise generated by a transonic rotor blade. The method is a combined approach involving computational fluid dynamics and geometrical acoustics. A full-potential finite-difference method is used to obtain the pressure field close to the blade. A Kirchhoff integral formulation is then used to extend these finite-difference results into the far field. This Kirchhoff formula is based on geometrical acoustics approximations. It requires initial data across a plane at the sonic radius in a blade-fixed coordinate system. This data is provided by the finite-difference solution. Acoustic pressure predictions show good agreement with hover experimental data for cases with hover tip Mach numbers of 0.88 through 0.96. The cases above 0.92 tip Mach number are dominated by non-linear transonic effects seen as strong shocks on and off the blade tip. This paper gives the first successful predictions of far-field acoustic pressures for high-speed impulsive noise over a range of Mach numbers after delocalization.

Isom, Morris↗

NASA NTRS1985

Lubrication of nonconformal contacts

Minimum film thickness results for piezoviscous-rigid regime of lubrication are developed for a compressible Newtonian fluid with Roelands viscosity. The results provide a basis for the analysis and design of a wide range of machine elements operating in the piezoviscous-rigid regime of lubrication. A new numerical method of calculating elastic deformation in contact stresses is developed using a biquadratic polynomial to approximate the pressure distribution on the whole domain analyzed. The deformation of every node is expressed as a linear combination of the nodal pressures whose coefficients can be combined into an influence coefficient matrix. This approach has the advantages of improved numerical accuracy, less computing time and smaller storage size required for influence matrix. The ideal elastohydrodynamic lubrication is extended to real bearing systems in order to gain an understanding of failure mechanisms in machine elements. The improved elastic deformation calculation is successfully incorporated into the EHL numerical scheme. Using this revised numerical technique and the flow factor model developed by Patir and Cheng (1978) the surface roughness effects on the elastohydrodynamic lubrication of point contact is considered. Conditions typical of an EHL contact in the piezoviscous-elastic regime entrained in pure rolling are investigated. Results are compared with the smooth surface solutions. Experiments are conducted to study the transient EHL effects in instrument ball bearings.

Jeng, Y. R.↗