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NASA NTRS1984

Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.

Cosentino, G. B.↗

NASA NTRS1985

Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure disributions and drag-to-lift ratio minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.

Cosentino, G. B.↗

DOE OSTI2021

Injection data analysis using material balance time for CO 2 storage capacity estimation in deep closed saline aquifers

Estimating the ultimate storage capacity of deep saline aquifers is important to address the formation potential to store the envisioned large volumes of CO 2 . Injection data (i.e. injection rate, bottomhole pressure, and cumulative injected volume of CO 2 ) are routinely recorded during storage operations. These data contain valuable information on the subsurface (e.g. the reservoir pore volume and the formation storage capacity) that can be extracted. In this paper, we present a two-step graphical technique to infer the pore volume and the ultimate storage capacity of closed saline aquifers by analyzing the available injection data. First, the pore volume is inferred through adapting the concept of the material balance time. Material balance time is an approximate superposition time function developed to interpret production data from oil and gas wells operating at variable pressure/rate conditions during the boundary-dominated flow period. Using material balance techniques, the ultimate storage capacity is then estimated through linear extrapolation of the average pressure trend to the maximum allowable pressure the formation can withstand. The average pressure is not available in practice, but is can be obtained from the injection data. Two approaches are presented in this study to calculate the average pressure; namely the rigorous and the approximate approaches. Unlike the rigorous approach, the approximate approach does not require a prior knowledge of some reservoir properties (e.g. relative permeability, absolute permeability, formation porosity and thickness) to calculate the average pressure. To investigate its potential and reliability in analyzing CO 2 injection data, the proposed technique is applied to four synthetic cases representing different well operating conditions. Results indicate that the approximate approach consistently overestimates the actual (simulated) storage capacity as compared to the rigorous approach. The agreement - between the inferred and the simulated reservoir pore volume, and between the analytical and numerical estimates of storage capacity - validates the potential application of the technique to CO 2 storage in closed saline aquifers. The technique is further substantiated through application to a field data set utilized from a commercial-scale geological storage (CGS) project. Finally, field data interpretation shows that the proposed technique can be utilized to identify the degree of hydraulic continuity and reservoir compartmentalization within a target formation by interpreting the corresponding pressure and rate responses.

02 PETROLEUM↗

DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗

DOE OSTI2021

Code and Solution Verification Assessment of the CTF Thermal Hydraulic Subchannel Code

CTF is a thermal-hydraulics subchannel code jointly developed by Oak Ridge National Laboratory and North Carolina State University. Over the past seven years, the Consortium for Advanced Simulation of Light Water Reactors (CASL) has made a significant investment in developing CTF so it can be used to model light water reactors, including nominal operating conditions, departure from nucleate boiling analysis, and transients ranging from loss of flow to reactivity insertion accidents. In addition to implementing new modeling capabilities and developing the user input and output interface, extensive work has been performed to improve the code’s quality assurance program, resulting in a development process that conforms with NQA-1 requirements. The CASL program follows the Predictive Capability Maturity Model (PCMM) approach for assessing code quality, which emphasizes performing code verification(ensuring the code converges to the correct answer) and solution verification (ensuring the code converges for the intended application). Code and solution verification are used to identify uncertainty errors introduced by numerical approximations in the code and are important for demonstrating that the model is coded without error, which is an important aspect of the Best Estimate plus Uncertainty method. This paper presents a comprehensive overview of the code and solution verification testing that has been performed on CTF. A top-down approach is taken in which the intended CTF applications are presented, followed by the code features required for their modeling. These features are then linked to the applicable code and solution verification tests that demonstrate proper functioning. Past testing efforts are summarized, and new tests are added to help close gaps in the presented test matrix. Rather than performing “one-off” exercises, these tests are added to the automated CTF regression test suite to ensure continual code quality.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1961

Method for Approximating the Vacuum Motions of Spinning Symmetrical Bodies with Nonconstant Spin Rates

A method for approximating the vacuum motions of spinning rigid symmetrical bodies with varying spin rates and inertias has been completed. The analysis includes the effects of time varying thrust misalignments, mass unbalance, and jet damping. Results are given in the form of equations for space referenced Euler angles, flight-path angles, body referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. The method consists of dividing the problem into intervals during which the time-dependent variables are assumed constant at their mean interval value. In order to check this procedure, solutions for various interval sizes are compared with solutions obtained with numerical methods. Although the method is somewhat lengthy for accurate hand computation in most cases, it is readily programed for machine solutions. Probably more important, the general solutions give insight into the separate effects of the variables and, in many cases, can be quickly used to determine the approximate ranges of the variables required for the desired solution to a given problem. In this respect, equations for determining maximum wobble have been derived for certain input conditions. The method has been shown to compare closely with the numerical solutions of two sample problems. The sample problems also illustrated the relatively large effect of pitch and yaw jet damping on body motions.

VACUUM↗

NASA NTRS1981

Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades

A linear unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, is being developed to predict the aerodynamic response to blade vibrations in the fan, compressor or turbine stages of modern jet engines. In previous work numerical solutions were restricted to cascades of sharp-edged blades aligned with the mean flow. Under the present effort the solution procedure has been extended to treat blades with rounded or blunt edges. As part of this effort an analytical model-problem study has been conducted to clarify the behavior of first-order perturbation solutions in the vicinity of airfoil edges. Further, a numerical approximation using concepts from singular perturbation theory has been developed to resolve the unsteady boundary value problem for cascades of blunt leading-edged blades. Numerical results for NACA 0012 cascades, including detailed results in the vicinity of a blade leading edge, are presented and evaluated.

Verdon, J. M.↗

NASA NTRS1993

A Realizable Reynolds Stress Algebraic Equation Model

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Shih, Tsan-Hsing↗

NASA NTRS2006

On the Rates of Coronal Mass Ejections: Remote Solar and In Situ Observations

We compare the rates of coronal mass ejections (CMEs) as inferred from remote solar observations and interplanetary CMEs (ICMEs) as inferred from in situ observations at both 1 AU and Ulyssses from 1996 through 2004. We also distinguish between those ICMEs that contain a magnetic cloud (MC) and those that do not. While the rates of CMEs and ICMEs track each other well at solar minimum, they diverge significantly in early 1998, during the ascending phase of the solar cycle, with the remote solar observations yielding approximately 20 times more events than are seen at 1 AU. This divergence persists through 2004. A similar divergence occurs between MCs and non-MC ICMEs. We argue that these divergences are due to the birth of midlatitude active regions, which are the sites of a distinct population of CMEs, only partially intercepted by Earth, and we present a simple geometric argument showing that the CME and ICME rates are consistent with one another. We also acknowledge contributions from (1) an increased rate of high-latitude CMEs and (2) focusing effects from the global solar field. While our analysis, coupled with numerical modeling results, generally supports the interpretation that whether one observes a MC within an ICME is sensitive to the trajectory of the spacecraft through the ICME (i.e., an observational selection effect), one result directly contradicts it. Specifically, we find no systematic offset between the latitudinal origin of ICMEs that contain MCs at 1 AU in the ecliptic plane and that of those that do not.

Riley, Pete↗

NASA NTRSDate not supplied

Hypersonic Boundary-Layer Transition over a Blunt Circular Cone in a Mach 8 Digital Wind Tunnel

To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, three-dimensional direct numerical simulations (DNS) were conducted to investigate the interaction of a tunnel-like acoustic disturbance field with a Mach 8 laminar boundary layer over a 7 deg half-angle blunt cone with a nose radius of 𝑅 𝑛 = 5.2 mm. The flow conditions and the axisymmetric cone geometry matched those measured in the Sandia Hypersonic Wind Tunnel at Mach 8 (Sandia HWT-8), and the incident freestream acoustic disturbances in the DNS were generated by acoustic radiation from the nozzle-wall turbulent boundary layer in the same tunnel. Consistent with the predictions of the nonmodal instability analysis, the study shows the emergence of a second spectral peak for moderately oblique waves between 150 kHz and 200 kHz in the aft part of the cone. The spectral energy of temperature and streamwise velocity fluctuations is initially concentrated within the entropy layer. These fluctiations are eventually “swallowed” by the boundary layer as the entropy-layer thickness 𝛿 𝑆 becomes similar to the boundary-layer thickness 𝛿h𝑡 at downstream locations. The numerical schlieren contours show the same inclined structures commonly observed in blunt cone experiments, and these structures are found to be three dimensional and advect with a constant speed approximately equal to the mean flow speed near the edge of the boundary layer.

Hypersonic Flow↗

NASA NTRSDate not supplied

Hypersonic Boundary-Layer Transition over a Blunt Circular Cone in a Mach 8 Digital Wind Tunnel

Hypersonic Flow↗

NASA NTRS2024

Filament Wound Composite Analysis Using the NASA Multiscale Analysis Tool (NASMAT) and Finite Element Analysis

Fiber reinforced composite materials, owing to their tailorable thermomechanical and functional properties, allow one to produce a structure that is stronger, stiffer, and lighter than its metal counterpart while performing the same function, yielding a more efficient structure. This not only allows for the improvement of current technologies like aircraft structures, but also enables new technologies like gaseous hydrogen storage for mobility applications, which are otherwise impractical when manufactured using traditional metals due to weight and space restrictions or material embrittlement. However, the use of composites imposes greater design and manufacturing challenges on an engineer, since they are heterogenous, having a distinct structure across multiple length scale, behave generally anisotropically at the structural level and require complex manufacturing and processing methods. Capturing this complex behavior requires detailed numerical simulations, including the modeling of microstructural features like undulations, voids, and fiber alignment. In this paper, multiple repeating unit cells (RUCs), representing filament wound composites, are developed (via a script provided in the Appendix) and analyzed. The refinement of these RUCs is varied, and the analyses are performed using both the Abaqus finite element software and the NASA Multiscale Analysis Tool (NASMAT). A study is undertaken to compare the predicted effective elastic properties of the wound RUC to a laminate representation of the wound RUC, which neglects the undulations. Additionally, two different sets of periodic boundary conditions (PBCs) have been examined. One approximates the real boundary conditions using a standard approach and the other represents the PBCs exactly through the use of an offset. Lastly, a comparison of the local elastic stress fields is made among the models and approaches. Since wound structures are often approximated as laminated structures, it is important to understand the degree to which this assumption is valid, namely by first comparing the elastic constants and local elastic fields. This will provide, on the one hand, information concerning the bulk mechanical behavior and, on the other hand, insights concerning local load distributions and likely damage initiation sites.

Composites↗

DOE OSTI2020

An extended/generalized phase-field finite element method for crack growth with global-local enrichment

In this paper, an extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction-correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two- and three-dimensional quasistatic fracture are provided to demonstrate the approach.

multiscale↗

NASA NTRS2025

Mind the Gap: Addressing Data Gaps and Assessing Noise Mismodeling in LISA

Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.

LISA↗

NASA NTRS1973

On the relationship between acoustic energy density flux near the jet axis and far field acoustic intensity

By measurement and analysis, the relationship between the distribution of the outflow of acoustic energy over the jet boundary and the far-field intensity is considered. The physical quantity used is the gradient of the pressure evaluated on a geometrical plane at the smallest possible radial distance from the jet axis, but outside the vortical region, in the area where the homogeneous wave equation is reasonably well satisfied. The numerical and experimental procedures involved have been checked out by using a known source. Results indicate that the acoustic power output per unit length of the jet, in the region from which the sound emanates, peaks at approximately 9 diameters downstream. The acoustic emission for a jet Strouhal number of about 0.3 exceeds the emission for all other Strouhal numbers nearly everywhere along the measurement plane. However, the far-field peak intensity distribution obtained from the contribution of each station was found to depend on the spatial extent of the region where sound emanates from the jet, which, in turn, depends more on the far-field angle than on the Strouhal number.

Maestrello, L.↗

NASA NTRS2018

Multi-Scale Modeling of Low-Density Carbon-Phenolic Ablators

Protecting a spacecraft during atmospheric entry is one of highest risk factors that needs to be mitigated during design of a space exploration mission. At entry speeds from space, air turns into high-temperature plasma, and spacecraft Thermal Protection Systems (TPS) are needed to protect the vehicle payload. Modern successful material architectures of spacecraft shields use a porous carbon fiber substrate impregnated with phenolic as an ablator material. In the lecture, efforts to build a Predictive Material Modeling framework for porous ablators from micro-scale to macro-scale will be presented. Several numerical methods and techniques will be summarized that use voxelized images to compute geometrical properties of the porous substrate. These computed properties include porosity, specific surface area and tortuosity that are otherwise indirectly measured through experimental techniques. Direct simulation Monte Carlo (DSMC), a particle-based method for approximating the Boltzmann equation, is used to compute the permeability coefficient of the porous substrate based on its digitized representation. The method computes the flow within the microstructure, where the size of the pores may approach the mean-free-path of the flow. Finally, a high-fidelity model implemented in PATO (Porous-material Analysis Toolbox) is discussed, and some examples of ablative material response are presented, including for the first time 3D simulations of the full tiled heat shield for the Mars Science Laboratory (MSL) capsule.

Ablators↗

NASA NTRS1994

Thermoviscoplastic analysis of fibrous periodic composites by the use of triangular subvolumes

The non-linear viscoplastic behavior of fibrous periodic composites is analyzed by discretizing the unit cell into triangular subvolumes. A set of these subvolumes can be configured by the analyst to construct a representation for the unit cell of a periodic composite. In each step of the loading history the total strain increment at any point is governed by an integral equation which applies to the entire composite. A Fourier series approximation allows the incremental stresses and strains to be determined within a unit cell of the periodic lattice. The non-linearity arising from the viscoplastic behavior of the constituent materials comprising the composite is treated as a fictitious body force in the governing integral equation. Specific numerical examples showing the stress distributions in the unit cell of a fibrous tungsten/copper metal-matrix composite under viscoplastic loading conditions are given. The stress distribution resulting in the unit cell when the composite material is subjected to an overall transverse stress loading history perpendicular to the fibers is found to be highly heterogeneous, and typical homogenization techniques based on treating the stress and strain distributions within the constituent phases as homogeneous result in large errors under inelastic loading conditions.

Walker, Kevin P.↗

NASA NTRS2004

Fracture Analysis of Semi-Elliptical Surface Cracks in Ductile Materials

Accurate life assessment of structural components may require advanced life prediction criteria and methodologies. Structural components often exhibit several different types of defects, among the most prevalent being surface cracks. A semi-elliptical surface crack subjected to monotonic loading will exhibit stable crack growth until the crack has reached a critical size, at which the crack loses stability and fracture ensues (Newman, 2000). The shape and geometry of the flaw are among the most influential factors. When considering simpler crack configurations, such as a through-the-thickness crack, a three-dimensional (3D) geometry may be modeled under the approximation of two-dimensional (2D) plane stress or plane strain. The more complex surface crack is typically modeled numerically with the Finite Element Method (FEM). A semi-elliptical surface crack is illustrated in Figure 1-1.

Daniewicz, S. R.↗