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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.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Evaluation of a Variable Facesheet Liner Configuration in Grazing Incidence for Broadband Noise Reduction

Tests were conducted in the NASA Langley Grazing Flow Impedance Tube (GFIT) to determine the broadband noise reduction capability of a variable facesheet liner. Three uniform liners were designed to achieve sound absorption over distinct frequency regimes at Mach 0.0. Each liner was fabricated and tested in the GFIT at sound pressure levels of 120 and 140 dB, and at tangential flow velocities up to Mach 0.5. A variable facesheet liner was fabricated to combine the geometries of these three liners, such that the facesheet geometry (hole diameter and porosity) was varied across the liner surface. The Prony method was used to educe the impedance of each sample, and these impedances were input to the CHE (Convected Helmholtz Equation) propagation code to predict the acoustic pressure profiles in the GFIT. Comparisons of predicted and measured acoustic pressure profiles were used to confirm the uniformity of all four liners, and to demonstrate the suitability of the CHE code in the analysis of the variable facesheet concept. Results showed good comparison at no flow and at Mach 0.3, and acceptable comparison at Mach 0.5. The variable facesheet liner provided enhanced broadband noise reduction at the no-flow condition for which it was designed, but further optimization is needed to target flow conditions.

acoustic↗
NASA NTRSDate not supplied

Assessment of Acoustic Behavior for Perforate-Over-Large-Cell Liners

This study explores the effects of increasing the cell size for large-cell acoustic liners. Tests are conducted in the NASA Langley Grazing Flow Impedance Tube to evaluate liners with increasingly larger cell dimensions (up to 2” x 4” cross-section). Conventional impedance eduction confirms that liners with 2” x 3” cells (or larger) must be evaluated using nonlocally reacting assumptions. In addition, due to the sound propagation within cavities, the liners must be modeled using higher fidelity techniques. Thus, grazing flow duct and acoustic liner are modeled simultaneously using finite element methods. The facesheet is modeled using a transfer impedance, while the rest of the domain is modeled using the convected Helmholtz equation. The acoustic pressures predicted are shown to compare favorably with those measured in the Grazing Flow Impedance Tube.

large diameter↗
NASA NTRS2024

An Experimental and Predictive Study of Bent-Chamber Acoustic Liners

Acoustic liner samples with rectangular, sharp chamber bends are 3D-printed and tested in the NASA Normal Incidence Tube. The angle of the bend is varied from 0 to 180 degrees. Four different methods are used to predict the impedance behavior of these samples: (1) midline-length assumption, (2) Cummings correction for curved duct bends, (3) Cummings prediction for 180 degrees sharp duct bends, and (4) Helmholtz equation via finite element method. Trends in the experimental data are discussed, predictions are compared to the experimental data, and recommendations are made on prediction method usage. Follow-on work is suggested, including capturing additional test points at higher frequencies and with different chamber geometries. Future modeling strategies are also briefly described.

chamber↗
DOE OSTI2020

Demonstration and performance testing of extreme-resolution simulations with static meshes on Summit (CPU & GPU) for a parked-turbine configuration and an actuator-line (mid-fidelity model) wind farm configuration (ECP-Q4 FY2020 Milestone Report)

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

17 WIND ENERGY↗
NASA NTRS1996

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Phillips, J. R.↗
NASA NTRS2006

Development of Experimental and Computational Aeroacoustic Tools for Advanced Liner Evaluation

Acoustic liners in aircraft engine nacelles suppress radiated noise. Therefore, as air travel increases, increasingly sophisticated tools are needed to maximize noise suppression. During the last 30 years, NASA has invested significant effort in development of experimental and computational acoustic liner evaluation tools. The Curved Duct Test Rig is a 152-mm by 381- mm curved duct that supports liner evaluation at Mach numbers up to 0.3 and source SPLs up to 140 dB, in the presence of user-selected modes. The Grazing Flow Impedance Tube is a 51- mm by 63-mm duct currently being fabricated to operate at Mach numbers up to 0.6 with source SPLs up to at least 140 dB, and will replace the existing 51-mm by 51-mm duct. Together, these test rigs allow evaluation of advanced acoustic liners over a range of conditions representative of those observed in aircraft engine nacelles. Data acquired with these test ducts are processed using three aeroacoustic propagation codes. Two are based on finite element solutions to convected Helmholtz and linearized Euler equations. The third is based on a parabolic approximation to the convected Helmholtz equation. The current status of these computational tools and their associated usage with the Langley test rigs is provided.

Jones, Michael G.↗
NASA NTRS1990

A multigrid solver for semi-implicit global shallow-water models

A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.

Barros, Saulo R. M.↗
NASA NTRS1973

Finite element analysis of unsteady incompressible flow around an oscillating obstacle of arbitrary shape.

An analytical procedure based on Navier-Stokes equations was developed for representing unsteady flow patterns around oscillating obstacles. A variational formulation of the Helmholtz vorticity equation was discretized in finite element form and integrated numerically. At each step of the numerical integration the velocity field around the obstacle was determined from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints at each time step of the numerical integration. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Bratanow, T.↗
DOE OSTI2025

Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multistage Training

The recent development of neural operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this article, we use the Fourier neural operator (FNO) model to directly solve the 3D Helmholtz wave equation for fast seismic ground-motion simulations on different frequencies and show the frequency bias of the FNO model, that is, it learns the lower frequencies better comparing to the higher frequencies. To reduce the frequency bias, we adopt the multistage FNO training, that is, after training a stage 1 FNO model for estimating the ground motion, we use a second FNO model as the stage 2 to learn from the residual, which greatly reduced the errors on the higher frequencies. By adopting this multistage training, the FNO models show reduced biases on higher frequencies, which enhanced the overall results of the ground-motion simulations. Thus the multistage training FNO improves the accuracy and realism of the ground-motion simulations.

earthquakes↗
NASA NTRS1981

Three-dimensional periodic disturbances acting upon airfoils in cascade

A theory is developed for three-dimensional periodic gusts interacting with loaded airfoils. The unsteady disturbances are linearized with respect to the mean potential flow of the airfoils. The vorticity transport equation is then integrated analytically in a Lagrangian form. The vorticity vector shows strong variations in its magnitude and wavelength as it interacts with the flowfield of a lifting airfoil. The streamwise component of the vorticity increases significantly with flow acceleration and flow turning. For simplicity the rectangular fan approximation is used and a single Helmholtz-like equation is derived to characterize the unsteady 3D flowfield. This is a new and significant result. The present theory is first applied to symmetric airfoils.

Atassi, H.↗
DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Solving Seismic Wave Equations on Variable Velocity Models With Fourier Neural Operator

Here, in the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning (DL) enables solving partial differential equations (PDEs), including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn the frequency domain seismic wavefields under the context of variable velocity models. We also propose a new framework paralleled FNO (PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.

58 GEOSCIENCES↗
DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗
DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

Damage models incorporated within FFT-based micromechanical methods have received much attention recently because of the need to better understand and predict brittle and ductile fracture. An important aspect of a damage model is non-local regularization, which removes the mesh dependence of the predictions that otherwise become physically unacceptable upon grid refinement. In this work, the Helmholtz-type equation for non-local gradient regularization of a damage model on a distorted grid is solved using an FFT-based approach. Further, the resulting system of equations is solved using the Jacobi iterative method. The model is applied to simulate brittle fracture of an intermetallic. The influence of the time and space discretization, the length-scale parameter, and intermetallic crystallographic orientation on crack evolution is studied.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Model Development and Analysis of a High-Fidelity Neutron Transport Sensor: The Quadrupole Detector Concept for Measurement of the Neutron Flux Gradient

Accurate reconstruction of the neutron flux distribution within a reactor core is essential for safe and efficient reactor operation. Traditional power shape synthesis in Light Water Reactors relies on hundreds of in-core detectors. However, this approach becomes impractical for Advanced Reactors and Microreactors due to limited space and harsh environments. To address this challenge, we propose a data-driven methodology that combines high-fidelity modeling with real-time ex-core sensor measurements, enabling the reconstruction of core power distribution while minimizing the reliance on intrusive in-core instrumentation. This project began in FY24 and achieved two initial milestones: (1) the definition of a three-year development plan for a Digital Twin framework and (2) the development of high-fidelity neutronics models of the Purdue University Reactor One (PUR-1) using both MCNP6 and OpenMC. The PUR-1 reactor, a zero-power facility, was selected due to its suitability for neutronics-focused modeling and the availability of experimental data for validation. Both models were benchmarked using neutron flux measurements obtained from irradiated gold foils, which were strategically placed within the core during a dedicated campaign in July 2024. This report marks the continuation and completion of those foundational tasks. The OpenMC model has been refined (improved geometric accuracy, expanded cross-section libraries, and refined sampling) and validated using additional experimental data. An updated sensor design—based on quadrupole configuration—was designed to measure both ex-core flux and its spatial gradient. These measurements will serve as inputs to a neural network-based reconstruction algorithm. Finally, the methodology was demonstrated on a two-dimensional test case representative of the heterogeneous material composition of the PUR-1 reactor core. A neural network implementation of the Kirchhoff-Helmholtz integral equation was employed to solve the boundary value problem using peripheral sensor measurements. The preliminary results confirm the strong potential of the proposed approach for accurate and minimally invasive neutron flux reconstruction.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗