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High Fidelity Adaptively Refined CFD and Reduced Order Models of a High Aspect Ratio Aeroelastic Wing Wind Tunnel Model

Robust adaptive mesh refinement for transonic conditions is one of the most difficult challenges to advancing CFD usage for certification by analysis. Transonic fluid-structure interaction cases represent an even more difficult challenge for adaptive mesh refinement. Production aircraft furthermore have structural models that have gaps and discontinuities that make the interdomain transfer of loads and deflections difficult. This adds to the challenge of adaptive mesh refinement. An initial attempt to create an adaptive mesh refinement process that refines regions of high flow gradient based around the HeldenMesh software is presented. The method is applied to the Integrated Adaptive Wing Technology Maturation (IAWTM) configuration. That has developed an aspect ratio 13.5 wing aeroelastic wind-tunnel model for testing in the Transonic Dynamics Tunnel (TDT). The high levels of deformation of this wing make the adaptation of meshes for the static shape difficult and has necessitated some creativity in how to efficiently adapt meshes. A time-domain identification of the unsteady system based on flexible modes using the adapted meshes is performed.

Robert E. Bartels↗

DOE OSTI2022

Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring consider several complex high-dimensional posterior densities and compare its performance to NUTS.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning

Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyse this dependence using multiple machine learning methods and a dataset of >200 000 nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence in diverse non-axisymmetric geometries. The dataset is generated using a large collection of both optimised and randomly generated stellarator equilibria. At fixed gradients and other input parameters, the turbulent heat flux varies between geometries by several orders of magnitude. Trends are apparent among the configurations with particularly high or particularly low heat flux. Regression and classification techniques from machine learning are then applied to extract patterns in the dataset. Due to a symmetry of the gyrokinetic equation, the heat flux and regressions thereof should be invariant to translations of the raw features in the parallel coordinate, similar to translation invariance in computer vision applications. Multiple regression models including convolutional neural networks (CNNs) and decision trees can achieve reasonable predictive power for the heat flux in held-out test configurations, with highest accuracy for the CNNs. Using Spearman correlation, sequential feature selection and Shapley values to measure feature importance, it is consistently found that the most important geometric lever on the heat flux is the flux surface compression in regions of bad curvature. The second most important geometric feature relates to the magnitude of geodesic curvature. These two features align remarkably with surrogates that have been proposed based on theory, while the methods here allow a natural extension to more features for increased accuracy. The dataset, released with this publication, may also be used to test other proposed surrogates, and we find that many previously published proxies do correlate well with both the heat flux and stability boundary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2016

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

Several improvements to the mixed-elementUSM3Ddiscretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Pandya, Mohagna J.↗

NASA NTRS2016

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Pandya, Mohagna J.↗

DOE OSTI2022

Characterization and visualization of grain boundary disconnections

We introduce a method to visualize dislocations along grain boundaries at the atomic level. It uses an atomic-level Nye tensor, representing the dislocation density. To calculate the Nye tensor at grain boundaries, we extend the Hartley-Mishin strain gradient calculation to the displacement shift complete lattice. We show that the method is effective in visualizing disconnections and the dislocation content of grain boundary phase junctions in body-centered cubic tungsten, as well as face-centered cubic copper. In addition, we use the method to characterize the morphology of a two-dimensional grain boundary phase nucleus in a symmetric tilt grain boundary in tungsten. This method can be applied to both bulk dislocations and grain boundary disconnections, which makes it ideal for studying the interactions and reactions of bulk dislocations with grain boundaries, and grain boundary disconnections.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Transport coefficient approach for characterizing nonequilibrium dynamics in soft matter

Nonequilibrium states in soft condensed matter require a systematic approach to characterize and model materials, enhancing predictability and applications. Among the tools, X-ray photon correlation spectroscopy (XPCS) provides exceptional temporal and spatial resolution to extract dynamic insight into the properties of the material. However, existing models might overlook intricate details. We introduce an approach for extracting the transport coefficient, denoted as $J(t)$, from the XPCS studies. This coefficient is a fundamental parameter in nonequilibrium statistical mechanics and is crucial for characterizing transport processes within a system. Our method unifies the Green–Kubo formulas associated with various transport coefficients, including gradient flows, particle–particle interactions, friction matrices, and continuous noise. We achieve this by integrating the collective influence of random and systematic forces acting on the particles within the framework of a Markov chain. We initially validated this method using molecular dynamics simulations of a system subjected to changes in temperatures over time. Subsequently, we conducted further verification using experimental systems reported in the literature and known for their complex nonequilibrium characteristics. The results, including the derived $J(t)$ and other relevant physical parameters, align with the previous observations and reveal detailed dynamical information in nonequilibrium states. This approach represents an advancement in XPCS analysis, addressing the growing demand to extract intricate nonequilibrium dynamics. Further, the methods presented are agnostic to the nature of the material system and can be potentially expanded to hard condensed matter systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1989

High resolution flow field prediction for tail rotor aeroacoustics

The prediction of tail rotor noise due to the impingement of the main rotor wake poses a significant challenge to current analysis methods in rotorcraft aeroacoustics. This paper describes the development of a new treatment of the tail rotor aerodynamic environment that permits highly accurate resolution of the incident flow field with modest computational effort relative to alternative models. The new approach incorporates an advanced full-span free wake model of the main rotor in a scheme which reconstructs high-resolution flow solutions from preliminary, computationally inexpensive simulations with coarse resolution. The heart of the approach is a novel method for using local velocity correction terms to capture the steep velocity gradients characteristic of the vortex-dominated incident flow. Sample calculations have been undertaken to examine the principal types of interactions between the tail rotor and the main rotor wake and to examine the performance of the new method. The results of these sample problems confirm the success of this approach in capturing the high-resolution flows necessary for analysis of rotor-wake/rotor interactions with dramatically reduced computational cost. Computations of radiated sound are also carried out that explore the role of various portions of the main rotor wake in generating tail rotor noise.

Quackenbush, Todd R.↗

NASA NTRS1972

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 2: Constant property turbulent boundary layer flow with simultaneous mass transfer and pressure gradient

An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.

Boccio, J.↗

NASA NTRS1983

Iterative PNS method for attached flows with upstream influence

A stable global-iteration procedure is developed by utilizing successive sweeps, from inflow to outflow boundaries, of a parabolized Navier-Stokes code for attached, steady supersonic flow. It is shown that the procedure converges in about ten or fewer iterations, and allows for the upstream influence within the subsonic region of a supersonic boundary layer. An implicit forward difference is employed in the subsonic region to evaluate the pressure-gradient term in the streamwise momentum equation. The pressure-gradient term is normally approximated in standard single-sweep parabolized methods, suppressing the upstream influence. The iterative results obtained demonstrate the validity of the single-sweep method for weak interactions. For hypersonic viscous interaction on a flat plate at a Mach number of 5.8, it is found that the single-sweep method has a small error that vanishes as the Reynolds number of the flow is increased. However, the skin friction has an error of about 10 percent for low Reynolds numbers and for hot wall conditions. The application of this method to laminar two-dimensional flow over weak expansion and compression corners shows that the pressure and skin friction results in the vicinity of the expansion corner compare favorably with a time-dependent Navier-Stokes numerical solution.

Rakich, J. V.↗

DOE OSTI2024

Identification of Kelvin-Helmholtz generated vortices in magnetised fluids

The Kelvin-Helmholtz Instability (KHI), arising from velocity shear across the magnetopause, plays a significant role in the viscous-like transfer of mass, momentum, and energy from the shocked solar wind into the magnetosphere. While the KHI leads to growth of surface waves and vortices, suitable detection methods for these applicable to magnetohydrodynamics (MHD) are currently lacking. A novel method is derived based on the well-established λ-family of hydrodynamic vortex identification techniques, which define a vortex as a local minimum in an adapted pressure field. The J × B Lorentz force is incorporated into this method by using an effective total pressure in MHD, including both magnetic pressure and a pressure-like part of the magnetic tension derived from a Helmholtz decomposition. The λ MHD method is shown to comprise of four physical effects: vortical momentum, density gradients, fluid compressibility, and the rotational part of the magnetic tension. A local three-dimensional MHD simulation representative of near-flank magnetopause conditions (plasma β’s 0.5 – 5 and convective Mach numbers M f ∼ 0.4) under northward interplanetary magnetic field (IMF) is used to validate λ MHD . Analysis shows it correlates well with hydrodynamic vortex definitions, though the level of correlation decreases with vortex evolution. Overall, vortical momentum dominates λ MHD at all times. During the linear growth phase, density gradients act to oppose vortex formation. By the highly nonlinear stage, the formation of small-scale structures leads to a rising importance of the magnetic tension. Compressibility was found to be insignificant throughout. Finally, a demonstration of this method adapted to tetrahedral spacecraft observations is performed.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1995

Investigation of Convection and Pressure Treatment with Splitting Techniques

Treatment of convective and pressure fluxes in the Euler and Navier-Stokes equations using splitting formulas for convective velocity and pressure is investigated. Two schemes - controlled variation scheme (CVS) and advection upstream splitting method (AUSM) - are explored for their accuracy in resolving sharp gradients in flows involving moving or reflecting shock waves as well as a one-dimensional combusting flow with a strong heat release source term. For two-dimensional compressible flow computations, these two schemes are implemented in one of the pressure-based algorithms, whose very basis is the separate treatment of convective and pressure fluxes. For the convective fluxes in the momentum equations as well as the estimation of mass fluxes in the pressure correction equation (which is derived from the momentum and continuity equations) of the present algorithm, both first- and second-order (with minmod limiter) flux estimations are employed. Some issues resulting from the conventional use in pressure-based methods of a staggered grid, for the location of velocity components and pressure, are also addressed. Using the second-order fluxes, both CVS and AUSM type schemes exhibit sharp resolution. Overall, the combination of upwinding and splitting for the convective and pressure fluxes separately exhibits robust performance for a variety of flows and is particularly amenable for adoption in pressure-based methods.

Thakur, Siddharth↗

NASA NTRS2017

SpaRibs Geometry Parameterization for Wings with Multiple Sections using Single Design

The SpaRibs topology of an aircraft wing has a significant effect on its structural behavior and stability as well as the flutter performance. The development of additive manufacturing techniques like Electron Beam Free Form Fabrication (EBF3) has made it feasible to manufacture aircraft wings with curvilinear spars, ribs (SpaRibs) and stiffeners. In this article a new global-local optimization framework for wing with multiple sections using curvilinear SpaRibs is described. A single design space is used to parameterize the SpaRibs geometry. This method has been implemented using MSC-PATRAN to create a broad range of SpaRibs topologies using limited number of parameters. It ensures C0 and C1 continuities in SpaRibs geometry at the junction of two wing sections with airfoil thickness gradient discontinuity as well as mesh continuity between all structural components. This method is advantageous in complex multi-disciplinary optimization due to its potential to reduce the number of design variables. For the global-local optimization the local panels are generated by an algorithm which is totally based on a set algebra on the connectivity matrix data. The great advantage of this method is that it is completely independent of the coordinates of the nodes of the finite element model. It is also independent of the order in which the elements are distributed in the FEM. The code is verified by optimizing of the CRM Baseline model at trim condition at Mach number equal to 0.85 for five different angle of attack (-2deg, 0deg,2deg,4deg and 6deg). The final weight of the wing is 19,090.61 lb. This value is comparable to that obtained by Qiang et al. 6 (19,269 lb).

wing sections↗

NASA NTRS2014

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle/Multi-Pixel Polarimetric Measurements

This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth's atmosphere.

linearization↗

NASA NTRS2014

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle Multi-Pixel Polarimetric Measurements

adjoint methods↗

DOE OSTI2022

Mapping the space of quasisymmetric stellarators using optimized near-axis expansion

A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and quasisymmetry, expanded in the small distance from the magnetic axis, as formulated by Garren & Boozer [ Phys. Fluids B, vol. 3, 1991, p. 2805]. Due to the reduction of the equations by the expansion, the computational cost is significantly reduced, to times of the order of 1 cpu second, enabling wide and high-resolution scans over parameter space. In contrast to traditional stellarator optimization, here, the cost function serves to maximize the volume in which the expansion is accurate. A key term in the cost function is $\| \boldsymbol {\nabla }\boldsymbol B \|$ , the norm of the magnetic field gradient, to maximize scale lengths in the field. Using this method, a database of $5\times 10^5$ optimized configurations is calculated and presented. Quasisymmetric configurations are observed to exist in continuous bands, varying in the ratio of the magnetic axis length to average major radius. Several qualitatively new types of configuration are found, including quasi-helically symmetric fields in which the number of field periods is two or more than six.

Landreman, Matt (ORCID:000000027233577X)↗

NASA NTRS1998

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Patniak, Surya N.↗