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NASA NTRS1997

Aerodynamic Shape Sensitivity Analysis and Design Optimization of Complex Configurations Using Unstructured Grids

A three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed and is extended to model geometrically complex configurations. The advantage of unstructured grids (when compared with a structured-grid approach) is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional geometry and a Gauss-Seidel algorithm for the three-dimensional; similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Simple parameterization techniques are utilized for demonstrative purposes. Once the surface has been deformed, the unstructured grid is adapted by considering the mesh as a system of interconnected springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR (which is an advanced automatic-differentiation software tool). To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for a two-dimensional high-lift multielement airfoil and for a three-dimensional Boeing 747-200 aircraft.

Taylor, Arthur C., III↗

NASA NTRSDate not supplied

Towards Aerodynamic Shape Optimization Using an Immersed Boundary Overset Grid Method

Traditional Reynolds-averaged Navier-Stokes grid methods applied to aerodynamic shapeoptimization can struggle with the deformation of surface and volume grids at componentintersections, such as at wing-fuselage junctions. To overcome this, we propose an approachwhich utilizes curvilinear overset grids for the discretization of the domain, with the presenceof the body modeled using an immersed boundary method. This approach handles complexgeometries without the need for their explicit integration into the grid. The goal of this approachis to reduce grid generation time and allow for greater geometric freedom for component-basedaerodynamic shape optimization. Two different methods are presented: a source-term-basedand a ghost-node-based immersed boundary method. Flow analyses and adjoint solutionsobtained using the proposed methods show promising comparisons with standard body-fittedgrid methods. Preliminary aerodynamic shape optimization results obtained using one of theimmersed boundary methods are also presented.

TTT↗

DOE OSTI2025

Extending TOUGH + HYDRATE with a parallel particle transport simulator: numerical investigation of sand production during gas production from hydrate deposits

A new parallel code for simulating particle transport in porous media is integrated with the TOUGH + HYDRATE simulator to investigate sand production associated with gas production from unconsolidated gas hydrate-bearing sediments (HBS). Here, the parallel coupled simulator is named THMPT and uses the integral finite difference method to describe the Darcian and non-Darcian flow of fluids and heat transport, the finite element method to describe the associated geomechanical changes, and the discrete element method to track the trajectory of individual sand particles within the HBS. The THMPT simulator is written in Fortran, incorporates multiple optimized algorithms, and can comprehensively address the coupled flow, thermal, chemical, geomechanical, and particle transport processes that characterize the system behaviors during gas production from HBS. The simulator can capture all processes involved in sand particle transport in porous media, including sand detachment, collision, clogging (i.e., bridging), and migration. A benchmark case study of sand production in the course of depressurization-induced gas production from a representative HBS reveals various distinct microscopic particle migration mechanisms and the adverse impact of sand particle detachment, transport, and clogging. The numerical investigation also examines the effect of bottomhole pressure on mitigating sand production. The simulation results indicate that sand clogging near the wellbore significantly reduces permeability, decreasing gas production by at least 50%. Lastly, the efficiency of gravel packing in mitigating sand production is numerically evaluated, revealing that the structure of the porous media appears to profoundly influence the macroscopic motion behavior of sand particles and sand clogging characteristics.

discrete element method↗

DOE OSTI2025

Low Cost High-Performance HRE-Free 3-in-1 Electric Drive Unit

The project team completed work to expand upon American Axle & Manufacturing’s (AAM) baseline technology and develop a high-speed, AC induction electric drive unit (EDU) with total direct-oil-cooling and integrated power electronics. The project accelerated advancements in EDU technology by allowing AAM to build upon the progress made in developing the underlying baseline technologies. The following seven improvements to AAM’s baseline technology were implemented in this research and development program: 1) Increased speed (30k RPM) AC induction motor, 2) Silver-sintering of discrete silicon carbide (SiC) metal-oxide-semiconductor field-effect transistors (MOSFET) to heat sinks, 3) Electrically insulated rotor bars, 4) Optimized lamination steel, 5) EDU-integrated 650VDC inverter package, 6) Over-molded stator with molded liners, and 7) 650VDC power-dense stator design. The successful development of the technology resulted in a meaningful cost reduction for EDU systems in the market. Coupled with falling battery system costs, lower EDU costs will likely accelerate the market acceptance and related production scaling of battery electric vehicles. The objective of this project was to research, develop, and test a Heavy Rare Earth (HRE)-free 3-In-1 electric drive unit (EDU) that has class leading power density and cost. The key technologies to be developed were anticipated to meet or exceed the Department of Energy (DOE) targets of a cost ≤ $\$$7/kilowatt (kW), power density ≥ 12 kW/liter, and operating voltage ≥ 600 VDC.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1988

Spatial compression of Seasat SAR imagery

The results of a study of techniques for spatial compression of synthetic-aperture-radar (SAR) imagery are summarized. Emphasis is on image-data volume reduction for archive and online storage applications while preserving the image resolution and radiometric fidelity. A quantitative analysis of various techniques, including vector quantization (VQ) and adaptive discrete cosine transform (ADCT), is presented. Various factors such as compression ratio, algorithm complexity, and image quality are considered in determining the optimal algorithm. The compression system requirements are established for electronic access of an online archive system based on the results of a survey of the science community. The various algorithms are presented and their results evaluated considering the effects of speckle noise and the wide dynamic range inherent in SAR imagery. The conclusion is that although the ADCT produces the best signal-to-distortion-noise ratio for a given compression ratio, the two-level tree-searched VQ technique is preferred due to its simplicity of decoding and near-optimal performance.

Chang, C. Y.↗

NASA NTRS1993

Real-time trajectory optimization on parallel processors

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

Psiaki, Mark L.↗

NASA NTRS1983

Low background IR detector and detector array evaluations

A technology program has been underway at Ames since 1978 to develop and evaluate detectors and integrated detector arrays for low-background astronomical applications. The approach is to evaluate existing (less than 24 micron) array technology under low-background conditions, with the aim of adapting and optimizing existing devices. For longer wavelengths, where the technology is much less mature, development is sponsored and devices are evaluated, in both discrete and array formats, for eventual applications. The status of this program has been reported previously. We rely on industrial and university sources for the detectors. Typically, after a brief functionality check in the supplier's laboratory, we work with the device at Ames to characterize its low-background performance. In the case of promising arrays or detectors, we conduct ground-based telescope testing to face the problems associated with real applications. A list of devices tested at Ames is given. In the array category, accumulation-mode charge-injection-devices (AMCIDs) appear repeatedly; this reflects our recent experience with the 2 x 64 and 16 x 16 arrays. Results from the 1 x 16 CID and InSb CCD have been reported. The status of our tests of the discrete Ge:x detectors from Lawrence Berkeley Laboratory are described below. Tests of a 1 x 2 switched sample photoconductor array are just beginning. A 32-channel CMOS multiplexer has been tested at 10 K. Low-temperature silicon MOSFETs and germanium JFETs have also been tested, primarily at Ball Aerospace. This paper describes results to date on three elements of this program: AMCID array, discrete Ge:Ga detectors, and Ge JFET preamplifiers.

Goebel, J. H.↗

NASA NTRS1999

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗

DOE OSTI2025

10-th order of accuracy for numerical solution of 3-D elasticity equations for heterogeneous materials on unfitted Cartesian meshes

We have developed the Optimal Local Truncation Error Method (OLTEM) with 10-th order of accuracy on unfitted Cartesian meshes for a system of 3-D elasticity equations with smooth irregular interfaces. 5 x 5 x 5 = 125-point stencils (similar to those for quadratic finite elements) for elastic heterogeneous materials are used for OLTEM. There are no unknowns at the interface points between different materials; the structure of the global discrete equations is the same for homogeneous and heterogeneous materials. The calculation of unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal 10-th order of accuracy for OLTEM on unfitted Cartesian meshes, i.e., the increase by 7 orders in accuracy compared to quadratic finite elements on conformal meshes. A new post-processing procedure provides the 9-th order of accuracy for stresses in the 3-D case. Similar to basic computations it uses OLTEM with the 125-point stencils, the interface conditions and the elasticity equations. It was shown that the use of the elasticity equations for post-processing improves the accuracy of 0.1% stresses by 6 orders compared to post-processing without the use of PDEs. At an accuracy of for stresses, OLTEM with the new post-processing procedure reduces the number of degrees of freedom by 360 - 8000 times compared to quadratic finite elements with similar stencils. OLTEM with the 125-point stencils yields even more accurate results than high-order finite elements with much wider stencils. OLTEM provides accurate numerical results for compressible and nearly incompressible materials.

elasticity equations↗

NASA NTRS1976

Digital controllers for VTOL aircraft

Using linear-optimal estimation and control techniques, digital-adaptive control laws have been designed for a tandem-rotor helicopter which is equipped for fully automatic flight in terminal area operations. Two distinct discrete-time control laws are designed to interface with velocity-command and attitude-command guidance logic, and each incorporates proportional-integral compensation for non-zero-set-point regulation, as well as reduced-order Kalman filters for sensor blending and noise rejection. Adaptation to flight condition is achieved with a novel gain-scheduling method based on correlation and regression analysis. The linear-optimal design approach is found to be a valuable tool in the development of practical multivariable control laws for vehicles which evidence significant coupling and insufficient natural stability.

Stengel, R. F.↗

DOE OSTI2026

Optimal Transfer Operators in Algebraic Two-Level Methods for Nonsymmetric and Indefinite Problems

Consider an algebraic two-level method applied to the 𝑛-dimensional linear system 𝐴⁢𝒙 = 𝒃 using fine-space preconditioner (i.e., “relaxation” or “smoother”) 𝑀, with 𝑀 ≈ 𝐴, restriction and interpolation 𝑅 and 𝑃, and algebraic coarse-space operator 𝐴 𝑐 : = 𝑅 ∗ ⁢𝐴⁢𝑃. Then, what are the best possible transfer operators 𝑅 and 𝑃 of a given dimension 𝑛 𝑐 < 𝑛? Brannick et al. [12] showed that when 𝐴 and 𝑀 are Hermitian positive definite (HPD), the optimal interpolation is such that its range contains the 𝑛 𝑐 smallest generalized eigenvectors of the matrix pencil (𝐴, 𝑀). Recently, in Ali et al. [5] we generalized this framework to the non-HPD setting, by considering both right (interpolation) and left (restriction) generalized eigenvectors of (𝐴, 𝑀) and defining corresponding nonsymmetric transfer operators {𝑅#, 𝑃#}. Tight convergence bounds for {𝑅#, 𝑃#} are derived in spectral radius, as well as a proof of pseudo-optimality. Note, {𝑅#, 𝑃#} are typically complex valued, which is not practical for real-valued problems. Here, in this work, we build on [5], first characterizing all inner products in which the coarse-space correction defined by {𝑅#, 𝑃#} is orthogonal. We then develop tight two-level convergence bounds in these norms, and prove that the underlying transfer operators {𝑅#, 𝑃#} are genuinely optimal. As a special case, our theory both recovers and extends the HPD results from [12]. Finally, we show how to construct optimal, real-valued transfer operators in the case of that 𝐴 and 𝑀 are real valued, but are not HPD. Numerical examples arising from a discretized advection-reaction equation, wave-equation, and Stokes equations are used to verify and illustrate the theory.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Packing and flow particle simulations

Granular material is present across natural and industrial processes on Earth and other planets. Granular particles show up in space exploration (lunar regolith), avalanches (boulders), food (coffee), construction (concrete powder) and manufacturing (additive manufacturing powder, battery slurries). Important phenomena emerge from large collections of granular particles. The size scales of the particles in granular material, 10 μm diameter or larger, makes particle-based simulations a tractable computational method. This seminar will present the packing and flow of granular matter using particle-based discrete element modeling simulations. Particles modeled with rotational friction only require as few as 2.6 contacts for mechanical stability, as opposed to 6 contacts for frictionless particles. Optimal parameters for in-space manufacturing particulate material are identified. Specifically, the maximum density and contacts occurs for a large-to-small particle volume ratio of 0.265. Stress and contact fabric fluctuations of flowing dry granular matter have power-law scaling with strain rate, and a kink. The pressure-dependent slope change kink could identify the transition between slower, quasistatic and faster, inertial flows.

granular↗

DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗

NASA NTRSDate not supplied

Packing and flow particle simulations

granular↗

NASA NTRS1984

Optimal maintenance center inventories for fault-tolerant repairable systems

A probabilistic approach is taken to determine the optimal repairable parts inventory for a maintenance center, servicing machines which contain several m-out-of-n systems of different parts, with a constraint on the total inventory investment. A model, based on the discrete Markov process, accounts for a typical ultrareliable avionics system, such as one presently being developed by NASA. The dynamic programming algorithm for minimizing the stockout and holding costs is applied to an exemplary maintenance center, and solutions for single-item and multi-item cases are given. The computational burden is noted to be reasonable and a computer program is used to generate optimal solutions.

Lawrence, S. H.↗

NASA NTRS1979

Human controller modeling in environments that include non-control tasks

In complex environments where the human operator is a supervisor, he must allocate his attention between different kinds of tasks for optimum overall performance. When a portion of the future reference trajectory for the control task is available for preview, scheduling various activities is possible. A model has been developed for this situation using dynamic programming to solve an optimal control problem. An experiment was conducted where subjects controlled an airplane symbol over a map, shown a fixed distance into the future. Discrete, non-control tasks were introduced as number entry tasks. Results from the model are compared with experimental results.

Govindaraj, T.↗

NASA NTRS1987

Galerkin/Runge-Kutta discretizations for semilinear parabolic equations

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

NASA NTRS1990

Technology development program for the Space Infrared Telescope Facility (SIRTF) science instruments

A coordinated technology program for the Space Infrared Telescope Facility (SIRTF) is described. The program encompasses detector technology, cryogenic mechanisms technology, and an adiabatic demagnetization refrigerator. Discrete detectors, detector arrays, detector readouts, and testing of engineering models under simulated flight environment conditions are considered. Several focal planes will be optimized at a particular wavelength range to make up over 247,000 detector pixels from about 1.8 to 1000 microns.

Ramos, Ruben↗