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NASA NTRS1982

Global differential geometry: An introduction for control engineers

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

Doolin, B. F.↗

NASA NTRS2013

Initial Assessment of a Variable-Camber Continuous Trailing-Edge Flap System on a Rigid Wing for Drag Reduction in Subsonic Cruise

In this paper, we describe an initial optimization study of a Variable-Camber Continuous Trailing-Edge Flap (VCCTEF) system. The VCCTEF provides a light-weight control system for aircraft with long flexible wings, providing efficient high-lift capability for takeoff and landing, and greater efficiency with reduced drag at cruising flight by considering the effects of aeroelastic wing deformations in the control law. The VCCTEF system is comprised of a large number of distributed and individually-actuatable control surfaces that are constrained in movement relative to neighboring surfaces, and are non-trivially coupled through structural aeroelastic dynamics. Minimzation of drag results in a constrained, coupled, non-linear optimization over a high-dimension search space. In this paper, we describe the modeling, analysis, and optimization of the VCCTEF system control inputs for minimum drag in cruise. The purpose of this initial study is to quantify the expected benefits of the system concept. The scope of this analysis is limited to consideration of a rigid wing without structural flexibility in a steady-state cruise condition at various fuel weights. For analysis, we developed an optimization engine that couples geometric synthesis with vortex-lattice analysis to automate the optimization procedure. In this paper, we present and describe the VCCTEF system concept, optimization approach and tools, run-time performance, and results of the optimization at 20%, 50%, and 80% fuel load. This initial limited-scope study finds the VCCTEF system can potentially gain nearly 10% reduction in cruise drag, provides greater drag savings at lower operating weight, and efficiency is negatively impacted by the severity of relative constraints between control surfaces.

trailing edge flaps↗

DOE OSTI2025

Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization

We present an optimized implementation of the recently proposed information geometric regularization (IGR) for unprecedented scale simulation of compressible fluid flows applied to multi-engine spacecraft boosters. We improve upon state-of-the-art computational fluid dynamics (CFD) techniques in terms of computational cost, memory footprint, and energy-to-solution metrics. Unified memory on coupled CPU–GPU or APU platforms increases problem size with negligible overhead. Mixed half/single-precision storage and computation are used on well-conditioned numerics. We simulate flow at 200 trillion grid points and 1 quadrillion degrees of freedom, exceeding the current record by a factor of 20. A factor of 4 wall-time speedup is achieved over optimized baselines. Ideal weak scaling is observed on OLCF Frontier, LLNL El Capitan, and CSCS Alps using the full systems. Strong scaling is near ideal at extreme conditions, including 80% efficiency on CSCS Alps with an 8 node baseline and stretching to the full system.

Wilfong, Benjamin [Georgia Institute of Technology↗

NASA NTRS1959

Flight Behavior of the X-2 Research Airplane to a Mach Number of 3.20 and a Geometric Altitude of 126,200 Feet

The maximum Mach number and altitude capabilities of the Bell X-2 research airplane were achieved during a program conducted by the U.S. Air Force with Bell Aircraft Corp. providing operational support and the National Aeronautics and Space Administration providing instrumentation and advisory engineering assistance. A maximum geometric altitude of 126,200 feet was attained at a static pressure of 9.4 pounds per square foot and a dynamic pressure of 19.1 pounds per square foot. During the last flight of the airplane, a maximum Mach number of 3.20 was reached. The directionally divergent maneuver which terminated the final high Mach number flight was precipitated by the loss in directional stability that resulted from increasing the angle of attack. The yawing moment from the lateral control was sufficient to initiate the divergence and also to cause,, indirectly, rolling moments that were greater than the aileron capabilities of the airplane. The ensuing violent motions-resulting from inertial roll coupling caused the loss of the aircraft.

Day, Richard E.↗

DOE OSTI2020

Aeroelastic oscillations of a pitching flexible wing with structural geometric nonlinearities: Theory and numerical simulation

In this paper, we focus on the derivation of an analytical model of the aeroelastic dynamics of an elastically mounted flexible wing. This equations of motion obtained serve to help understand the behaviour of the aeroelastic wind tunnel setup in question, which consists of a rectangular wing with a uniform NACA 0012 airfoil profile, whose base is free to rotate rigidly about a longitudinal axis. Of particular interest are the structural geometric nonlinearities primarily introduced by the coupling between the rigid body pitch degree-of-freedom and the continuous system. A coupled system of partial differential equations (PDEs) coupled with an ordinary differential equation (ODE) describing axial-bending-bending-torsion-pitch motion is derived using Hamilton's principle. A finite dimensional approximation of the system of coupled differential equations is obtained using the Galerkin method, leading to a system of coupled nonlinear ODEs. Subsequently, these nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Adopting a linear unsteady aerodynamic model, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. Finally, the behaviour of the limit cycle oscillations is primarily influenced by the structural geometric nonlinear terms in the coupled system of PDEs and ODE.

42 ENGINEERING↗

NASA NTRSDate not supplied

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method (FEM) models. Geometry measurement methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps of how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the preprocessing methods and results from Py_TIGIRS are provided and compared for Composite Test Articles (CTA) 8.2, 8.2B, and 8.3. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future developments of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Geometric imperfections↗

NASA NTRSDate not supplied

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

Geometric imperfections↗

NASA NTRS1979

Advanced General Aviation Turbine Engine (GATE) concepts

Concepts are discussed that project turbine engine cost savings through use of geometrically constrained components designed for low rotational speeds and low stress to permit manufacturing economies. Aerodynamic development of geometrically constrained components is recommended to maximize component efficiency. Conceptual engines, airplane applications, airplane performance, engine cost, and engine-related life cycle costs are presented. The powerplants proposed offer encouragement with respect to fuel efficiency and life cycle costs, and make possible remarkable airplane performance gains.

Lays, E. J.↗

NASA NTRS1979

A review of Curtiss-Wright rotary engine developments with respect to general aviation potential

Aviation related rotary (Wankel-type) engine tests, possible growth directions and relevant developments at Curtiss-Wright have been reviewed. Automotive rotary engines including stratified charge are described and flight test results of rotary aircraft engines are presented. The current 300 HP engine prototype shows basic durability and competitive performance potential. Recent parallel developments have separately confirmed the geometric advantages of the rotary engine for direct injected unthrottled stratified charge. Specific fuel consumption equal to or better than pre- or swirl-chamber diesels, low emission and multi-fuel capability have been shown by rig tests of similar rotary engine.

Jones, C.↗

NASA NTRS2010

High-Fidelity Roadway Modeling and Simulation

Roads are an essential feature in our daily lives. With the advances in computing technologies, 2D and 3D road models are employed in many applications, such as computer games and virtual environments. Traditional road models were generated by professional artists manually using modeling software tools such as Maya and 3ds Max. This approach requires both highly specialized and sophisticated skills and massive manual labor. Automatic road generation based on procedural modeling can create road models using specially designed computer algorithms or procedures, reducing the tedious manual editing needed for road modeling dramatically. But most existing procedural modeling methods for road generation put emphasis on the visual effects of the generated roads, not the geometrical and architectural fidelity. This limitation seriously restricts the applicability of the generated road models. To address this problem, this paper proposes a high-fidelity roadway generation method that takes into account road design principles practiced by civil engineering professionals, and as a result, the generated roads can support not only general applications such as games and simulations in which roads are used as 3D assets, but also demanding civil engineering applications, which requires accurate geometrical models of roads. The inputs to the proposed method include road specifications, civil engineering road design rules, terrain information, and surrounding environment. Then the proposed method generates in real time 3D roads that have both high visual and geometrical fidelities. This paper discusses in details the procedures that convert 2D roads specified in shape files into 3D roads and civil engineering road design principles. The proposed method can be used in many applications that have stringent requirements on high precision 3D models, such as driving simulations and road design prototyping. Preliminary results demonstrate the effectiveness of the proposed method.

Wang, Jie↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Aero-Acoustic Analyses and Experimental Validation - Part 3

A unique assessment of acoustic similarity scaling laws and acoustic analogy methodologies in predicting the far-field acoustic signature from a sub-scale altitude rocket test facility at the NASA Stennis Space Center was performed. A directional, point-source similarity analysis was implemented for predicting the acoustic far-field. In this approach, experimental acoustic data obtained from "similar" rocket engine tests were appropriately scaled using key geometric and dynamic parameters. The accuracy of this engineering-level method is discussed by comparing the predictions with acoustic far-field measurements obtained. In addition, a CFD solver was coupled with a Lilley's acoustic analogy formulation to determine the improvement of using a physics-based methodology over an experimental correlation approach. In the current work, steady-state Reynolds-averaged Navier-Stokes calculations were used to model the internal flow of the rocket engine and altitude diffuser. These internal flow simulations provided the necessary realistic input conditions for external plume simulations. The CFD plume simulations were then used to provide the spatial turbulent noise source distributions in the acoustic analogy calculations. Preliminary findings of these studies will be discussed.

Allgood, Daniel C.↗

DOE OSTI2021

Magnetic skyrmion diode: Unidirectional skyrmion motion via symmetry breaking of potential energy barriers

In this work, we realize a magnetic skyrmion diode operated by a unidirectional skyrmion transport that flows in only one direction, which is highly significant for information processing in spintronic and nanoelectronic devices. We easily control the skyrmion transport by engineering asymmetric shapes of geometric structures. Here, we present a simple method to describe the underlying mechanism behind the unidirectional skyrmion transport by characterizing the topography of potential energy surfaces from a purely geometric perspective. Our approach enables a deeper physical insight into skyrmion transport manipulation and efficient design of skyrmion-based devices in geometric structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

A Vertex-Aligned Model for Packing 4-Hexagonal Clusters in a Regular Hexagonal Container

This paper deals with a problem the packing polyhex clusters in a regular hexagonal container. It is a common problem in many applications with various cluster shapes used, but symmetric polyhex is the most useful in engineering due to its geometrical properties. Hence, we concentrate on mathematical modeling in such an application, where using the “bee” tetrahex is chosen for the new Compact Muon Solenoid (CMS) design upgrade, which is one of four detectors used in Large Hadron Collider (LHC) experiment at European Laboratory for Particle Physics (CERN). We start from the existing hexagonal containers with hexagonal cells packed inside, and uniform clustering applied. We compare the center-aligned (CA) and vertex-aligned (VA) models, analyzing cluster rotations providing the increased packing efficiency. We formally describe the geometrical properties of clustering approaches and show that cluster sharing is inevitable at the container border with uniform clustering. In addition, we propose a new vertex-aligned model decreasing the number of shared clusters in the uniform scenario, but with a smaller number of clusters contained inside the container. Also, we describe a non-uniform tetrahex cluster packing scheme in the proposed container model. With the proposed cluster packing solution, it is accomplished that all clusters are contained inside the container region. Since cluster-sharing is completely avoided at the container border, the maximal packing efficiency is obtained compared to the existing models.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

The design of a wind tunnel VSTOL fighter model incorporating turbine powered engine simulators

A wind-tunnel model of a supersonic VSTOL fighter aircraft configuration has been developed for use in the evaluation of airframe-propulsion system aerodynamic interactions. The model may be employed with conventional test techniques, where configuration aerodynamics are measured in a flow-through mode and incremental nozzle-airframe interactions are measured in a jet-effects mode, and with the Compact Multimission Aircraft Propulsion Simulator which is capable of the simultaneous simulation of inlet and exhaust nozzle flow fields so as to allow the evaluation of the extent of inlet and nozzle flow field coupling. The basic configuration of the twin-engine model has a geometrically close-coupled canard and wing, and a moderately short nacelle with nonaxisymmetric vectorable exhaust nozzles near the wing trailing edge, and may be converted to a canardless configuration with an extremely short nacelle. Testing is planned to begin in the summer of 1982.

Bailey, R. O.↗

NASA NTRS2005

Predicting Noise From Aircraft Turbine-Engine Combustors

COMBUSTOR and CNOISE are computer codes that predict far-field noise that originates in the combustors of modern aircraft turbine engines -- especially modern, low-gaseous-emission engines, the combustors of which sometimes generate several decibels more noise than do the combustors of older turbine engines. COMBUSTOR implements an empirical model of combustor noise derived from correlations between engine-noise data and operational and geometric parameters, and was developed from databases of measurements of acoustic emissions of engines. CNOISE implements an analytical and computational model of the propagation of combustor temperature fluctuations (hot spots) through downstream turbine stages. Such hot spots are known to give rise to far-field noise. CNOISE is expected to be helpful in determining why low-emission combustors are sometimes noisier than older ones, to provide guidance for refining the empirical correlation model embodied in the COMBUSTOR code, and to provide insight on how to vary downstream turbinestage geometry to reduce the contribution of hot spots to far-field noise.

Gliebe, P.↗

NASA NTRS1991

Engine Structures Modeling Software System (ESMOSS)

Engine Structures Modeling Software System (ESMOSS) is the development of a specialized software system for the construction of geometric descriptive and discrete analytical models of engine parts, components, and substructures which can be transferred to finite element analysis programs such as NASTRAN. The NASA Lewis Engine Structures Program is concerned with the development of technology for the rational structural design and analysis of advanced gas turbine engines with emphasis on advanced structural analysis, structural dynamics, structural aspects of aeroelasticity, and life prediction. Fundamental and common to all of these developments is the need for geometric and analytical model descriptions at various engine assembly levels which are generated using ESMOSS.

Source record↗

NASA NTRS1996

TSS-Thermal Synthesizer System

Thermal Synthesizer System (TSS) is integrated set of thermal-analysis application programs designed to solve problems encountered by thermal engineers. Combines functionality of Systems Improved Numerical Differencing Analyzer/Fluid Integrator (SINDA/FLUINT) and radiation analysis with friendly and easily understood user-interface environment coupled with powerful interactive color graphics and geometric modeling capability. Enables thermal engineers to spend more time solving engineering problems instead of laboriously constructing and verifying math models. Written in FORTRAN and C language.

Chimenti, Edward↗

NASA NTRSDate not supplied

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric surface imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method models. Data collection methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps on how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the pre-processing methods and results from Py_TIGIRS are provided and compared for Composite Test Article (CTA) 8.2B. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future development of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Sandwich structures↗