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NASA NTRS2000

The Design of a Templated C++ Small Vector Class for Numerical Computing

We describe the design and implementation of a templated C++ class for vectors. The vector class is templated both for vector length and vector component type; the vector length is fixed at template instantiation time. The vector implementation is such that for a vector of N components of type T, the total number of bytes required by the vector is equal to N * size of (T), where size of is the built-in C operator. The property of having a size no bigger than that required by the components themselves is key in many numerical computing applications, where one may allocate very large arrays of small, fixed-length vectors. In addition to the design trade-offs motivating our fixed-length vector design choice, we review some of the C++ template features essential to an efficient, succinct implementation. In particular, we highlight some of the standard C++ features, such as partial template specialization, that are not supported by all compilers currently. This report provides an inventory listing the relevant support currently provided by some key compilers, as well as test code one can use to verify compiler capabilities.

Moran, Patrick J.↗

NASA NTRS2007

Experimental Study of an Axisymmetric Dual Throat Fluidic Thrust Vectoring Nozzle for Supersonic Aircraft Application

An axisymmetric version of the Dual Throat Nozzle concept with a variable expansion ratio has been studied to determine the impacts on thrust vectoring and nozzle performance. The nozzle design, applicable to a supersonic aircraft, was guided using the unsteady Reynolds-averaged Navier-Stokes computational fluid dynamics code, PAB3D. The axisymmetric Dual Throat Nozzle concept was tested statically in the Jet Exit Test Facility at the NASA Langley Research Center. The nozzle geometric design variables included circumferential span of injection, cavity length, cavity convergence angle, and nozzle expansion ratio for conditions corresponding to take-off and landing, mid climb and cruise. Internal nozzle performance and thrust vectoring performance was determined for nozzle pressure ratios up to 10 with secondary injection rates up to 10 percent of the primary flow rate. The 60 degree span of injection generally performed better than the 90 degree span of injection using an equivalent injection area and number of holes, in agreement with computational results. For injection rates less than 7 percent, thrust vector angle for the 60 degree span of injection was 1.5 to 2 degrees higher than the 90 degree span of injection. Decreasing cavity length improved thrust ratio and discharge coefficient, but decreased thrust vector angle and thrust vectoring efficiency. Increasing cavity convergence angle from 20 to 30 degrees increased thrust vector angle by 1 degree over the range of injection rates tested, but adversely affected system thrust ratio and discharge coefficient. The dual throat nozzle concept generated the best thrust vectoring performance with an expansion ratio of 1.0 (a cavity in between two equal minimum areas). The variable expansion ratio geometry did not provide the expected improvements in discharge coefficient and system thrust ratio throughout the flight envelope of typical a supersonic aircraft. At mid-climb and cruise conditions, the variable geometry design compromised thrust vector angle achieved, but some thrust vector control would be available, potentially for aircraft trim. The fixed area, expansion ratio of 1.0, Dual Throat Nozzle provided the best overall compromise for thrust vectoring and nozzle internal performance over the range of NPR tested compared to the variable geometry Dual Throat Nozzle.

Flamm, Jeffrey D.↗

DOE OSTI2024

Real space iterative reconstruction for vector tomography (RESIRE-V)

Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method. To make the algorithm accessible to a broad user community, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V.

47 OTHER INSTRUMENTATION↗

NASA NTRS1987

Multiaxis control power from thrust vectoring for a supersonic fighter aircraft model at Mach 0.20 to 2.47

The aeropropulsive characteristics of an advanced twin-engine fighter aircraft designed for supersonic cruise have been studied in the Langley 16-Foot Tansonic Tunnel and the Lewis 10- by 10-Foot Supersonic Tunnel. The objective was to determine multiaxis control-power characteristics from thrust vectoring. A two-dimensional convergent-divergent nozzle was designed to provide yaw vector angles of 0, -10, and -20 deg combined with geometric pitch vector angles of 0 and 15 deg. Yaw thrust vectoring was provided by yaw flaps located in the nozzle sidewalls. Roll control was obtained from differential pitch vectoring. This investigation was conducted at Mach numbers from 0.20 to 2.47. Angle of attack was varied from 0 to about 19 deg, and nozzle pressure ratio was varied from about 1 (jet off) to 28, depending on Mach number. Increments in force or moment coefficient that result from pitch or yaw thrust vectoring remain essentially constant over the entire angle-of-attack range of all Mach numbers tested. There was no effect of pitch vectoring on the lateral aerodynamic forces and moments and only very small effects of yaw vectoring on the longitudinal aerodynamic forces and moments. This result indicates little cross-coupling of control forces and moments for combined pitch-yaw vectoring.

Capone, Francis J.↗

NASA NTRS1994

Static performance investigation of a skewed-throat multiaxis thrust-vectoring nozzle concept

The static performance of a jet exhaust nozzle which achieves multiaxis thrust vectoring by physically skewing the geometric throat has been characterized in the static test facility of the 16-Foot Transonic Tunnel at NASA Langley Research Center. The nozzle has an asymmetric internal geometry defined by four surfaces: a convergent-divergent upper surface with its ridge perpendicular to the nozzle centerline, a convergent-divergent lower surface with its ridge skewed relative to the nozzle centerline, an outwardly deflected sidewall, and a straight sidewall. The primary goal of the concept is to provide efficient yaw thrust vectoring by forcing the sonic plane (nozzle throat) to form at a yaw angle defined by the skewed ridge of the lower surface contour. A secondary goal is to provide multiaxis thrust vectoring by combining the skewed-throat yaw-vectoring concept with upper and lower pitch flap deflections. The geometric parameters varied in this investigation included lower surface ridge skew angle, nozzle expansion ratio (divergence angle), aspect ratio, pitch flap deflection angle, and sidewall deflection angle. Nozzle pressure ratio was varied from 2 to a high of 11.5 for some configurations. The results of the investigation indicate that efficient, substantial multiaxis thrust vectoring was achieved by the skewed-throat nozzle concept. However, certain control surface deflections destabilized the internal flow field, which resulted in substantial shifts in the position and orientation of the sonic plane and had an adverse effect on thrust-vectoring and weight flow characteristics. By increasing the expansion ratio, the location of the sonic plane was stabilized. The asymmetric design resulted in interdependent pitch and yaw thrust vectoring as well as nonzero thrust-vector angles with undeflected control surfaces. By skewing the ridges of both the upper and lower surface contours, the interdependency between pitch and yaw thrust vectoring may be eliminated and the location of the sonic plane may be further stabilized.

Wing, David J.↗

NASA NTRS2006

Implementing Scientific Simulation Codes Highly Tailored for Vector Architectures Using Custom Configurable Computing Machines

The motivation for this work comes from an observation that amidst the push for Massively Parallel (MP) solutions to high-end computing problems such as numerical physical simulations, large amounts of legacy code exist that are highly optimized for vector supercomputers. Because re-hosting legacy code often requires a complete re-write of the original code, which can be a very long and expensive effort, this work examines the potential to exploit reconfigurable computing machines in place of a vector supercomputer to implement an essentially unmodified legacy source code. Custom and reconfigurable computing resources could be used to emulate an original application's target platform to the extent required to achieve high performance. To arrive at an architecture that delivers the desired performance subject to limited resources involves solving a multi-variable optimization problem with constraints. Prior research in the area of reconfigurable computing has demonstrated that designing an optimum hardware implementation of a given application under hardware resource constraints is an NP-complete problem. The premise of the approach is that the general issue of applying reconfigurable computing resources to the implementation of an application, maximizing the performance of the computation subject to physical resource constraints, can be made a tractable problem by assuming a computational paradigm, such as vector processing. This research contributes a formulation of the problem and a methodology to design a reconfigurable vector processing implementation of a given application that satisfies a performance metric. A generic, parametric, architectural framework for vector processing implemented in reconfigurable logic is developed as a target for a scheduling/mapping algorithm that maps an input computation to a given instance of the architecture. This algorithm is integrated with an optimization framework to arrive at a specification of the architecture parameters that attempts to minimize execution time, while staying within resource constraints. The flexibility of using a custom reconfigurable implementation is exploited in a unique manner to leverage the lessons learned in vector supercomputer development. The vector processing framework is tailored to the application, with variable parameters that are fixed in traditional vector processing. Benchmark data that demonstrates the functionality and utility of the approach is presented. The benchmark data includes an identified bottleneck in a real case study example vector code, the NASA Langley Terminal Area Simulation System (TASS) application.

Rutishauser, David↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

A new method was developed to extract surface flow vectors from an oilflow visualization image that has oil streaklines. The method is analogous to the PIV processing where the image is divided into interrogation windows. A representative flow direction is obtained for each interrogation window using image processing with a line-detection algorithm. Repeating the process for the entire image, one can find the surface vector field. The Hough transformation, Radon transformation and Machine Learning were used as line-detection algorithms. The obtained vector field is then postprocessed to filter spurious vectors and to apply smoothing. The method was tested on 2D and 3D models with different flow complexities. The method was able to predict surface flow vectors for all cases tested. The predicted surface flow vectors were used in obtaining the surface skin friction. The successful implementation of the surface flow vectors enables interferometric skin friction measurements on surfaces beneath 3D complex flows. In addition, the surface flow vectors can be superimposed on the oilflow visualization images to better explain the surface flow topology.

Surface flow vectors↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

Surface flow vectors↗

NASA NTRS1995

Multiaxis Thrust-Vectoring Characteristics of a Model Representative of the F-18 High-Alpha Research Vehicle at Angles of Attack From 0 deg to 70 deg

An investigation was conducted in the Langley 16-Foot Transonic Tunnel to determine the multiaxis thrust-vectoring characteristics of the F-18 High-Alpha Research Vehicle (HARV). A wingtip supported, partially metric, 0.10-scale jet-effects model of an F-18 prototype aircraft was modified with hardware to simulate the thrust-vectoring control system of the HARV. Testing was conducted at free-stream Mach numbers ranging from 0.30 to 0.70, at angles of attack from O' to 70', and at nozzle pressure ratios from 1.0 to approximately 5.0. Results indicate that the thrust-vectoring control system of the HARV can successfully generate multiaxis thrust-vectoring forces and moments. During vectoring, resultant thrust vector angles were always less than the corresponding geometric vane deflection angle and were accompanied by large thrust losses. Significant external flow effects that were dependent on Mach number and angle of attack were noted during vectoring operation. Comparisons of the aerodynamic and propulsive control capabilities of the HARV configuration indicate that substantial gains in controllability are provided by the multiaxis thrust-vectoring control system.

Asbury, Scott C.↗

NASA NTRS2004

An Algorithm for Converting Static Earth Sensor Measurements into Earth Observation Vectors

An algorithm has been developed that converts penetration angles reported by Static Earth Sensors (SESs) into Earth observation vectors. This algorithm allows compensation for variation in the horizon height including that caused by Earth oblateness. It also allows pitch and roll to be computed using any number (greater than 1) of simultaneous sensor penetration angles simplifying processing during periods of Sun and Moon interference. The algorithm computes body frame unit vectors through each SES cluster. It also computes GCI vectors from the spacecraft to the position on the Earth's limb where each cluster detects the Earth's limb. These body frame vectors are used as sensor observation vectors and the GCI vectors are used as reference vectors in an attitude solution. The attitude, with the unobservable yaw discarded, is iteratively refined to provide the Earth observation vector solution.

Harman, R.↗

NASA NTRS2011

GPU Accelerated Vector Median Filter

Noise reduction is an important step for most image processing tasks. For three channel color images, a widely used technique is vector median filter in which color values of pixels are treated as 3-component vectors. Vector median filters are computationally expensive; for a window size of n x n, each of the n(sup 2) vectors has to be compared with other n(sup 2) - 1 vectors in distances. General purpose computation on graphics processing units (GPUs) is the paradigm of utilizing high-performance many-core GPU architectures for computation tasks that are normally handled by CPUs. In this work. NVIDIA's Compute Unified Device Architecture (CUDA) paradigm is used to accelerate vector median filtering. which has to the best of our knowledge never been done before. The performance of GPU accelerated vector median filter is compared to that of the CPU and MPI-based versions for different image and window sizes, Initial findings of the study showed 100x improvement of performance of vector median filter implementation on GPUs over CPU implementations and further speed-up is expected after more extensive optimizations of the GPU algorithm .

Aras, Rifat↗

DOE OSTI2020

The direct and indirect effects of copper on vector-borne disease dynamics

Metal pollution is a growing concern that affects the health of humans and animals globally. Copper is an essential insect micronutrient required for respiration, pigmentation and oxidative stress protection but can also act as a potentially toxic trace element. While several studies have focused on the negative fitness effects of copper on the aquatic larvae of mosquitoes, the effects of larval copper exposure on adult mosquito fitness (i.e., survival and fecundity) and their ability to transmit parasites (i.e., vector competence) remains unclear. Here, using a well-studied model vector-parasite system, the mosquito Aedes aegypti and parasite Dirofilaria immitis, we show that sublethal copper exposure in larval mosquitoes alters adult female fecundity and vector competence. Specifically, mosquitoes exposed to copper had a hormetic fecundity response and mosquitoes exposed to 600 μg/L of copper had significantly fewer infective parasite larvae than control mosquitoes not exposed to copper. Therefore, exposure of mosquito larvae to copper levels far below EPA-mandated safe drinking water limits (1300 μg/L) can impact vector-borne disease dynamics not only by reducing mosquito abundance (through increased larval mortality), but also by reducing parasite transmission risk. Our results also demonstrated that larval copper is retained through metamorphosis to adulthood in mosquitoes, indicating that these insects could transfer copper from aquatic to terrestrial foodwebs, especially in urban areas where they are abundant. To our knowledge this is the first study to directly link metal exposure with vector competence (i.e., ability to transmit parasites) in any vector-parasite system. Additionally, it also demonstrates unequivocally that mosquitoes can transfer contaminants from aquatic to terrestrial ecosystems. These results have broad implications for public health because they directly linking contaminants and vector-borne disease dynamics, as well as linking mosquitoes and contaminant dynamics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The development of Gibbs's dyadic and implications for the gradient of a vector field

In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

A vectorization of the Jameson-Caughey NYU transonic swept-wing computer program FLO-22-V1 for the STAR-100 computer

The computer program FLO-22 for analyzing inviscid transonic flow past 3-D swept-wing configurations was modified to use vector operations and run on the STAR-100 computer. The vectorized version described herein was called FLO-22-V1. Vector operations were incorporated into Successive Line Over-Relaxation in the transformed horizontal direction. Vector relational operations and control vectors were used to implement upwind differencing at supersonic points. A high speed of computation and extended grid domain were characteristics of FLO-22-V1. The new program was not the optimal vectorization of Successive Line Over-Relaxation applied to transonic flow; however, it proved that vector operations can readily be implemented to increase the computation rate of the algorithm.

Smith, R. E.↗

NASA NTRS1983

A static investigation of yaw vectoring concepts on two-dimensional convergent-divergent nozzles

The flow-turning capability and nozzle internal performance of yaw-vectoring nozzle geometries were tested in the NASA Langley 16-ft Transonic wind tunnel. The concept was investigated as a means of enhancing fighter jet performance. Five two-dimensional convergent-divergent nozzles were equipped for yaw-vectoring and examined. The configurations included a translating left sidewall, left and right sidewall flaps downstream of the nozzle throat, left sidewall flaps or port located upstream of the nozzle throat, and a powered rudder. Trials were also run with 20 deg of pitch thrust vectoring added. The feasibility of providing yaw-thrust vectoring was demonstrated, with the largest yaw vector angles being obtained with sidewall flaps downstream of the nozzle primary throat. It was concluded that yaw vector designs that scoop or capture internal nozzle flow provide the largest yaw-vector capability, but decrease the thrust the most.

Berrier, B. L.↗

NASA NTRS1986

Multiaxis aircraft control power from thrust vectoring at high angles of attack

Extensive research programs conducted at the Langley Research Center have shown that thrust vectoring can be provided by multifunction (nonaxisymmetric) nozzles. Most of this research has been conducted on pitch vectoring at both static and forward flight conditions. Recent efforts have been aimed at evaluating yaw vectoring concepts at static (wind off) conditions. This paper summarizes results for three different twin-engine fighter configurations tested over a Mach number range of 0.15 to 2.47 at angles of attack up to 35 deg. The objective of these investigations was to determine the multiaxis control power characteristics provided by thrust vectoring. All three configurations employed two-dimensional convergent-divergent nozzles which provided pitch vectoring by differential deflection of the upper and lower nozzle divergent flaps. Three different means of yaw vectoring were tested: (1) a translating nozzle sidewall; (2) yaw flaps located in the nozzle sidewalls; and (3) canted nozzles. These investigations were conducted in the Langley 16-Foot Transonic Tunnel and the Lewis 10x10-Foot Supersonic Tunnel. Longitudinal and direction control power from thrust vectoring was greater than that provided by aerodynamic control effectors at low speed or at high angles of attack.

Capone, F. J.↗

NASA NTRS1986

Multiaxis aircraft control power from thrust vectoring at high angles of attack

Extensive research programs conducted at the Langley Research Center have shown that thrust vectoring can be provided by multifunction (nonaxisymmetric) nozzles. Most of this research has been conducted on pitch vectoring at both static and forward flight conditions. Recent efforts have been aimed at evaluating yaw vectoring concepts at static (wind off) conditions. This paper summarizes results for three different twin-engine fighter configurations tested over a Mach number range of 0.15 to 2.47 at angles of attack up to 35 deg. The objective of these investigations was to determine the multiaxis control power characteristics provided by thrust vectoring. All three configurations employed two-dimensional convergent-divergent nozzles which provided pitch vectoring by differential deflection of the upper and lower nozzle divergent flaps. Three different means of yaw vectoring were tested: (1) a translating nozzle sidewall; (2) yaw flaps located in the nozzle sidewalls; and (3) canted nozzles. These investigations were conducted in the Langley 16-Foot Transonic Tunnel and the Lewis 10 x 10-Foot Supersonic Tunnel. Longitudinal and direction control power from thrust vectoring was greater than that provided by aerodynamic control effectors at low speed or at high angles of attack.

Capone, Francis J.↗