Search NASA⌕ Search

SEARCH · Search NASA

Results for “gradient”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

Crosswind Shear Gradient Affect on Wake Vortices

Parametric simulations with a Large Eddy Simulation (LES) model are used to explore the influence of crosswind shear on aircraft wake vortices. Previous studies based on field measurements, laboratory experiments, as well as LES, have shown that the vertical gradient of crosswind shear, i.e. the second vertical derivative of the environmental crosswind, can influence wake vortex transport. The presence of nonlinear vertical shear of the crosswind velocity can reduce the descent rate, causing a wake vortex pair to tilt and change in its lateral separation. The LES parametric studies confirm that the vertical gradient of crosswind shear does influence vortex trajectories. The parametric results also show that vortex decay from the effects of shear are complex since the crosswind shear, along with the vertical gradient of crosswind shear, can affect whether the lateral separation between wake vortices is increased or decreased. If the separation is decreased, the vortex linking time is decreased, and a more rapid decay of wake vortex circulation occurs. If the separation is increased, the time to link is increased, and at least one of the vortices of the vortex pair may have a longer life time than in the case without shear. In some cases, the wake vortices may never link.

Proctor, Fred H.↗

The NTF Inlet Guide Vanes Thermal Gradient Problem and Its Mitigation

The National Transonic Facility (NTF) utilizes Inlet Guide Vanes (IGV) to provide precise, quick response Mach number control for the tunnel. During cryogenic operations, the massive IGV structure can experience large thermal gradients, measured as "Delta T or (Delta)T", between the IGV ring and its support structure called the transfer case. If these temperature gradients are too large, the IGV structure can be stressed beyond its safety limit and cease operation. In recent years, (Delta)T readings exceeding the prescribed safety limits were observed frequently during cryogenic operations, particularly during model access. The tactical operation methods of the tunnel to minimize (Delta)T did not always succeed. One obvious option to remedy this condition is to warm up the IGV structure by disabling the main drive operation, but this "natural" warm up method can takes days in some cases, resulting in productivity loss. This paper documents the thermal gradient problem associated with the IGV structure during cryogenic operation and how the facility has recently achieved an acceptable mitigation which has resulted in improved efficiency of operations.

Venkat, Venki S.↗

Sudden Intensity Increases and Radial Gradient Changes of Cosmic Ray Mev Electrons and Protons Observed at Voyager 1 Beyond 111 AU in the Heliosheath

Voyager 1 has entered regions of different propagation conditions for energetic cosmic rays in the outer heliosheathat a distance of about 111 AU from the Sun. The low energy 614 MeV galactic electron intensity increased by 20over a time period 10 days and the electron radial intensity gradient abruptly decreased from 19AU to 8AU at2009.7 at a radial distance of 111.2 AU. At about 2011.2 at a distance of 116.6 AU a second abrupt intensity increase of25 was observed for electrons. After the second sudden electron increase the radial intensity gradient increased to18AU. This large positive gradient and the 13 day periodic variations of 200 MeV particles observed near theend of 2011 indicate that V1 is still within the overall heliospheric modulating region. The implications of these resultsregarding the proximity of the heliopause are discussed.

protons↗

Interpretation of CHAMP Magnetic Anomaly Data over the Pannonian Basin Region Using Lower Altitude Horizontal Gradient Data

The ESA SWARM mission will have three earth orbiting magnetometer bearing satellites one in a high orbit and two side-by-side in lower orbits. These latter satellites will record a horizontal magnetic gradient. In order to determine how we can use these gradient measurements for interpretation of large geologic units we used ten years of CHAMP data to compute a horizontal gradient map over a section of southeastern Europe with our goal to interpret these data over the Pannonian Basin of Hungary.

CHAMP↗

Methods for Fabricating Gradient Alloy Articles with Multi-Functional Properties

Systems and methods for fabricating multi-functional articles comprised of additively formed gradient materials are provided. The fabrication of multi-functional articles using the additive deposition of gradient alloys represents a paradigm shift from the traditional way that metal alloys and metal/metal alloy parts are fabricated. Since a gradient alloy that transitions from one metal to a different metal cannot be fabricated through any conventional metallurgy techniques, the technique presents many applications. Moreover, the embodiments described identify a broad range of properties and applications.

Hofmann, Douglas C.↗

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Leone, Frank A., Jr.↗

Evolution of a Planar Wake in Adverse Pressure Gradient

In the interest of improving the predictability of high-lift systems at maximum lift conditions, a series of fundamental experiments were conducted to study the effects of adverse pressure gradient on a wake flow. Mean and fluctuating velocities were measured with a two-component laser-Doppler velocimeter. Data were obtained for several cases of adverse pressure gradient, producing flows ranging from no reversed flow to massively reversed flow. While the turbulent Reynolds stresses increase with increasing size of the reversed flow region, the gradient of Reynolds stress does not. Computations using various turbulence models were unable to reproduce the reversed flow.

Wake↗

Solution of Ordinary Differential Equations in Gradient-Based Multidisciplinary Design Optimization

A gradient-based approach to multidisciplinary design optimization enables efficient scalability to large numbers of design variables. However, the need for derivatives causes difficulties when integrating ordinary differential equations (ODEs) in models. To simplify this, we propose the use of the general linear methods framework, which unifies all Runge-Kutta and linear multistep methods. This approach enables rapid implementation of integration methods without the need to differentiate each one, even in a gradient-based optimization context. We also develop a new parallel time integration algorithm that enables vectorization across time steps. We present a set of benchmarking results using a stiff ODE, a non-stiff nonlinear ODE, and an orbital dynamics ODE, and compare integration methods. In a modular gradient-based multidisciplinary design optimization context, we find that the new parallel time integration algorithm with high-order implicit methods, especially Gauss-Legendre collocation, is the best choice for a broad range of problems.

Hwang, John T.↗

Through Thickness Thermal Gradients in Thick Laminates During Cure, Influence on Tg and Modulus

Carbon fiber composites are materials of great interest to the aerospace industry because of their light weight and high strength properties. Composite use in high load bearing applications such as roto-craft gearing requires manufacturing parts that are 1.5 inches thick and beyond. Very thick composite parts (laminates) produce thermal gradients and temperature spikes due to the heat released by resin polymerization and cross-linking during composite cure. It is believed that these thermal gradients will cause internal stresses to build-up inside these ultra-thick laminates during the cure-cycle, yielding parts with non-uniform mechanical properties throughout the thickness of the laminate. The goal of this study is to identify these thermal gradients and determine the magnitude of difference in mechanical properties generated by them.

Mechanical Properties↗

Numerical Study of Turbulent Separation Bubbles with Varying Pressure Gradient and Reynolds Number

A family of cases each containing a small separation bubble is treated by direct numerical simulation (DNS), varying two parameters: the severity of the pressure gradients, generated by suction and blowing across the opposite boundary, and the Reynolds number. Each flow contains a well-developed entry region with essentially zero pressure gradient, and all are adjusted to have the same value for the momentum thickness, extrapolated from the entry region to the centre of the separation bubble. Combined with fully defined boundary conditions this will make comparisons with other simulations and turbulence models rigorous; we present results for a set of eight Reynolds-averaged Navier–Stokes turbulence models. Even though the largest Reynolds number is approximately 5.5 times higher than in a similar DNS study we presented in 1997, the models have difficulties matching the DNS skin friction very closely even in the zero pressure gradient, which complicates their assessment. In the rest of the domain, the separation location per se is not particularly difficult to predict, and the most definite disagreement between DNS and models is near reattachment. Curiously, the better models tend to cluster together in their predictions of pressure and skin friction even when they deviate from the DNS, although their eddy-viscosity levels are widely different in the outer region near the bubble (or they do not rely on an eddy viscosity). Stratford’s square-root law is satisfied by the velocity profiles, both at separation and reattachment. The Reynolds-number range covers a factor of two, with the Reynolds number based on the extrapolated momentum thickness equal to approximately 1500 and 3000. This allows tentative estimates of the improvements that even higher values will bring to the model comparisons. The solutions are used to assess models through pressure, skin friction and other measures; the flow fields are also used to produce effective eddy-viscosity targets for the models, thus guiding turbulence-modelling work in each region of the flow.

Coleman, G. N.↗

Fast Aircraft Separation Calculations for Gradient Based Optimization of Airspace Simulations

Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.

Optimization↗

Simulation and Modeling of Hypersonic Turbulent Boundary Layers Subject to Adverse Pressure Gradients due to Concave Streamline Curvature

Direct numerical simulations (DNS) of adverse-pressure-gradient turbulent boundary layers over a planar concave wall are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models. The wall geometry and flow conditions of the DNS are representative of the experimental data for a Mach 4.9 turbulent boundary layer that was tested on a two-dimensional planar concave wall model in the high-speed blow-down wind tunnel located at the National Aerothermochemistry Laboratory at Texas A&M University (TAMU). The DNS was validated against the experimental results of TAMU for the same flow conditions and wall geometry. An analysis of the DNS datasets was also conducted to provide an assessment of the validity of Morkovin’s hypothesis and the strong Reynolds analog for turbulence subject to mechanical nonequilibrium. In addition to the DNS results, RANS predictions are obtained by using the Baldwin-Lomax (BL), Spalart-Allmaras (SA), and the k - w SST turbulence models. The comparisons between RANS and DNS showed little impact of an adverse pressure gradient on the accuracy of these models, at least up to an incompressible Clauser pressure gradient parameter of beta(sub inc) 1.22. While the Boussinesq assumption provided reasonable predictions for the Reynolds shear stress, it failed to adequately predict the normal components of the Reynolds stress.

turbulent boundary layers↗

Gradient-Enhanced Reliability Analysis of Transonic Aeroelastic Flutter

Reliability computation for transonic aeroelastic systems is a challenging task, given the complex physical mechanisms involved, and broader challenges associated with computing small probabilities of failure/flutter. This paper demonstrates the use of four different reliability estimation tools, with a particular focus on tools that can utilize gradient information: the derivative of flutter boundaries with respect to random parametric inputs. Results are shown for two test cases: the AGARD 445.6 case and the Common Research Model, and the strength and weaknesses of each UQ tool are compared in terms of cost and accuracy. Two of the UQ tools used here require gradients as part of a search process, but the other two are sample-based, and are able to leverage the existence of gradients for improved performance.

Bret K Stanford↗

Aviary: An Open-Source Multidisciplinary Design, Analysis, and Optimization Tool for Modeling Aircraft With Analytic Gradients

Demands on aircraft design methods in recent years have begun to require increasingly higher amounts of coupling between disciplines and have also begun to require optimization in order to satisfy competing objectives involving large numbers of parameters that define unconventional configurations. These expanding requirements have amplified a need for new and improved aircraft design, analysis, and optimization codes that are capable of performing coupled design exploiting analytic gradients where possible. Aviary is a multidisciplinary design optimization and analysis framework which allows for tightly coupled simultaneous aircraft and subsystem design using analytic gradients. Aviary has employed the methods of two legacy aircraft analysis tools to provide native analytically differentiated calculations for five different disciplines, and it also has the ability to couple in external discipline analysis tools, whether or not those tools can provide analytic gradients. Preliminary examples and modeling efforts have shown Aviary’s ability to effectively model novel concepts and explore large and non-intuitive design spaces. Finally, a multi-level user interface in Aviary creates an easy entry point for users with any level of multidisciplinary design, analysis, and optimization experience.

multidisciplinary↗

Gradient-Based Optimization of the Common Research Model Wing Subject to CFD-Based Gust and Flutter Constraints

The linearized frequency-domain method was recently implemented in the stabilized finite element solver in NASA’s FUN3D code. Previous work by the authors used this method for enforcing flutter constraints during gradient-based optimizations. More recently, the solver was expanded to account for continuous (also known as stochastic) gust responses. This paper expands on recent Common Research Model wing optimization work, which demonstrated gradient-based optimization with flutter and stochastic gust constraints, among others. While that work utilized FUN3D for static aeroelastic solutions but relied on doublet lattice aerodynamics for gust and flutter responses, the present work replaces these unsteady aerodynamic analyses with those of FUN3D’s linearized frequency-domain solver. With analytic derivatives available, gradient-based optimization is performed through the use of the OpenMDAO/MPhys libraries with over 700 shape, structural, and aerodynamic design variables and over 10 nonlinear constraints. Comparisons of analysis results and optimized designs are made between doublet lattice and linearized frequency-domain solutions.

aeroelasticity↗

Robust Trajectory Optimization Techniques Using a Sweeping Gradient Method and Linear Covariance Analysis

We present robust trajectory optimization techniques using a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov). SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve robust optimal trajectory design problems. We describe the individual methods and some details on how they can be combined. Then we apply the combined techniques to a variety of orbital trajectory design problems to demonstrate its use, including minimum fuel transfer and mid-course correction burn scheduling.

Benjamin W L Margolis↗

Co-Optimization of Navigation System Requirements and Trajectory Design Using a Sweeping Gradient Method and Linear Covariance Analysis

We describe the application of a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov) to the co-optimization of navigation system requirement generation and robust trajectory design. SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve a combined robust optimal trajectory and navigation system design problem. In this paper, we formulate the required models to apply the combined SGM and LinCov techniques to a Near-Rectilinear Halo Orbit rendezvous approach scenario and show results for several intermediate problems.

Benjamin W L Margolis↗