Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differential Geometry”

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 685 records · Page 38

Single-pulse x-ray diffraction using polycapillary optics for in situ dynamic diffraction

Diagnostic use of single-pulse x-ray diffraction (XRD) at pulsed power facilities can be challenging due to factors such as the high flux and brightness requirements for diffraction and the geometric constraints of experimental platforms. By necessity, the x-ray source is usually positioned very close, within a few inches of the sample. On dynamic compression platforms, this puts the x-ray source in the debris field. We coupled x-ray polycapillary optics to a single-shot needle-and-washer x-ray diode source using a laser-based alignment scheme to obtain high-quality x-ray diffraction using a single 16 ns x-ray pulse with the source >1 m from the sample. Additionally, the system was tested on a Mo sample in reflection geometry using 17 keV x-rays from a Mo anode. We also identified an anode conditioning effect that increased the x-ray intensity by 180%. Quantitative measurements of the x-ray focal spot produced by the polycapillary yielded a total x-ray flux on the sample of 3.3 ± 0.5 × 10 7 molybdenum Kα photons.

47 OTHER INSTRUMENTATION↗

Analysis of a finite composite plate with smooth rigid pin

An elastic continuum method of analysis developed for a smooth rigid pin in a finite composite plate by using complex potentials that satisfy the governing orthotropic differential equation is presented. The plate is subjected to uniaxial loading and the nonlinear problems of partial contact in the pin-plate are studied. Three types of pin fits are examined: interference, push, and clearance. The problems of stresses due to pure interference, load contact behavior, and stresses variations are addressed. The effects of the rectangular geometry and the orthotropic property of the plate are demonstrated through numerical results. It is found that the use of large hole diameter/plate width ratios have deleterious effects and the use of interference has beneficial effects. The solutions obtained will help in the development of special finite elements for fastener joints. Finally, the boundary conditions on the finite outer boundaries are found to be satisfied by a successive integration technique.

Naidu, A. C. B.↗

An assessment of CFD-based wall heat transfer models in piston engines

The lack of accurate submodels for in-cylinder heat transfer has been identified as a key shortcoming in developing truly predictive, physics-based computational fluid dynamics (CFD) models that can be used to develop combustion systems for advanced high-efficiency, low-emissions engines. Only recently have experimental methods become available that enable accurate near-wall measurements to enhance simulation capability via advancing models. Initial results show crank-angle dependent discrepancies with respect to previously used boundary-layer models of up to 100%. However, available experimental data is quite sparse (only few data points on engine walls) and limited (available measurements are those of heat flux only). Predictive submodels are needed for medium-resolution ("engineering") LES and for unsteady Reynolds-averaged simulations (URANS). Recently, some research groups have performed DNS studies on engine-relevant conditions using simple geometries. These provide very useful data for benchmarking wall heat transfer models under such conditions. Further, a number of new and more sophisticated models have also become available in the literature which account for these engine-like conditions. Some of these have been incorporated while others of a more complex nature, which include solving additional partial differential equations (PDEs) within the thin boundary layer near the wall, are underway. These models will then be tested against the available DNS/experimental data in both SI (spark-ignition) and CI (compression-ignition) engines.

33 ADVANCED PROPULSION SYSTEMS↗

Resonant torque differential magnetometry with high frequency quartz oscillators

Sensitive magnetometry has been a powerful probe for investigating quantum materials. Extreme conditions, such as sub-kelvin cryogenic temperatures and ultrahigh magnetic fields, demand further durability for sensitive magnetometry. However, significant mechanical vibrations and rapid magnetic field changes give enormous challenges to conventional magnetometry. Here, this article presents a possible solution to this problem by developing a new magnetometry technique using high-frequency quartz oscillators. The technique takes advantage of the symmetry and geometry of mechanical vibration configurations of standard commercially available MHz quartz oscillators, and the setup keeps the high quality factor resonance with the sample mounted on the oscillator. We further demonstrate the sensitivity of the technique using bismuth single crystals and a Fe 0.25 TaS 2 ferromagnetic material. Quantum oscillations are observed in the magnetometry response below 1 T, and the detected oscillation frequency is shown to come from the electron pockets of the bismuth.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Rindler fluids from gravitational shockwaves

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Small-scale production of bespoke accelerated aging plutonium alloy

Here, this study demonstrates the 100 g scale manufacture of a plutonium alloy that ages at an accelerated rate. The resulting alloy ages six times faster than typical weapons-grade plutonium due to the addition of 238 Pu. As a major innovation, the process involved using a partial direct oxide reduction technique. This method was achieved by developing a new, complex geometry stirrer using additive manufacturing to reduce the 238Pu oxide and efficiently incorporate it into weapons-grade plutonium metal. The material was then purified by molten salt extraction and electrorefining before being alloyed with gallium. The alloy was then cold-rolled and annealed in a homogenization heat treatment. The resulting disk was characterized by metallography and differential scanning calorimetry, and the impurity content was determined using analytical chemistry techniques. The results show that a homogeneous delta phase plutonium alloy was achieved with expected microstructure and minimal impurities. This study was also successful in changing the plutonium isotopic composition by incorporating additional 238 Pu to accelerate the effects of radiation damage. This enables researchers to study long-term aging phenomena in a reduced time frame, thus avoiding the need for large-scale material production and circumventing the limitations of using naturally aged, archived plutonium.

Aging theory↗

Accelerating FEM-Based Corrosion Predictions Using Machine Learning

Atmospheric corrosion of metallic parts is a widespread materials degradation phenomena that is challenging to predict given its dependence on many factors (e.g. environmental, physiochemical, and part geometry). For materials with long expected service lives, accurately predicting the degree to which corrosion will degrade part performance is especially difficult due to the stochastic nature of corrosion damage spread across years or decades of service. The Finite Element Method (FEM) is a computational technique capable of providing accurate estimates of corrosion rate by numerically solving complex differential Eqs. characterizing this phenomena. Nevertheless, given the iterative nature of FEM and the computational expense required to solve these complex equations, FEM is ill-equipped for an efficient exploration of the design space to identify factors that accelerate or deter corrosion, despite its accuracy. In this work, a machine learning based surrogate model capable of providing accurate predictions of corrosion with significant computational savings is introduced. Specifically, this work leverages AdaBoosted Decision trees to provide an accurate estimate of corrosion current per width given different values of temperature, water layer thickness, molarity of the solution, and the length of the cathode for a galvanic couple of aluminum and stainless steel.

36 MATERIALS SCIENCE↗

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

Baker, A. J.↗

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.

Barth, Timothy J.↗

Automated fiber placement composite manufacturing: The mission at MSFC's Productivity Enhancement Complex

Automated fiber placement is a manufacturing process used for producing complex composite structures. It is a notable leap to the state-of-the-art in technology for automated composite manufacturing. The fiber placement capability was established at the Marshall Space Flight Center's (MSFC) Productivity Enhancement Complex in 1992 in collaboration with Thiokol Corporation to provide materials and processes research and development, and to fabricate components for many of the Center's Programs. The Fiber Placement System (FPX) was developed as a distinct solution to problems inherent to other automated composite manufacturing systems. This equipment provides unique capabilities to build composite parts in complex 3-D shapes with concave and other asymmetrical configurations. Components with complex geometries and localized reinforcements usually require labor intensive efforts resulting in expensive, less reproducible components; the fiber placement system has the features necessary to overcome these conditions. The mechanical systems of the equipment have the motion characteristics of a filament winder and the fiber lay-up attributes of a tape laying machine, with the additional capabilities of differential tow payout speeds, compaction and cut-restart to selectively place the correct number of fibers where the design dictates. This capability will produce a repeatable process resulting in lower cost and improved quality and reliability.

Vickers, John H.↗

Fiber Optic Sensors for Smart Materials and Structures

In this paper we describe recently developed fiber sensors which are capable of monitoring the health of smart-structures. The unobstrusive geometry of these sensors make them an excellent choice for embedding the sensor in composite materials to measure internal states of strain in structures and materials. Some of these sensors have gage lengths that can be tailored from tens of microns to many meters. We will describe various demodulation schemes (Pseudo-Heterodyne, Synthetic-Heterodyne, Homodyne, Differential-Cross Multiplier, and Single Channel Phase-Tracker) to obtain high bandwidth measurements, enabling measurement of static to high frequency impact generated strains with a dynamic response exceeding tens of thousands of microstrains. In addition, we will show that we can tailor the fiber sensor to either measure only strain and reject temperature response or measure only the temperature, or measure both temperature and strain simultaneously. We will also demonstrate the ability to measure multiple strain components inside a host simultaneously using a single fiber sensor embedded in the host using a certain sensor type and transverse strain immunity using another sensor type. Additionally we will show the ability to measure temperature up to 100 C using fiber optic sensors.

Singh, H.↗

Spinning the fuzzy sphere

Here, we construct various exact analytical solutions of the SO(3) BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori. These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the N = 1* field theory with a non-trivial chargedensity. The solutions we construct have a Ζ N symmetry, where N is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in 2N real variables. These equations have a discrete set of solutions for each value of the angular momentum. We study the phase structure of the solutions for various values of N . Also the continuum limit where N → ∞, where the problem reduces to finding periodic solutions of a set of coupled differential equations. We also study the topology change transition from the sphere to the torus.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗

First Temperature Profile of a Stellar Flare Using Differential Chromatic Refraction

We present the first derivation of a stellar flare temperature profile from single-band photometry. Stellar flare DWF 030225.574−545707.45129 was detected in 2015 by the Dark Energy Camera as part of the Deeper, Wider, Faster program. The brightness (Δm g = −6.12) of this flare, combined with the high air mass (1.45 ≲ X ≲ 1.75) and blue filter (DES g, 398–548 nm) in which it was observed, provided ideal conditions to measure the zenithward apparent motion of the source due to differential chromatic refraction (DCR) and, from that, infer the effective temperature of the event. We model the flare’s spectral energy distribution as a blackbody to produce the constraints on flare temperature and geometric properties derived from single-band photometry. We additionally demonstrate how simplistic assumptions on the flaring spectrum, as well as on the evolution of flare geometry, can result in solutions that overestimate the effective temperature. Exploiting DCR enables studying chromatic phenomena with ground-based astrophysical surveys, and stellar flares on M dwarfs are a particularly enticing target for such studies due to their ubiquity across the sky and the heightened color contrast between their red quiescent photospheres and the blue flare emission. Our novel method will enable similar temperature constraints for a large sample of objects in upcoming photometric surveys like the Vera C. Rubin Legacy Survey of Space and Time.

Clarke, Riley W. [University of Delaware, Newark, ↗

A viscous-inviscid interaction algorithm for three-dimensional turbulent subsonic aerodynamic juncture region flow

An order-of magnitude analysis of the subsonic, three-dimensional, steady time-averaged Navier-Stokes equations for semibounded aerodynamic juncture geometries yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three-dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement first-order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. The algorithm is employed to predict the three-dimensional turbulent flowfield in the juncture region formed by two intersecting parabolic arcs at a free-stream Mach-number of 0.08, and Re/C = 600,000/m.

Baker, A. J.↗

Towards Robust Designs Via Multiple-Objective Optimization Methods

Fabricating and operating complex systems involves dealing with uncertainty in the relevant variables. In the case of aircraft, flow conditions are subject to change during operation. Efficiency and engine noise may be different from the expected values because of manufacturing tolerances and normal wear and tear. Engine components may have a shorter life than expected because of manufacturing tolerances. In spite of the important effect of operating- and manufacturing-uncertainty on the performance and expected life of the component or system, traditional aerodynamic shape optimization has focused on obtaining the best design given a set of deterministic flow conditions. Clearly it is important to both maintain near-optimal performance levels at off-design operating conditions, and, ensure that performance does not degrade appreciably when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. The basic ideas involved in robust optimal design will be included in this lecture. The imposition of the additional requirement of robustness results in a multiple-objective optimization problem requiring appropriate solution procedures. Typically the costs associated with multiple-objective optimization are substantial. Therefore efficient multiple-objective optimization procedures are crucial to the rapid deployment of the principles of robust design in industry. Hence the companion set of lecture notes (Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks ) deals with methodology for solving multiple-objective Optimization problems efficiently, reliably and with little user intervention. Applications of the methodologies presented in the companion lecture to robust design will be included here. The evolutionary method (DE) is first used to solve a relatively difficult problem in extended surface heat transfer wherein optimal fin geometries are obtained for different safe operating base temperatures. The objective of maximizing the safe operating base temperature range is in direct conflict with the objective of maximizing fin heat transfer. This problem is a good example of achieving robustness in the context of changing operating conditions. The evolutionary method is then used to design a turbine airfoil; the two objectives being reduced sensitivity of the pressure distribution to small changes in the airfoil shape and the maximization of the trailing edge wedge angle with the consequent increase in airfoil thickness and strength. This is a relevant example of achieving robustness to manufacturing tolerances and wear and tear in the presence of other objectives.

Man Mohan, Rai↗

Interaction between laser radiation and metallic powder of 316L austenitic steel during selective laser melting

Highlights: • Single and multiple tracks on a loose bulk powder substrate were generated. • Understanding of the microstructure development during SLM was achieved. • Single tracks reveal a nearly symmetrical crystallography with elongated grains. • Multiple tracks show elongated grains perpendicular to the build direction. - Abstract: During selective laser melting (SLM), a complex heat state develops that leads to a characteristic crystallography and microstructure of the processed materials. Depending on the geometry of the processed part, most scan tracks of a new layer, so-called hatches, are located above a dense substrate or already solidified structures whereas others are located above loose powder. This is, inter alia, the case for overhanging structures. Attributable to the lower thermal conductivity of loose powder, temperature gradients and cooling rates of the melt pool differentiate in these areas, resulting in a different microstructural build-up. In this work, the microstructure and the crystallographic orientation of grade 316L austenitic stainless steel processed by SLM was investigated to understand the interaction between the laser radiation and the metallic powder during SLM-processing and to investigate the remelting of a track on a previous SLM-densified track. Single and multiple tracks on a loose bulk powder substrate, as well as single tracks on a dense substrate plate, were generated. A parameter study revealed that high energy densities are necessary to build continuous tracks on a loose bulk powder substrate. In addition, the amount of adhered particles, which are sintered on the fully melted and solidified tracks, is determined in comparison to the melted powder because the sintered particles strongly influence the surface roughness. To understand the microstructure development and, particularly, the influence of adjacent hatches during SLM-processing, investigations on the resulting microstructure and crystallographic orientation of a single track and two connected multiple tracks were carried out. During SLM processing of the tracks, the substrate plate and the solidified structures influence the temperature gradient and cooling rate of the melt pool, thus directionally solidified and elongated grains occur. Furthermore, the solidification is characterized by an epitaxial growth due to a distinct thermal gradient between the melt pool and the surrounding elements.

36 MATERIALS SCIENCE↗

The Global and Small-scale Magnetic Fields of Fully Convective, Rapidly Spinning M Dwarf Pair GJ65 A and B

The nearby M dwarf binary GJ65 AB, also known as BL Cet and UV Cet, is a unique benchmark for investigation of dynamo-driven activity of low-mass stars. Magnetic activity of GJ65 was repeatedly assessed by indirect means, such as studies of flares, photometric variability, X-ray, and radio emission. Here, we present a direct analysis of large-scale and local surface magnetic fields in both components. Interpreting high-resolution circular polarization spectra (sensitive to a large-scale field geometry) we uncovered a remarkable difference of the global stellar field topologies. Despite nearly identical masses and rotation rates, the secondary exhibits an axisymmetric, dipolar-like global field with an average strength of 1.3 kG while the primary has a much weaker, more complex, and non-axisymmetric 0.3 kG field. On the other hand, an analysis of the differential Zeeman intensification (sensitive to the total magnetic flux) shows the two stars having similar magnetic fluxes of 5.2 and 6.7 kG for GJ65 A and B, respectively, although there is evidence that the field strength distribution in GJ65 B is shifted toward a higher field strength compared to GJ65 A. Based on these complementary magnetic field diagnostic results, we suggest that the dissimilar radio and X-ray variability of GJ65 A and B is linked to their different global magnetic field topologies. However, this difference appears to be restricted to the upper atmospheric layers but does not encompass the bulk of the stars and has no influence on the fundamental stellar properties.

79 ASTRONOMY AND ASTROPHYSICS↗