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At least 181 records · Page 10

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DOE OSTI2016

Cohesive phase-field fracture and a PDE constrained optimization approach to fracture inverse problems

In recent years there has been a proliferation of modeling techniques for forward predictions of crack propagation in brittle materials, including: phase-field/gradient damage models, peridynamics, cohesive-zone models, and G/XFEM enrichment techniques. However, progress on the corresponding inverse problems has been relatively lacking. Taking advantage of key features of existing modeling approaches, we propose a parabolic regularization of Barenblatt cohesive models which borrows extensively from previous phase-field and gradient damage formulations. An efficient explicit time integration strategy for this type of nonlocal fracture model is then proposed and justified. In addition, we present a C++ computational framework for computing in- put parameter sensitivities efficiently for explicit dynamic problems using the adjoint method. This capability allows for solving inverse problems involving crack propagation to answer interesting engineering questions such as: 1) what is the optimal design topology and material placement for a heterogeneous structure to maximize fracture resistance, 2) what loads must have been applied to a structure for it to have failed in an observed way, 3) what are the existing cracks in a structure given various experimental observations, etc. In this work, we focus on the first of these engineering questions and demonstrate a capability to automatically and efficiently compute optimal designs intended to minimize crack propagation in structures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗

DOE OSTI2017

Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

Here, we study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interface is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.

42 ENGINEERING↗

NASA NTRS2012

Low-Gain Circularly Polarized Antenna with Torus-Shaped Pattern

The Juno mission to Jupiter requires an antenna with a torus-shaped antenna pattern with approximately 6 dBic gain and circular polarization over the Deep Space Network (DSN) 7-GHz transmit frequency and the 8-GHz receive frequency. Given the large distances that accumulate en-route to Jupiter and the limited power afforded by the solar-powered vehicle, this toroidal low-gain antenna requires as much gain as possible while maintaining a beam width that could facilitate a +/-10deg edge of coverage. The natural antenna that produces a toroidal antenna pattern is the dipole, but the limited approx. = 2.2 dB peak gain would be insufficient. Here a shaped variation of the standard bicone antenna is proposed that could achieve the required gains and bandwidths while maintaining a size that was not excessive. The final geometry that was settled on consisted of a corrugated, shaped bicone, which is fed by a WR112 waveguide-to-coaxial- waveguide transition. This toroidal low-gain antenna (TLGA) geometry produced the requisite gain, moderate sidelobes, and the torus-shaped antenna pattern while maintaining a very good match over the entire required frequency range. Its "horn" geometry is also low-loss and capable of handling higher powers with large margins against multipactor breakdown. The final requirement for the antenna was to link with the DSN with circular polarization. A four-layer meander-line array polarizer was implemented; an approach that was fairly well suited to the TLGA geometry. The principal development of this work was to adapt the standard linear bicone such that its aperture could be increased in order to increase the available gain of the antenna. As one increases the aperture of a standard bicone, the phase variation across the aperture begins to increase, so the larger the aperture becomes, the greater the phase variation. In order to maximize the gain from any aperture antenna, the phase should be kept as uniform as possible. Thus, as the standard bicone fs aperture increases, the gain increase becomes less until one reaches a point of diminishing returns. In order to overcome this problem, a shaped aperture is used. Rather than the standard linear bicone, a parabolic bicone was found to reduce the amount of phase variation as the aperture increases. In fact, the phase variation is half of the standard linear bicone, which leads to higher gain with smaller aperture sizes. The antenna pattern radiated from this parabolic-shaped bicone antenna has fairly high side lobes. The Juno project requested that these sidelobes be minimized. This was accomplished by adding corrugations to the parabolic shape. This corrugated-shaped bicone antenna had reasonably low sidelobes, and the appropriate gain and beamwidth to meet project requirements.

Amaro, Luis R.↗

NASA NTRS1995

A Fundamental Study of Smoldering with Emphasis on Experimental Design for Zero-G

A research program to study smoldering combustion with emphasis on the design of an experiment to be conducted in the space shuttle was conducted at the Department of Mechanical Engineering, University of California, Berkeley. The motivation of the research is the interest in smoldering both as a fundamental combustion problem and as a serious fire risk. Research conducted included theoretical and experimental studies that have brought considerable new information about smolder combustion, the effect that buoyancy has on the process, and specific information for the design of a space experiment. Experiments were conducted at normal gravity, in opposed and forward mode of propagation and in the upward and downward direction to determine the effect and range of influence of gravity on smolder. Experiments were also conducted in microgravity, in a drop tower and in parabolic aircraft flights, where the brief microgravity periods were used to analyze transient aspects of the problem. Significant progress was made on the study of one-dimensional smolder, particularly in the opposed-flow configuration. These studies provided enough information to design a small-scale space-based experiment that was successfully conducted in the Spacelab Glovebox in the June 1992 USML-1/STS-50 mission of the Space Shuttle Columbia.

Fernandez-Pello, Carlos↗

NASA NTRS1977

On the problem of constructing a modern, economic radiotelescope complex

Criteria for comparing and planning the technical and economic characteristics of large parabolic reflector antenna systems and other types used in radioastronomy and deep space communications are discussed. The experience gained in making and optimizing a series of highly efficient parabolic antennas in the USSR is reviewed. Several ways are indicated for further improving the complex characteristics of antennas similar to the original TNA-1500 64m radio telescope. The suggestions can be applied in planning the characteristics of radiotelescopes which are now being built, in particular, the TNA-8000 with a diameter of 128 m.

Bogomolov, A. F.↗

NASA NTRS1984

Incompressible Navier-Stokes and parabolized Navier-Stokes formulations and computational techniques

The differential formulations and computational techniques currently used for the incompressible Navier-Stokes (NS) and parabolic Navier-Stokes (PNS) equations are reviewed. In particular, attention is given to problems associated with the choice of difference equations, the method of solution and the choice of algorithm, the coupling of dependent variables and discretized equations, the application of boundary conditions, and grid generation. A new composite velocity NS and PNS formulation in (u,v,p) variables is presented, and the applicability of a 'forward' difference global pressure iteration for the (u,v,p) PNS system is demonstrated.

Rubin, S. G.↗

NASA NTRS1988

Focal region fields of distorted reflectors

The problem of the focal region fields scattered by an arbitrary surface reflector under uniform plane wave illumination is solved. The physical optics (PO) approximation is used to calculate the current induced on the reflector. The surface of the reflector is described by a number of triangular domain-wise 5th degree bivariate polynomials. A 2-dimensional Gaussian quadrature is employed to numerically evaluate the integral expressions of the scattered fields. No Freshnel or Fraunhofer zone approximations are made. The relation of the focal fields problem to surface compensation techniques and other applications are mentioned. Several examples of distorted parabolic reflectors are presented. The computer code developed is included, together with instructions on its usage.

Buris, N. E.↗

NASA NTRS1989

A numerical study of hypersonic propulsion/airframe integration problem

A numerical analysis procedure useful in the propulsion-airframe integration problem has been established. Flow around a generic hypersonic vehicle forebody is solved using Parabolized Navier-Stokes equations and Thin Layer Navier-Stokes equations. Forebody cross sectional geometry corresponds to a two-ellipse configuration. Effect of forebody geometry on the flow structure, especially at the engine inlet location, is analyzed.

Narayan, J. R.↗

NASA NTRS1989

Guidance analysis of the aeroglide plane change maneuver as a turning point problem

The development of guidance approximations for the atmospheric (aeroglide) portion of the minimum fuel, orbital plane change, trajectory optimization problem is described. Asymptotic methods are used to reduce the two point, boundary value, optimization problem to a turning point problem from the bank angle control. The turning point problem solution, which yields an approximate optimal control policy, is given in terms of parabolic cylinder functions, which are tabulated, and integral expressions, which must be numerically computed. Comparisons of the former, over their region of validity, with optimal control solutions show good qualitative agreement. Additional work and analysis is needed to compute the guidance approximation work.

Gracey, Christopher↗

NASA NTRS1993

Stability of mixing layers

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Tam, Christopher↗

NASA NTRS2017

Presentation Annotated

This Report is not the latest word on an old idea but the first word on a new one. The new idea reverses the old one, the axiom that the best primary objective for an astronomical telescope exhibits the least chromatic aberration. That axiomatic distinction goes back to a young Isaac Newton who knew from experiments with prisms and mirrors in the 1660's that magnification with a reflection primary was completely free of the dispersion he saw with refraction. The superiority of reflection primary objectives for eyeball or photographic viewing is now considered obvious. It was this piece of wisdom on achromatic primary objectives that led to the dominance of the parabolic mirror as the means to collect star light. Newton was aware of the problem when he introduced his telescope to the scientific world in 1670.This Report is not the latest word on an old idea but the first word on a new one. The new idea reverses the old one, the axiom that the best primary objective for an astronomical telescope exhibits the least chromatic aberration. That axiomatic distinction goes back to a young Isaac Newton who knew from experiments with prisms and mirrors in the 1660's that magnification with a reflection primary was completely free of the dispersion he saw with refraction. The superiority of reflection primary objectives for eyeball or photographic viewing is now considered obvious. Actually, Newton's design innovation was in a secondary mirror, a plane mirror far more easily fabricated than Gregory's embodiment of 1663 which required two curved mirrors.

Astronomical telescope↗

NASA NTRS1959

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

The analysis of super-circular entry is developed around a new dimensionless parameter which combines certain conditions at the conic perigee altitude with certain characteristics of the vehicle; this parameter conveniently determines either deceleration-limited or heating limited corridor widths for elliptic, parabolic, or hyperbolic approach trajectories. Illustrative calculations of corridor widths and the associated guidance problems are presented for Venus, Earth, Mars, Jupiter, and Titan. Generalized curves are presented for application to various entry conditions.

Chapman, Dean R.↗

DOE OSTI2025

Design Basis Document / Owner’s Technical Specification for Nitrate Salt Systems in CSP Projects (Final Technical Report)

The number of commercial coal, gas, and nuclear projects built over the past 100 years number in the thousands. As such, there is a large database, available to a wide range of commercial engineering contractors, on proven designs. In essence, unsuccessful designs have, through generations of iterations, been identified and then deleted from further consideration. In contrast, the number of commercial parabolic trough projects using nitrate salt for the thermal storage media is perhaps 60. Further, the number of commercial central receiver projects using nitrate salt as the working fluid is on the order of 20, including estimates for China. Given the relative immaturity of salt technology, and commercial pressures to successfully bid new solar projects into a mature electricity market, solar projects often promise more than has been delivered. The Design Basis Document / Owner’s Technical Specification is a first step in the iteration process. The report describes the successful features of commercial projects, outlines a range equipment and system failures in projects that didn’t operate as intended, and provides a draft set of design changes intended to correct the known problems. The product of the study is 3 volumes of technical material; one volume is on parabolic trough technologies; a second is on central receiver technologies, and the third is on potential design changes to parabolic trough and central receiver projects. The 3 volumes, which total some 590 pages, can be found at https://www.solardynllc.com/csp-plant-technologies. One of the principal topics in the report is the use of functional or prescriptive specifications. Functional specifications describe what the equipment needs to do, consistent with the minimum legal requirements of the local jurisdictions. The details of how this is to be accomplished is developed by the engineering contractor. Prescriptive specifications, which are developed by the Owner, prescribe to the engineering contractor how the functional requirements are to be met. This arrangement ensures that the favorable experience from a previous project is repeated. One example is the design code for the hot salt tank in central receiver projects. The closest design basis is API Standard 650 Welded Steel Tanks for Oil Storage. However, the maximum design temperature in API 650 is 260 °C. As such, solar projects have typically adopted a hybrid Code approach, in which allowable material stresses are taken from ASME Section II Materials. Further, since the tanks experience daily changes in temperature and in (static) pressure, and since portions of the tank can operate at stresses beyond the elastic range, the low cycle fatigue life of the tank is conducted using the rules of Section VIII Division 2. However, in a recent study by NREL, the principal damage mechanism was identified as creep rather than fatigue. Further, design stresses permitted under Section VIII Division 2, corresponding to a fatigue life of 30 years, result in projected creep lifetimes of only 2 to 5 years. An alternate design approach, prescribed by the Owner, would be based on Code sections intended for high temperature service in the creep regime. A candidate is Section III Division 5. Granted, this is a nuclear code section, and it’s use would not likely be mandated by local jurisdictions. However, the effects of creep have been deemed to be of sufficient importance that one nuclear project developer, and one central receiver project developer, have stipulated in the tank design specification that the equipment be designed to the requirements of Section III Division 5.

14 SOLAR ENERGY↗

NASA NTRS1983

Interactive phenomena in supersonic jet mixing problems

The interactive phenomena that occur in the plume flowfield produced by a supersonic jet exhausting into a supersonic or subsonic external stream are discussed. A spatial marching parabolized Navier-Stokes approach is used to analyze the coupled viscous/inviscid interactive processes in supersonic flow regions. A 'partially parabolic' spatial marching procedure is used to analyze embedded subsonic regions (viz. the flow behind Mach discs) and the subsonic portion of the plume mixing layer for subsonic external flows. Coupling between the two-regions utilizes viscous-characteristic techniques and appropriate iterative procedures. Applications to a variety of jet mixing problems are presented. The importance of accounting for compressibility effects on the turbulence is demonstrated via comparisons of predictions employing several two-equation turbulence models with detailed laboratory data.

Dash, S. M.↗

NASA NTRS1986

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.↗

NASA NTRS1988

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

Gibson, J. S.↗

DOE OSTI2018

Ray Expansions and Identities for Second Order Equations. Applications to Inverse Problems

We develop a new method for studying inverse problems of mathematical physics by using systems of equations of ray expansion of solutions to parabolic and hyperbolic equations with variable coefficients.

97 MATHEMATICS AND COMPUTING↗