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At least 325 records · Page 18

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NASA NTRS1985

A theory for the core of a three-dimensional leading-edge vortex

A theory is presented for the flow in the core of a separation-induced leading-edge vortex. The theory is based on matching inner and outer representations of the vortex. The inner representation models continuously distributed vorticity and includes an asymptotic viscous subcore. The outer representation models concentrated spiral sheets of vorticity and is fully three dimensional. A parameter is identified which closely tracks the vortex breakdown stability boundary for delta, arrow, and diamond wings.

Luckring, J. M.↗

NASA NTRS1986

A theory for the core flow of leading-edge vortices

Separation-induced leading-edge vortices can dominate the flow about slender wings at moderate to high angles of attack, often with favorable aerodynamic effects. However, at the high angles of attack which are desirable for takeoff and landing as well as subsonic-transonic maneuver the vortices can breakdown or burst in the vicinity of the aircraft causing many adverse effects; these include lift loss, pitchup, and buffet. The flow in the core of leading-edge vortices is generally affiliated with the vortex breakdown phenomenon. A theory is presented for the flow in the core of separation-induced, leading-edge vortices at practical Reynolds numbers. The theory is based on matching inner and outer representations of the vortex. The inner representation models continuously distributed vorticity and includes an asymptotic viscous subcore. The outer representation models concentrated spiral sheets of vorticity and is fully three dimensional. A parameter is identified which closely tracks the vortex breakdown stability boundary for delta, arrow, and diamond wings.

Luckring, James M.↗

NASA NTRS2009

Stability Analysis of Roughness Array Wake in a High-Speed Boundary Layer

Computations are performed to examine the effects of both an isolated and spanwise periodic array of trip elements on a high-speed laminar boundary layer, so as to identify the potential physical mechanisms underlying an earlier transition to turbulence as a result of the trip(s). In the context of a 0.333 scale model of the Hyper-X forebody configuration, the time accurate solution for an array of ramp shaped trips asymptotes to a stationary field at large times, indicating the likely absence of a strong absolute instability in the mildly separated flow due to the trips. A prominent feature of the wake flow behind the trip array corresponds to streamwise streaks that are further amplified in passing through the compression corner. Stability analysis of the streaks using a spatial, 2D eigenvalue approach reveals the potential for a strong convective instability that might explain the earlier onset of turbulence within the array wake. The dominant modes of streak instability are primarily sustained by the spanwise gradients associated with the streaks and lead to integrated logarithmic amplification factors (N factors) approaching 7 over the first ramp of the scaled Hyper-X forebody, and substantially higher over the second ramp. Additional computations are presented to shed further light on the effects of both trip geometry and the presence of a compression corner on the evolution of the streaks.

Choudhari, Meelan↗

NASA NTRS1987

Adaptive proximate time optimal servomechanisms: Discrete time case

Following a review of the continuous time proximate time-optimal servomechanism (PTOS), a discrete-time PTOS is developed, along with conditions for its stability. An algorithm is proposed for adapting PTOS when the plant parameters are not known yielding APTOS (adaptive PTOS). Under ideal conditions APTOs is shown to be uniformly asymptotically stable. Simulation results demonstrate the predicted performance, and experimental results validate the practically of APTOS.

Workman, M. L.↗

NASA NTRS1990

Multivariable flight control synthesis and literal robustness analysis for an aeroelastic vehicle

An integrated flight/aeroelastic control law is developed analytically for a hypothetical large supersonic transport aircraft in which the first aeroelastic mode frequency of the fuselage (6 rad/sec) is near the short-period mode (2 rad/sec). The approach employed is based on a linear-quadratic-regulator (LQR) formulation (yielding model-following state-feedback gains), followed by asymptotic loop-transfer recovery of LQR robustness (to produce an output-feedback control law). The derivation is outlined, and numerical results comparing the performance and multivariate stability robustness of the present controller with those of a classical controller are presented in graphs. The two controllers are shown to have similar characteristics, even with respect to the sources of limitations on robustness.

Schmidt, David K.↗

NASA NTRS1995

On the Dynamics of Implicit Linear Multistep Methods

Some new guidelines on the usage of implicit linear multistep methods (LMMs) as time-dependent approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) are explored. The commonly used implicit LMMs in CFD belong to the class of superstable time discretizations. It can be shown that the nonlinear asymptotic behavior in terms of bifurcation diagrams and basins of attractions of these schemes can provide an improved range of initial data and time step over the linearized stability limit.

Yee, H. C.↗

NASA NTRS1987

Adaptive proximate time-optimal servomechanisms - Continuous time case

A Proximate Time-Optimal Servo (PTOS) is developed, along with conditions for its stability. An algorithm is proposed for adapting the PTOS (APTOS) to improve performance in the face of uncertain plant parameters. Under ideal conditions APTOS is shown to be uniformly asymptotically stable. Simulation results demonstrate the predicted performance.

Workman, M. L.↗

DOE OSTI2020

Asymptotic solutions and convergence studies of the resistive inner region equations

A recent publication presents a detailed prescription for constructing global eigenfunctions and complex growth rates for resistive instabilities in axisymmetric toroidal systems, using the method of matched asymptotic expansions. At each singular surface in the plasma, the small-x asymptotic solutions of the ideal MHD outer-region equations are matched to the large-x asymptotic solutions of the resistive inner-region equations, with x being the distance from the singular surface. The success of this method depends upon accurate asymptotic solutions of the resistive inner region equations. Extensive studies have shown that there are not only regimes of excellent agreement with straight-through methods, without asymptotic matching, but also regimes of strong disagreement. As such, in an effort to find the cause of this discrepancy, we present here a different method of constructing asymptotic solutions of the inner region equations and we study the convergence properties of the new and old solutions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1984

Heat and mass transfer in combustion - Fundamental concepts and analytical techniques

Fundamental combustion phenomena and the associated flame structures in laminar gaseous flows are discussed on physical bases within the framework of the three nondimensional parameters of interest to heat and mass transfer in chemically-reacting flows, namely the Damkoehler number, the Lewis number, and the Arrhenius number which is the ratio of the reaction activation energy to the characteristic thermal energy. The model problems selected for illustration are droplet combustion, boundary layer combustion, and the propagation, flammability, and stability of premixed flames. Fundamental concepts discussed include the flame structures for large activation energy reactions, S-curve interpretation of the ignition and extinctin states, reaction-induced local-similarity and non-similarity in boundary layer flows, the origin and removal of the cold boundary difficulty in modeling flame propagation, and effects of flame stretch and preferential diffusion on flame extinction and stability. Analytical techniques introduced include the Shvab-Zeldovich formulation, the local Shvab-Zeldovich formulation, flame-sheet approximation and the associated jump formulation, and large activation energy matched asymptotic analysis. Potentially promising research areas are suggested.

Law, C. K.↗

NASA NTRS1987

On a finite element CFD algorithm for compressible, viscous and turbulent aerodynamic flows

This paper develops and analyses individual construction aspects of an efficient and accurate finite element algorithm for prediction of viscous and turbulent flow fields of impact in aerodynamics. The theoretical construction employs a Taylor weak statement (TWS) for coincident embedding of stability mechanisms within a classic Galerkin finite element formulation of semidiscrete approximation error orthogonalization. A wide variety of the stabilizing mechanisms of independently derived CFD algorithms are contained within the TWS theory. An implicit construction that meets the requirement of efficient convergence to steady state is developed. The theoretical asymptotic error estimates of the TWS finite element algorithm for supersonic and viscous boundary layer flows are verified. Application to a three-dimensional turbulent flow is cited.

Baker, A. J.↗

NASA NTRS2023

Evaluation of Voronoi Meshes for Large Eddy Simulations of High Lift Aerodynamics

Numerical sensitivity to 3 different Voronoi seeding methods is investigated for Large Eddy Simulations (LES). A second order accurate, non-dissipative finite volume discretization is used to systematically investigate the effects of different polyhedral Voronoi mesh types using a sequence of three canonical problems with increasing complexity. First, inviscid isentropic vortex propagation is studied to demonstrate the substantial reduction of errors for rhombic dodecahedron and truncated octahedral cell types over Cartesian hexagonal cells of identical spacing. Furthermore, the reduction of errors induced at cell-size transitions (grid-coarsening interfaces) due to Lloyd smoothing iterations is quantified. It is shown that by utilizing an appropriate viscous flux discretization, a constant coefficient subgrid scale model is sufficient for non-linear stability at the 2:1 cell-size transitions on polyhedral grids, although some further error reduction does occur when smoothing is utilized. Next, forced homogeneous isotropic turbulence at an asymptotically large Reynolds number is studied to demonstrate the non-dissipative character of the inviscid flux discretization, and the non-linear robustness and accuracy offered by the viscous flux discretization using a subgrid scale model for all three Voronoi grid types. Finally,Wall-Modeled Large Eddy Simulations (WMLES) are performed to study the high-lift aerodynamics on the McDonnell Douglas 30P30N multi-element airfoil at two distinct grid levels and for two distinct Voronoi cell types. The formulation is shown to predict the aerodynamic loading with high accuracy at all angles of attack when sufficient resolution is reached, and the hexagonal prism grid topology, while computationally more expensive, has higher effective resolution compared to the Cartesian grid topology with the same spacing.

TTT↗

NASA NTRS2023

Evaluation of Voronoi Meshes for Large Eddy Simulations of High Lift Aerodynamics

Numerical sensitivity to 3 different Voronoi seeding methods is investigated for Large Eddy Simulations (LES). A second order accurate, non-dissipative finite volume discretization is used to systematically investigate the effects of different polyhedral Voronoi mesh types using a sequence of three canonical problems with increasing complexity. First, inviscid isentropic vortex propagation is studied to demonstrate the substantial reduction of errors for rhombic dodecahedron and truncated octahedral cell types over Cartesian hexagonal cells of identical spacing. Furthermore, the reduction of errors induced at cell-size transitions (grid-coarsening interfaces) due to Lloyd smoothing iterations is quantified. It is shown that by utilizing an appropriate viscous flux discretization, a constant coefficient subgrid scale model is sufficient for non-linear stability at the 2:1 cell-size transitions on polyhedral grids, although some further error reduction does occur when smoothing is utilized. Next, forced homogeneous isotropic turbulence at an asymptotically large Reynolds number is studied to demonstrate the non-dissipative character of the inviscid flux discretization, and the non-linear robustness and accuracy offered by the viscous flux discretization using a subgrid scale model for all three Voronoi grid types. Finally, Wall-Modeled Large Eddy Simulations (WMLES) are performed to study the high-lift aerodynamics on the McDonnell Douglas 30P30N multi-element airfoil at two distinct grid levels and for two distinct Voronoi cell types. The formulation is shown to predict the aerodynamic loading with high accuracy at all angles of attack when sufficient resolution is reached, and the hexagonal prism grid topology, while computationally more expensive, has higher effective resolution compared to the Cartesian grid topology with the same spacing.

TTT↗

NASA NTRS1975

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

Smith, L. L.↗

NASA NTRS1987

The fully nonlinear development of Goertler vortices in growing boundary layers

The fully nonlinear development of small wavelength Goertler vortices in a growing boundary layer is investigated using a combination of asymptotic and numerical methods. The starting point for the analysis is the weakly nonlinear theory of Hall (1982b) who discussed the initial development of small amplitude vortices in a neighborhood of the location where they first become linearly unstable. That development is unusual in the context of nonlinear stability theory in that it is not described by the Stuart-Watson approach. In fact the development is governed by a pair of coupled nonlinear partial differential evolution equations for the vortex flow and the mean flow correction. Here the further development of this interaction is considered for vortices so large that the mean flow correction driven by them is as large as the basic state. Surprisingly it is found that such a nonlinear interaction can still be described by asymptotic means. It is shown that the vortices spread out across the boundary layer and effectively drive the boundary layer. In fact the system obtained by writing down the equations for the fundamental component of the vortex generate a differential equation for the basic state. Thus the mean flow adjusts so as to make these large amplitude vortices locally neutral. Moreover in the region where the vortices exist the mean flow has a square-root profile and the vortex velocity field can be written down in closed form. The upper and lower boundaries of the region of vortex activity are determined by a free-boundary problem involving the boundary layer equations. In general it is found that this region ultimately includes almost all of the original boundary layer and much of the free-stream. In this situation the mean flow has essentially no relationship to the flow which exists in the absence of the vortices.

Hall, Philip↗

NASA NTRS1989

A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

Chulya, A.↗

NASA NTRS1991

A new uniformly valid asymptotic integration algorithm for elasto-plastic creep and unified viscoplastic theories including continuum damage

Chulya, Abhisak↗

DOE OSTI2021

Simultaneous Decomposition and Dewetting of Nanoscale Alloys: A Comparison of Experiment and Theory

In this work, we consider the coupled process of phase separation and dewetting of metal alloys of nanoscale thickness deposited on solid substrates. The experiments involve applying nanosecond laser pulses that melt the Ag40Ni60 alloy films in two setups: either on thin supporting membranes or on bulk substrates. These two setups allow for extracting both temporal and spatial scales on which the considered processes occur. The theoretical model involves a longwave version of the Cahn–Hilliard formulation used to describe spinodal decomposition, coupled with an asymptotically consistent longwave-based description of dewetting that occurs due to destabilizing interactions between the alloy and the substrate, modeled using the disjoining pressure approach. Careful modeling, combined with linear stability analysis and fully nonlinear simulations, leads to results consistent with the experiments. In particular, we find that the two instability mechanisms occur concurrently, with the phase separation occurring faster and on shorter temporal scales. The modeling results show a strong influence of the temperature dependence of relevant material properties, implying that such a dependence is crucial for the understanding of the experimental findings. The agreement between theory and experiment suggests the utility of the proposed theoretical approach in helping to develop further experiments directed toward formation of metallic alloy nanoparticles of desired properties.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Stabilizer Rank Strong Simulation v.0.1

This software improves upon the Clifford gate+T gate magic state strong simulation algorithm by Brayvi and Gosset. It provides a better stabilizer state decomposition that scales as 2^{0.463t}, an improvement over 2^{0.468t}, for t T gate magic states. This code enables simulations of universal quantum computing with that asymptotic scaling cost. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525 SAND2020-14293 O

SciDAC↗