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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.

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NASA NTRS1988

Development of a computerized analysis for solid propellant combustion instability with turbulence

A multi-dimensional numerical model has been developed for the unsteady state oscillatory combustion of solid propellants subject to acoustic pressure disturbances. Including the gas phase unsteady effects, the assumption of uniform pressure across the flame zone, which has been conventionally used, is relaxed so that a higher frequency response in the long flame of a double-base propellant can be calculated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition with no condensed phase reaction. In a given geometry, the Galerkin finite element solution shows the strong resonance and damping effect at the lower frequencies, similar to the result of Denison and Baum. Extended studies deal with the higher frequency region where the pressure varies in the flame thickness. The nonlinear system behavior is investigated by carrying out the second order expansion in wave amplitude when the acoustic pressure oscillations are finite in amplitude. Offset in the burning rate shows a negative sign in the whole frequency region considered, and it verifies the experimental results of Price. Finally, the velocity coupling in the two-dimensional model is discussed.

Chung, T. J.↗

NASA NTRS1993

Dynamics of aging magnetic clouds

The dynamics of radially expanding magnetic clouds is rigorously analyzed within the framework of ideal MHD. The cloud is modelled as a cylindrically symmetric magnetic flux rope. In the force balance we include the gas pressure gradient and the Lorentz force. Interaction with the ambient solar wind due to expansion of the magnetic cloud is represented by a drag force proportional to the bulk velocity. We consider the self-similar expansion of a polytrope, and reduce the problem to an ordinary nonlinear differential equation for the evolution function. Analyzing the asymptotic behavior of the evolution function, we formulate theoretical expectations for the long-term behavior of cloud parameters. We focus on the temporal evolution of (1) the magnetic field strength; (2) the twist of the field lines; (3) the asymmetry of the total field profile; and (4) the bulk flow speed. We present data from two magnetic clouds observed at 1 AU and 2 AU, respectively, and find good agreement with theoretical expectations. For a peak magnetic field strength at 1 AU of 25 nT and a polytropic index of 0.5, we find that a magnetic cloud can be distinguished from the background interplanetary field up to a distance of about 5 AU. Taking larger magnetic fields and bigger polytropic indices this distance can double.

Osherovich, V. A.↗

DOE OSTI2026

An Integrated Computational Materials Engineering (ICME) Approach to Design Nonlinear Transition Zones Between Dissimilar Metals

Current approaches to designing graded transition joints (GTJs) between dissimilar metals often rely on linear changes in both composition profiles and thickness of each sublayer. This increases fabrication cost and may not be optimal with respect to residual stress or the formation of undesirable phases. Here, in this study, GTJs between P91 ferritic/martensitic steel and 347H austenitic stainless steel were designed using Integrated Computational Materials Engineering (ICME) principles with nonlinear composition and length profiles. Guided by inputs from classical mechanics and CALPHAD predictions of carbon chemical potential, a novel transition zone consisting of five discrete compositions was proposed, with the thickness of each sublayer varying according to a brachistochrone-inspired distribution. In addition to carbon potential gradients, CALPHAD was used to predict coefficients of thermal expansion, which were incorporated into finite element models to evaluate stress evolution. The proposed nonlinear design resulted in a smoother carbon potential gradient, lower carbon depletion at the P91 interface, and a comparable residual stress under long-term thermal exposure, compared to a conventional linear design using ten sublayers with equal thickness. This work introduces a brachistochrone-inspired distribution for GTJ design, offering a general framework for optimizing graded interfaces between dissimilar metals.

Directed Energy Deposition↗

NASA NTRS1972

Instabilities in uranium plasma and the gas-core nuclear rocket engine

The nonlinear evolution of unstable sound waves in a uranium plasma has been calculated using a multiple time-scale asymptotic expansion scheme. The fluid equations used include the fission power density, radiation diffusion, and the effects of the changing degree of ionization of the uranium atoms. The nonlinear growth of unstable waves is shown to be limited by mode coupling to shorter wavelength waves which are damped by radiation diffusion. This mechanism limits the wave pressure fluctuations to values of order delta P/P approximates 0.00001 in the plasma of a typical gas-core nuclear rocket engine. The instability is thus not expected to present a control problem for this engine.

Tidman, D. A.↗

NASA NTRS1971

Instabilities in uranium plasma.

The nonlinear evolution of unstable sound waves in a uranium plasma has been calculated using a multiple time-scale asymptotic expansion scheme. The fluid equations used include the fission power density, radiation diffusion, and the effects of the changing degree of ionization of the uranium atoms. The nonlinear growth of unstable waves is shown to be limited by mode coupling to shorter wavelength waves which are damped by radiation diffusion. This mechanism limits the wave pressure fluctuations to values of order delta P/P equal to about .00001 in the plasma of a typical gas-core nuclear rocket engine. The instability is thus not expected to present a control problem for this engine.

Tidman, D. A.↗

NASA NTRS1971

The nonlinear instability in flap-lag of rotor blades in forward flight

The nonlinear flap-lag coupled oscillation of torsionally rigid rotor blades in forward flight is examined using a set of consistently derived equations by the asymptotic expansion procedure of multiple time scales. The regions of stability and limit cycle oscillation are presented. The roles of parametric excitation, nonlinear oscillation, and forced excitation played in the response of the blade are determined.

Tong, P.↗

NASA NTRS1996

Mixing and Transition Control Studied

Considerable progress in understanding nonlinear phenomena in both unbounded and wallbounded shear flow transition has been made through the use of a combination of high- Reynolds-number asymptotic and numerical methods. The objective of this continuing work is to fully understand the nonlinear dynamics so that ultimately (1) an effective means of mixing and transition control can be developed and (2) the source terms in the aeroacoustic noise problem can be modeled more accurately. Two important aspects of the work are that (1) the disturbances evolve from strictly linear instability waves on weakly nonparallel mean flows so that the proper upstream conditions are applied in the nonlinear or wave-interaction streamwise region and (2) the asymptotic formulations lead to parabolic problems so that the question of proper out-flow boundary conditions--still a research issue for direct numerical simulations of convectively unstable shear flows--does not arise. Composite expansion techniques are used to obtain solutions that account for both mean-flow-evolution and nonlinear effects. A previously derived theory for the amplitude evolution of a two-dimensional instability wave in an incompressible mixing layer (which is in quantitative agreement with available experimental data for the first nonlinear saturation stage for a plane-jet shear layer, a circular-jet shear layer, and a mixing layer behind a splitter plate) have been extended to include a wave-interaction stage with a three-dimensional subharmonic. The ultimate wave interaction effects can either give rise to explosive growth or an equilibrium solution, both of which are intimately associated with the nonlinear self-interaction of the three dimensional component. The extended theory is being evaluated numerically. In contrast to the mixing-layer situation, earlier comparisons of theoretical predictions based on asymptotic methods and experiments in wall-bounded shear-flow transition have been somewhat lacking in one aspect or another. The current work strongly suggests that the main weakness is the underlying asymptotic representation of the linear "part" of the problem and not the explicit modeling of the nonlinear/wave-interaction effects. Consequently, the long-wave-length/high-Reynolds-number asymptotic limit for the Blasius boundary-layer stability problem was reexamined, and a new dispersion relationship for the instability waves that is uniformly valid for both the upper- and lower branch regions to the required order of approximation was obtained. A comparison with numerical results, obtained by solving the Orr-Sommerfeld stability problem, shows that the asymptotic formula provides surprisingly good results, even for values of the frequency parameter usually encountered in experimental investigations. This is particularly evident in the dynamically important upper-branch region, where much of the nonlinear interactions in transition experiments are believed to take place. The result is important in that it can be used to greatly improve the accuracy of weakly nonlinear critical-layer-based theories, and a consistent nonlinear theory is currently under evaluation.

Source record↗

NASA NTRS1980

On the pressure field of nonlinear standing water waves

The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.

Schwartz, L. W.↗

NASA NTRS1998

Complete Galilean-Invariant Lattice BGK Models for the Navier-Stokes Equation

Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (theta = 3) and two dimensions (theta = 1) for the Navier-Stokes equation have been obtained.

Qian, Yue-Hong↗

NASA NTRS1998

The Development of Kolmogoroff-Like Power Spectra in the Expanding Solar Wind

Power spectra of the solar wind fluctuations consistently exhibit a -5/3 power-law slope consistent with the idea that the medium is undergoing a turbulent cascade as seen in ordinary fluids. This is surprising both because the radial streams and the magnetic field threading the plasma will induce anisotropies and because the expansion of the wind will tend to lead to the suppression of nonlinear cascades. These conditions violate the assumptions used by Kolmogoroff to derive the -5/3 law. We have studied this issue using a compressible IMHD code in spherical coordinates and have shown that a -5/3 spectrum results from a broad-band flat-spectrum input condition that is sheared and distorted by a current sheet as the wind expands. We determine spectra from time series taken at selected points in the domain as is done with observational spacecraft data. The spectra are very like those we have seen in nonexpanding runs and exhibit evolution and compressive characteristics very similar to those seen in observations. We will report on these results in addition to a new set of runs intended to constrain the necessary and sufficient conditions for the spectra to have this form. The simulation also allows us to examine the anisotropy for the spectra to attempt to determine why the result of an isotropic magnetofluid is obtained in a highly anisotropic situation.

Goldstein, M. L.↗

NASA NTRS1989

An Entropy-Based Approach to Nonlinear Stability

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Merriam, Marshal L.↗

NASA NTRS1990

Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations

A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.

Johnson, Forrester T.↗

NASA NTRS1977

Effect of chordwise forces and deformations and deformations due to steady lift on wing flutter

This investigation explores the effects of chordwise forces and deformations and steady-state deformation due to lift on the static and dynamic aeroelastic stability of a uniform cantilever wing. Results of this analysis are believed to have practical applications for high-performance sailplanes and certain RPV's. The airfoil cross section is assumed to be symmetric and camber bending is neglected. Motions in vertical bending, fore-and-aft bending, and torsion are considered. A differential equation model is developed, which included the nonlinear elastic bending-torsion coupling that accompanies even moderate deflections. A linearized expansion in small time-dependent deflections is made about a steady flight condition. The stability determinant of the linearized system then contains coefficients that depend on steady displacements. Loads derived from two-dimensional incompressible aerodynamic theory are used to obtain the majority of the results, but cases using three-dimensional subsonic compressible theory are also studied. The stability analysis is carried out in terms of the dynamically uncoupled natural modes of vibration of the uniform cantilever.

Boyd, W. N.↗

NASA NTRS1982

Anharmonic properties of solids from measurements of the stress acoustic constant

The equations of elastic motion and their solutions are generalized in order to include nonzero homogeneous initial stresses and redefine the stress acoustic constants to include the effect of initial stress. In deriving the relationship between the stress acoustic constants and the strain-generalized Gruneisen parameters, implications in material anharmonicity and nonlinear thermoelasticity are discovered. It is found that the linear change in velocity obtained from these measurements is a nonlinear process resulting from anharmonicity in the interatomic potential. In addition, the thermal expansion coefficient can also be expressed in terms of linear combinations.

Cantrell, J. H., Jr.↗

NASA NTRS1992

Improvements to the missile aerodynamic prediction code DEMON3

The computer program DEMON3 was developed for the aerodynamic analysis of nonconventional supersonic configurations comprising a body with noncircular cross section and up to two wing or fin sections. Within a wing or fin section, the lifting surfaces may be cruciform, triform, planar, or low profile layouts; the planforms of the lifting surfaces allow for breaks in sweep. The body and fin sections are modeled by triplet and constant u-velocity panels, respectively, accounting for mutual body-fin interference. Fin thickness effects are included for the use of supersonic planar source panels. One of the unique features of DEMON3 is the modeling of high angle of attack vortical effects associated with the lifting surfaces and the body. In addition, shock expansion and Newtonian pressure calculation methods can be optionally engaged. These two dimensional nonlinear methods are augmented by aerodynamic interference determined from the linear panel methods. Depending on the geometric details of the body, the DEMON3 program can be used to analyze nonconventional configurations at angles of attack up to 25 degrees for Mach numbers from 1.1 to 6. Calculative results and comparisons with experimental data demonstrate the capabilities of DEMON3. Limitations and deficiencies are listed.

Dillenius, Marnix F. E.↗

NASA NTRS1999

A Viscoelastic Hybrid Shell Finite Element

An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

Johnson, Arthur↗

NASA NTRSDate not supplied

Determining Aircraft Moments of Inertia from Flight Test Data

Flight test maneuver design and dynamic modeling techniques were developed for determining aircraft moments of inertia from flight test data. Full nonlinear rigid-body rotational equations of motion were used in the analysis, with aerodynamic moment dependencies modeled by linear expansions in the aircraft states and controls. Aerodynamic parameters were estimated simultaneously with inertia parameters using equation-error modeling applied to flight test data from maneuvers designed specifically for this problem. The approach was demonstrated using a nonlinear F-16 simulation, then applied to a remotely-piloted subscale aircraft flight test. Errors in the aircraft moment of inertia parameters determined from simulated F-16 flight test maneuver data were less than 6 percent compared to the true values in the simulation. Flight test results for the subscale aircraft were within 6 percent of ground-test values obtained using the same aircraft.

moments of inertia↗

NASA NTRSDate not supplied

Determining Aircraft Moments of Inertia from Flight Test Data

Flight test maneuver design and dynamic modeling techniques were developed for determining aircraft moments of inertia from flight test data. Full nonlinear rigid-body rotational equations of motion were used in the analysis, with aerodynamic moment dependencies modeled by linear expansions in the aircraft states and controls. Aerodynamic parameters were estimated simultaneously with inertia parameters using equation-error modeling applied to flight test data from maneuvers designed specifically for this problem. The approach was demonstrated using a nonlinear F 16 simulation, then applied to a remotely piloted subscale aircraft flight test. Errors in the aircraft moment of inertia parameters determined from simulated F-16 flight test maneuver data were less than 6 percent compared to the true values in the simulation. Flight test results for the subscale aircraft were within 6 percent of ground-test values obtained using the same aircraft.

Aircraft Moments of Inertia↗