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NASA NTRS1975

A method for the dynamic and thermal stress analysis of space shuttle surface insulation

The thermal protection system of the space shuttle consists of thousands of separate insulation tiles bonded to the orbiter's surface through a soft strain-isolation layer. The individual tiles are relatively thick and possess nonuniform properties. Therefore, each is idealized by finite-element assemblages containing up to 2500 degrees of freedom. Since the tiles affixed to a given structural panel will, in general, interact with one another, application of the standard direct-stiffness method would require equation systems involving excessive numbers of unknowns. This paper presents a method which overcomes this problem through an efficient iterative procedure which requires treatment of only a single tile at any given time. Results of associated static, dynamic, and thermal stress analyses and sufficient conditions for convergence of the iterative solution method are given.

Ojalvo, I. U.↗

NASA NTRS1987

Analysis of structures with rotating, flexible substructures

A new methodology has been developed for the dynamic analysis of flexible structures, parts of which may be experiencing discrete motion relative to other parts. This methodology provides the capability of representing the continuum deformations typically treated using finite element methods. In addition, it provides the capability of representing the discrete motion at joints traditionally available with multibody methods. After decomposing the structure into substructures and associating a frame of reference with each substructure, the equations of motion for each substructure can be written explicitly including contributions due to the frame of reference generalized coordinates. By expanding the set of constraints to include constraints that eliminate the redundancy introduced by the frame generalized coordinates, the equations of motion become amenable to solution. The first digital computer program using this methodology, the General Rotorcraft Aeromechanical Stability Program (GRASP), was introduced in 1986. Although GRASP is limited to applications involving steady-state rotation, extension to arbitrary motions (including spin-up) can be accomplished by the selective retention of nonlinear terms in this formulation.

Hopkins, A. Stewart↗

NASA NTRS1989

A finite element approach for large motion dynamic analysis of multibody structures in space

A three-dimensional finite element formulation for modeling the transient dynamics of constrained multibody space sructures with truss-like configurations is presented. Convected coordinate systems are used to define rigid-body motion of individual elements in the system. These systems are located at one end of each element and are oriented such that one axis passes through the other end of the element. Deformation of each element, relative to its convected coordinate system, is defined by cubic flexural shape functions as used in finite element methods of structural analysis. The formulation is oriented toward joint dominated structures and places the generalized coordinates at the joint. A transformation matrix is derived to integrate joint degree-of-freedom into the equations of motion of the element. Based on the derivation, a general-purpose code LATDYN (Large Angle Transient DYNamics) was developed. Two examples are presented to illustrate the application of the code. For the spin-up of a flexible beam, results are compared with existing solutions available in the literature. For the deployment of one bay of a deployable space truss (the Minimast), results are verified by the geometric knowledge of the system and converged solution of a successively refined model.

Chang, Che-Wei↗

NASA NTRS1983

Energetics and the resistive tearing mode - Effects of Joule heating and radiation

The contribution of energy flux to the dynamics of magnetic field reconnection is analytically studied in order to determine the influence of Joule heating and radiation on the linear development of the tearing instability in slab geometry. A temperature-dependent Coulomb-like resistivity is used to provide the coupling between the dynamics and the energy equation. Analytical expressions are derived for the growth rates utilizing constant-psi and long-wavelength approximations. The solutions indicate the occurrence of several modes in addition to the usual tearing mode, several of which have relatively slow, complex growth rates. At large values of the magnetic Reynolds number, there are at least two modes with purely exponential growth when the radiative loss decreases with increasing temperature. If the radiation is neglected, the Joule heating alone also results in two modes with real, positive growth at large S. Below a particular value of S, all the modes are generally stabilized.

Steinolfson, R. S.↗

NASA NTRS1985

The Scaling of Coronal Models from One Star to Another

The requirements that must be met in order that stationary numerical corona models can be scaled from one star to another are discussed. A corona model is a solution of the conservation equations for mass, momentum, and energy, subject to appropriate boundary conditions, and of the equation of state. In general, the mass M and radius R of the star enter these equations and boundary conditions as free parameters. A given solution can be scaled to other stars only if all equations can be rewritten in such a form that M and R do no longer appear explicitly as free parameters, but only implicitly as scaling factors of the variables. An adequate means to find these scaling factors is a homologous transformation: one multiplies all variables and parameters by separate constants (i.e., scaling factors) and requires that the equations and boundary conditions remain valid. This leads to a set of nonlinear relations between the transformation constants. Only if in this set the two constants associated with M and R can be chosen independently, can a given numerical corona model be scaled to arbitrary stars.

Hammer, R.↗

NASA NTRS1985

Whirl and whip: Rotor/bearing stability problems

A mathematical model of a symmetric rotor supported by one rigid and one fluid lubricated bearing is proposed. The rotor model is represented by generalized (modal) parameters of its first bending mode. The rotational character of the bearing fluid force is taken into account. The model yields synchronous vibrations due to rotor unbalance as a particular solution of the equations of motion, rotor/bearing system natural frequencies and corresponding self-excited vibrations known as oil whirl and oil whip. The stability analysis yields rotative speed threshold of stability. The model also gives the evaluation of stability of the rotor synchronous vibrations. In the first balance resonance speed region two more thresholds of stability are yielded. The width of this stability region is directly related to the amount of rotor unbalance. The results of the analysis based on this model stand with very good agreement with field observations of rotor dynamic behavior and the experimental results.

Muszynska, A.↗

NASA NTRS1991

Plasma expansion characteristics of ionized clouds in the ionosphere - Macroscopic formulation

A macroscopic plasma expansion model, based on a numerical solution of the type-dependent nonlinear coupled continuity and momentum equations for background O(+) ions and several released ion species, was used to examine plasma expansion characteristics of ionized clouds in the ionosphere. Information is obtained on Ba(+), Li(+), and Ba(+) - Li(+) clouds; different cloud sizes (Gaussian half widths of 0.1, 0.5, and 1 km); cloud/background ion density ratios covering two orders of magnitude; electron/ion temperature ratios of 1, 5, and 10; and several cloud-background relative velocities along B (0, 1, 2, 4, 6, and 8 km/sec). The macroscopic expansion features obtained were found to be in general agreement with those obtained from the small-scale numerical simulations.

Schunk, R. W.↗

NASA NTRS1991

Hybrid accretion disks in active galactic nuclei. I - Structure and spectra

A unified treatment is presented of the two distinct states of vertically thin AGN accretion disks: a cool (about 10 to the 6th K) optically thick solution, and a hot (about 10 to the 9th K) optically thin solution. A generalized formalism and a new radiative cooling equation valid in both regimes are introduced. A new luminosity limit is found at which the hot and cool alpha solutions merge into a single solution of intermediate optical depth. Analytic solutions for the disk structure are given, and output spectra are computed numerically. This is used to demonstrate the prospect of fitting AGN broadband spectra containing both the UV bump as well as the hard X-ray and gamma-ray tail, using a single accretion disk model. Such models are found to make definite predictions about the observed spectrum, such as the relation between the hard X-ray spectral index, the UV-to-X-ray luminosity ratio, and a feature of about 1 MeV.

Wandel, Amri↗

NASA NTRS1950

The solution of the laminar-boundary-layer equation for the flat plate for velocity and temperature fields for variable physical properties and for the diffusion field at high concentration

In connection with Pohlhausen's solution for the temperature field on the flat plate, a series of formulas were indicated by means of which the velocity and temperature field for variable physical characteristics can be computed by an integral equation and an iteration method based on it. With it, the following cases were solved: On the assumption that the viscosity simply varies with the temperature while the other fluid properties remain constant, the velocity and temperature field on the heated and cooled plate, respectively, was computed at the Prandtl numbers 12.5 and 100 (viscous fluids). A closer study of these two cases resulted in general relations: The calculations for a gas of Pr number 0.7 (air) were conducted on the assumption that all fluid properties vary with the temperature, and the velocities are low enough for the heat of friction to be discounted. The result was a thickening of the boundary layers, but no appreciable modification in shearing stress or heat-transfer coefficient.

BOUNDARY LAYER, LAMINAR - PLATES, FLAT↗

NASA NTRS1982

Jacchia-Lineberry upper atmosphere density model

A series of increasingly accurate models which are a careful blend of empirical and theoretical formulae were developed. The exospheric temperature is assumed to be a function of: (1) the average and daily variations in the solar flux, (2) the average and three hourly variations in the geomagnetic index, (3) the angle between the position vector and the axis of the unsymmetric atmospheric bulge, and (4) the angle between the position vector and the geomagnetic pole. The exospheric temperature is related to the density by the solution of the diffusion equilibrium equations for the different constituents of the atmosphere as a function of altitude. Other variations are modeled directly as changes in the density. They are: (1) changes due to the semiannual effect, and (2) changes due to the seasonal latitudinal effect. The causes for these variations are not exactly known but may be modeled sufficiently by empirical formulae. The Jacchia model is assumed to be valid over the altitude range of 90 to 2500 km. The residuals between the observed density from satellite drag observations and the computed densities show the mean relative error to be generally less than 10 percent with occasional peak errors near 50 percent.

Mueller, A. C.↗

NASA NTRS1986

Satellite attitude motion models for capture and retrieval investigations

The primary purpose of this research is to provide mathematical models which may be used in the investigation of various aspects of the remote capture and retrieval of uncontrolled satellites. Emphasis has been placed on analytical models; however, to verify analytical solutions, numerical integration must be used. Also, for satellites of certain types, numerical integration may be the only practical or perhaps the only possible method of solution. First, to provide a basis for analytical and numerical work, uncontrolled satellites were categorized using criteria based on: (1) orbital motions, (2) external angular momenta, (3) internal angular momenta, (4) physical characteristics, and (5) the stability of their equilibrium states. Several analytical solutions for the attitude motions of satellite models were compiled, checked, corrected in some minor respects and their short-term prediction capabilities were investigated. Single-rigid-body, dual-spin and multi-rotor configurations are treated. To verify the analytical models and to see how the true motion of a satellite which is acted upon by environmental torques differs from its corresponding torque-free motion, a numerical simulation code was developed. This code contains a relatively general satellite model and models for gravity-gradient and aerodynamic torques. The spacecraft physical model for the code and the equations of motion are given. The two environmental torque models are described.

Cochran, John E., Jr.↗

NASA NTRS1988

Numerical Simulation of Subsonic and Transonic Propeller Flow

The numerical simulation of 3-D transonic flow about a system of propeller blades is investigated. In particular, it is shown that the use of helical coordinates significantly simplifies the form of the governing equation when the propeller system is assumed to be surrounded by an irrotational flow field of an inviscid fluid. The unsteady small disturbance equation, valid for lightly loaded blades and expressed in helical coordinates, is derived from the general blade-fixed potential equation, given for an arbitrary coordinate system. The use of a coordinate system which inherently adapts to the mean flow results in a disturbance equation requiring relatively few terms to accurately model the physics of the flow. Furthermore, the helical coordinate system presented here is novel in that it is periodic in the circumferential direction while, simultaneously, maintaining orthogonal properties at the mean blade locations. The periodic characteristic allows a complete cascade of blades to be treated, and the orthogonality property affords straightforward treatment of blade boundary conditions. An ADI numerical scheme is used to compute the solution of the steady flow as an asymptotic limit of an unsteady flow. As an example of the method, solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an 8-bladed cascade. Both high and low advance ratio cases are computed and include a lifting as well as nonlifting cases. The nonlifting solutions obtained are compared to solutions from a Euler code.

Snyder, Aaron↗

NASA NTRS1993

On the stability of nongyrotropic ion populations - A first (analytic and simulation) assessment

The wave and dispersion equations for perturbations propagating parallel to an ambient magnetic field in magnetoplasmas with nongyrotropic ion populations show, in general, the occurrence of coupling between the parallel (left- and right-hand circularly polarized electromagnetic and longitudinal electrostatic) eigenmodes of the associated gyrotropic medium. These interactions provide a means to driving linearly one mode with free-energy sources of other modes in homogeneous media. Different types of nongyrotropy bring about distinct classes of coupling. The stability of a hydrogen magnetoplasma with anisotropic, nongyrotropic protons that only couple the electromagnetic modes to each other is investigated analytically (via solution of the derived dispersion equation) and numerically (via simulation with a hybrid code). Nongyrotropy enhances growth and enlarges the unstable spectral range relative to the corresponding gyrotropic situation. The relevance of the properties of nongyrotropic populations to space plasma environments is also discussed.

Brinca, A. L.↗

NASA NTRS2021

Transition Analysis for the CRM-NLF Wind Tunnel Configuration

This paper presents the results of an ongoing study into the linear stability characteristics of the boundary layer flow over the common research model with natural laminar flow (CRMNLF) aircraft configuration. The flow conditions match selected test conditions from a recent wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. Previous work involving parallel stability computations of a boundary layer flow based on the conical flow approximation has shown that the measured onset of laminar-turbulent transition during the experiments can be correlated with the linear amplification of Tollmien- Schlichting (TS) and stationary crossflow (CF) instabilities in the swept wing boundary layer. Here, we examine the effects of the simplifying approximations in both basic state computation and the stability analysis, with the goal of quantifying the resulting changes in the N-factor correlations. Specifically, the basic states are computed by using full Navier-Stokes equations and the stability analysis is performed by using a nonorthogonal coordinate system that allows a clear distinction between planar TS and CF instabilities. Furthermore, the effects of curvature and nonparallel mean flow have been included in the stability computations based on the parabolized stability equations (PSE). The fully turbulent Reynolds-Averaged-Navier-Stokes (RANS) mean flow solutions show good agreement with the measured wall pressure distribution. Viscous-inviscid interactive effects are observed to be important because the shock fronts along the suction surface are influenced by the imposed transition front. The stability results confirm the previous findings related to TS amplification within the inboard region of the wing and the dominance of stationary CF modes in the outboard region. However, given the close proximity of the measured transition front and the dual shock system within the outer part of the wing, the onset of transition may well be shock limited within the outboard region. In general, the transition criterion based on the dual N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at Re MAC = 15 million and AoA = 1.5, 2 degrees; however, the low values of the correlating N-factors at Re MAC = 17.5 million support the hypothesis that the measured transition at the higher Reynolds number may have been strongly influenced by the merging of turbulent wedges that originate from surface imperfections near the leading edge.

Boundary layer transition↗

NASA NTRS1987

Observation of millimeter-wave oscillations from resonant tunneling diodes and some theoretical considerations of ultimate frequency limits

Recent observations of oscillation frequencies up to 56 GHz in resonant tunneling structures are discussed in relation to calculations by several authors of the ultimate frequency limits of these devices. It is found that calculations relying on the Wentzel-Kramers-Brillouin (WKB) approximation give limits well below the observed oscillation frequencies. Two other techniques for calculating the upper frequency limit were found to give more reasonable results. One method employs the solution of the time-dependent Schroedinger equation obtained by Kundrotas and Dargys (1986); the other uses the energy width of the transmission function for electrons through the double-barrier structure. This last technique is believed to be the most accurate since it is based on general results for the lifetime of any resonant state. It gives frequency limits on the order of 1 THz for two recently fabricated structures. It appears that the primary limitation of the oscillation frequency for double-barrier resonant-tunneling diodes is imposed by intrinsic device circuit parameters and by the transit time of the depletion layer rather than by time delays encountered in the double-barrier region.

Sollner, T. C. L. G.↗

NASA NTRS1974

First order latitude effects in the solar wind

The Weber-Davis model of the solar wind is generalized to include the effects of latitude. The principal assumptions of perfect electrical conductivity, rotational symmetry, a polytropic relation between pressure and density, and a flow aligned magnetic field in a system rotating with the Sun, are retained. The original three dimensional magnetohydrodynamic flow problem is reduced to a two dimensional hydrodynamic flow problem. The solution at 1 Au is most sensitive to a latitudinal dependence in the coronal boundary temperature and least sensitive to a latitudinal dependence in the magnetic field magnitude. A solution obtained for an approximate dipolar variation in the coronal magnetic field magnitude predicts that the latitudinal flow is initially toward the equator due to magnetic channeling; however, this effect is rapidly overcome and the latitudinal flow at 1 Au is toward the pole and not significantly different from the solution for constant boundary conditions.

Winge, C. R., Jr.↗

NASA NTRS1986

Fugacity and concentration gradients in a gravity field

Equations are reviewed which show that at equilibrium fugacity and concentration gradients can exist in gravitational fields. At equilibrium, the logarithm of the ratio of the fugacities of a species at two different locations in a gravitational field is proportional to the difference in the heights of the two locations and the molecular weight of the species. An analogous relation holds for the concentration ratios in a multicomponent system. The ratio is calculated for a variety of examples. The kinetics for the general process are derived, and the time required to approach equilibrium is calculated for several systems. The following special topics are discussed: ionic solutions, polymers, multiphase systems, hydrostatic pressure, osmotic pressure, and solubility gradients in a gravity field.

May, C. E.↗

NASA NTRSDate not supplied

Improvements in Iterative Convergence of FUN3D Solutions

This paper presents a hierarchical adaptive nonlinear iteration method (HANIM) implemented in the NASA computational fluid dynamics code, FUN3D, to improve robustness and computational efficiency. In contrast to the legacy FUN3D iterative solver that relies on an approximate Jacobian, a simple multicolor Gauss-Seidel point-implicit iteration scheme, and linear Courant-Friedrichs-Lewy number (CFL) ramping, HANIM is based upon a hierarchy of modules including preconditioner, generalized conjugate residual, realizability check, nonlinear control, and CFL adaption modules. HANIM performance is systematically compared with the performance of the legacy solver of FUN3D and a baseline solver based on a preconditioner alone. Iterative solutions are compared for three benchmark cases: a subsonic separated flow around a hemisphere cylinder, a supersonic flow through a long duct, and a subsonic flow over the NASA wing-fuselage juncture model. Two Reynolds-averaged Navier-Stokes turbulence models are used in these computations, namely, the negative variant of the linear one-equation Spalart-Allmaras model and its nonlinear extension based on quadratic constitutive relations.

CFD↗