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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 NTRS1986

The effect of beam-driven return current instability on solar hard X-ray bursts

The problem of electrostatic wave generation by a return current driven by a small area electron beam during solar hard X-ray bursts is discussed. The marginal stability method is used to solve numerically the electron and ion heating equations for a prescribed beam current evolution. When ion-acoustic waves are considered, the method appears satisfactory and, following an initial phase of Coulomb resistivity in which T sub e/T sub i rise, predicts a rapid heating of substantial plasma volumes by anomalous ohmic dissipation. This hot plasma emits so much thermal bremsstrahlung that, contrary to previous expectations, the unstable beam-plasma system actually emits more hard X-rays than does the beam in the purely collisional thick target regime relevant to larger injection areas. Inclusion of ion-cyclotron waves results in ion-acoustic wave onset at lower T sub e/T sub i and a marginal stability treatment yields unphysical results.

Cromwell, D.↗

NASA NTRS1986

Heat-flux measurements for the rotor of a full-stage turbine. II - Description of analysis technique and typical time-resolved measurements

An analytical technique for obtaining the time-resolved heat flux of a turbine blade is applied to the case of a TFE 731-2 hp full-stage rotating turbine. In order to obtain the heat flux values from the thin film gage temperature histories, a finite difference procedure is used to solve the heat equation with variable thermal properties. After setting out the data acquisition and analysis procedures, their application is illustrated for three midspan locations on the blade and operation at the design flow function. Results demonstrate that the magnitude of the heat flux fluctuation due to vane-balde interaction is large by comparison to the time-averaged heat flux at all investigated locations; FFT of a portion of the heat flux record illustrates that the dominant frequencies occur at the wake-cutting frequency and its harmonics.

Dunn, M. G.↗

NASA NTRSDate not supplied

Realistic Thermographic Simulation of Impact Damage with Quadrupole Method

Flash thermography has been shown to be an effective method for detection of delaminations in carbon fiber reinforced polymer (CFRP) composite structures. Improved understanding of the limitations of the technique can be obtained by simulating the inspection process. Time domain finite difference and finite element methods are well suited for such simulations but can be computationally intensive. An alternate method is to solve the Laplace transform of the heat equation, then invert the Laplace transform to produce a time domain response. Often this is referred to as the thermal quadrupole method and is well suited for simulating flash thermography. The quadrupole method has been used extensively for simulating one-dimensional heat flow in multilayer systems with contact resistances at the interfaces. It is also applicable for three dimensional configurations, in particular for simulation of changes in thermographic response due to delaminations in composites. This presentation discusses three-dimensional simulations with realistic shapes and contact resistances at the interfaces between layers. The results of these simulations are compared to thermography measurements on composites specimens with impact induced delaminations.

thermography↗

NASA NTRSDate not supplied

Realistic Thermographic Simulation of Impact Damage with Quadrupole Method

Flash thermography has been shown to be an effective method for detection of delaminations in carbon fiber reinforced polymer (CFRP) composite structures. Improved understanding of thelimitations of the technique can be obtained by simulating the inspection process. Time domainfinite difference and finite element methods are well suited for such simulations but can be computationally intensive. An alternate method is to solve the Laplace transform of the heat equation, then invert the Laplace transform to produce a time domain response. Often this is referred to as the thermal quadrupole method and is well suited for simulating flash thermography. The quadrupole method has been used extensively for simulating one-dimensional heat flow in multilayer systems with contact resistances at the interfaces. It is also applicable for three dimensional configurations, in particular for simulation of changes in thermographic response due to delaminations in composites. This presentation discusses three-dimensional simulations with realistic shapes and contact resistances at the interfaces between layers. The results of these simulations are compared to thermography measurements on composites specimens with impact induced delaminations.

Thermography↗

NASA NTRS1992

An Engineering Method for Interactive Inviscid-Boundary Layers in Three-Dimensional Hypersonic Flows

An engineering method has been developed that couples an approximate three dimensional inviscid technique with the axisymmetric analog and a set of approximate convective heating equations. The displacement effect on the boundary layer on the outer inviscid flow is calculated and included as a boundary condition in the inviscid technique. This accounts for the viscous interaction present at lower Reynolds numbers. The method is applied to blunted axisymmetric and three dimensional elliptic cones at angle of attack for the laminar hypersonic flow of a perfect gas. The method is applied to turbulent and equilibrium-air conditions. The present technique predicts surface heating rates, pressures, and shock shapes that compare favorably with experimental (ground-test and flight) data and numerical solutions of the Navier-Stokes and viscous shock-layer equations. In addition, the inclusion of viscous interaction significantly improves results obtained at lower Reynolds numbers. The new technique represents a major improvement over current engineering aerothermal methods with only a modest increase in computational effort.

Riley, Christopher J.↗

NASA NTRS1993

Convection equation modeling: A non-iterative direct matrix solution algorithm for use with SINDA

The determination of the boundary conditions for a component-level analysis, applying discrete finite element and finite difference modeling techniques often requires an analysis of complex coupled phenomenon that cannot be described algebraically. For example, an analysis of the temperature field of a coldplate surface with an integral fluid loop requires a solution to the parabolic heat equation and also requires the boundary conditions that describe the local fluid temperature. However, the local fluid temperature is described by a convection equation that can only be solved with the knowledge of the locally-coupled coldplate temperatures. Generally speaking, it is not computationally efficient, and sometimes, not even possible to perform a direct, coupled phenomenon analysis of the component-level and boundary condition models within a single analysis code. An alternative is to perform a disjoint analysis, but transmit the necessary information between models during the simulation to provide an indirect coupling. For this approach to be effective, the component-level model retains full detail while the boundary condition model is simplified to provide a fast, first-order prediction of the phenomenon in question. Specifically for the present study, the coldplate structure is analyzed with a discrete, numerical model (SINDA) while the fluid loop convection equation is analyzed with a discrete, analytical model (direct matrix solution). This indirect coupling allows a satisfactory prediction of the boundary condition, while not subjugating the overall computational efficiency of the component-level analysis. In the present study a discussion of the complete analysis of the derivation and direct matrix solution algorithm of the convection equation is presented. Discretization is analyzed and discussed to extend of solution accuracy, stability and computation speed. Case studies considering a pulsed and harmonic inlet disturbance to the fluid loop are analyzed to assist in the discussion of numerical dissipation and accuracy. In addition, the issues of code melding or integration with standard class solvers such as SINDA are discussed to advise the user of the potential problems to be encountered.

Schrage, Dean S.↗

NASA NTRS1983

Moving finite elements in 2-D

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

Gelinas, R. J.↗

NASA NTRS1992

Practical aspects of spatially high accurate methods

The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.

Godfrey, Andrew G.↗

NASA NTRS2021

A Study of Layered Structural Configurations as Thermal and Impact Shielding of Lunar Habitats

The focus of this study is the analysis of a proposed multilayer material configuration as lunar habitat shielding so as to assess its ability to resist temperature extremes and impact. In order to resist this environmental hazard, the analysis will compare various configurations of potential shielding layers using both in-situ resource utilization (ISRU) and Earth-based materials. The technology for implementation of in-situ resources in construction is developing, though not yet able to produce a functional lunar habitat. As the lunar infrastructure is developed, ISRU techniques for manufacturing and construction may become more viable. Therefore, both types of materials are considered due to potential for application towards both near-term and long-term commencements of habitat construction. The thermal analysis in this paper utilizes the nonlinear heat equation to produce a depth-dependent temperature gradient from the habitat exterior to the interior that changes continuously with time during the lunar diurnal cycle. Static loading conditions meant to simulate the impact force of a 77.9 g meteorite were used to analyze the ability of a proposed multilayer shielding configuration to resist impact. A thermal stress analysis was performed to observe the effects of heat transfer through the proposed multilayer configuration. The results of this study should be useful in determining the potential for implementation of efficient shielding layers for the initial lunar base.

Layered systems↗

NASA NTRS1971

Two examples in the time optimal control theory of distributed parameter systems.

The behavior of hyperbolic and parabolic partial differential equations is contrasted by studying the point-to-point time-optimal control problem for the equation of heat conduction and the equation of motion of a vibrating string. A maximal principle is obtained for the time-optimal control of the one-dimensional heat equation, and it is proven that time optimal controls are weakly bang-bang. The bang-bang principle is proven to be invalid for hyperbolic equations because of the finite speed of wave propagation. In the case of boundary value control of the vibrating spring, the latter is demonstrated by deriving an explicit formula for the time optimal control.

Quinn, J. P.↗

NASA NTRS1996

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

GREENS FUNCTIONS↗

NASA NTRS1968

Two-fluid model of the solar wind.

Solar wind studied with two fluid model, using proton and electron fluid type heat equations, equation of motion and continuity equation

Hartle, R. E.↗

NASA NTRS1977

Mercury's helium exosphere after Mariner 10's third encounter

From Mariner 10 third encounter UV data, a value of .00045 was calculated as the fraction of the solar wind He++ flux intercepted and captured by Mercury's magnetosphere if the observed He atmosphere is maintained by the solar wind. If an internal source for He prevails, the corresponding upper bound for the global outgassing rate is estimated to be 4.5 x 10 to the 22nd power per sec. A surface temperature distribution was used which satisfies the heat equation over Mercury's entire surface using Mariner 10 determined mean surface thermal characteristics. The means stand off distance of Mercury's magnetopause averaged over Mercury's orbit was also used.

Curtis, S. A.↗

NASA NTRS1977

CAVE: A computer code for two-dimensional transient heating analysis of conceptual thermal protection systems for hypersonic vehicles

A digital computer code CAVE (Conduction Analysis Via Eigenvalues), which finds application in the analysis of two dimensional transient heating of hypersonic vehicles is described. The CAVE is written in FORTRAN 4 and is operational on both IBM 360-67 and CDC 6600 computers. The method of solution is a hybrid analytical numerical technique that is inherently stable permitting large time steps even with the best of conductors having the finest of mesh size. The aerodynamic heating boundary conditions are calculated by the code based on the input flight trajectory or can optionally be calculated external to the code and then entered as input data. The code computes the network conduction and convection links, as well as capacitance values, given basic geometrical and mesh sizes, for four generations (leading edges, cooled panels, X-24C structure and slabs). Input and output formats are presented and explained. Sample problems are included. A brief summary of the hybrid analytical-numerical technique, which utilizes eigenvalues (thermal frequencies) and eigenvectors (thermal mode vectors) is given along with aerodynamic heating equations that have been incorporated in the code and flow charts.

Rathjen, K. A.↗

NASA NTRS1978

On acceleration of MacCormack's scheme

An acceleration of MacCormack's scheme due to Desideri and Tannehill is analyzed. It is found that for hyperbolic problems one cannot improve upon the efficiency of MacCormack's method. For parabolic problems the time step can be chosen arbitrarily large without loss of stability by an appropriate choice of the acceleration parameters. When applied to the heat equation this method is equivalent to both the Dufort-Frankel scheme and to MSOR.

Gottlieb, D.↗

NASA NTRS1978

Mercury's helium exosphere after Mariner 10's third encounter

From a comparison of the Mariner 10 third encounter UV spectrometer data with intensities generated from a newly constructed model exosphere, a new value of 4.5 x 10 to the -4th power for the fraction of the solar wind He(++) flux to be intercepted and captured by Mercury's magnetosphere, if the observed He atmosphere is maintained by the solar wind, has been derived. If an internal source for He prevails, the corresponding upper bound for the global outgassing rate is estimated to be 4.5 x 10 to the 22nd power/s. These values differ from those given earlier because of the present use of a surface temperature distribution satisfying the heat equation over Mercury's entire surface which employs Mariner-10-determined mean surface thermal characteristics. The mean standoff distance of Mercury's magnetopause averaged over Mercury's orbit is also used. Agreement between the observed and calculated intensities is found to be good. Minor discrepancies on the nightside of the terminator are explicable in terms of differences between actual and computed temperatures and scale height structure changes.

Curtis, S. A.↗

NASA NTRS1986

Reduction of the effects of the communication delays in scientific algorithms on message passing MIMD architectures

The efficient implementation of algorithms on multiprocessor machines requires that the effects of communication delays be minimized. The effects of these delays on the performance of a model problem on a hypercube multiprocessor architecture is investigated and methods are developed for increasing algorithm efficiency. The model problem under investigation is the solution by red-black Successive Over Relaxation YOUN71 of the heat equation; most of the techniques described here also apply equally well to the solution of elliptic partial differential equations by red-black or multicolor SOR methods. Methods for reducing communication traffic and overhead on a multiprocessor are identified and results of testing these methods on the Intel iPSC Hypercube reported. Methods for partitioning a problem's domain across processors, for reducing communication traffic during a global convergence check, for reducing the number of global convergence checks employed during an iteration, and for concurrently iterating on multiple time-steps in a time-dependent problem. Empirical results show that use of these models can markedly reduce a numewrical problem's execution time.

Saltz, J. H.↗

NASA NTRS1987

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗