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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 NTRS2022

Earth System Model Parameter Adjustment Using a Green's Functions Approach

We demonstrate the practicality and effectiveness of using a Green's functions estimation approach for adjusting uncertain parameters in an Earth system model (ESM). This estimation approach has previously been applied to an intermediate-complexity climate model and to individual ESM components, e.g., ocean, sea ice, or carbon cycle components. Here, the Green's functions approach is applied to a state-of-the-art ESM that comprises a global atmosphere/land configuration of the Goddard Earth Observing System (GEOS) coupled to an ocean and sea ice configuration of the Massachusetts Institute of Technology general circulation model (MITgcm). Horizontal grid spacing is approximately 110 km for GEOS and 37–110 km for MITgcm. In addition to the reference GEOS-MITgcm simulation, we carried out a series of model sensitivity experiments, in which 20 uncertain parameters are perturbed. These “control” parameters can be used to adjust sea ice, microphysics, turbulence, radiation, and surface schemes in the coupled simulation. We defined eight observational targets: sea ice fraction, net surface shortwave radiation, downward longwave radiation, near-surface temperature, sea surface temperature, sea surface salinity, and ocean temperature and salinity at 300 m. We applied the Green's functions approach to optimize the values of the 20 control parameters so as to minimize a weighted least-squares distance between the model and the eight observational targets. The new experiment with the optimized parameters resulted in a total cost reduction of 9 % relative to a simulation that had already been adjusted using other methods. The optimized experiment attained a balanced cost reduction over most of the observational targets. We also report on results from a set of sensitivity experiments that are not used in the final optimized simulation but helped explore options and guided the optimization process. These experiments include an assessment of sensitivity to the number of control parameters and to the selection of observational targets and weights in the cost function. Based on these sensitivity experiments, we selected a specific definition for the cost function. The sensitivity experiments also revealed a decreasing overall cost as the number of control variables was increased. In summary, we recommend using the Green's functions estimation approach as an additional fine-tuning step in the model development process. The method is not a replacement for modelers' experience in choosing and adjusting sensitive model parameters. Instead, it is an additional practical and effective tool for carrying out final adjustments of uncertain ESM parameters.

Green's Function↗
NASA NTRS1989

Green's function solution to heat transfer of a transparent gas through a tube

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

Frankel, J. I.↗
NASA NTRS1984

Structural sensitivity analysis: Methods, applications and needs

Innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. The techniques include a finite difference step size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Some of the critical needs in the structural sensitivity area are indicated along with plans for dealing with some of those needs.

Adelman, H. M.↗
NASA NTRS1981

An analytic formulation for heating source memory in the thermospheric composition

Numerical calculations from a spectral circulation model are utilized to construct an analytic Green's function formulation describing the meridional, time-dependent thermospheric composition and temperature response during magnetic storms. The purpose is to develop a formulation that embodies source memory while being sufficiently simple to serve as a heuristic guide for empirical modeling. By passing from the discrete Fourier series representation, utilized for the numerical circulation model, to a continuous Fourier integral representation, explicit waves are obtained for the thermospheric response times. The response times are altitude and species dependent and can exceed two days below 200 km. Thus, for certain storm scenarios, pronounced source memory signatures for the composition and temperature are predicted. Response times obtained from the formulation are shown to give a response consistent with previously published neutral composition data from AE-C for the February 1974 storm when an ap dependent heat source is employed.

Porter, H. S.↗
NASA NTRS1984

Structural sensitivity analysis: Methods, applications, and needs

Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs.

Adelman, H. M.↗
NASA NTRS2015

Analytic Thermoelectric Couple Modeling: Variable Material Properties and Transient Operation

To gain a deeper understanding of the operation of a thermoelectric couple a set of analytic solutions have been derived for a variable material property couple and a transient couple. Using an analytic approach, as opposed to commonly used numerical techniques, results in a set of useful design guidelines. These guidelines can serve as useful starting conditions for further numerical studies, or can serve as design rules for lab built couples. The analytic modeling considers two cases and accounts for 1) material properties which vary with temperature and 2) transient operation of a couple. The variable material property case was handled by means of an asymptotic expansion, which allows for insight into the influence of temperature dependence on different material properties. The variable property work demonstrated the important fact that materials with identical average Figure of Merits can lead to different conversion efficiencies due to temperature dependence of the properties. The transient couple was investigated through a Greens function approach; several transient boundary conditions were investigated. The transient work introduces several new design considerations which are not captured by the classic steady state analysis. The work helps to assist in designing couples for optimal performance, and also helps assist in material selection.

Seebeck Effect↗
NASA NTRS1993

Unsteady three-dimensional thermal field prediction in turbine blades using nonlinear BEM

A time-and-space accurate and computationally efficient fully three dimensional unsteady temperature field analysis computer code has been developed for truly arbitrary configurations. It uses boundary element method (BEM) formulation based on an unsteady Green's function approach, multi-point Gaussian quadrature spatial integration on each panel, and a highly clustered time-step integration. The code accepts either temperatures or heat fluxes as boundary conditions that can vary in time on a point-by-point basis. Comparisons of the BEM numerical results and known analytical unsteady results for simple shapes demonstrate very high accuracy and reliability of the algorithm. An example of computed three dimensional temperature and heat flux fields in a realistically shaped internally cooled turbine blade is also discussed.

Martin, Thomas J.↗
NASA NTRS1997

Global Analysis of Empirical Relationships Between Annual Climate and Seasonality of NDVI

This study describes the use of satellite data to calibrate a new climate-vegetation greenness function for global change studies. We examined statistical relationships between annual climate indexes (temperature, precipitation, and surface radiation) and seasonal attributes of the AVHRR Normalized Difference Vegetation Index (NDVI) time series for the mid-1980s in order to refine our empirical understanding of intraannual patterns and global abiotic controls on natural vegetation dynamics. Multiple linear regression results using global l(sup o) gridded data sets suggest that three climate indexes: growing degree days, annual precipitation total, and an annual moisture index together can account to 70-80 percent of the variation in the NDVI seasonal extremes (maximum and minimum values) for the calibration year 1984. Inclusion of the same climate index values from the previous year explained no significant additional portion of the global scale variation in NDVI seasonal extremes. The monthly timing of NDVI extremes was closely associated with seasonal patterns in maximum and minimum temperature and rainfall, with lag times of 1 to 2 months. We separated well-drained areas from l(sup o) grid cells mapped as greater than 25 percent inundated coverage for estimation of both the magnitude and timing of seasonal NDVI maximum values. Predicted monthly NDVI, derived from our climate-based regression equations and Fourier smoothing algorithms, shows good agreement with observed NDVI at a series of ecosystem test locations from around the globe. Regions in which NDVI seasonal extremes were not accurately predicted are mainly high latitude ecosystems and other remote locations where climate station data are sparse.

Potter, C. S.↗
NASA NTRS1987

Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth

Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.

Revenaugh, Justin↗
NASA NTRS1971

On strain energy and constitutive relations for alkali metals.

An expression for the strain energy as a continuous differentiable function of the Green-Cauchy deformation tensor is obtained for the alkali metals at absolute zero temperature. The development is based on well established quantum and classical calculations of the various contributions to the crystal energy. Stress-deformation relations are next obtained. As a check on the accuracy of the strain energy, theoretical calculations of the values of the second-order elastic coefficients are obtained and compared to known experimental data. The predicted values are shown to compare quite well with the experimental values.

Eftis, J.↗
NASA NTRS1994

Computational modeling of properties

A simple model was developed to calculate the electronic transport parameters in disordered semiconductors in strong scattered regime. The calculation is based on a Green function solution to Kubo equation for the energy-dependent conductivity. This solution together with a rigorous calculation of the temperature-dependent chemical potential allows the determination of the dc conductivity and the thermopower. For wide-gap semiconductors with single defect bands, these transport properties are investigated as a function of defect concentration, defect energy, Fermi level, and temperature. Under certain conditions the calculated conductivity is quite similar to the measured conductivity in liquid 2-6 semiconductors in that two distinct temperature regimes are found. Under different conditions the conductivity is found to decrease with temperature; this result agrees with measurements in amorphous Si. Finally the calculated thermopower can be positive or negative and may change sign with temperature or defect concentration.

Franz, Judy R.↗
NASA NTRS1994

Computational modeling of properties

A simple model was developed to calculate the electronic transport parameters in disordered semiconductors in strong scattered regime. The calculation is based on a Green function solution to Kubo equation for the energy-dependent conductivity. This solution together with a rigorous calculation of the temperature-dependent chemical potential allows the determination of the dc conductivity and the thermopower. For wise-gap semiconductors with single defect bands, these transport properties are investigated as a function of defect concentration, defect energy, Fermi level, and temperature. Under certain conditions the calculated conductivity is quite similar to the measured conductivity in liquid II-VI semiconductors in that two distinct temperature regimes are found. Under different conditions the conductivity is found to decrease with temperature; this result agrees with measurements in amorphous Si. Finally the calculated thermopower can be positive or negative and may change sign with temperature or defect concentration.

Franz, Judy R.↗
NASA NTRS2013

Jet Surface Interaction-Scrubbing Noise

Generation of sound due to scrubbing of a jet flow past a nearby solid surface is investigated within the framework of the generalized acoustic analogy theory. The analysis applies to the boundary layer noise generated at and near a wall, and excludes the scattered noise component that is produced at the leading or the trailing edge. While compressibility effects are relatively unimportant at very low Mach numbers, frictional heat generation and thermal gradient normal to the surface could play important roles in generation and propagation of sound in high speed jets of practical interest. A general expression is given for the spectral density of the far-field sound as governed by the variable density Pridmore- Brown equation. The propagation Green's function should be solved numerically starting with the boundary conditions on the surface and subject to specified mean velocity and temperature profiles between the surface and the observer. The equivalent sources of aerodynamic sound are associated with non-linear momentum flux and enthalpy flux terms that appear in the linearized Navier-Stokes equations. These multi-pole sources should be modeled and evaluated with input from a Reynolds-Averaged Navier-Stokes (RANS) solver with an appropriate turbulence model.

Khavaran, Abbas↗
NASA NTRS1983

The relationship between surface topography, gravity anomalies, and temperature structure of convection

Consideration is given to the relationship between the temperature structure of mantle convection and the resulting surface topography and gravity anomalies, which are used in its investigation. Integral expressions relating the three variables as a function of wavelength are obtained with the use of Green's function solutions to the equations of motion for the case of constant-viscosity convection in a plane layer subject to a uniform gravitational field. The influence of the boundary conditions, particularly at large wavelengths, is pointed out, and surface topographies and gravity produced by convection are illustrated for a number of simple temperature distributions. It is shown that the upper thermal boundary layer plays an important role in determining the surface observables, while temperatures near the bottom of the layer affect mainly that boundary. This result is consistent with an explanation of geoid anomalies over mid-ocean swells in terms of convection beneath the lithosphere.

Parsons, B.↗
NASA NTRS2000

Thermal Edge-Effects Model for Automated Tape Placement of Thermoplastic Composites

Two-dimensional thermal models for automated tape placement (ATP) of thermoplastic composites neglect the diffusive heat transport that occurs between the newly placed tape and the cool substrate beside it. Such lateral transport can cool the tape edges prematurely and weaken the bond. The three-dimensional, steady state, thermal transport equation is solved by the Green's function method for a tape of finite width being placed on an infinitely wide substrate. The isotherm for the glass transition temperature on the weld interface is used to determine the distance inward from the tape edge that is prematurely cooled, called the cooling incursion Delta a. For the Langley ATP robot, Delta a = 0.4 mm for a unidirectional lay-up of PEEK/carbon fiber composite, and Delta a = 1.2 mm for an isotropic lay-up. A formula for Delta a is developed and applied to a wide range of operating conditions. A surprise finding is that Delta a need not decrease as the Peclet number Pe becomes very large, where Pe is the dimensionless ratio of inertial to diffusive heat transport. Conformable rollers that increase the consolidation length would also increase Delta a, unless other changes are made, such as proportionally increasing the material speed. To compensate for premature edge cooling, the thermal input could be extended past the tape edges by the amount Delta a. This method should help achieve uniform weld strength and crystallinity across the width of the tape.

Costen, Robert C.↗
NASA NTRS2013

Towards a Comprehensive Model of Jet Noise Using an Acoustic Analogy and Steady RANS Solutions

An acoustic analogy is developed to predict the noise from jet flows. It contains two source models that independently predict the noise from turbulence and shock wave shear layer interactions. The acoustic analogy is based on the Euler equations and separates the sources from propagation. Propagation effects are taken into account by calculating the vector Green's function of the linearized Euler equations. The sources are modeled following the work of Tam and Auriault, Morris and Boluriaan, and Morris and Miller. A statistical model of the two-point cross-correlation of the velocity fluctuations is used to describe the turbulence. The acoustic analogy attempts to take into account the correct scaling of the sources for a wide range of nozzle pressure and temperature ratios. It does not make assumptions regarding fine- or large-scale turbulent noise sources, self- or shear-noise, or convective amplification. The acoustic analogy is partially informed by three-dimensional steady Reynolds-Averaged Navier-Stokes solutions that include the nozzle geometry. The predictions are compared with experiments of jets operating subsonically through supersonically and at unheated and heated temperatures. Predictions generally capture the scaling of both mixing noise and BBSAN for the conditions examined, but some discrepancies remain that are due to the accuracy of the steady RANS turbulence model closure, the equivalent sources, and the use of a simplified vector Green's function solver of the linearized Euler equations.

Miller, Steven A. E.↗