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Siegel, Robert

Publications and source records attributed to Siegel, Robert.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Analysis of Thermal Radiation Effects on Temperatures in Turbine Engine Thermal Barrier Coatings

Thermal barrier coatings are important, and in some instances a necessity, for high temperature applications such as combustor liners, and turbine vanes and rotating blades for current and advanced turbine engines. Some of the insulating materials used for coatings, such as zirconia that currently has widespread use, are partially transparent to thermal radiation. A translucent coating permits energy to be transported internally by radiation, thereby increasing the total energy transfer and acting like an increase in thermal conductivity. This degrades the insulating ability of the coating. Because of the strong dependence of radiant emission on temperature, internal radiative transfer effects are increased as temperatures are raised. Hence evaluating the significance of internal radiation is of importance as temperatures are increased to obtain higher efficiencies in advanced engines.

Siegel, Robert↗
NASA NTRS1997

Thermal Radiation Effects Analyzed in Translucent Composite and Thermal Barrier Coating

Ceramic parts and coatings are needed to withstand high temperatures in advanced aircraft engines. In hot environments, such as in the combustion chambers of these engines, infrared and visible radiation can penetrate into some ceramics and heat them internally. The internal temperatures depend on radiative effects combined with heat conduction, and on convection and radiation at the material boundaries. Since engine temperatures are high, radiant emission can be large from within translucent parts and coatings, and this must be included in the analysis. Transient and steady-state behavior are both important. During a transient, radiant penetration provides more rapid internal heating than conduction alone, and the temperature distributions are usually considerably different than for steady-state conditions; this can produce transient thermal stresses. Analytical and numerical methods are being used at the NASA Lewis Research Center to predict transient temperatures and heat flows in translucent materials. A transient analysis was done for a composite of two translucent layers. The layer refractive indices were larger than 1, producing internal reflections at the boundaries and at the internal interface. In addition, steady-state results were computed for a two-layer composite with one layer opaque. The results were used to assess the importance of internal radiation in a zirconia thermal barrier coating on a cooled metal wall. Since the radiative transfer equations are rather complex, especially when internal scattering is included, approximate methods are being investigated that might be convenient for computer design programs. An approximate two-flux method was used and verified by comparisons with solutions that used exact radiative transfer relations. The two-flux equations include scattering without increasing solution difficulty.

Siegel, Robert↗
NASA NTRS1997

Temperature Distribution in a Composite of Opaque and Semitransparent Spectral Layers

The analysis of radiative transfer becomes computationally complex for a composite when there are multiple layers and multiple spectral bands. A convenient analytical method is developed for combined radiation and conduction in a composite of alternating semitransparent and opaque layers. The semi- transparent layers absorb, scatter, and emit radiation, and spectral properties with large scattering are included. The two-flux method is used, and its applicability is verified by comparison with a basic solution in the literature. The differential equation in the two-flux method Is solved by deriving a Green's function. The solution technique is applied to analyze radiation effects in a multilayer zirconia thermal barrier coating with internal radiation shields for conditions in an aircraft engine combustor. The zirconia radiative properties are modeled by two spectral bands. Thin opaque layers within the coating are used to decrease radiant transmission that can degrade the zirconia insulating ability. With radiation shields, the temperature distributions more closely approach the opaque limit that provides the lowest metal wall temperatures.

Siegel, Robert↗
NASA NTRS1996

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗
NASA NTRS1996

Internal Radiation Effects in Zirconia Thermal Barrier Coatings

Using thermal barrier coatings on combustor liners, turbine vanes, and rotating blades is important for reducing metal temperatures in current and advanced aircraft engines. Zirconia is a common coating material, and it is partially transparent to thermal radiation. Radiation becomes more significant as temperatures are raised for higher efficiency in advanced engines. Calculations are often made with radiation effects neglected inside the coating. The effect of radiation is illustrated here, where an analytical procedure is provided by using the two-flux method for the radiative contribution. A detailed study was made of ceramic thermal barrier coatings for diesel engines, and a two-flux analysis was developed for radiation in semitransparent multilayer composites. These efforts provide the basis for the present analysis where illustrative solutions are obtained for typical conditions in an aircraft engine. The formulation and solution of the exact spectral radiative transfer equations including large scattering, as is characteristic of zirconia, are rather complicated. The two-flux method is used here to provide a simplified method.

Siegel, Robert↗
NASA NTRS1996

Transient Heat Transfer in a Semitransparent Radiating Layer with Boundary Convection and Surface Reflections

Surface convection and refractive index are examined during transient radiative heating or cooling of a grey semitransparent layer with internal absorption, emission and conduction. Each side of the layer is exposed to hot or cold radiative surroundings, while each boundary is heated or cooled by convection. Emission within the layer and internal reflections depend on the layer refractive index. The reflected energy and heat conduction distribute energy across the layer and partially equalize the transient temperature distributions. Solutions are given to demonstrate the effect of radiative heating for layers with various optical thicknesses, the behavior of the layer heated by radiation on one side and convectively cooled on the other, and a layer heated by convection while being cooled by radiation. The numerical method is an implicit finite difference procedure with non-uniform space and time increments. The basic method developed in earlier work is expanded to include external convection and incident radiation.

Siegel, Robert↗
NASA NTRS1996

Two-Flux Method for Transient Radiative Transfer in a Semitransparent Layer

The two-flux method was used to obtain transient solutions for a plane layer including internal reflections and scattering. The layer was initially at uniform temperature, and was heated or cooled by external radiation and convection. The two-flux equations were examined as a means for evaluating the radiative flux gradient in the transient energy equation. Comparisons of transient temperature distributions using the two-flux method were made with results where the radiative flux gradient was evaluated from the exact radiative transfer equations. Good agreement was obtained for optical thicknesses from 0.5 to 5 and for refractive indices of 1 and 2. Illustrative results obtained with the two-flux method demonstrate the effect of isotropic scattering coupled with changing the refractive index. For small absorption with large scattering the maximum layer temperature is increased when the refractive index is increased. For larger absorption the effect is opposite, and the maximum temperature decreases with increased refractive index .

Siegel, Robert↗
NASA NTRS1995

Temperature Distributions in Semitransparent Coatings: A Special Two-Flux Solution

Radiative transfer is analyzed in a semitransparent coating on an opaque substrate and in a semitransparent layer for evaluating thermal protection behavior and ceramic component performance in high temperature applications. Some ceramics are partially transparent for radiative transfer, and at high temperatures internal emission and reflections affect their thermal performance. The behavior is examined for a ceramic component for which interior cooling is not provided. Two conditions are considered: (1) the layer is heated by penetration of radiation from hot surroundings while its external surface is simultaneously film cooled by convection, and (2) the surface is heated by convection while the semitransparent material cools from within by radiant emission leaving through the surface. By using the two-flux method, which has been found to yield good accuracy in previous studies, a special solution is obtained for these conditions. The analytical result includes isotropic scattering and requires only an integration to obtain the temperature distribution within the semitransparent material. Illustrative results are given to demonstrate the nature of the thermal behavior.

Siegel, Robert↗
NASA NTRS1995

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗
NASA NTRS1992

Boundary Heat Fluxes for Spectral Radiation from a Uniform Temperature Rectangular Medium

The effect of spectral behavior is analytically shown for radiation in a 2D rectangular geometry. The solution provides exact boundary heat flux values that can be used for comparison with values obtained from general computer programs. The spectral solution presented can be easily evaluated by numerical integration for complex variations of the spectral absorption coefficient with wavelength.

Siegel, Robert↗
NASA NTRS1992

Finite difference solution for transient cooling of a radiating-conducting semitransparent layer

Transient solutions were obtained for cooling a semitransparent material by radiation and conduction. The layer is in a vacuum environment so the only means for heat dissipation is by radiation from within the medium leaving through the boundaries. Heat conduction serves only to partially equalize temperatures across the layer. As the optical thickness is increased, steep temperature gradients exist near the boundaries when conduction is relatively small. A solution procedure is required that will provide accurate temperature distributions adjacent to the boundaries, or radiative heat losses will be in error. The approach utilized numerical Gaussian integration to obtain the local radiative source term, and a finite difference procedure with variable space and time increments to solve the transient energy equation.

Siegel, Robert↗
NASA NTRS1992

Thermal radiation heat transfer (3rd revised and enlarged edition)

This book first reviews the overall aspects and background information related to thermal radiation heat transfer and incorporates new general information, advances in analytical and computational techniques, and new reference material. Coverage focuses on radiation from opaque surfaces, radiation interchange between various types of surfaces enclosing a vacuum or transparent medium, and radiation including the effects of partially transmitting media, such as combustion gases, soot, or windows. Boundary conditions and multiple layers are discussed with information on radiation in materials with nonunity refractive indices.

Siegel, Robert↗
NASA NTRS1991

Transient cooling of a square region of radiating medium

A time-accurate numerical solution was carried out for transient radiative cooling of a gray emitting and absorbing medium in a square two-dimensional region. The integro-differential energy equation for transient temperature distributions was solved in two stages. At each time increment, the local radiative source term was obtained by numerical integration of the temperature field using two-dimensional Gaussian integration over rectangular subregions. Then the differential portion of the equation was integrated forward in time by use of the local first and second time derivatives. The results were compared with available limiting case, and excellent agreement was obtained. Transient results are given for a wide range of optical thicknesses of the region. Optimum transient cooling is obtained when the optical side length is about 4.

Siegel, Robert↗
NASA NTRS1990

Emittance bounds for transient radiative cooling of a scattering rectangular region

Transient cooling was analyzed for a two-dimensional gray rectangular region that emits, absorbs, and isotropically scatters radiation. The region, initially at uniform temperature, is placed in surroundings at a much lower temperature. The cooling analysis yields two simultaneous equations for the transient temperature and scattering source function distributions. The region starts to cool with the medium at uniform temperature. For this condition, the local emittance around the perimeter was obtained by a numerical solution of the radiative equations, and the rate of heat loss from the entire medium was evaluated. As cooling continues, the emissive ability decreases because of the lower temperatures in the outer regions of the rectangle. Based on some previous work, a lower limit for the transient overall emittance was found by obtaining a similarity solution. For some ranges of optical thickness and scattering albedo, the lower limit is only a small amount below the initial emittance. For these conditions, the initial emittance can be used to compute the entire transient resulting in a considerable simplification.

Siegel, Robert↗
NASA NTRS1989

Some aspects of transient cooling of a radiating rectangular medium

The emission from a gray radiating medium is analyzed for transient cooling in surroundings at a low temperature. The medium is rectangular with no variations in the direction normal to the cross section. The integral equation for the transient temperature distribution is solved numerically using a two-dimensional Gaussian integration subroutine. The emissive ability for a rectangle at uniform temperature is compared with that for transient cooling where the temperature distribution of the region has reached a fully developed shape, as shown by a separation of variables solution. The two solutions provide the upper and lower bounds for the emittance of a rectangle during transient cooling. The emittances for various aspect ratios are presented as a function of the mean length of the rectangle and are compared with results for a plane layer and a cylinder.

Siegel, Robert↗
NASA NTRS1989

Solidification by radiative cooling of a cylindrical region filled with drops

Transient cooling by radiation is analyzed for a cylindrical region filled with axially flowing streams of drops that are becoming solidified. This is of interest for the dissipation of waste heat from orbiting power system in space. The drops absorb, emit, and scatter radiation, and the surroundings are at a lower uniform temperature. The radiative properties are assumed gray, and the scattering is isotropic. The radiating region is a two-phase mixture that remains at the melting temperature of the drops. Its temperature uniformity maintains a high emissive power as energy is lost. This is an advantage over a sensible heat radiator in which the temperature decreases, thereby reducing the emissive power. The results provide the axial length that remains two-phase and the fraction of energy dissipated within this length in which the emissive power has not decreased because of sensible cooling. It is also shown how the radial distribution of the axial velocity of the drops can be modified to increase this energy fraction.

Siegel, Robert↗
NASA NTRS1989

Radiative cooling performance of a converging liquid drop radiator

The liquid drop radiator consists of many directed streams of hot liquid drops that are cooled by passing through space and are then collected for reuse. To facilitate the collection of the cooled liquid, a converging geometry might be useful. As the streams converge toward the collector, the density and optical thickness of the droplet cloud are increased. The increase of optical thickness in the flow direction is shown to reduce the local emittance along the length of the radiator.

Siegel, Robert↗