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Technical Paper

Node Geometries and Conductances in Spacecraft Thermal Models

Thermal conductances are computed for relatively simple node geometries that are typical of analytical models of spacecraft. Heat-transfer rates computed with these conductances are compared to heat-transfer rates computed from exact, closed-form mathematical formulas. The comparisons show that most accurate results are obtained with rectangular nodal arrangements and with triangular arrangements with interior angles less than ninety degrees. For rectangles, the conductances obtained from finite-difference, finite-element and centroid methods are identical. For triangles, the finite-element conductances are best. For other quadrilateral arrangements and triangles, the centroid method is the most reliable.
Technical Paper

Difficulties with Obtuse-Angled Elements in Finite-Element Thermal Models

Thermal conductances are computed by finite-element techniques for typical triangular elements.. Heat-transfer rates computed with these conductances are compared to heat-transfer rates computed from exact, closed-form mathematical formulas and from refined models. The comparisons show that significant simulation errors can occur in triangular elements that have an internal angle greater than 90 degrees. An alternative, centroid method is shown to give smaller errors by some measures and in some cases but larger errors in most cases.
Technical Paper

Detecting Fencing Errors in Radiant Heat-Transfer Calculations

The classical fencing problem occurs in radiant heat-transfer computations when a surface extends from one compartment to another, with the two compartments otherwise exchanging little heat. The surface that separates the two compartments is called a “fence.” If the gap between the bottom of the fence and the surface that extends under the fence is small, the potential for a large fencing error is evident from an examination of the drawings. In large models, with many surfaces forming many compartments, the fencing error is less evident. In this paper we examine the fencing errors in two prototype geometries. If the fenced surface is adiabatic, the error is found to be significant for surprisingly large gaps. A surface can be adiabatic due either to a high reflectance or a layer of insulation. The error is found to become insignificant when there is no reflectance.
Technical Paper

BIFAC: A Program for Computing Thermal Radiant Interchange Among Non-Idealized Surfaces

A new, general-purpose computer program (BIFAC) has been developed for computing thermal radiant interchange among opaque surfaces that need not be perfectly diffuse or perfectly specular. The method uses the full bi-directional reflectance distribution function (BRDF) to determine directional radiosities, and thence heat fluxes, between surfaces. The method gives more accurate average interchange factors for diffuse surfaces, because it better represents interaction in corners. The maximum error in a stringent test using a specular surface was 8.9%, in great part because the exact specular solution does not include the real specular cone that is used in BIFAC.
Technical Paper

Accuracy of Various Methods for Reducing the Number of Radiation Factors

Simulation of radiant heat transfer in large systems results in perhaps millions of radiant-interchange factors. In the interest of reducing computation times, some engineers frequently omit the smallest factors. Others combine the smallest factors into effective radiation nodes. Still others reduce the number of radiation factors by introducing fictitious partitions, known as multiple enclosure simplification shields that divide the large system into smaller systems. In this paper we examine the errors introduced by these various techniques and offer a new method that has the same accuracy as incorporating all of the radiation factors but requires little increase in computation time. The methods are compared by application to three simple models that clearly illustrate how significant errors can be generated if the methods are incorrectly applied.