Numerical model of solar dynamic radiator for parametric analysis

Extensive thermal and power cycle modeling have been developed for Space Station Freedom electric power system design and analysis. A simple and flexible numerical model simulates heat transfer and fluid flow performance of the radiator and calculates area, mass, and impact survivability for many combinations of flow tube and panel configurations, fluid and material properties, and environmental and cycle variations. A brief description and discussion are presented of the numerical model, its capabilities and limitations, and results of the parametric studies performed to date.<<ETX>>


OF POOR QlJALtlY
flux models to predict the population o f particles at least as large as the lethal particle size: and determine the probabi I i ty of no penetration of the vu'nerable area over the component lifetime.

Lethal Particle Size Model
The minimum particle diameter which would penetrate the radiator fluid tube wall is calculated for micrometeoroids and space debris using a model which is considered to yield a conservative prediction [161 for double-walled (bumpered) structures. The calculation is based o n empirical resulrs o f Nycmith [171 for a normal impact to bumpered aluminum, where the particle diameter is predicted as a furction of target wall thickness, wall spacing, anc particle velocity, with modification f o r material density. Micrometeoroids and space debris have different average densities and impact velocities, thus the model predicts different threshold diameters for each type of particle [181.
Hypervelocity impact testing of the preliminary design configuration of the SD radiator is currently underway. Results of these tests are expected to further define the radiator's survivability from orbital debris impacts.

Particle Flux Model
Once the threshold penetration diameter is known, the flux (impacts per year per unit area) of both micrometeoroids and space debris particles large enough to penetrate the radiator is found froin the flux models in Ref. 19. These models weri developed in particular f o r the Space Station Freidom orbital altitude and inclination.
The flux of micrometeoroids is based on an 'exposed' area [ 1 8 1 , which for a radiator with round tubes, is the product of the tube circumference, tube length. and number of radiator tubes. The flux of space debris is based on a 'projected' ared [181, which is the total tube area projected on (1 plane perpendicular to the space debris plane. For simplicity, the projected area is taken as the product of the tube diameter, tube length and number of tubes.

Survival Probabi 1 i ty
The probability o f no impact of a particle gre?.ter than or equal to the lethal particle size is calculated according to the method in Ref. 18 usirlg d 10 year expected lifetime, where sep3rate protlabi 1 i ties are found for micrometeoroidr and space debris, and the total probability is the product of the two. Since the radiator has an entirely redundant fluid loop, the survival prot'ability is based on loss of both loops.

EXAMPLES OF RESULTS
Initial runs o f the model were made to examine convergence and accuracy of the model. I t wds found that a convergence of the nodal root temperatures to 0.5 "R was adequate for parametric study purposes. Division of the tube length into 100 nodes yields consistent values for heat rejection. Next, the model was verifiea again;t results qf other numerical models [ 2 0 , 211. These results are shown in Table 1 for the baseline radiator and show good agreement.
Several parametric studies have been performed to examine optimization of the baseline radiator configuration. One study examined the variation of face-sheet thickness versus spacing between active radiator tubes. Face-sheet thickness was incrementally increased from the baseline thickness of 0.01 in., and the number of active tubes in a radiator panel was incrementally decreased from the baseline value of 18. The width o f the radiator-panel was held at a constant 7.5 ft. This effectively varied the fin performance. It was found that a thicker face-sheet provided a slight performance improvement at a cost of much increased mas:.
Reduced mass and equivalent thermal performance could be achieved by reducing the numoer of tubes per panel and increasing frictional head loss (at a constant mass flow rate). The model indicated that a 16 percent mass reduction can be obtained using 1 6 tubes per panel and a frictional head loss increase of 40 percent.
This information prompted a study of a parametric variation o f the flow-tube diameter and the number of active tubes per panel, holding all other parametsrs constant. This also effectively varies the fin length. it was found that mass can be reduced by decreasing the number of tubes per panel and increasing the tube diameter, at a cost o f slightly increased pumping power (within the current 25 psi allotment).
One of the recent design efforts focused on improvement of radiator performance (especially convective heat transfer in the flow-tubes) i s the selection of a fluid. Rocketdyne conducted a fiuid trade study analysis [221 in which fluids were evaluated against performance, safety, and material criteria. The numerical model was used to verify the performance results of the contractor's w a l u ation for the final fluid candidates: FC-75. toluene, and N-heptane. These results are shown in Tables 1 and 2. Small performance differences are attributed to the small differences in fluid properties used in each model and the 'overestimating' fin model used ( s e e radiation model discussion). The results are in agreement with the contractor's conclusion that toluene and N-heptane exceed FC-75 in performance.

SUMMA RL
A simple, flexible numerical model has been developed to analyze a variety o f SD radiator configurations by parametric study. The model has been verified against results of other available models, and has proven useful in verification of contractor trade-study analyses and preliminary design studies.

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