Nonimaging Behavior of Circular Trough Concentrators With Tubular Receivers
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Bibliographic record
Abstract
Abstract This paper presents a detailed analysis of the optical performance of circular trough concentrators with tubular receivers. First, a simple analytical formula for the achievable geometric concentration ratio as a function of the rim angle and acceptance angle is developed. Notably, the development reveals the existence of three distinct concentration ratio regimes: a first regime where the receiver is sized based on the reflection of the edge rays from the rim alone, a second regime where the receiver is sized based on the rim and the edge ray caustics, and a third regime where two reflections from the mirror are permitted. Several exemplary designs are proposed and further analyzed using Monte Carlo ray tracing to obtain transmission angle curves and receiver flux distributions. For an acceptance angle of 1 deg, the circular trough concentrator with circular receiver is found to achieve a maximum geometric concentration ratio of 7.695× with a peak flux of 30 suns. For large acceptance angles (10 deg), the circular trough achieves a geometric concentration ratio as high as 82% of that of a parabolic trough. This noteworthy performance, along with the fact that a circular mirror is amenable to an inflated polymer construction, makes this configuration promising for low-cost, low-concentration solar thermal applications.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it