Bibliographic record
Abstract
The simplest aerodynamic model of horizontal-axis wind turbines is blade element-momentum theory. The blades are divided radially into small elements which are assumed to behave as airfoils when determining the lift and drag. Since all blades have neighbours, a more accurate two-dimensional representation is an infinite cascade of identical, equispaced lifting bodies. In this study, cascades of airfoils1 at spacings and pitch angles typical of wind turbine applications, are analyzed using the conventional and impulse forms of the force equations for two-dimensional, steady, incompressible flow. The flow at a Reynolds number of 6×106 through cascades of NACA 0012 airfoils was simulated using OpenFOAM software. The results of the force equations agree well (less than 1 % error) with the body forces determined directly from OpenFOAM for four spacing ratios. Examining the terms of these equations reveals the importance of the circulation, the viscous drag, and the displacement effect of the body's wake due to its finite width. We focus on the "wake vorticity" term, which is ignored in blade element-momentum analysis. At a pitch angle of 90°, this term balances the viscous drag when the angle of attack is zero. At zero pitch, which models the outer region of a wind turbine blade at high tip speed ratio, the term can account for 27 % of the axial thrust when angle of attack is about 4°. This condition represents the rotor entering the high thrust region after the maximum power point. A simple equation is proposed for the wake vorticity term that is suitable for incorporation in blade element-momentum analysis. The normal force equation, like the angular momentum equation for wind turbines, has no viscous term which forces the body drag to contribute to the circulation in the wake. It is shown that the airfoil assumption is conservative in that cascade elements always have higher lift:drag ratios than airfoils at the same angle of attack. An associated result is that separation occurs at higher angles of attack on a cascade element compared to an airfoil.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.016 | 0.009 |
| Insufficient payload (model declined to judge) | 0.133 | 0.123 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".