Bibliographic record
Abstract
Abstract. Using the concept of impulse in control volume (CV) analysis, we derive a new equation for steady wind turbine thrust in a constant, spatially uniform wind. This equation contains the circumferential velocity and tip speed ratio. We determine the conditions under which the new equation reduces to the standard equation involving only the axial velocity. A major advantage of an impulse formulation is that it removes the pressure and introduces the vorticity, allowing the equation to be used unambiguously immediately behind the blades. Using two CVs with this downwind end – one rotating with the blades, and one stationary – highlights different aspects of the analysis. We assume that the vorticity is frozen relative to an observer rotating with the blades, so the vortex lines follow the local streamlines in the rotating frame and vorticity does not appear explicitly in the impulse equation for force. In the stationary frame, streamlines and vortex lines intersect, and one of the thrust terms can be interpreted as the effect of wake rotation. The impulse analysis also shows the significance of the radial velocity in wind turbine aerodynamics. By assuming both the radial and axial velocities are continuous through the rotor disk, their contributions to the final thrust expression cancel to leave an expression dependent on azimuthal velocity alone. The final integral equation for thrust can be viewed as a generalization of the Kutta–Joukowsky theorem for the rotor forces. We give a proof, for the first time, for the conditions under which the Kutta–Joukowsky equations apply. The analysis is then extended to the blade elements comprising the rotor. The new formulation gives a very simple, exact equation for blade element thrust which is the major contribution of this study. By removing the pressure partly through the kinetic energy contribution of the radial velocity, the new equation circumvents the long-standing concern over the role the pressure forces acting on the expanding annular streamtube intersecting each blade element. It is shown that the necessary condition for blade-element independence of the conventional thrust equation – that which involves the axial induction factor – is the constancy of the vortex pitch in the wake.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".