Some effects of domain size and boundary conditions on the accuracy of airfoil simulations
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Bibliographic record
Abstract
Abstract This paper investigates a specific case of one of the most popular fluid dynamic simulations, the incompressible flow around an airfoil (NACA 0012 here) at a high Reynolds number ( $$6 \times 10^6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>6</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> ). OpenFOAM software was used to study the effect of domain size and four common choices of boundary conditions on airfoil lift, drag, surface friction, and pressure. We also examine the relation between boundary conditions and the velocity, pressure, and vorticity distributions throughout the domain. In addition to the common boundary conditions, we implement the “point vortex” boundary condition that was introduced many years ago but is now rarely used. We also applied the point vortex condition for the outlet pressure instead of using the traditional Neumann condition. With the airfoil generating significant lift at incidence angles of $$5^\circ , 10^\circ$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> </mml:math> , and $$14^\circ$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>14</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> , we confirm a previous finding that the boundary conditions combine with domain size to produce an induced (pressure) drag. The change in the pressure drag with domain size is significant for the commonly-used boundary conditions but is much smaller for the point vortex alternative. The point vortex boundary condition increases the execution time, but this is more than offset by the reduction in domain size needed to achieve a specified accuracy in the lift and drag. This study also estimates the error in total drag and lift due to domain size and shows it can be almost eliminated using the point vortex boundary condition. We also used the impulse form of the momentum equations to study the relation between drag and lift and spurious vorticity, which is generated as a result of using non-exact boundary conditions. These equations reveal that the spurious vorticity throughout the domain is associated with cancelling circulation around the domain boundaries.
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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 | 0.000 |
| 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