Shock reflection in internal axisymmetric flow
Bibliographic record
Abstract
A new model to predict internal axisymmetric shocks with Mach reflections at their centreline is developed.The model combines the method of characteristics and the quasi-one-dimensional flow equations.A method to extend the model for cases with extremely small Mach stems, generated by weak incident shocks, is developed and applied.Model predictions are compared with those from inviscid CFD, for a range of axisymmetric wedge geometries, and the effects of wedge length and shock angle at the wedge leading edge are studied.These various wedge geometries are found to generate flowfields with similar flow features, with Mach discs that vary greatly in size.This observation forms the basis of a method that uses the results from a CFD mesh convergence study, conducted for a single wedge geometry, to determine the mesh resolution requirements and uncertainty due to finite mesh resolution for all other wedge geometries.The model indicates that these geometries generate a flowfield that can be treated as two separate parts: one supported by the wedge surface and another supported by the sharp corner at the wedge trailing edge.The influence 5-3 Characteristic lines at a point, P ; η and ξ represent the local C + and C -directions, respectively, x 1 is the local flow direction, θ is the flow inclination angle relative to the x-axis, and µ is the Mach angle.120 xv 5-4 Schematic showing the situation where mass flow rate at b is computed by integration along the local C + characteristic.The mass flow rate at a is known and the mass flow rate through the segment a to b, d ṁ′ , is computed. . . . . . . . . . . . . . . . . . . . . . . . . . . . .124 5-5 MOC prediction of a Prandtl-Meyer expansion fan (planar twodimensional) generated at a 20 • sharp corner, with a freestream Mach number of 3.0, γ = 1.4.The pink marker indicates the node at which the MOC solution is taken. . . . . . . . . . . . . . . . . .126 5-6 Discretization error, DE, plotted against MOC grid spacing, ∆c. . . .126 5-7 Error in MOC predicted average shock angle, β, in comparison to the theoretical value of β t = 150 • . . . . . . . . . . .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 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) | 0.001 | 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 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".