The Formulation of the RANS Equations for Hypersonic Turbulent Flows
Bibliographic record
Abstract
Accurate prediction of hypersonic turbulent flows is essential to the design of high-speed aerospace vehicles. Such flows are mainly predicted using the Reynolds-Averaged-Navier-Stokes (RANS) approach in general and in particular turbulence models using the effective viscosity approximation. Several terms involving the turbulent kinetic energy (TKE) appear explicitly in the RANS equations through the modelling of the Reynolds stresses and mean total energy and the molecular and turbulent diffusion terms. Some of these terms are often ignored in low, or even supersonic, speed simulations with zero-equation models, as well as some one-or twoequation models. The omission of these terms may not be suitable under hypersonic conditions, but there are nevertheless codes and software packages that still make such approximations, even for very high-speed turbulent flow simulations. To clarify the impact of ignoring the TKE terms in the RANS equations, two linear two-equation models and one nonlinear two-equation model are applied to the computation of two hypersonic benchmark cases, a 2D zero-pressure gradient flat plate case and an axisymmetric shock wave boundary layer interaction (SWBLI) case. The predicted surface friction coefficients and velocity profiles with different combinations of TKE terms showed little differences in the zero-pressure gradient case. However, in the SWBLI case, comparisons show that the flow separation would be delayed or accelerated with different combinations of TKE compared to the one with all the TKE terms included. Therefore, it is highly recommended to include all the TKE terms in the mean flow equations when dealing with simulations of hypersonic turbulent flows, especially for flows with shock wave boundary layer interactions. As a further consequence, since the TKE terms may not be obtained explicitly in zero-equation, or some one-equation, models, it is debatable whether these models are suitable for simulations of hypersonic turbulent flows with SWBLIs.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".