Fluid-Structure Interactions in a Tube Bundle Subject to Cross-Flow. Part A: Porous Medium Approach
Bibliographic record
Abstract
The objective of this paper is to develop a Eulerian porous medium formulation to model the fluid-structure interactions of a tube bundle in a two-phase cross-flow. This is the first part of a two-part paper. Part A. deals with the model developed to account for the fluid-structure interactions. In Part B. (see Ref. 1) the current model will be extended to two-phase flows. Using volume averaging, we develop transport equations for the conservation of mass and momentum. In these equations the effects of the tubes on the flow are lumped into the porosity model. This porous variant of the Navier–Stokes equations greatly simplifies the computational model. First, the volume averaging process filters many details of the flow such as the geometry of the tubes and small-scale vortices. The resulting macroscopic model presents smoother variations so that coarser meshes may be used. Second, the fluid mesh and the tubes are independent. Therefore, fixed meshes may be used to simulate unsteady problems. The averaging process is described and the resulting equations for momentum and mass conservation are developed. The averaged equations are solved by a finite element method. Simulations are performed using an implicit and fully coupled formulation. The same high order time integration schemes are used for both the fluid and the structure equations. The code is verified by the method of manufactured solutions. The ability of the porous medium model to represent the two-way coupling is assessed by comparing its predictions to DNS predictions of laminar cross-flow interactions with a tube bundle. The proposed methodology is then applied to sample problems of practical interest.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".