A new utility calculation model for axial flow of non‐Newtonian fluid in concentric annuli
Bibliographic record
Abstract
A new utility approach that is independent of the rheological model is presented for the flow of non‐Newtonian fluids in concentric annulus. The novel model was developed without assuming that the generalised flow index remains constant over all shear rate ranges. Based on the slot model, the flow rate expressions for all common rheological models flowing in annuli were obtained, such as the Herschel–Bulkley model, the Robertson–Stiff model, and the Four‐parameter model, and they all can be solved numerically to obtain accurate wall shear rate and shear stress. Following Metzner and Reed's study, we defined a generalised flow index for non‐Newtonian fluid flow in annuli. Through a theoretical analysis, we also defined a new effective diameter for non‐Newtonian fluid flow in annuli, which accounts for the effects both of annulus geometry and fluid rheology but which is different from that was proposed by Reed and Pilehvari. Through the generalised effective diameter we linked non‐Newtonian annular flow with Newtonian pipe flow. A general annular Reynolds number expression was derived from this method for conditions under which the generalised flow index is variable. A theoretical calculation method for the generalised flow index and a uniform pressure loss calculation model for non‐Newtonian flow in concentric annuli were developed, which are applicable to all time‐independent non‐Newtonian fluid. The predictions of this model have been compared with an extensive set of data from the literature. The comparisons of different fluids in different size annuli show very good agreement over the entire range of flow types.
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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 | 0.001 |
| 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".