Linear stability analysis of pressure-driven flows in channels with porous walls
Bibliographic record
Abstract
We present the three-dimensional linear stability analysis of a pressure-driven, incompressible, fully developed, laminar flow in a channel delimited by rigid, homogeneous, isotropic, porous layers. We consider porous materials of small permeability in which the maximum fluid velocity is small compared to the mean velocity in the channel region and for which inertial effects may be neglected. We analyse the linear stability of symmetric laminar velocity profiles in channels with two identical porous walls as well as skewed laminar velocity profiles in channels with only one porous wall. We solve the fully coupled linear stability problem, arising from the adjacent channel and porous flows, using a spectral collocation technique. We validate our results by recovering the linear stability results of a flow in a channel with impermeable walls as the permeabilities of the porous layers tend to zero. We also verify that our results are consistent with the assumption of negligible inertial effects in the porous regions. We characterize the stability of pressure-driven flows by performing a parametric study in which we vary the permeability, porosity, and height of the porous layers as well as an interface coefficient, τ, associated with the momentum transfer process at the interfaces between the channel and porous regions. We find that very small amounts of wall permeability significantly affect the Orr–Sommerfeld spectrum and can dramatically decrease the stability of the channel flow. Within our assumptions, in channels with two porous walls, permeability destabilizes up to two Orr–Sommerfeld wall modes and introduces two new damped wall modes on the left branch of the spectrum. In channels with only one porous wall, permeability destabilizes up to one wall mode and introduces one new damped wall mode on the left branch of the spectrum. In both cases, permeability also introduces a new class of damped modes associated with the porous regions. The size of the unstable region delimited by the neutral curve grows substantially, and the critical Reynolds number can decrease to only 10% of the corresponding value for a channel flow with impermeable walls. We conclude our study by considering two real materials: foametal and aloxite. We fit the porosity and interface coefficient τ to published data so that the porous materials we model behave like foametal and aloxite, and we compare our results with previously published numerical and experimental results.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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".