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arxiv: 2604.06913 · v2 · submitted 2026-04-08 · ⚛️ physics.flu-dyn

Quantifying Flow separation for ellipse and von-K\'arm\'an Airfoil: A dataset of surface pressure and skin friction

Christian Bak Winther , Peter Ammundsen , Fynn Jerome Aschmoneit This is my paper

Pith reviewed 2026-05-10 18:39 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords flow separationRANS simulationellipsevon Karman airfoilsurface pressureskin frictionbenchmark datasetpotential flow models
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The pith

Steady RANS simulations provide surface pressure and skin friction data for an ellipse and von-Kármán airfoil to benchmark extended potential flow models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper performs steady-state Reynolds-averaged Navier-Stokes simulations of two-dimensional flow around an ellipse and a von-Kármán-Trefftz airfoil. Data is generated for seven angles of attack and two Reynolds numbers using the k-ω SST turbulence model. The output includes distributions of surface pressure and skin friction, along with lift and drag coefficients and locations of stagnation and separation points. A sympathetic reader would care because these numerical results could serve as a standard reference set for testing and improving simpler flow models without needing full turbulence computations.

Core claim

Steady-state RANS simulations are reported for 2D flow around an ellipse and a von-Kármán-Trefftz airfoil at seven different angles of attack and two different Reynolds numbers, computed using the k ω SST turbulence model in OpenFOAM. The dataset contains surface pressure distribution, skin friction distribution, lift and drag coefficients, stagnation point location and separation point locations. The results serve as a benchmark for calibration and evaluation of extended potential flow models.

What carries the argument

The dataset of surface pressure distributions, skin friction distributions, lift and drag coefficients, stagnation point locations and separation point locations from the RANS simulations.

If this is right

  • Extended potential flow models can be calibrated and evaluated against the reported separation point locations and surface quantities.
  • The data allows quantification of how well simplified models capture flow separation without running full RANS simulations.
  • Design processes for airfoils or similar shapes could use these benchmarks to validate quick approximations at low computational cost.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar datasets for other airfoil shapes could extend the benchmarking approach to a wider range of geometries.
  • If the separation data proves reliable, it might guide the development of hybrid models that combine potential flow with empirical separation corrections.
  • Future experiments matching these conditions would directly test the dataset's accuracy for real-world applications.

Load-bearing premise

The k-ω SST turbulence model accurately captures the real flow separation locations and surface pressure and skin friction for these geometries and flow conditions.

What would settle it

Experimental measurements of surface pressure, skin friction, or separation locations on physical models of the ellipse and airfoil at the same angles of attack and Reynolds numbers; disagreement beyond numerical or experimental uncertainty would falsify the benchmark reliability.

Figures

Figures reproduced from arXiv: 2604.06913 by Christian Bak Winther, Fynn Jerome Aschmoneit, Peter Ammundsen.

Figure 1
Figure 1. Figure 1: Ellipse geometry 0.0 0.2 0.4 0.6 0.8 1.0 x/c −0.1 0.0 0.1 y/c [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ellipse mesh 4 TURBULENCE SENSITIVITY Selecting the appropriate ambient turbulence level in RANS simulations can be a non-trivial task. Generally, the turbulent kinetic energy field should only contain the turbulent energy at a length-scale relevant to boundary-layer [6]. For this turbulence sensitivity study the same case is considered as for the mesh convergence study. In external flows the ambient turbu… view at source ↗
Figure 4
Figure 4. Figure 4: Airfoil mesh 5 RESULTS Simulations results are presented in the following order: First distributions of local force coefficients, friction and pressure. These data are found in the Supplementary Material, in file ”Results.zip”. Then, integral values of these values are presented in tables. Finally stagnation points and separation points are reported. Pressure coefficient and skin friction coefficient Surfa… view at source ↗
Figure 5
Figure 5. Figure 5: Simulation results for the ellipse, Each row, from top to bottom; α = 0 ◦ , α = 5 ◦ , α = 10◦ , α = 15◦ and α = 20◦ . Each column, from left to right; streamlines at Re = 107 , Pressure coefficient and Skin friction coefficient. 5/9 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Simulation results for the airfoil, Each row, from top to bottom; α = 0 ◦ , α = 5 ◦ , α = 10◦ , α = 15◦ and α = 20◦ . Each column, from left to right; streamlines at Re = 107 , Pressure coefficient and Skin friction coefficient. 6/9 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Sign convention for stagnation- and separation angles. The stagnation points are identified as the point where the Cp takes on its maximum value. Separation points are found where Cf changes sign from positive to negative. Tabulated results for the stagnation points, and separation points and angles for the ellipse can be found in tables 5 and 6 for Re = 106 and Re = 107 respectively. Stagnation and separa… view at source ↗
read the original abstract

Steady-state RANS simulations are reported for 2D flow around an ellipse and a von-K\'arm\'an-Trefftz airfoil at seven different angles of attack and two different Reynolds numbers, computed using the $k \omega SST$ turbulence model in OpenFOAM. The dataset contains surface pressure distribution, skin friction distribution, lift and drag coefficients, stagnation point location and separation point locations. The results serve as a benchmark for calibration and evaluation of extended potential flow models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports steady-state 2D RANS simulations of flow over an ellipse and a von-Kármán-Trefftz airfoil at seven angles of attack and two Reynolds numbers, performed with the k-ω SST turbulence model in OpenFOAM. The resulting dataset comprises surface pressure coefficient distributions, skin-friction distributions, lift and drag coefficients, stagnation-point locations, and separation-point locations. The authors position this dataset as a benchmark for calibration and evaluation of extended potential-flow models that incorporate flow separation.

Significance. If the reported separation locations and surface quantities prove accurate, the dataset would supply a concrete numerical reference for testing and tuning reduced-order aerodynamic models that extend classical potential flow to separated regimes. Such benchmarks are currently scarce for these particular geometries and conditions, so the work could accelerate development of hybrid potential-flow/RANS or data-driven separation models. The paper supplies direct simulation outputs without self-referential derivations or fitted parameters, which is a methodological strength.

major comments (2)
  1. [Numerical methods and Results sections] The central claim that the dataset constitutes a reliable benchmark rests on the assumption that the chosen k-ω SST RANS setup faithfully reproduces separation locations and surface quantities at the stated Re and AoA. However, the manuscript provides neither a grid-convergence study nor any comparison against experimental data or higher-fidelity simulations for the ellipse or von-Kármán-Trefftz airfoil. Without these anchors, systematic RANS biases (e.g., delayed separation at high AoA) could propagate into any subsequent model calibration.
  2. [Results and Dataset description] No uncertainty estimates, sensitivity analysis to turbulence-model constants, or mesh-resolution details are reported for the extracted separation points and Cp/Cf distributions. This omission makes it impossible for users to assess the numerical uncertainty of the benchmark values they would employ for model calibration.
minor comments (2)
  1. [Abstract] The abstract and introduction should explicitly state the exact Reynolds numbers and angle-of-attack range used, rather than referring only to “two different Reynolds numbers” and “seven different angles of attack.”
  2. [Figures] Figure captions for the surface-pressure and skin-friction plots should include the precise mesh size, y+ values, and any convergence criteria employed.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and describe the revisions we will make to improve the presentation and utility of the dataset.

read point-by-point responses

  1. Referee: [Numerical methods and Results sections] The central claim that the dataset constitutes a reliable benchmark rests on the assumption that the chosen k-ω SST RANS setup faithfully reproduces separation locations and surface quantities at the stated Re and AoA. However, the manuscript provides neither a grid-convergence study nor any comparison against experimental data or higher-fidelity simulations for the ellipse or von-Kármán-Trefftz airfoil. Without these anchors, systematic RANS biases (e.g., delayed separation at high AoA) could propagate into any subsequent model calibration.

    Authors: We agree that the absence of a grid-convergence study limits the strength of the benchmark claim. In the revised manuscript we will add a dedicated subsection in Numerical Methods describing the mesh parameters (cell count, refinement regions, and y+ values) employed for all cases. We will also include a limited grid-convergence assessment for one representative high-AoA case to quantify changes in separation location and integrated forces when the mesh is coarsened or refined by a factor of two. Regarding experimental or higher-fidelity comparisons, no suitable datasets exist in the literature for these exact geometries and flow conditions; we will therefore add an explicit limitations paragraph stating that the provided data represent standard RANS results rather than validated ground truth, and that users should treat them accordingly when calibrating reduced-order models. revision: partial

  2. Referee: [Results and Dataset description] No uncertainty estimates, sensitivity analysis to turbulence-model constants, or mesh-resolution details are reported for the extracted separation points and Cp/Cf distributions. This omission makes it impossible for users to assess the numerical uncertainty of the benchmark values they would employ for model calibration.

    Authors: We accept this criticism. The revised manuscript will report the mesh-resolution details (including total cell counts and near-wall spacing) for every simulation. We will also add a short sensitivity study on the k-ω SST constants for the ellipse at the highest angle of attack, showing the variation in separation location when the constants are perturbed within their commonly accepted ranges. For the extracted quantities we will include estimated uncertainties derived from the grid-sensitivity test and from the finite resolution of the surface sampling; these will be tabulated alongside the separation-point and Cp/Cf data. revision: yes

standing simulated objections not resolved
  • Direct comparison of the RANS results against experimental measurements or higher-fidelity simulations, because no such reference data are available for the precise geometries and conditions examined.

Circularity Check

0 steps flagged

No circularity: direct RANS dataset with no derivations or self-referential claims

full rationale

The paper reports steady-state RANS simulation outputs (surface pressure, skin friction, lift/drag, separation points) for ellipse and von-Kármán-Trefftz airfoils at specified Re and AoA using k-ω SST in OpenFOAM. No derivation chain, fitted parameters, predictions, or mathematical reductions are claimed. The benchmark claim is an external-use statement, not a self-referential derivation. No self-citations or ansatzes are load-bearing. This is a standard data-release paper whose content is independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only abstract available; standard CFD assumptions apply but cannot be audited in detail.

axioms (2)
  • domain assumption Steady-state RANS assumption holds for the reported angles and Reynolds numbers
    Invoked for all seven angles of attack and both Reynolds numbers in the abstract.
  • domain assumption k-ω SST turbulence model sufficiently represents separation physics
    Chosen without further justification in the abstract; central to all surface data.

pith-pipeline@v0.9.0 · 5390 in / 1168 out tokens · 42900 ms · 2026-05-10T18:39:58.063817+00:00 · methodology

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Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

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    work page 2007