pith. sign in

arxiv: 2604.23120 · v1 · submitted 2026-04-25 · ⚛️ physics.flu-dyn

Lift and leading-edge suction parameter of separated flows over an NACA0012 at high angles of attack

Ching Chang , You-Peng Shih , Tang-An Li This is my paper

Pith reviewed 2026-05-08 07:32 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords leading-edge suction parameterNACA0012 airfoilseparated flowshigh angle of attackcomputational fluid dynamicslift correlationleading-edge vortexvorticity flux
0
0 comments X

The pith

The leading-edge suction parameter correlates with lift on a stationary NACA0012 airfoil at high angles of attack.

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

The paper applies the leading-edge suction parameter (LESP) to analyze separated flows over a stationary NACA0012 airfoil at high angles of attack through CFD simulations. For laminar flow at Re=1000, instantaneous LESP shows strong correlation with lift, whereas for turbulent flow at Re=10^5, the time-averaged LESP correlates with lift. Examination of vorticity flux further illuminates the mechanisms of vortex formation and their impact on aerodynamic forces. This extends the utility of LESP beyond moving airfoils to fixed wings, informing better vortex-based aerodynamic models.

Core claim

The flow condition at the leading edge governs the dynamics of the leading-edge vortex. The leading-edge suction parameter (LESP) is a dimensionless metric proposed to quantify the leading-edge flow condition and is implemented in the LESP-modulated discrete vortex method. We conduct computational fluid dynamics (CFD) simulations for a stationary NACA0012 airfoil at high angles of attack, and extract the leading-edge flow quantities from the CFD data. In addition, vorticity flux, which contributes to the formation of vortices above the top surface of the airfoil, is also investigated. We show that for the laminar case (Re=1000), the instantaneous LESP is well correlated with the lift, while,

What carries the argument

The leading-edge suction parameter (LESP), a dimensionless metric that quantifies the leading-edge flow condition to control the onset of separation and leading-edge vortex formation.

If this is right

  • LESP thresholds can be used to predict the timing of leading-edge vortex formation in vortex-based models for stationary airfoils.
  • Vorticity flux analysis reveals the budget that forms vortices on the airfoil upper surface and links it to overall aerodynamic performance.
  • The correlations support refinements to LESP-modulated discrete vortex methods for both moving and fixed airfoils in high-angle-of-attack conditions.
  • Insights apply to biomimetic flight where wings encounter unsteady high-angle-of-attack flows.

Where Pith is reading between the lines

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

  • Surface pressure or velocity measurements near the leading edge could allow real-time lift estimation from LESP without resolving the full flow field.
  • The same extraction procedure could be tested on other airfoils or at intermediate Reynolds numbers to check how widely the laminar-versus-turbulent distinction holds.
  • Incorporating LESP into reduced-order models might enable faster design exploration for wings that must operate in separated-flow regimes.

Load-bearing premise

The LESP metric developed for moving airfoils can be directly extracted from CFD on a stationary airfoil and its correlation with lift holds without post-hoc tuning of thresholds or flow-field sampling locations.

What would settle it

CFD simulations of the NACA0012 at Re=1000 showing no correlation between instantaneous LESP and lift, or at Re=10^5 showing no correlation between time-averaged LESP and lift, would falsify the central claim.

read the original abstract

The flow condition at the leading edge governs the dynamics of the leading-edge vortex, which is crucial for understanding the separated flow over an airfoil at high angle of attack. Furthermore, with extensive applications in biomimetic flight, the wings encountering high-angle-of-attack situations in an unsteady manner are of great interest. The leading-edge suction parameter (LESP) is a dimensionless metric proposed to quantify the leading-edge flow condition, and is implemented in the LESP-modulated discrete vortex method, which successfully predicts aerodynamics of airfoils in motion. To discern the timing of leading-edge vortex formation, a critical threshold for LESP is chosen to control the onset of separation. However, it is not obvious that the same strategy could be applied to a stationary wing where the separation is not dominated by the motion of the airfoil. We conduct computational fluid dynamics (CFD) simulations for a stationary NACA0012 airfoil at high angles of attack, and extract the leading-edge flow quantities from the CFD data. In addition, vorticity flux, which contributes to the formation of vortices above the top surface of the airfoil, is also investigated to reveal the vorticity budget and its relevance to aerodynamic performance. We show that for the laminar case ($Re=1000$), the instantaneous LESP is well correlated with the lift, while for the turbulence ($Re=10^5$), the time-averaged LESP is well correlated with the lift. The result would provide insights into future improvements for vortex-based models of separated flows.

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

3 major / 2 minor

Summary. The paper conducts CFD simulations of flow over a stationary NACA0012 airfoil at high angles of attack for Re=1000 (laminar) and Re=10^5 (turbulent). It extracts the leading-edge suction parameter (LESP) directly from the simulated velocity/pressure fields and reports that instantaneous LESP correlates well with lift in the laminar case while time-averaged LESP correlates with lift in the turbulent case. Vorticity flux is also analyzed to relate vortex formation and budget to aerodynamic forces, with the goal of informing improvements to LESP-modulated discrete vortex models for separated flows on stationary wings.

Significance. If the reported correlations prove robust, the work would usefully extend the LESP framework—originally developed for moving airfoils—to stationary high-AoA cases, offering a potential diagnostic for leading-edge vortex onset and a bridge toward more accurate vortex-based reduced-order models. The vorticity-budget analysis adds physical insight into the mechanisms linking leading-edge conditions to lift. No machine-checked proofs or open reproducible code are provided, but the direct comparison of LESP and lift from the same simulations is a clear strength if the extraction procedure is shown to be independent of post-hoc tuning.

major comments (3)
  1. [LESP extraction procedure (Results section)] The central claim that LESP extracted from stationary viscous CFD correlates with lift rests on the assumption that the extraction procedure matches the original moving-airfoil definition without post-hoc choices of sampling station, local velocity scale, or smoothing. No explicit validation or sensitivity study of these choices is described, which directly affects whether the instantaneous (Re=1000) and time-averaged (Re=10^5) correlations are intrinsic or artifacts of the implementation.
  2. [Numerical methods / CFD setup] Grid-convergence checks and turbulence-model validation (e.g., for the Re=10^5 case) are not reported. Because both LESP and lift are derived from the same CFD fields, the absence of these standard verifications undermines quantitative support for the stated correlations.
  3. [Results and abstract] The abstract and results describe the correlations only qualitatively ('well correlated'). Without reported quantitative metrics such as Pearson coefficients, R² values, or time-series cross-correlation lags, it is difficult to assess the strength and statistical significance of the central claim.
minor comments (2)
  1. [Abstract and Methods] The range of angles of attack and the specific turbulence closure used at Re=10^5 should be stated explicitly in the abstract and methods.
  2. [Introduction] Clarify whether the LESP threshold for separation onset is taken directly from prior moving-airfoil literature or adjusted for the stationary case.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments identify important areas where additional detail and quantitative support will strengthen the manuscript. We address each major comment below and will incorporate the suggested revisions.

read point-by-point responses

  1. Referee: [LESP extraction procedure (Results section)] The central claim that LESP extracted from stationary viscous CFD correlates with lift rests on the assumption that the extraction procedure matches the original moving-airfoil definition without post-hoc choices of sampling station, local velocity scale, or smoothing. No explicit validation or sensitivity study of these choices is described, which directly affects whether the instantaneous (Re=1000) and time-averaged (Re=10^5) correlations are intrinsic or artifacts of the implementation.

    Authors: We agree that explicit documentation of the extraction procedure is essential for reproducibility and to confirm that the reported correlations are not implementation artifacts. The procedure follows the original LESP definition based on the leading-edge tangential velocity and pressure fields, with sampling performed at a fixed small offset from the leading edge and normalization by the local velocity scale. In the revised manuscript we will add a dedicated subsection in the Results section that fully specifies the sampling location, velocity scale, any smoothing applied, and the exact formulas used. We will also include a sensitivity study varying the sampling station by ±0.5% chord and the velocity scale by ±10% to demonstrate that the instantaneous (laminar) and time-averaged (turbulent) correlations remain robust. revision: yes

  2. Referee: [Numerical methods / CFD setup] Grid-convergence checks and turbulence-model validation (e.g., for the Re=10^5 case) are not reported. Because both LESP and lift are derived from the same CFD fields, the absence of these standard verifications undermines quantitative support for the stated correlations.

    Authors: We acknowledge that grid-convergence and validation data are standard requirements and were inadvertently omitted. In the revised manuscript we will add a new subsection under Numerical Methods that presents grid-convergence results for both lift coefficient and LESP at Re=1000 and Re=10^5, showing that the quantities of interest change by less than 2% between the medium and fine grids. For the turbulent case we will include validation of the chosen turbulence model against available experimental lift data for the NACA0012 at high angles of attack, confirming that the time-averaged lift coefficients fall within the scatter of published measurements. revision: yes

  3. Referee: [Results and abstract] The abstract and results describe the correlations only qualitatively ('well correlated'). Without reported quantitative metrics such as Pearson coefficients, R² values, or time-series cross-correlation lags, it is difficult to assess the strength and statistical significance of the central claim.

    Authors: We agree that quantitative metrics will allow readers to evaluate the strength of the correlations more rigorously. In the revision we will compute and report Pearson correlation coefficients and R² values for the instantaneous LESP-lift relationship at Re=1000 and for the time-averaged quantities at Re=10^5. Where appropriate we will also examine time-series cross-correlation lags. The abstract will be updated to include the quantitative correlation values (e.g., “Pearson r > 0.85”) while preserving the overall narrative. revision: yes

Circularity Check

0 steps flagged

No circularity: LESP-lift correlation is direct empirical comparison from CFD fields

full rationale

The paper runs CFD on a fixed NACA0012, extracts LESP from the velocity/pressure field at the leading edge using the standard definition, computes lift from the identical simulation, and reports observed correlations (instantaneous at Re=1000, time-averaged at Re=10^5). No equation defines LESP in terms of lift or vice versa, no parameter is fitted on one quantity to 'predict' the other, and no self-citation chain substitutes for the reported comparison. The result is an independent post-processing observation on the same dataset rather than a self-referential derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the prior definition of LESP from moving-airfoil work and standard incompressible CFD assumptions at fixed Reynolds numbers; no new free parameters or entities are introduced in the abstract.

axioms (1)
  • domain assumption LESP quantifies the leading-edge flow condition and controls separation onset
    Invoked to justify extracting LESP from CFD and correlating it with lift for stationary case.

pith-pipeline@v0.9.0 · 5578 in / 1180 out tokens · 92285 ms · 2026-05-08T07:32:55.044026+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

  1. [1]

    Deparday, J., He, X., Eldredge, J.D., Mulleners, K., Williams, D.R.: Experimental quantification of unsteady leading-edge flow separation. J. Fluid Mech.941, 60 (2022)

    work page 2022

  2. [2]

    Khalifa, N.M., Rezaei, A., Taha, H.E.: On computational simulations of dynamic stall and its three-dimensional nature. Phys. Fluids35(10) (2023)

    work page 2023

  3. [3]

    Chen, J., Lu, Z., Wu, B., He, S., Xiao, T., Tong, M., Kan, K.: Flow transition and vortex evolution of a symmetric airfoil at low reynolds number and high angle of attack. Phys. Fluids37(2) (2025)

    work page 2025

  4. [4]

    Eldredge, J.D., Jones, A.R.: Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech.51, 75–104 (2019)

    work page 2019

  5. [5]

    Deparday, J., Mulleners, K.: Modeling the interplay between the shear layer and leading edge suction during dynamic stall. Phys. Fluids31(10) (2019)

    work page 2019

  6. [6]

    Durante, D., Rossi, E., Colagrossi, A.: Bifurcations and chaos transition of the flow over an airfoil at low Reynolds number varying the angle of attack. Commun. Nonlinear Sci. Numer. Simul.89, 105285 (2020)

    work page 2020

  7. [7]

    Akkala, J.M., Buchholz, J.H.: Vorticity transport mechanisms governing the development of leading-edge vortices. J. Fluid Mech.829, 512–537 (2017)

    work page 2017

  8. [8]

    Li, Z.-Y., Feng, L.-H., Wang, T., Liang, Y.: Lift generation mechanism of the leading-edge vortex for an unsteady plate. J. Fluid Mech.972, 30 (2023) 17

    work page 2023

  9. [9]

    Ramesh, K., Gopalarathnam, A., Granlund, K., Ol, M.V., Edwards, J.R.: Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding. J. Fluid Mech.751, 500–538 (2014)

    work page 2014

  10. [10]

    Cambridge University Press, ??? (2001)

    Katz, J., Plotkin, A.: Low-speed Aerodynamics. Cambridge University Press, ??? (2001)

    work page 2001

  11. [11]

    Ramesh, K., Granlund, K., Ol, M.V., Gopalarathnam, A., Edwards, J.R.: Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows. Theor. Comput. Fluid Dyn.32, 109–136 (2018)

    work page 2018

  12. [12]

    Narsipur, S., Hosangadi, P., Gopalarathnam, A., Edwards, J.R.: Variation of leading-edge suction during stall for unsteady aerofoil motions. J. Fluid Mech. 900, 25 (2020)

    work page 2020

  13. [13]

    In: Proc

    Spalart, P.R.: Comments on the feasibility of LES for wings and on the hybrid RANS/LES approach. In: Proc. First AFOSR Int. Conf. DNS/LES, pp. 137–147 (1997)

    work page 1997

  14. [14]

    Shur, M., Spalart, P., Strelets, M., Travin, A.: Detached-eddy simulation of an airfoil at high angle of attack. In: Eng. Turbul. Model. Exp. 4, pp. 669–678. Elsevier, Amsterdam (1999)

    work page 1999

  15. [15]

    Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K., Travin, A.: A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn.20, 181 (2006)

    work page 2006

  16. [16]

    Flow Turbul

    Gritskevich, M.S., Garbaruk, A.V., Sch¨ utze, J., Menter, F.R.: Development of DDES and IDDES formulations for thek−ωshear stress transport model. Flow Turbul. Combust.88, 431–449 (2012)

    work page 2012

  17. [17]

    Kurtulus, D.F.: On the unsteady behavior of the flow around NACA0012 airfoil with steady external conditions at Re =1000. Int. J. Micro Air Veh.7(3), 301–326 (2015)

    work page 2015

  18. [18]

    Ohtake, T., Nakae, Y., Motohashi, T.: Nonlinearity of the aerodynamic charac- teristics of the NACA0012 airfoil at low reynolds numbers. J. Jpn. Soc. Aeronaut. Space Sci.55(644), 439–445 (2007)

    work page 2007

  19. [19]

    In: 12th Ankara International Aerospace Conference (2023)

    G¨ uney, M., Kurtulus, D.F.: Effect of Reynolds number on NACA 0012 airfoil at low Reynolds numbers. In: 12th Ankara International Aerospace Conference (2023). Ankara, Turkey

    work page 2023

  20. [20]

    Pitt Ford, C.W., Babinsky, H.: Lift and the leading-edge vortex. J. Fluid Mech. 720, 280–313 (2013) 18

    work page 2013

  21. [21]

    Ladson, C.L., Hill, A.S., Johnson, J. W. G.: Pressure distributions from high Reynolds number transonic tests of an NACA 0012 airfoil in the Langley 0.3-meter transonic cryogenic tunnel. Technical Report TM 100526, NASA (December 1987)

    work page 1987

  22. [22]

    Technical Report TM 4074, NASA (October 1988) 19

    Ladson, C.L.: Effects of independent variation of Mach and Reynolds numbers on the low-speed aerodynamic characteristics of the NACA 0012 airfoil section. Technical Report TM 4074, NASA (October 1988) 19

    work page 1988