pith. sign in

arxiv: 1907.05500 · v1 · pith:ART3OKLEnew · submitted 2019-07-11 · ⚛️ physics.flu-dyn

Active Flow Control for Drag Reduction of a Plunging Airfoil under Deep Dynamic Stall

Brener D'L\'elis Oliveira Ramos , William Roberto Wolf , Chi-An Yeh , Kunihiko Taira This is my paper

Pith reviewed 2026-05-24 22:29 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords active flow controldynamic stallplunging airfoildrag reductionvortex disruptionblowing and suctionSD7003 airfoil
0
0 comments X

The pith

Blowing and suction at specific frequencies on a plunging airfoil's leading edge disrupts dynamic stall vortex formation and reduces mean drag while preserving lift.

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

The paper uses high-fidelity simulations to test active flow control via leading-edge blowing and suction on a plunging SD7003 airfoil at Reynolds number 60,000. It reports that actuation within a particular frequency band, especially in a spanwise-uniform 2D arrangement, lowers both average drag and its fluctuations while leaving mean lift nearly unchanged. The mechanism is prevention of the dynamic stall vortex, which raises suction-side pressure near the trailing edge and lowers it near the leading edge. Readers interested in rotorcraft or turbine performance would see this as a route to mitigating the performance penalty of deep stall without sacrificing lift.

Core claim

For a specific frequency range of actuation, mean drag and drag fluctuations are substantially reduced while mean lift is maintained almost unaffected, especially for a 2D actuator setup. For this frequency range, 2D flow actuation disrupts the formation of the dynamic stall vortex, what leads to drag reduction due to a pressure increase along the airfoil suction side, towards the trailing edge region. At the same time, pressure is reduced on the suction side near the leading edge, increasing lift and further reducing drag.

What carries the argument

Spanwise-uniform 2D blowing-and-suction actuators at the leading edge that prevent dynamic stall vortex formation.

If this is right

  • Mean drag drops substantially and its fluctuations are suppressed for the identified actuation frequencies.
  • Mean lift coefficient remains nearly the same as the uncontrolled plunging case.
  • The 2D actuator arrangement outperforms spanwise-varying 3D arrangements in drag reduction.
  • Pressure recovery on the aft suction surface is the direct cause of the observed drag drop.

Where Pith is reading between the lines

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

  • If the actuation power cost is low enough, the net energy budget for sustained operation could become favorable in periodic plunging devices.
  • The same leading-edge placement and frequency scaling might transfer to other unsteady motions such as pitching or combined pitch-plunge.
  • Because the benefit is tied to vortex disruption rather than direct momentum injection, the approach may remain effective at modestly higher Reynolds numbers where the stall vortex still dominates.

Load-bearing premise

The high-order finite-difference solver on a staggered grid accurately reproduces the three-dimensional vortex dynamics and surface pressures under active control at this Reynolds number.

What would settle it

Wind-tunnel measurements of time-averaged drag coefficient on the same plunging airfoil with matching leading-edge blowing and suction at the reported frequencies that show no net drag reduction relative to the uncontrolled case.

Figures

Figures reproduced from arXiv: 1907.05500 by Brener D'L\'elis Oliveira Ramos, Chi-An Yeh, Kunihiko Taira, William Roberto Wolf.

Figure 1
Figure 1. Figure 1: FIG. 1: Actuator setup [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Profiles of function [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Grids considered in the mesh refinement study (only every other grid point in the [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Aerodynamic coefficients obtained using grids 1 and 2 and from Ref. [12] as [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Cycle to cycle variations in aerodynamic coefficients (grid 1). [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Airfoil position for different phase angles [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Spanwise-averaged vorticity contours at different phases of the plunging motion [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Iso-surfaces of Q criterion colored by [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Variations in aerodynamic coefficients for different actuation frequencies ( [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Mean aerodynamic loads compared to the baseline flow, mean lift to mean drag [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Aerodynamic coefficients versus effective angle of attack for 2D actuated flows [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Comparison between span-averaged values of [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Position [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Comparison of [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Comparison of [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Spanwise-averaged vorticity contours at different phase angles for the [PITH_FULL_IMAGE:figures/full_fig_p024_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Comparison of aerodynamic coefficients obtained by 2D and 3D actuation with [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Q-criterion colored by [PITH_FULL_IMAGE:figures/full_fig_p026_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: Distribution of [PITH_FULL_IMAGE:figures/full_fig_p027_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: Distribution of [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: Spanwise-averaged values of [PITH_FULL_IMAGE:figures/full_fig_p028_22.png] view at source ↗
read the original abstract

High-fidelity simulations are performed to study active flow control techniques for alleviating deep dynamic stall of a SD7003 airfoil in plunging motion. The flow Reynolds number is $Re=60{,}000$ and the freestream Mach number is $M=0.1$. Numerical simulations are performed with a finite difference based solver that incorporates high-order compact schemes for differentiation, interpolation and filtering on a staggered grid. A mesh convergence study is conducted and results show good agreement with available data in terms of aerodynamic coefficients. Different spanwise arrangements of actuators are implemented to simulate blowing and suction at the airfoil leading edge. We observe that, for a specific frequency range of actuation, mean drag and drag fluctuations are substantially reduced while mean lift is maintained almost unaffected, especially for a 2D actuator setup. For this frequency range, 2D flow actuation disrupts the formation of the dynamic stall vortex, what leads to drag reduction due to a pressure increase along the airfoil suction side, towards the trailing edge region. At the same time, pressure is reduced on the suction side near the leading edge, increasing lift and further reducing drag.

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 / 1 minor

Summary. The manuscript reports high-fidelity simulations of active flow control on a plunging SD7003 airfoil at Re=60,000 and M=0.1 using a high-order compact finite-difference solver on a staggered grid. Different spanwise arrangements of leading-edge blowing/suction actuators are tested; for a specific frequency range, especially with 2D actuation, mean drag and drag fluctuations decrease substantially while mean lift is nearly unaffected. The mechanism is identified as disruption of the dynamic stall vortex, producing a suction-side pressure rise toward the trailing edge and a pressure drop near the leading edge.

Significance. If the controlled-flow results hold, the work demonstrates a targeted active-control strategy that achieves drag reduction in deep dynamic stall without lift penalty. Mesh convergence and baseline coefficient agreement with prior data provide a credible foundation for the uncontrolled case and credit the numerical setup; the actuated results would extend this to practical flow-control applications in unsteady aerodynamics if the vortex-disruption mechanism is confirmed.

major comments (3)
  1. [Abstract] Abstract and results: the reported drag reduction and pressure changes for actuated cases are presented without error bars, ensemble statistics, or quantitative uncertainty estimates, in contrast to the mesh-convergence study performed for the baseline; this directly affects in the quantitative magnitude of the claimed reductions for the 2D actuator configuration.
  2. [Numerical method] Numerical method and validation sections: mesh convergence and agreement with available data are shown only for the uncontrolled plunging case; no controlled-experiment comparison or actuator-specific sensitivity study is referenced for the 2D leading-edge blowing/suction, leaving the capture of 3D vortex disruption and resulting pressure integrals unvalidated at Re=60,000.
  3. [Results] Mechanism discussion: the central claim that 2D actuation disrupts dynamic-stall vortex formation (leading to the reported suction-side pressure rise toward the trailing edge) rests on the compact-scheme solver accurately resolving spanwise structures under 2D actuation; without additional resolution or boundary-condition checks for the actuated cases, this mechanism remains a potential numerical artifact.
minor comments (1)
  1. [Abstract] The abstract refers to 'a specific frequency range' without stating the nondimensional values or the corresponding Strouhal numbers; adding these would improve reproducibility.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results: the reported drag reduction and pressure changes for actuated cases are presented without error bars, ensemble statistics, or quantitative uncertainty estimates, in contrast to the mesh-convergence study performed for the baseline; this directly affects in the quantitative magnitude of the claimed reductions for the 2D actuator configuration.

    Authors: The reported results are from deterministic high-fidelity simulations, with coefficients obtained by time-averaging over multiple plunging periods after initial transients have decayed. While explicit ensemble statistics or error bars were not included for the actuated cases, the drag reductions are consistent across the tested frequency band and actuator setups. We will revise the manuscript to include a quantitative discussion of cycle-to-cycle variations and the statistical convergence of the time averages for the actuated configurations. revision: partial

  2. Referee: [Numerical method] Numerical method and validation sections: mesh convergence and agreement with available data are shown only for the uncontrolled plunging case; no controlled-experiment comparison or actuator-specific sensitivity study is referenced for the 2D leading-edge blowing/suction, leaving the capture of 3D vortex disruption and resulting pressure integrals unvalidated at Re=60,000.

    Authors: Mesh convergence and validation against available data are presented for the baseline plunging case using the same numerical method and grids employed for all actuated simulations. The 2D leading-edge actuation is imposed via a time-dependent boundary condition on the existing mesh. No experimental data are available for the controlled SD7003 plunging case at this Reynolds number. We will add an actuator-specific grid-sensitivity study for the 2D configuration to the revised manuscript. revision: yes

  3. Referee: [Results] Mechanism discussion: the central claim that 2D actuation disrupts dynamic-stall vortex formation (leading to the reported suction-side pressure rise toward the trailing edge) rests on the compact-scheme solver accurately resolving spanwise structures under 2D actuation; without additional resolution or boundary-condition checks for the actuated cases, this mechanism remains a potential numerical artifact.

    Authors: The mechanism is supported by instantaneous and phase-averaged flow-field visualizations showing clear suppression of the dynamic-stall vortex under 2D actuation, together with the corresponding surface-pressure distributions. The high-order compact scheme and staggered-grid discretization have been validated on the baseline unsteady flow, and the 3D domain permits spanwise structures even when actuation is spanwise uniform. We will include an additional resolution and domain-size sensitivity check for the actuated 2D case in the revision. revision: yes

standing simulated objections not resolved
  • Absence of experimental data for the actively controlled plunging airfoil at Re=60,000, which precludes direct experimental validation of the actuated results.

Circularity Check

0 steps flagged

No circularity: results are direct numerical outputs from NS solver

full rationale

The paper reports aerodynamic coefficients and flow structures obtained by solving the compressible Navier-Stokes equations with a high-order compact finite-difference scheme on a staggered grid. A mesh-convergence study and comparison to existing (uncontrolled) data are stated, but no analytical derivation, fitted parameter, or self-referential equation is present. The central observations (drag reduction via disruption of the dynamic-stall vortex under 2D actuation) are computed quantities, not quantities that reduce to the input data or to a prior self-citation by construction. No load-bearing self-citation, ansatz smuggling, or renaming of known results occurs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The study rests on standard low-Mach compressible flow assumptions and numerical discretization choices rather than new physical postulates. No free parameters are fitted to produce the central claim; actuation frequencies are explored parametrically. No new entities are introduced.

axioms (2)
  • domain assumption The finite-difference solver with high-order compact schemes on a staggered grid resolves the relevant vortical structures at Re=60,000 and M=0.1
    Invoked by the choice of numerical method and the reported mesh-convergence study
  • domain assumption The SD7003 airfoil geometry and prescribed plunging kinematics are representative of the target unsteady flow regime
    Stated directly in the problem setup

pith-pipeline@v0.9.0 · 5743 in / 1493 out tokens · 31965 ms · 2026-05-24T22:29:32.260388+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

54 extracted references · 54 canonical work pages

  1. [1]

    W. J. McCroskey, Unsteady airfoils, Annual Review of Fluid Mechanics 14, 285 (1982)

    work page 1982

  2. [2]

    Carr, Progress in analysis and prediction of dynamic stall, Journal of Aircraft 25, 6 (1988)

    L. Carr, Progress in analysis and prediction of dynamic stall, Journal of Aircraft 25, 6 (1988)

    work page 1988

  3. [3]

    Ekaterinaris and M

    J. Ekaterinaris and M. Platzer, Computational prediction of airfoil dynamic stall, Progress in Aerospace Sciences 33, 759–846 (1998)

    work page 1998

  4. [4]

    T. C. Corke and F. O. Thomas, Dynamic stall in pitching airfoils: Aerodynamic damping and compressibility effects, Annual Review of Fluid Mechanics 47, 479–505 (2015)

    work page 2015

  5. [5]

    Eldredge and A

    J. Eldredge and A. Jones, Leading-edge vortices: Mechanics and modeling, Annual Review of Fluid Mechanics 51, 75–104 (2019)

    work page 2019

  6. [6]

    N. D. Ham and M. I. Young, Limit cycle torsional motion of helicopter blades due to stall, Journal of Sound and Vibration 4, 431–432 (1966)

    work page 1966

  7. [7]

    M. R. Visbal and J. S. Shang, Investigation of the flow structure around a rapidly pitching airfoil, AIAA Journal 27, 1044–1051 (1989)

    work page 1989

  8. [8]

    M. R. Visbal, On the formation and control of the dynamic stall vortex on a pitching airfoil, in AIAA Paper 1991-6 (1991). 30

    work page 1991

  9. [9]

    P. G. Choudhuri, D. D. Knight, and M. R. Visbal, Two-dimensional unsteady leading-edge separation on a pitching airfoil, AIAA Journal 32, 673–681 (1994)

    work page 1994

  10. [10]

    M. R. Visbal, Dynamic stall of a constant-rate pitching airfoil, Journal of Aircraft 27, 400–407 (1990)

    work page 1990

  11. [11]

    R. R., J. Windte, and S. U., Numerical and experimental flow analysis of moving airfoils with laminar separation bubbles, AIAA Journal 45, 1346–1356 (2007)

    work page 2007

  12. [12]

    M. R. Visbal, Numerical investigation of deep dynamic stall of a plunging airfoil, AIAA Journal 49, 2152–2170 (2011)

    work page 2011

  13. [13]

    M. R. Visbal, Numerical exploration of flow control for delay of dynamic stall on a pitching airfoil, in AIAA Paper 2014-2044 (2014)

    work page 2014

  14. [14]

    M. R. Visbal, Control of dynamic stall on a pitching airfoil using high-frequency actuation, in AIAA Paper 2015-1267 (2015)

    work page 2015

  15. [15]

    M. R. Visbal and D. J. Garmann, Control of dynamic stall over a pitching finite-aspect-ratio wing, in AIAA Paper 2017-4118 (2017)

    work page 2017

  16. [16]

    S. I. Benton and M. R. Visbal, Evaluation of thermoacoustic-based forcing for control of dynamic stall, in AIAA Paper 2018-3683 (2018)

    work page 2018

  17. [17]

    Visbal and S

    M. Visbal and S. Benton, Exploration of high-frequency control of dynamic stall using large- eddy simulations, AIAA Journal 56, 2974–2991 (2018)

    work page 2018

  18. [18]

    McCroskey, The phenomenon of dynamic stall, National Aeronautics and Space Adminis- tration (1981)

    W. McCroskey, The phenomenon of dynamic stall, National Aeronautics and Space Adminis- tration (1981)

    work page 1981

  19. [19]

    C.-K. Kang, Y. S. Baik, Bernal, L. P., M. V., and W. Shyy, Fluid dynamics of pitching and plunging airfoils for Reynolds number between 1 x 10 4 and 6 x 10 4, in AIAA Paper 2009-536 (2009)

    work page 2009

  20. [20]

    Y. S. Baik, J. M. Rausch, L. P. Bernal, and Ol., Experimental investigation of pitching and plunging airfoils at Reynolds number between 1 x 10 4 and 6 x 10 4, in AIAA Paper 2009-4030 (2009)

    work page 2009

  21. [21]

    V. M. Ol, L. P. Bernal, C.-K. Kang, and W. Shyy, Shallow and deep dynamic stall for flapping low Reynolds number airfoils, Experiments in Fluids 46, 883–901 (2009)

    work page 2009

  22. [22]

    Lorber, D

    P. Lorber, D. McCormick, T. Anderson, B. Wake, D. MacMartin, M. Pollack, T. Corke, and K. Breuer, Rotorcraft retreating blade stall control, in AIAA Paper 2000-2475 (2000). 31

    work page 2000

  23. [23]

    Greenblatt and I

    D. Greenblatt and I. Wygnanski, Dynamic stall control by periodic excitation, part 1: Naca 0015 parametric study, Journal of Aircraft 38, 430–438 (2001)

    work page 2001

  24. [24]

    Sun and S

    M. Sun and S. R. Sheikh, Dynamic stall suppression on an oscillating airfoil by steady and unsteady tangential blowing, Aerospace Science and Technology , 355–366 (1999)

    work page 1999

  25. [25]

    Weaver, K

    D. Weaver, K. W. McAlister, and J. Tso, Control of vr-7 dynamic stall by strong steady blowing, Journal of Aircraft 41, 1404–1413 (2004)

    work page 2004

  26. [26]

    T. C. Corke, P. O. Bowles, C. He, and E. H. Matlis, Sensing and control of flow separation using plasma actuators, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, 1459–1475 (2011)

    work page 2011

  27. [27]

    Lombardi, P

    A. Lombardi, P. Bowles, and T. Corke, Closed-loop dynamic stall control using a plasma actuator, AIAA Journal 51, 1130–1141 (2013)

    work page 2013

  28. [28]

    M. L. Post and T. C. Corke, Separation control using plasma actuators: Dynamic stall vortex control on oscillating airfoil, AIAA Journal 44, 3125–3135 (2006)

    work page 2006

  29. [29]

    Heine, M

    B. Heine, M. K., G. Joubert, and M. Raffel, Dynamic stall control by passive disturbance generators, AIAA Journal 51, 2086–2097 (2013)

    work page 2086

  30. [30]

    Martin, J

    P. Martin, J. Wilson, J. Berry, T. Wong, M. Moulton, and M. McVeigh, Passive control of compressible dynamic stall, in AIAA Paper 2008-7506 (2008)

    work page 2008

  31. [31]

    Traub, A

    L. Traub, A. Miller, and O. Rediniotis, Effects of active and passive flow control on dynamic stall vortex formation, Journal of Aircraft 41, 405–408 (2004)

    work page 2004

  32. [32]

    Ekaterinaris, Numerical investigations of dynamic stall active control for incompressible and compressible flows, Journal of Aircraft 39, 71–78 (2002)

    J. Ekaterinaris, Numerical investigations of dynamic stall active control for incompressible and compressible flows, Journal of Aircraft 39, 71–78 (2002)

    work page 2002

  33. [33]

    Florea and B

    R. Florea and B. Wake, Parametric analysis of directed-synthetic jets for improved dynamic- stall performance, 41st Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings (2003)

    work page 2003

  34. [34]

    L. Carr, M. Chandrasekhara, M. Wilder, and K. Noonan, Effect of compressibility on sup- pression of dynamic stall using a slotted airfoil, Journal of Aircraft 38, 296–309 (2001)

    work page 2001

  35. [35]

    Chandrasekhara, M

    M. Chandrasekhara, M. Tung, and P. Martin, Aerodynamic flow control using a variable droop leading edge airfoil, AVT Specialists’ Meet. Enhanc. NATO Mil. Flight Perform., Pap. RTO-MP-AVT-111 (2004)

    work page 2004

  36. [36]

    Joo, B.-S

    W. Joo, B.-S. Lee, K. Yee, and D.-H. Lee, Combining passive control method for dynamic stall control, Journal of Aircraft 43, 1120–1128 (2006). 32

    work page 2006

  37. [37]

    Feszty, E

    D. Feszty, E. Gillies, and M. Vezza, Alleviation of airfoil dynamic stall moments via trailing- edge-flap flow control, AIAA Journal 42, 17–25 (2004)

    work page 2004

  38. [38]

    Gerontakos and T

    P. Gerontakos and T. Lee, Dynamic stall flow control via a trailing-edge flap, AIAA Journal 44, 469–480 (2006)

    work page 2006

  39. [39]

    Greenblatt, I

    D. Greenblatt, I. J. Wygnanski, and C. L. Rumsey, Aerodynamic flow control, Encyclopedia of Aerospace Engineering (2010)

    work page 2010

  40. [40]

    Z. U. A. Warsi, K. Devarayalu, and J. F. Thompson, Numerical solution of the Navier-Stokes equations for arbitrary blunt bodies in supersonic flows, Numerical Heat Transfer 1, 499–516 (1978)

    work page 1978

  41. [41]

    Yamamoto and H

    S. Yamamoto and H. Daiguji, A numerical method for the transonic cascade flow problem, Computers and Fluids 19, 461–477 (2001)

    work page 2001

  42. [42]

    Orlandi, A numerical method for direct simulation of turbulence in complex geometries, CTR Annual Research Briefs , 215–229 (1989)

    P. Orlandi, A numerical method for direct simulation of turbulence in complex geometries, CTR Annual Research Briefs , 215–229 (1989)

    work page 1989

  43. [43]

    Choi, Turbulent Drag Reduction: Studies of Feedback Control and Flow Over Riblets, Ph.D

    H. Choi, Turbulent Drag Reduction: Studies of Feedback Control and Flow Over Riblets, Ph.D. thesis, Stanford University (1992)

    work page 1992

  44. [44]

    Yang and Voke, Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature, Journal of Fluid Mechanics 439, 305–333 (2001)

    Z. Yang and Voke, Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature, Journal of Fluid Mechanics 439, 305–333 (2001)

    work page 2001

  45. [45]

    Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics (Dover Publications, 1989)

    R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics (Dover Publications, 1989)

    work page 1989

  46. [46]

    S. K. Lele, Compact finite difference schemes with spectral-like resolution, Journal of Com- putational Physics 103, 16–42 (1992)

    work page 1992

  47. [47]

    Nagarajan, Leading Edge Effects in Bypass Transition , Ph.D

    S. Nagarajan, Leading Edge Effects in Bypass Transition , Ph.D. thesis, Stanford University (2004)

    work page 2004

  48. [48]

    See supplemental material at [url to be inserted by publisher] for a movie showing spanwise- averaged vorticity contours at different phases of the plunging motion with and withour ac- tuation. ()

    work page

  49. [49]

    See supplemental material at [url to be inserted by publisher] for a movie showing contours of spanwise-averaged pressure coefficient with iso-contours of z-vorticity with and withour actuation. ()

    work page

  50. [50]

    Yeh and K

    C. Yeh and K. Taira, Resolvent-analysis-based design of airfoil separation control, Journal of Fluid Mechanics 867, 572–610 (2019). 33

    work page 2019

  51. [51]

    Munday and K

    P. Munday and K. Taira, Effects of wall-normal and angular momentum injections in airfoil separation control, AIAA Journal 56, 1830–1842 (2018)

    work page 2018

  52. [52]

    See supplemental material at [url to be inserted by publisher] for a movie showing iso-surfaces of q-criterion colored by pressure coefficient comparing 2d and 3d actuations. ()

    work page

  53. [53]

    See supplemental material at [url to be inserted by publisher] for a movie showing the impact of different types of actuation on pressure coefficient along the airfoil suction side. ()

    work page

  54. [54]

    See supplemental material at [url to be inserted by publisher] for a movie showing the impact of different types of actuation on friction coefficient along the airfoil suction side. (). 34

    work page