Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

Theoretical and Computational Fluid Dynamics, Aug 2017

A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.

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Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

Theoretical and Computational Fluid Dynamics April 2018, Volume 32, Issue 2, pp 109–136 | Cite as Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows AuthorsAuthors and affiliations Kiran RameshKenneth GranlundMichael V. OlAshok GopalarathnamJack R. Edwards Open Access Original Article First Online: 14 August 2017 5 Shares 580 Downloads Abstract A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements. KeywordsLESP LEV Vortex dynamics Unsteady aerodynamics Low Reynolds number Flow separation  List of symbols \(\alpha \) Angle between the airfoil and inertial horizontal \(\dot{\alpha }\) Pitch rate \(\dot{h}\) Plunge rate \(\eta \) Variation of camber along airfoil \(\gamma \) Chordwise distribution of bound vorticity on airfoil \(\varGamma _b\) Bound circulation of airfoil at time t \(\varGamma _{\mathrm{tev}_m}\) Strength of mth wake/trailing-edge vortex \(\omega \) Angular frequency \(\phi \) Velocity potential \(\phi _\mathrm{B}\) Velocity potential from bound circulation \(\phi _\mathrm{tev}\) Velocity potential from trailing-edge vorticity (wake circulation) \(\theta \) Variable of transformation of chordwise distance \(A_{0},A_{1},A_{2}\ldots \) Fourier coefficients Bxyz Body frame c Airfoil chord \(C_\mathrm{f}\) Skin friction coefficient \(C_\mathrm{p}\) Pressure coefficient h Plunge displacement in the inertial Z direction \(K = \dot{\alpha } c/2U\) Reduced frequency (ramp) \(k = \omega c/2U\) Reduced frequency (sinusoidal) LESP Leading-edge suction parameter \(\hbox {LESP}_\mathrm{crit}\) Critical value of LESP corresponding to LEV initiation OXYZ Inertial frame Re Reynolds number t Time \(t^*\) Nondimensional time \(=tU/c\) U Freestream velocity W Local downwash \(x_\mathrm{p}\) Pivot location on the airfoil from 0 to c Communicated by Jeff D. Eldredge. Download to read the full article text References 1. Abbott, I.H., von Doenhoff, A.E.: Theory of Wing Sections. Dover, New York (1959)Google Scholar 2. Acharya, M., Metwally, M.H.: Unsteady pressure field and vorticity production over a pitching airfoil. AIAA J. 30(2), 403–411 (1992)CrossRefGoogle Scholar 3. Baik, Y.S., Bernal, L.P., Granlund, K., Ol, M.V.: Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J. Fluid Mech. 709(1), 37–68 (2012). doi: 10.1017/jfm.2012.318 MathSciNetCrossRefzbMATHGoogle Scholar 4. Beddoes, T.S.: Onset of leading edge separation effects under dynamic conditions and low Mach number. In: 34th Annual forum of the American Helicopter Society (1978)Google Scholar 5. Bos, F.M., van Oudheusden, B.W., Bijl, H.: Wing performance and 3-D vortical structure formation in flapping flight. J. Fluids Struct. 42, 130–151 (2013)CrossRefGoogle Scholar 6. Brunton, S.L., Rowley, C.W., Williams, D.R.: Reduced-order unsteady aerodynamic models at low Reynolds numbers. J. Fluid Mech. 724(1), 203–233 (2013)CrossRefzbMATHGoogle Scholar 7. Carr, L.: Progress in analysis and prediction of dynamic stall. J. Aircr. 25(1), 6–17 (1988)MathSciNetCrossRefGoogle Scholar 8. Carr, L.W., Platzer, M.F., Chandrasekhara, M.S., Ekaterinaris, J.: Experimental and computational studies of dynamic stall. In: Cebeci, T. (ed.) Numerical and Physical Aspects of Aerodynamic Flows IV, pp. 239–256. Springer, Berlin (1990). doi: 10.1007/978-3-662-02643-4_15 CrossRefGoogle Scholar 9. Carr, Z.R., Chen, C., Ringuette, M.J.: Finite-span rotating wings: three-dimensional vortex formation and variations with aspect ratio. Exp. Fluids 54(2), 1–26 (2013)CrossRefGoogle Scholar 10. Cassidy, D.A., Edwards, J.R., Tian, M.: An investigation of interface-sharpening schemes for multi-phase mixture flows. J. Comput. Phys. 228(16), 5628–5649 (2009). doi: 10.101 (...truncated)


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Kiran Ramesh, Kenneth Granlund, Michael V. Ol, Ashok Gopalarathnam, Jack R. Edwards. Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows, Theoretical and Computational Fluid Dynamics, 2017, pp. 109-136, Volume 32, Issue 2, DOI: 10.1007/s00162-017-0442-0