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.
Highlights
Low-Reynolds-number flows at low speeds and small scales, despite being incompressible and nonthermodynamic, are rife with complexity owing to the effects of viscosity and flow separation [49]
It was seen that there is a critical value of the leading-edge suction parameter (LESP) for a given airfoil and Reynolds number at which leading-edge vortex (LEV) formation is initiated, except for motions with varying pitch rates that have varying degrees of trailing-edge flow separation
The use of LESP must be restricted to kinematics with high pitch rates (K > 0.1), well beyond those typical of dynamic stall, where the influence of trailing-edge separation is comparatively small
Summary
Low-Reynolds-number flows at low speeds and small scales, despite being incompressible and nonthermodynamic, are rife with complexity owing to the effects of viscosity and flow separation [49]. A new theoretical method based on the unsteady thin-airfoil theory developed by Katz and Plotkin [38], accounting for large amplitudes of motion and nonplanar wakes was developed by the Ramesh et al [57] and applied to a ramp-hold-return pitching maneuver The results from this model were compared against those from Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) and experimental (water tunnel) methods. We study the LESP concept in more detail using a large set of experimental and CFD studies involving LEV formation, spanning a broad range of relevant parameters, with an aim toward establishing the envelope of applicability of the LESP criterion and to isolate the effect of various parameters on LEV formation It has been known for several decades, especially among the dynamic stall community, that onset of separation at the leading edge is governed by the criticality of flow properties at the leading edge. Using the observation that LEV formation occurs only when the LESP reaches the critical value, it is shown that the motion kinematics can be designed to either avoid or intentionally trigger LEV formation by tailoring the LESP variation
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