Aerodynamic Hysteresis of a Low-Reynolds-Number Airfoil

Abstract

L OW-REYNOLDS-NUMBER airfoil aerodynamics is important for bothmilitary and civilian applications. The applications include propellers, sailplanes, ultralight man-carrying/man-powered aircraft, high-altitude vehicles, wind turbines, unmanned aerial vehicles (UAVs), and micro air vehicles (MAVs). For the applications just listed, the combination of small length scale and low flight velocities results in airfoils operating at low chord Reynolds numbers of Re < 500; 000. It is well known that many significant aerodynamic problems occur below chord Reynolds numbers of about 500,000. Hysteresis phenomena have been found to be relatively common for roundnosed airfoils at low Reynolds numbers. Aerodynamic hysteresis of an airfoil refers to airfoil aerodynamic characteristics as it becomes history dependent, i.e., dependent on the sense of change of the angle of attack, near the airfoil stall angle. The coefficients of lift, drag, and moment of the airfoil are found to be multiple-valued rather than single-valued functions of the angle of attack. Aerodynamic hysteresis is of practical importance because it produces widely different values of lift coefficient and lift-to-drag ratio for a given angle of attack. It could also affect the recovery from stall and/or spin flight conditions. Whereas aerodynamic hysteresis associated with the pitchingmotion of airfoils (also known as dynamic stall) has been investigated extensively as summarized in the review article of McCorskey [1], hysteresis phenomena observed for static stall of an airfoil have received much less attention. Mueller [2] investigated the aerodynamic characteristics of Lissaman 7769 and Miley M06-13-128 airfoils at low Reynolds numbers, and found both airfoils produced hysteresis loops in the profiles of measured lift and drag forces when they operated below chord Reynolds numbers of 300,000. Based on qualitative flow visualization with smoke, he suggested that airfoil hysteresis is closely related to laminar boundary-layer transition and separation on the airfoils. Hoffmann [3] studied the aerodynamic characteristics of a NACA 0015 airfoil at a chord Reynolds number of 250,000, and hysteresis loopwas observed in themeasured coefficients of drag and lift. He also found that hysteresis was observed for low-freestream turbulence cases but disappeared for high-freestream turbulence cases. More recently, Mittal and Saxena [4] conducted a numerical study to predict the aerodynamic hysteresis near the static stall angle of a NACA 0012 airfoil in comparison with the experimental data of Thibert et al. [5]. In the present study, we report the measurement results of an experimental study to investigate aerodynamic hysteresis near the static stall angle of a low-Reynolds-number airfoil. In addition to mapping surface pressure distribution around the airfoil with pressure sensors, a high-resolution particle image velocimetry (PIV) system was used to make flowfield measurements to quantify the occurrence and behavior of boundary-layer transition and/or separation on the airfoil when aerodynamic hysteresis occurs. To the best knowledge of the authors, this is the first effort of its nature. The primary objective of the present study is to gain further insight into fundamental physics of aerodynamic hysteresis. In addition, the quantitative flowfield measurements will be used as the database for the validation of computational fluid dynamics (CFD) simulations of such complex phenomena for the optimum design of low-Reynoldsnumber airfoils.