# Numerical Investigation of Jet Angle Effect on Airfoil Stall Control
## 1 Introduction  
Stall occurs when a lifting surface loses its aerodynamic lift. A well-known reason of the stall is the flow separation from the surface. An airfoil would be the best example to describe the stall phenomenon. As the angle of attack \(\alpha\) increases beyond the stall angle \(\alpha_{stall}\), the flow is detached from the airfoil surface. The flow may separate from the trailing edge or the leading edge, depending on the specific design of an airfoil and the flow condition including the Reynolds and Mach numbers [1]. The stall phenomenon associated with a lifting body at fixed angles of attack is called static stall. In contrast to static stall, dynamic stall occurs when the angle of attack changes rapidly due to airfoil motion. In this study, both static and dynamic stall are investigated. For dynamic stall, a pitching motion is assigned to an airfoil with the maximum pitch angle being significantly larger than the static stall angle. Static and dynamic stall of an airfoil are depicted in Figure 1. Several key stages of the dynamic stall are compared to the static stall for the OA209 airfoil at the Mach number \(Ma=0.3\) and the Reynolds number \(Re=\frac{\rho U_{\infty}c}{h}=1.15\times 10^{6}\) where \(\rho\) is the density, \(U_{\infty}\) is the freestream velocity, \(c\) is the airfoil chord length, and \(\mu\) is the viscosity. The non-dimensionalized pitching frequency \(k=2\pi fc/(2U_{\infty})\) is determined for a rotor-relevant pitch frequency. Stage 1 in the upstroke region, which is still before the static stall angle, is similar to the static airfoil. Around stage 2, dynamic stall vortex (DSV) is formed near the leading edge. DSV reduces the pressure on the suction side further, compared to the static case, which results in the lift increase. From stage 2 to 3, DSV convects downstream, inducing more lift. Such additional lift is accompanied with the drag increase. From stage 2 to 3, the moment stall occurs as DSV moves to the trailing edge. The moment stall indicates a significant pitching-down moment because of the additional lift near the trailing edge. From stage 3 to 4, DSV is finally detached from the surface, which results in the lift stall. At stage 5, near the peak angle, shedding vortices produce the load fluctuation. In the downstroke region, the airfoil undergoes the severe stall until a small enough angle for the flow to reattach on the airfoil from the leading edge, which occurs around stage 6. The cycle restarts, as the angle reaches to the minimum. Stall phenomena, typically dynamic stall, impact on designing and analyzing lift surfaces. For example, conventional helicopter main rotor blades frequently encounter dynamic stall in high-speed forward flight conditions [2; 3; 4; 5; 6; 7]. The blade stall can occur in the retreating side because the blade needs to pitch up in order to balance aerodynamic forces. The retreating blade stall can decrease the performance of the helicopter and cause structural damage in the main rotor system. In contrast to the rotary wing, fixed-wing aircraft can use dynamic stall to improve performance such as super-maneuverability [8; 9; 10]. Wind turbine blades also experience dynamic stall under highly unsteady conditions [11; 12; 13; 14]. Stall suppression with an active flow control technique is of interest in this study. Various active flow control techniques using fluidic actuators have been studied to mitigate flow separation [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. Among numerous methods, steady-blowing jet would be the simplest fluidic actuation, ejecting a jet flow continuously into the surrounding. Recently, [PERSON] et al. investigated steady-blowing jet of high jet momentum in both simulation and wind tunnel tests [16; 17; 18; 19]. Their experiments demonstrate  
Figure 1: Static and dynamic stalls of OA209 airfoil at \(Ma=0.3\), \(Re=1.15\times 10^{6}\) and \(k=0.05\). that the steady-blowing jet which is normal to the airfoil chord is able to suppress the moment stall.