# Numerical Study of Flow Separation Control over a Hump Airfoil Using a Novel Sweeping Jet Actuator
## 1 Introduction  
A boundary layer separates when the fluid within it lacks the energy to counteract the kinetic energy losses caused by adverse pressure gradients and viscous dissipation in a given application. This separation can lead to substantial energy losses, resulting in increased drag, decreased lift, or reduced total pressure recovery, thus diminishing system performance. To mitigate this, separation control methods [1, 2, 3] are often implemented to energize the slowed fluid near the wall within the boundary layer. The main approaches for energizing the boundary layer and controlling flow separation involve adding momentum and vorticity to the boundary layer. This vorticity can be introduced either passively or actively. Passive control methods such as vortex generators [4, 5] and winglets [6, 7] have been widely used in various scenarios to suppress boundary layer separation. However, passive control methods have the problem of modifying the geometric surface and not being able to suppress boundary layer separation according to actual operating conditions, and may even have side effects. On the contrary, active control methods can effectively suppress boundary layer separation by transmitting an additional momentum, which can be turned on and off according to actual operating conditions. Currently, it has become a research hotspot, and many active flow control methods and technologies have been proposed and validated, such as Synthetic jet [8, 9], Plasma [10, 11], Sweeping jet (SWJ) actuator [12, 13, 14], and so on. In the flow control of synthetic jets, many studies have focused on momentum coefficient (Cu) and frequency, as well as the position of actuators. [PERSON] et al. [15] investigated the impact of synthetic jets at various frequencies and momentum coefficients on the size of separation vortices and the drag resistance of a cylinder. Theydiscovered that the maximum reduction in drag resistance occurred when the momentum coefficient, C\(\upmu\), was 10.8% and the frequency, \(f^{+}\), was 0.98. The definition of \(f^{+}\) is the ratio of the synthesized jet frequency to the Karman vortex street frequency. [PERSON] et al. [16] studied the response of turbulent separation bubbles (TSB) to three driving frequencies of synthetic jets through direct numerical simulation. It was found that when the sinusoidal frequency was the two natural frequencies of the undisturbed separated bubbles, a very large scale lateral rotating vortex was formed, resulting in a 50% reduction in the average TSB length. In addition to synthetic jets, SWJ actuators also have frequency characteristics. As effective tools for flow control [17], sweeping jet actuators have been extensively studied [18; 19; 20; 21]. Figure 1 illustrates the fundamental mechanism of the SWJ actuator. SWJ actuators without moving parts can generate a self-induced and self-sustaining oscillating jet, making it more practical and appealing than other flow control methods [23]. Significant research has been conducted to deepen the understanding of the jet oscillation mechanism in SWJ actuators [24; 25; 26] and their role in active flow control. [PERSON] et al. [27; 28] used phase-averaged particle image velocimetry (PIV) and time-resolved pressure measurements to visualize internal flow field structures within an enlarged SWJ actuator, providing detailed insights into the jet oscillation pattern. [PERSON] et al. [29] conducted experiments using water as the working fluid to simultaneously measure the internal and external flow fields of an SWJ actuator, examining the synchronization and interaction of twin SWJ actuators. [PERSON] and [PERSON] [30] also explored the synchronization of a pair of opposed actuators. On the other hand, numerical studies conducted by [PERSON] et al. [31; 32] in a quiescent environment have validated the feasibility of using an SWJ actuator for flow separation control. Efforts have also been made to develop SWJ actuator systems for suppressing flow separation over trailing edge flap [33], vertical tail [32; 34], and hump [35].