# Numerical Study of Flow Separation Control over a Hump Airfoil Using a Novel Sweeping Jet Actuator
## 2 Set Up and Numerical Simulation Methods
Therefore, a sinusoidal function was chosen for the waveform of the synthetic jet. The velocity variation between synthetic jets A and B is defined as follows: Equation (11) represents the velocity of synthetic jet A, and Equation (12) represents the velocity of synthetic jet B. In these equations, \"\(a_{0}\)\" stands for the amplitude, and \"\(b_{0}\)\" corresponds to the mean velocity. \"F\({}^{+}\)\" signifies the dimensionless frequency. The F\({}^{+}\) is defined as follows:  
Figure 2:4  
where \(f\) represents the frequency of the novel Sweeping jet actuator, c is the chord of the Hump airfoil, and \(U_{\infty}\) is the freestream velocity. c and \(U_{\infty}\) will be provided later in this study. Figure 2:5  
Figure 2:6  
Grid independence verification was conducted, and the grid sizes selected for this study are shown in Figure 2:7 Figure 5 illustrates the variation of internal velocity over time for several grids under control frequencies of 1 and 10. The monitoring point location for the SWJ actuator is shown in Figure 2:8 It can be observed that increasing the grid size slightly enhances the internal velocity, but the frequencies remain consistent across different grid sizes, confirming grid independence. Therefore, to save computational time while maintaining quality in the numerical simulations presented in this study, mesh2 grid size was chosen. The operational principle of the SWJ actuator is depicted in the provided Figure 8 as follows:  
At T* = 0, the jet adheres to the lower wall. Due to the interaction between the jet and the wall, the jet's direction at the exit is upwards. Subsequently, synthetic jet B initiates air  
Figure 2:9 Periodic flow field of the internal velocity within the SWJ actuator. Figure 3.0 Disturbance in the velocity flow field. expulsion, inducing the creation of separation vortices on the wall at that location. The energy from the synthetic jet promotes the growth of these separation vortices, propelling the jet to move toward the upper wall. By T* = 1/2T, the jet is observed to be fully attached to the upper wall, and its direction at the exit becomes downward. As synthetic jet A comes into play, the jet commences its downward motion towards the wall. By T* = T, a cyclic oscillation is achieved, completing a full period. In this study, the location of the SWJ actuator and the hump model are shown in Figure 3.1 The chord length of the Hump airfoil is 420 mm. The height of the Hump airfoil is 50 mm. The position of the Hump separation point is around 65% of the chord length, so in order to better control the flow separation. The novel SWJ actuator model is positioned at 65% of the chord length and angled at 30\({}^{\circ}\) relative to the freestream direction. In this configuration, the size of the SWJ actuator is scaled down to 25%. The left boundary of the calculation domain is defined as the velocity inlet and the right boundary is defined as the pressure outlet. Similar to the experiment [40], the inlet velocity is V\({}_{\infty}\) = 34.6 m/s (M = 0.1), which is horizontal to the right. [PERSON] et al. conducted the experiment in a subsonic wind tunnel on a wall-mounted hump at chord Reynolds numbers of 0.68 \(\times\) 10\({}^{6}\) \(<\) Re \(<\) 2.02 \(\times\) 10\({}^{6}\) (Ma \(<\) 0.2). They only studied the efficiency of traditional sweeping jet actuators in a spanwise direction compared to fixed-length jets. The boundary conditions and numerical simulation methods for the oscillating jet device are consistent with the calculations mentioned above. To investigate the influence of frequency and velocity ratio on flow control using the SWJ actuator, this paper focuses on studying F\({}^{+}\) = 0.375, 1, and 10. Velocity ratios (VR) of 1.1, 1.8, 2.3, and 3.1 were chosen. The VR is defined as follows:  
Figure 3.2  
where Ujet refers to the average velocity at the outlet of the SWJ actuator, while U\({}_{\infty}\) denotes the freestream velocity.