## 1 Introduction  
Governments' demands for pollutant emissions and fuel efficiency have led to many studies on reducing automotive aerodynamic drag, which is responsible for most fuel consumption for high speeds above 80 km/h [1]. However, assessing the aerodynamic characteristics of realistic automotive vehicles is a challenge due to the complexities of flow around the vehicles, associated with the instability and unsteady phenomena. To solve this problem, simplified automotive models are designed in place of actual vehicle geometries to study important flow characteristics while reducing the impact of the complex vehicle design. The Ahmed body, originally proposed to explore the influences of the rear slant angle on the near-wake flow structure is a widely studied model [2]. In more recent studies, because of the increase in interest in commercial minivans, trucks, and buses, the Ahmed square-back model has been focused on investigation. Both numerical and experimental studies have been conducted on the flow physics of this model. The aerodynamic drag of the bluff body, such as the square-back Ahmed model, is dominated by pressure deficiency due to flow separation, and unsteady vortex formation in the wake region at the rear surface of the vehicle. This leads to the development of control flow methods that can modify the flow at the rear end of the model to delay the separated flow and thereby reduce the aerodynamic drag. These techniques vary from passive control device to active control device usage. Passive devices localized on the rear surface of the vehicle, such as boat tailing, splitter plates, and vortex generators have shown an ability of significant aerodynamic drag reduction [3; 4; 5; 6; 7]. However, the application of passive methods requires a substantial modification of the vehicle shape, leading to conflicts with constraints of the length and the exterior aesthetics. The drawbacks of the passive methods put more focus on the active control strategy. The active control devices require additional energy to modify the flow around the model without considerable interference in its shape. Various active flow control studies have been conducted both on the simplified model and realistic vehicles, and promising results in drag reduction have been obtained. For instance, dielectric barrier discharge plasma actuators have been used as a flow control device on the [PERSON] model [8; 9; 10]. [PERSON] et al. used a tangential blowing jet on the rear end of a tractor-trailer to reduce aerodynamic drag by more than 30 percent [11]. Numerical studies were performed by [PERSON] et al. [12] and [PERSON] et al. [13], in which a steady blowing jet was used to change the wake structure of the square-back [PERSON] model. The numerical results showed that the aerodynamic drag reduction was approximately 17-29%, depending on the jet angle and velocity. [PERSON] et al. [14] performed experimental and computational studies to evaluate the ability of a microjet device to control flow on a simple vehicle geometry. They showed a drag reduction of 3%. Another study conducted by [PERSON] et al. [15] pointed out that a drag reduction of 12% was achieved when using a steady jet on the rear edges of a simple truck model. According to the above studies, the active flow control method using the steady blowing jet has shown promising results in reducing aerodynamic drag with various operating conditions, especially when considering simple vehicle geometries. However, they often require vast energy input, even greater than the energy saved due to reduced drag. Therefore, the control energy efficiency of this method is still not clear. Recently, another promising active flow control technique, i.e., a synthetic jet, that generates the periodic blowing and suction in a jet cycle has been vastly studied. The average mass flow rate in a cycle (blowing and suction) is zero; thus such a device is called a zero-net-mass-flux actuator [16]. For instance, [PERSON] et al. [17] and [PERSON] et al.