## 5 Conclusions  
WMLES simulations based on a 3D finite element solver were performed on a square-back Ahmed model with and without flow control devices. Three active flow control techniques were applied: steady blowing, synthetic, and unsteady jets. The influence of jet angle and control frequency was also considered. A detailed analysis of the near-wake structure was performed. Some conclusions are summarized as follows:  
* The application of control jets deviates the streamlines behind the model, and thus reduces the size of the near-wake section. In addition, the momentum from the control jets introduces the wake region, shrinks the recirculation zones, and then pushes them away from the surface rear of the model. This leads to a limitation of backward flow and static pressure recovery on the back surface of the model.
* The largest drag coefficient reduction of \(\Delta\mathrm{C}_{\mathrm{D}}=26.51\%\) is achieved using a steady blowing jet at jet angle of \(\beta=45^{\circ}\). When using a synthetic jet, the drag reduction is negligible with all operating conditions, except for the high control frequency case (\(\Delta\mathrm{C}_{\mathrm{D}}=5.62\%\) at \(\mathrm{f}_{\mathrm{c}}=272\) Hz). Meanwhile, a significant drag reduction is observed with an unsteady jet (\(\Delta\mathrm{C}_{\mathrm{D}}=8.03\%\) at low control frequency \(\mathrm{f}_{\mathrm{c}}=34\) Hz and \(\Delta\mathrm{C}_{\mathrm{D}}=17.27\%\) at high control frequency \(\mathrm{f}_{\mathrm{c}}=272\) Hz, with optimal jet angle \(\beta=45^{\circ}\)). The application of a steady blowing jet helps to achieve an impressive drag reduction; however, a large energy input is also required. Therefore, the unsteady jet can be considered as a promising candidate for active flow control method when considering the control energy efficiency.
* The optimal jet angle \(\beta=45^{\circ}\) is determined for steady blowing and unsteady jets, while jet angle \(\beta=60^{\circ}\) is the optimal case with synthetic jets. Due to the influence of the interaction between the control jet and the rear surface of the model, the drag coefficient reduction at jet angle \(\beta=30^{\circ}\) in all control cases is the smallest.
* The aerodynamic drag coefficient of the model is most reduced when synthetic and unsteady jets with high control frequencies are used. These control jets interact with the shear layer and delay the formation of small-scale vortices in this layer. The number and size of vortices in the shear layer are also significantly reduced when a high-frequency control jet is applied.  
Conceptualization, T.-L.P.; methodology, T.-L.P. and Q.T.P.; software, T.-L.P. and T.T.N.; validation, T.-L.P.; formal analysis, T.-L.P. and T.T.N.; investigation, T.-L.P.; resources, T.-L.P. and Q.T.P.; data curation, T.-L.P. and T.K.L.N.; writing--original draft preparation, T.-L.P.; writing--review and editing, Q.T.P., T.T.N. and T.K.L.N.; visualization, T.-L.P. and T.K.L.N.; supervision, T.-L.P.; project administration, T.-L.P.; funding acquisition, T.-L.P. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Ministry of Education and Training, grant number B2020-DNA-03.  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.