# A Numerical Aerodynamic Analysis on the Effect of Rear Underbody Diffusers on Road Cars
## 1 Introduction
### Literature Review and Diffusers' Fundamental Theory
In addition, some studies on the relationship between the reversal zone behind the body and the diffuser upsweeping angle at a fixed slant angle yielded relevant results on  
Figure 6: Active diffuser scheme of a Porsche car [33]. Figure 7: Wake vorticity comparison after using the adjoint solver [34]. the flow. In fact, in [17] it is shown that the reversal zone moves upward with the increase in upsweeping angle and that the turbulent kinetic energy density follows the same trend. In conjunction with the effect of the counter-rotating vortices generated by the diffuser, a reduction in turbulence behind the car can be achieved which grants a reduction in vortex intensity, better pressure recovery, and thus less drag. The last important consideration is the effect of the presence of the wheels in proximity of the diffuser. Since they are rotating elements, which greatly interfere with the flow, their effect is considerable. Indeed, for a body without wheels, this study reveals that there would be continuous and predictable variations in lift and drag for an angle of the diffuser of \(\alpha\leq 7^{\circ}\). Above this value, separation of the airstream might occur because of the growth of vortex structure generated by lateral inflows on the sides of the diffuser surface into the underbody region, which can significantly alter the flow behind the body [35]. A subsequent study on a hatchback car with wheels at varying diffuser lengths and angles was done afterwards [36]. It was concluded that the vortices originating from the wheelhouse have a significant effect on the aerodynamic loads of the car, and that there is a possibility of reaching a minimal drag by choosing the right diffuser combination. The key factor to choose is the diffuser angle, which focuses on the diffuser itself and additional underbody elements. To achieve this purpose, some studies on the diffuser angle's effect on the flow are considered. A particularly pertinent work is presented in [37]. The authors studied the flow over a diffuser at angles of 5, 10, 15, 17, and 20\({}^{\circ}\). The results for the 5, 10, and 15\({}^{\circ}\) cases are shown in Figure 8. It was observed that for the 5\({}^{\circ}\) case, there was no separation bubble and the flow was slow and unsteady at the exit. For the 10\({}^{\circ}\) case, the separation bubble formed at the inlet and closed just ahead of the outlet with something similar to the onset of a longitudinal vortex breakdown. For the three remaining cases, the separation bubble was closer to the inlet, and since it was open, the vortex breakdown happened earlier. Therefore, since the first case was not prone to separation and the second case was deemed transitional, for this study the diffuser angle was chosen to be inferior to 10\({}^{\circ}\). Furthermore, in the works of [PERSON] [4], study to reduce the drag of a sedan car was performed by CFD for various diffuser angles, and it was demonstrated that the drag coefficient decreased as the diffuser angle increased, until a limit of approximately 7\({}^{\circ}\). This is the consequence of an increased underbody mass flow, which leads to better velocity recovery, and this effect is eliminated at larger diffuser angles because of separated flow. In addition, in an investigation on using diffusers for maximal downforce to reduce incidents on highways [38], it was shown that for a 7\({}^{\circ}\) angle there is an improvement in drag  
Figure 2:0 Surface flow visualisation at diffuser angles of (**a**) 5\({}^{\circ}\), (**b**) 10\({}^{\circ}\) and (**c**) 15\({}^{\circ}\) (Reprinted with permission from the University of Southampton [15]). coefficient with respect to the other choices of at least 1.3-1.4% and that for angles superior to 10\({}^{\circ}\), flow might separate, since the separation bubble is near opening at such angle.