# A Numerical Aerodynamic Analysis on the Effect of Rear Underbody Diffusers on Road Cars
## 1 Introduction
### Literature Review and Diffusers' Fundamental Theory
It is interesting to note that the contribution of [PERSON] [27] describes perfectly the flow behaviour under the surface of a diffuser-equipped geometry in terms of pressure coefficient (see Equation (1)). \[C_{p}=1-\frac{U}{U_{\infty}} \tag{1}\]  
As can be observed in Figure 5, interpreted from [28], that the flow experiences an acceleration after the inlet of the underbody (low-pressure zone) for both cases, the baseline and the diffuser setting. That zone is followed by a pressure recovery phenomenon [18] that finally adopts the free stream pressure value. The main difference is that for the flat underbody, that process is undertaken continuously, whereas for the diffuser configuration it is done in two stages, where a pressure peak is found. Through the diffuser, a portion of the kinetic energy of the fluid is turned into potential pressure energy, also called pumping effect, as described in [29]. The pressure drop at the exit is almost identical for both cases, but the lower it is, the less drag it would cause, since vorticity would be smaller. Hence,  
Figure 4: Downforce generation at different ride heights [8]. diffusers may also be employed adequately with the idea of controlling the boundary layer separation of the flow on the undertray. This can, if done properly, avoid the large turbulence phenomenon of the wake. Various additional elements have been studied to improve the aerodynamic performances of vehicles. Examples of such research are presented in [30]: the analysis of a bluff body shaped underbody diffuser with side plates and moving ground. The conclusion drawn was that the diffuser can benefit the drag reduction of the body and the correct upper slant angle can enhance the improvement. More ambitious projects were also done with active flow control devices such as pulsed jets activation and decreased the drag by about 6-8% [31]. In the work of [PERSON] et al. [32] the concept of actively translating diffusers was introduced, as can be seen in Figure 6. When active, within the range of 70-160 km/h, drag was reduced by about 4%, as the diffuser blocked the low-pressure air from the underbody, which filled the rear end with high pressure from the sides, consequently raising the base pressure of the car and creating a smoother recovery. Figure 5: Pressure coefficient curve around a bluff body. Before proceeding to the analysis of the diffuser of this paperwork, it is relevant to contemplate the physics of the flow involved in the relevant flow. Therefore, an adequate reference is an investigation of the aerodynamic behaviour of an underbody diffuser fitted to a wind tunnel model of a wheel-less, simple body of passenger car proportions [5]. The three major aerodynamic phenomena are hence identified and explained: first, the ground effect previously mentioned as a consequence of the asymmetry of the flow; then, the upsweep of the rear underbody produces the effect of a camber, resulting in significant downforce; finally, the pumping effect of the diffuser, which naturally accelerates the flow because of its geometry. Moreover, in a subsequent study [20], an analytical model based on a simple diffuser/body combination was developed to generalise the experiment. It was demonstrated that an effective underbody can include a relatively short diffuser (half of the length of the underbody), that the optimum diffuser length decreases as the area ratio of the diffuser decreases, and that the optimum area increases as the ride height increases. An interesting example from race car optimisation via the adjoint method has been reported in [34]. The results can be seen in Figure 7. In fact, after adding the diffuser, the larger longitudinal vortices of the wake were reduced and dissipated earlier because of the underbody-induced counter-rotating vortices, which led to a significant drag reduction.