# A Numerical Aerodynamic Analysis on the Effect of Rear Underbody Diffusers on Road Cars
## 1 Introduction  
A proper and adequate design of the underbody of a road car is by no means an easy task, and usually represents a resource-demanding duty for aerodynamicists and car manufacturers. The high complexity of incompressible but turbulent flows observed around a sophisticated and detailed underbody of a road vehicle may generate notorious and undesired air resistance that in turn will cause a non-suble increase in the fuel consumption [1]. In fact, aerodynamic drag is responsible for more than \(50\%\) of the propulsive fuel consumption of a typical car running on a highway [2]. Moreover, it has been shown that a reduction in aerodynamic drag specifically is achievable at a relatively low cost compared to improving other car mechanisms, such as the development of a more efficient power train system; therefore, it is an economical target [3]. Some publications, such as the works of [PERSON] [4] and [PERSON] et al. [5], suggest that some acoustic phenomena may also be originated as a result of a poor underbody treatment when conceiving of the designs of road cars. Again, the complex wake and strong vorticity that are generated due to the underfloor being in the vicinity of problematic rotating elements, such as wheels, deserve special attention and study. The evolution of underbodies and diffusers in the automotive sector cannot be explained without the contributions of several motorsport categories, such as Can-Am and Formula One, where the works of [PERSON] and [PERSON] (among others) traced the paths for future aerodynamic development. Over the years, multiple body shapes for race cars have been conceptualised to create downforce with minimal drag-induced penalties. For an example, see the basic catamaran shape illustrated in Figure 1.  
The core shape covers the wheels. There is a central channel with an offset from the ground that ends in a venturi qualified by an upward rear slope. The goal is to maintain an undisturbed free stream under the car and prevent flow separation at the rear end [6]. Furthermore, some studies of ground effect diffusers have been performed to improve performance due to the major aerodynamic contribution of the diffusers to downforce generation (up to 50%) [7]. This effect is due to the longitudinal counter-rotating vortices generated that roll up along the diffuser's endplates within the diffuser's flow channel, which enhances suction by accelerating the streamwise diffuser flow. In recent years, the easy access to CFD solvers [8] and the generalisation of wind tunnel testing [9] has allowed interesting research and publications. Generalised geometries such as the _Ahmed Body_ have been extensively evaluated. A pertinent example is the study of the coherent flow structures generated in the wake of the Ahmed body. Effectively, a recirculating bubble over the slanted surface can be distinguished, along with longitudinal C-Pillar vortices originating from the side edges of the rear window and a recirculation torus behind the vertical base [10]. Another remarkable study was presented by [PERSON] [11], where rear flow separation was evaluated as a function of slant angle. The analysis of the flow depicts two primary types of vortices in the wake: a ring vortex, running perpendicularly to the flow direction, and a longitudinal horseshoe-shaped vortex, which is associated with a large increase in drag. The relevant idea was to use the car's geometry to counteract these vortices by modifying the slant angle. Some studies have also been conducted on diverse aerodynamic passive control devices, for instance, splitter plates [12] and flaps [13; 14]. However, sometimes disagreements have been encountered regarding the aesthetics and the performances of the cars, and these concepts were not applied. Other experimental approaches, such as the one led by [PERSON] et al. [15], have evaluated the usage of sealing skirts on the underbody to channelise and direct the flow towards the exit diffuser section.