# A Numerical Aerodynamic Analysis on the Effect of Rear Underbody Diffusers on Road Cars
## 1 Introduction
### Literature Review and Diffusers' Fundamental Theory  
As explicitly stated by [PERSON] et al. [PERSON] et al. (2018), diffusers may easily be understood as aerodynamic elements, usually mounted on the rear area of the underbody of a ground transport vehicle, whose main function is to increase the downforce and facilitate a smooth transition from the underbody flow back to free stream conditions. The downforce on the underbody area is created mainly due to the presence of a suction area originated by a [PERSON]'s effect, which in turn is greatly intensified with the presence of a diffuser. This process mimics the flow over a constricted tube as shown in Figure 2, interpreted from [1]. The role of the diffuser is to raise the low pressure of the air underneath the car back to atmospheric pressure. The slope of the diffuser is critical to increasing the flow speed and reducing the pressure locally ([PERSON] et al., 2018), and that is why the diffuser also acts as an expansion chamber to smoothly recover the free stream conditions from the vehicle's influence. By smoothing this transition, turbulence and drag in the vehicle's wake are improved. Figure 3 shows the adoption of a typical diffuser automotive's configuration. Again, the works of [PERSON] et al. [PERSON] et al. (2018) reflect some fundamental fluid-mechanical sources of downforce found when evaluating closely the flow behaviour of diffusers. If a perfectly symmetric bluff body at the zero-angle of attack, such as the _Almed body_, is considered for evaluation, it will be clearly visible that no downforce is generated due to it not generating any pressure differential between the upper and lower surfaces, just as in a symmetric airfoil. However, when testing the body close to the ground, the airflow under the body experiences an increase in its velocity caused by the ground constraint, a phenomena called  
Figure 3: Schematic representation of a bluff body with an added diffuser ([PERSON], 2018). Figure 2: Pressure distribution along the centreline of a generic body of car with an underbody diffuser and a Venturi tube. ground interaction. This phenomenon has been studied rigorously in vehicle aerodynamics [16]. Descriptions of the major flow structures for different ride heights have been obtained, along with insights on the flow's physics. The acceleration of the flow because of the ground effect causes, in turn, a pressure gradient between the upper and lower surface, and originates a resulting aerodynamic lifting force, as seen in [21]. Figure 4 shows the variation in the loads generated at different ride heights. It is important to note that such an increase in downforce when decreasing the ride height is limited due to fluid viscosity. These viscous effects are not dominant at large ride heights; therefore, downforce reaches its maximum at a certain low ride height, as stated by [PERSON] [22]. The second mechanism for the generation of downforce on the underbody is the curved non-symmetrical zones at the rear of the body. That cambered shape creates a flow asymmetry that gives rise to the apparition of a suction peak at the inlet of the diffuser. Nonetheless, it is extremely important to model and design the diffuser angle \(\theta\) to avoid flow separation, which is mathematically expressed by an adverse pressure gradient in the axial flow direction. To prevent flow separation in an expanding rectangular duct, an equivalent conical section is calculated, based on relevant length, inlet, and outlet areas [23]. This angle must normally not exceed \(7^{\circ}\), to avoid flow separation [24]. Nevertheless, racing diffusers can achieve attached flow with angles superior to \(20^{\circ}\)[25], but it is typically accepted that the optimum value is often found around \(7^{\circ}\)[26]. The cambered geometry of the diffuser counters the non-clockwise, rotating, streamwise vortical structure pair upward, created by the pressure gradient between the diffuser and the outer region [7].