Aerodynamic Basics

Aerodynamics in FSAE can be used to describe the interaction of air and the racecar, in particular its bodywork and aerodynamic elements such as wings, diffusers and fins. It can be analysed by the use of Computational Fluid Dynamics. The performance of aerodynamic elements can be described by parameters such as the coefficient of Lift ($C_{l}$), coefficient of Drag ($C_{d}$) and the ratio of $C_{l}/C_{d}$.

Conceptual aspect of Aerodynamics

Aerodynamics is not necessary to make a car go around a racetrack. Check beforehand if your car benefits from aerodynamic elements. Simple laptime simulation usually includes lift and drag coefficents and helps you determine your target goals.

Key Parameters

Coefficient of Lift, $C_{l}$

Coefficient of Drag, $C_{d}$

Lift to Drag ratio, $C_{l}/C_{d}$

Boundary Layers

There are many resources available about what exactly boundary layers are, why they exist, and other useful information. This will focus on FSAE applications, as they are fairly unique.

Beyond "what is a boundary layer" type questions, I highly recommend reading High Lift Aerodynamics, as it contains many of the fundamentals for the limitations of downforce generation. Most of what follows is a summary of the paper.

Laminar, Turbulent, and Transition

• Boundary layers (BL) can be either laminar, or turbulent
  • Neither is "worse" or "better" than the other. They are simply different and have different effects aero systems.
• When a BL initially forms, it is laminar. Gradually fluctuations destabilize the flow and it becomes turbulent.
  • This is known as (BL) transition
• The fluctuations may come naturally (from atmospheric turbulence or surface imperfections) or be induced artificially by "BL trips" or vortex generators
  • The artificial methods force the transition to occur sooner than it would otherwise

• Determining when a boundary layer transitions is a function of it's Reynolds Number, $Re_{x}$, using $x$ (distance along a wall) as its characteristic length scale. The boundary layer thickness can also be described non-dimensionally as $Re_{\theta }$ where $\theta$ is the local boundary layer thickness; this defines the boundary layer properties strictly in terms of local variables, as the meaning of "x" becomes less useful when the streamwise pressure gradient varies over the surface of the airfoil.
  
  • The higher the Reynolds number the more likely it is to be turbulent (over a certain level, it is more-or-less guaranteed)
  • Therefore, increasing flow velocity decreases the distance at which BL transition occurs

Pressure Gradients and Separation

• Flow separation occurs as a direct result of the existence of boundary layers
  • Hence why "flow separation" and "boundary layer separation" are synonymous
• Pressure gradients describe the force being applied to the fluid as it moves
  • A pressure gradient that pushes with the (bulk) fluid motion is known as a Favorable Pressure Gradient (FPG)
  • A pressure gradient that pushes against the (bulk) fluid motion is known as an Adverse Pressure Gradient (APG)
• APGs are what cause flow separation
  • The APG pushes against the boundary layer such that the flow close to the wall (which is significantly slower than the flow outside the BL) begins to move backwards. At incipient separation, the shear stress at the wall reaches 0.
    

Low-$Re$ effects

• Laminar and Turbulent BL react to APGs differently:
  • Laminar BLs are more susceptible to separation than turbulent BLs

• Airfoils feature an initial FPG, followed by an APG (also known as pressure recovery)
• If the Reynolds number is high enough for an airfoil, BL transition occurs before the APG region
  • This means that the "stronger" turbulent BL will resist the APG well
  • If the Reynolds number is too low, the BL will not transition and a (weak) laminar BL will be forced to go through the APG region.
  • FSAE cars generally run in this Low-$Re$ regime

• Low-$Re$ phenomenon include:
  • "Premature" separation (compared to running the airfoil at higher $Re$)
  • Hysteresis
    • The AoA at which separation occurs is different when increasing AoA than decreasing AoA
    • See the UIUC LSAT database for plots demonstrating this effect (ie. compare the differences in polar plots between different $Re$)

• Unless your airfoil is operating outside the Low-$Re$ regime (generally around $Re_{c}\approx 25,000$, though this is airfoil dependent), use airfoils explicitly designed for Low-$Re$ regime
  • These are meant to place the boundary layer transition point ahead of the APG region of the airfoil (or to "help" the BL transition sooner)
  • S1223 airfoil is the quintessential airfoil design for this regime (at least for high lift applications, as would be found in FSAE cars)

Important Note for CFD:

• Low-$Re$ effects are generally NOT well-captured by CFD, as many common turbulence models treat the BL as always turbulent. Modern commercial CFD codes do include transitional RANS models which are of some utility.
  • There are special "transition" models, but they require empirical calibration to work correctly.
    
  • Even if you have the empirical calibration data, BL transitions is very sensitive to surface roughness, surface shape, atmospheric conditions, etc. FSAE manufacturing processes can be rather crude and a defect near the leading edge has a massive effect on the flow over the rest of the airfoil chord.
    
  • My advice is to simply trust wind tunnel data (such as UIUC LSAT) to determine whether airfoils operating in Low-$Re$. If they are not, then the CFD assumptions aren't broken. If they are, then don't rely on CFD. CFD can arguably provide very good results pointing you towards a relatively optimal design even in the transitional regime, but not necessarily for providing a precise number for lift and drag coefficients. Like any other engineering tool, it has its purpose, but must be supplemented by sound engineering reasoning and experimental testing and validation.