Aerodynamic theory

 

Aerodynamic Factors

 
 
  • Streamlines
  • Velocity Distribution
  • Laminar Flow
  • Turbulent Flow
  • Viscosity
  • Reynolds Number
  • Boundary Layer
  • Skin Friction Bernoulli’s Principle
  • Pitot Tube
  • Pressure Coefficient
 

 

 

Streamlines

 
  • Curves associated with a pictorial representation of air flow
  • Smoke is commonly used in wind tunnels to represent the streamlines
  • Streamlines are used to study air flow

 

 

Velocity Distribution

 
  • The nature of the fluid flow
  • A measure of changes in air flow’s velocity close to the vehicle

 

 

Laminar Flow

 
  • Fluid motion that is "well organized"
  • Fluid with parallel velocity vectors
  • Generally, laminar flow has the ideal aerodynamic properties

 

 

Turbulent Flow

 
  • Fluid motion that is not "well organized"
  • Fluid with parallel and other velocity vectors
  • Generally, turbulent flow has undesirable properties

 

 

Viscosity

 
  • The fluid’s resistance to motion
  • Internal fluid forces at the molecular level
 
 
  • Where, F= fluid viscosity force, m = coefficient of viscosity, V¥ = fluid velocity, h= separation distance, and A= contact area
  • Pictorial of fluid viscosity

 

 

Reynolds Number

 
  • Quantifies the product of speed times size
  • A dimensionless number
 
 
  • Where, r is fluid density, m is the viscosity, V is the velocity, and L is the length of the object
  • Represents the ratio between inertial and viscous forces
  • Compensates for scale differences
  • Example
    • A car has a length of 4 m, travelling at 30 m/s
    • Air density is 1.22 Kg/m3
    • Air viscosity is 1.8x10-5
    • Re = 1.22 x 30 x 4 / (1.8x10-5) = 8.1x106
  • Re can indicate the nature of the fluid flow
  • Higher values indicate turbulent flow
  • Lower values indicate laminar flow
  • Different flows can be considered the same if they have similar Re values
  • Allows scale models to be accurately tested in wind tunnels using different fluids and or velocities

 

 

Boundary Layer

 
  • The thin layer of rapid tangential velocity change close to an object’s surface
  • Generally increases in thickness (d ) with the length of the object
 
 
  • Relative velocity
    • Zero at the object’s surface
    • V¥ at the outer edge of the boundary layer
  • Example
    • At 60 mph, the boundary layer is about an inch close to the rear of a vehicle
    • A thicker boundary layer creates more viscous friction
  • A too sudden a change in thickness (transition) can cause flow separation,
  • Additional drag (skin friction)
  • Loss of down force
 

 

 

 

Skin Friction

 
 
  • Cf, skin friction coefficient
  • Non-dimensional
  • Indicates the level of friction between the vehicle’s skin and the air
  • t = Friction resistance

 

 

- Dynamic Pressure

 
 
  • Where V¥ is the velocity, and r is the fluid density
  • Boundary layer is thicker for turbulent flows
  • Skin friction (Cf) decreases with Re
  • At certain speeds, both laminar and turbulent flows are possible
  • Flow separation can be delayed in turbulent flow, resulting in a preference for turbulent boundary conditions

 

 

- Bernoulli’s Principle

 
  • Pressure drop: P1 > P2 > P3
  • Height of the fluid decreases with drop in pressure
   
 
  • Fluid Velocity is greater at the neck, V1 > V¥
  • Pressure drop, P1 > P3 > P2
  • Fluid pressure drops as fluid velocity increases
  • Fluid pressure is inversely proportional to fluid velocity

 

 

- Bernoulli’s Equation

 
 
  • where, V = velocity, p = local static pressure, and r = density, for any point on a streamline
 
  • Usually used to compare and calculate pressure and velocity at two different points

 

 

Pitot Tube

 
  • Bernoulli’s equation allows measuring any fluid velocity by measuring its pressure

 

 

Pressure Coefficient

 
  • Non-dimensional
  • Used to measure aerodynamic loads (lift, drag, and side forces)