Aerodynamic Theory

• TEC452 Home
• Aero Index
• Introduction
• Aerodynamic Theory
• Wind Tunnel
• Computational Fluid Dynamics
• Vehicle Aerodynamics

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

Example

• What is the force required to pull the upper plate at 5 m/s, if the plate area is 2 m², and the fluid between the surfaces is water with the separation distance of 0.04 m (water’s coef. of viscosity is 1.0x10^-3 Ns/m²)

Example

• Using the previous diagram and dimensions,
• How fast will the upper plate move, if the fluid is SAE 30 motor oil with the coef. of viscosity of 4.0x10^-3 Ns/m² and an applied force of 2 N

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

Skin Friction

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

Example

• What is the friction resistance (t ) of a plate moving at 30 m/s, with coef. of friction of 0.002 through air with a density of 1.22 Kg/m³?

t = C_f (0.5r V²) = 0.002 x 0.5 x 1.22 x 30²

t = 1.098 N/m²

 

• Where V¥ is the velocity, and r is the fluid density
• Boundary layer is thicker for turbulent flows
• Skin friction (C_f) 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

• 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

Example

• What is the pressure difference on the surface of a vehicle’s grill (V_grill=0), if the vehicle travels at 30 m/s. Air density is 1.22 Kg/m³

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)

• TEC452 Home
• Aero Index
• Introduction
• Aerodynamic Theory
• Wind Tunnel
• Computational Fluid Dynamics
• Vehicle Aerodynamics